׉?ׁB!XבCט{u׉׉ 7cassandra://-X-92faCdrjR2toerQKX_vuD81As003MbLO0ufGcGvoLi` ׉ 7cassandra://3r5wzqdX72YirA9Oy4nQL2xqYR30WXUQBYte6ut7y0g*`S׉ 7cassandra://fXR3QRN_-s1jmwTaZsYxKm6DB7Gc40txSSoZB94RicE`̵׉ 7cassandra://R00UnUCjQ9PcR-9WFkzBMCmpcwCt1LYNzN3JAnJ5rgMz͠ay=!׈Eay=!׉E׉ 7cassandra://fXR3QRN_-s1jmwTaZsYxKm6DB7Gc40txSSoZB94RicE`̵ay=!ay=!{בCט{u׉׉ 7cassandra://HOj2zoUDSuw8E-lCQI0GOImxgJGREHzR7vIT9atU5l4` ׉ 7cassandra://BMZTyESWD-SBXyboD5JdHJCi_iwHSsDwinjnSuZjdt45S`S׉ 7cassandra://RsXa5heqwVZ1C9L2TNGTyToqAziorm4L0aQgtCqIAeQ`̵׉ 7cassandra://0helaj0nTgDY_WZuCnrSsG-A9c8g87sI3HM7K3fmlyg̀Z͠ay=!ט{u׉׉ 7cassandra://5JYnn7aVmUQbhHdFqToOZyTRHDfBfy2rM3oWTs-xcno ` ׉ 7cassandra://cmazznjm79tpFik6PMDnlPqhRIAOyRwWrlU82DbxxJI">`S׉ 7cassandra://UHNnl9ZYUzHEvXY3e6uQgsEXM5QQegE3TSvMCRaAz98 `̵׉ 7cassandra://Cy1RCkjQ9DXP3j2Q-RHCmY57poEdZ2quiWYltIfqSoM3MZ͠ay=!נay=!ˁ9׉SG ׁ ׁ rנay=!́9׉SG ׁ ׁ rנay=!́!9׉SG ׁ ׁ rנay=!΁?9׉SG ׁ ׁ rנay=!ρ]9׉SG ׁ ׁ rנay=!Ёs(9׉SG ׁ ׁ rנay=!с9׉SG ׁ ׁ rנay=!ҁˁ9׉S G ׁ ׁ rנay=!Ӂ9׉S#G ׁ ׁ rנay=!ԁ ̄(9׉S=G ׁ ׁ rנay=!Ձ99׉S=G ׁ ׁ rנay=!ցW9׉SLG ׁ ׁ rנay=!ׁu9׉S]G ׁ ׁ rנay=!؁̄(9׉SmG ׁ ׁ rנay=!فŁ9׉SmG ׁ ׁ rנay=!ځ9׉S̎G ׁ ׁ rנay=!ہ9׉S̖G ׁ ׁ rנay=!܁9׉S̠G ׁ ׁ rנay=!݁=9׉S̭G ׁ ׁ rנay=!!9ׁH#mailto:info@tolerantiemanagement.nlׁ ׁ Ј׉EAdvanced Geometrical Tolerancing Preface The intend of the syllabus is being a book for self study or as a book used on Geometric Dimensioning and Tolerancing. trainings. Knowledge and best practice in this field are constantly changing. Therefor regular updates will become necessary. There are two major standards when it gets to “Geometrical Dimensioning and Tolerancing” (GD&T). There are the American ASME Y14.5 standards ‘Dimensioning and Tolerancing’ and the ISO series of standards. The relation between the several ISO standards is defined in ISO 14638 which is a matrix of the Geometrical Product Specification Standards (GPS). ASME and ISO have different philosophies and can have different interpretation of a geometric characteristic. The syllabus is updated to the GD&T standards as released up to 2021 Drawings in the syllabus are for illustration purposes only. All drawings are dimensioned and tolerated with the metric system of measurement. Hans van Kimmenade info@tolerantiemanagement.nl 2021: GDT_adv release 1.01 II ׉ 7cassandra://RsXa5heqwVZ1C9L2TNGTyToqAziorm4L0aQgtCqIAeQ`̵ay=!׉EAdvanced Geometrical Tolerancing Table of conTenT Preface II Table of content Icons used Abbreviations Glossery of terms Module I 1 Introduction 2 Concepts, Terms and Symbols 3 Modifying Symbols Module II 4 Tolerances of Form 5 Datum System 6 Tolerances of Orientation Module III 7 Tolerances of Location 8 Tolerances of Run-out 9 Tolerances of Profile 10 3D PMI MBD 11 References VI III IV V 1 7 30 56 71 88 104 137 145 155 168 III ׉ 7cassandra://UHNnl9ZYUzHEvXY3e6uQgsEXM5QQegE3TSvMCRaAz98 `̵ay=!ay=!{בCט{u׉׉ 7cassandra://XM_F4q34a23vIx6Nz70GfFwJWJmPmNrYvy4OFDK1EKo%` ׉ 7cassandra://7Aa8n0jsQrUkbUat-qYSD5mq3ia7KN3yIGVNyllTPjg"`S׉ 7cassandra://nojcSIPYZ8LLY9xM4_hVL3QCkl3_ZLJJd16J_95mgp0 `̵׉ 7cassandra://5hAROZTKaDwa5kSLmNBy4DMH4YspHxGo2mYrCTB8ssUJ; L͠ay=!ט{u׉׉ 7cassandra://NjYKzQuerrAUUeD_tzKt3K7cU018T6KtQqlxu_Ctry4 o` ׉ 7cassandra://TwZsleclB4DYFpO7w8_k9Z6RqFGuvN8dIt3IXuufvHE$`S׉ 7cassandra://AidsAiJ_B3prQCYHbz0WeU9NbkFGTwEIfMfGDND1xkA \`̵׉ 7cassandra://1cvR7Dh_E-0IVnk0xgtb_m03B-WpC8YVTbisT21SwAM5Z͠ay=!׉EyAdvanced Geometrical Tolerancing Icons used This icon refers to important information or definitions that are worthwhile to remember. Exercises. The information symbol indicates more complex examples and broadened information. Subjects will result in more in-depth knowledge. The information can be interesting but is not necessarily required for understanding the subject. IV ׉ 7cassandra://nojcSIPYZ8LLY9xM4_hVL3QCkl3_ZLJJd16J_95mgp0 `̵ay=!׉EAdvanced Geometrical Tolerancing abbrevIaTIons A Derived feature ACS CZ E F GPS L LD M P PD R RFS SIM SZ TED UF UZ Any Cross Section Combined Zone Envelope requirement Free state Geometrical Product Specification Least material requirement Least (minimum) Diameter Maximum material requirement Projected tolerance zone Pitch Diameter Reciprocity requirement Regardless of feature size Simultaneous requirement Seperate zone Theoretical Exact Dimension United feature Unequal Zone V ׉ 7cassandra://AidsAiJ_B3prQCYHbz0WeU9NbkFGTwEIfMfGDND1xkA \`̵ay=!ay=!{בCט{u׉׉ 7cassandra://Vj32wXAg-7UwwY3M6LkAv9GgX10Hqogz805It_i9Ajk?U` ׉ 7cassandra://Ue0tmo1gXZRfYanh6uOn409t8CL8L6EvvNWTvujtOkUa`S׉ 7cassandra://wb-WEHGKZSsA4YawEs0ffvd_jfvyY87gOI1kJzVSGuY`̵׉ 7cassandra://g-kcVsvKLBPTlnc5EteBgT3maf6tTVomH2l3IQZUwLYGZ͠ay=!ט{u׉׉ 7cassandra://jdFHP3oCYPn1LxkUkYe0IqG_nng-Kgl4bZ1Cm1MQHgE ` ׉ 7cassandra://TThWOFVEF-cUqj-8INp-cTZY8JEt5DNDr_xvSYNiqrAZh`S׉ 7cassandra://2OghaGvZLJJneXznpY-JNnnlm9atgLBvlI525CmvqgA`̵׉ 7cassandra://vnH0vFqTg8UwyIG54O6s--1LkC0JumKM9RvbfMKkz4cѻ͠ay=!׉E cAdvanced Geometrical Tolerancing Glossery of Terms Datum - A theoretical exact point, axis or plane derived from a true geometric counter part of the specified datum feature Datum axis - The theoretical axis derived from the true geometric counter part of a specified datum feature Datum plane - A datum established from the datum feature simulator of a nominal flat datum feature Datum system - A set of symbols and rules on how to constrain a part to establish a relation between the part and geometric tolerance zones Datum targets - A set of symbols that describe the shape, size and location of datum feature simulators that are used to establish datum planes, axis or points. Feature - The physical portion of the workpiece, such as a point, hole, pin or a surface; these features can be integral features (e.g. the external surface of a cylinder) or derived (e.g. a median line or median surface). Definitions of features are taken from ISO 14660-1 and ISO 14660-2 Feature of size - The shape defined by a linear or angular dimension that is a size. Typically, a feature of size is a cylinder, a sphere, two opposite parallel surfaces, a cone or wedge. (ISO 14660-1). Gage - A device to measure a part characteristics. Geometric tolerance - The general term applied to the category of tolerances used to control form, profile, orientation, location and run-out. Least Material Condition (LMC) - The condition in which a feature of size contains the least amount of material within the stated limits of size Maximal Material Condition (MMC) - The condition in which a feature of size contains the maximum amount of material within the stated limits of size. Modifiers - Symbols or keywords that communicate additional information about the tolerancing of a part. Simulated datum - A datum established from a physical datum feature simulator. Theoretical Exact Dimension (TED) - A dimension which is not affected by an individual or general tolerance. Tolerance zone - the area (zone) that represents the total amount that part features are allowed to vary from their specified dimension. True position - The theoretical exact location of a feature of size as established by its theoretical exact dimension (TED). Virtual condition - A fixed size boundary generated by the collective effects of a feature of size’s specified MMC or LMC and the geometric tolerance for that material condition. VI ׉ 7cassandra://wb-WEHGKZSsA4YawEs0ffvd_jfvyY87gOI1kJzVSGuY`̵ay=!׉EAdvanced Geometrical Tolerancing module I 1 InTroducTIon 1.1 GeomeTrIcal TolerancInG objecTIves Geometric Tolerancing is an international language that is used on engineering drawings to accurately describe the size, form, orientation, and location of part features. It is also a design dimensioning philosophy to define a part based on its functions. GD&T will improve product designs and result in lower cost. Machine operators and manufacturing engineers use the language to interpret the design intent and to determine the best manufacturing approach. Quality control and inspection use the GD&T language to determine proper set-up and part verification. GPS reduces controversy, guesswork, and assumptions throughout the design, manufacturing and inspection process. 1.2 HIsTory Frederick Winslow Taylor 1856 in Germantown, Pennsylvania. He was born into a wealthy family. Taylor became an apprentice pattern maker and machinist. He finished his four-year apprenticeship and became a machine-shop laborer. He was quickly promoted to chief engineer. He joined Bethlehem Steel in 1893 in order to solve an expensive machine shop capacity problem. Frederick Taylor (1856 -1915) Taylor focused the rest of his career on promoting his management and machining methods. Frederick Winslow Taylor caught pneumonia and died on March 21, 1915. Taylor is one of the pioneers on Scientific management a theory of management that analyzes and synthesizes workflows. Its main objective is improving economic efficiency, especially labor productivity. It was one of the earliest attempts to apply science to the engineering of processes to management. Taylor also influenced Henri Ford where the Fordism was developed. Fordism is a manufacturing technology that serves as the basis of modern economic and social systems in industrialized, standardized mass production and mass consumption. Related to GD&T Taylor developed limit gauges. A ‘GO’ gauge should check all related dimensions (form and size) simultaneously the ‘NOGO’ gauge should check only one dimension at a time. We know this GO requirement as envelope requirement. After leaving the company, Figure 1.2 Taylor gauge 24H7 1 ׉ 7cassandra://2OghaGvZLJJneXznpY-JNnnlm9atgLBvlI525CmvqgA`̵ay=! ay=!{בCט{u׉׉ 7cassandra://MQkCR271-bjuBAlPjxNgcwFVg-QsrZH-1P4erHkcyP4I` ׉ 7cassandra://L7_8BfAGzMPs7r-kPPVBsYiz2YGgDGdl7GFh9eH05MoC`S׉ 7cassandra://Qde_o2XsqgD_v3uOxgEc1Rc1EF5VQx_pNnBXbWOsAME`̵׉ 7cassandra://gYoJ59L7dhEtfL5TbLa90N_fGG_F6l2uJ_VRxQoBzdUU͠ay=!ט{u׉׉ 7cassandra://CDfhx0BFVnP5Ei9Wfb0ySnoIHI9ugZ3L66Q2t203pn0` ׉ 7cassandra://1F08q9unmvy-KTHY7T8Fw1bJOVD6Le_CDZATcUdLDG04'`S׉ 7cassandra://9h5jjcXmaBcOrheLT7F9U8XW39KyJjmQGZEQPrE_bzU`̵׉ 7cassandra://HdS1VuhHyIAxjqHy_HhTPXUpbzeLui47kKeFEZqIEnoS ͠ay=!׉EAdvanced Geometrical Tolerancing Driven by the demands of the 2nd World War the British innovated and standardized. Stanley Parker of the Royal Torpedo Factory created in 1940 a positional tolerancing system. He found that coordinate tolerances result in a square tolerance zone, but that parts outside the square might be actually be good, as long as they are within a circle that encompasses the square’s corners. Parker came up with a concept on defining allowed deviations on a workpiece. This concept developed into what know as Geometrical Dimensioning and Tolerancing. From here a concept symbol language was developed. In the US as first ANSI GD&T standard. The British set up the first standard on position tolerancing published in 1948 “Dimensional Analysis of Engineering Design”. The American National Standards Institute publication in 1982 of ANSI Y14.5M-1982 was a turning point in standardization of the methodology. Today we know two major dimensioning and tolerancing standards the ASME Y14.5 published by the American Society of Mechanical Engineers and the ISO GPS standards defined in ISO matrix 14638 published by International Organization of Standards. A few examples of GD&T standards are ISO 1101; ISO 5458; ISO 5459 and ISO 1660. The ASME and ISO standards look similar but are very different in application and interpretation. reject from square tolerance zone accept from round tolerance zone Figure 1.3 Square and round tolerance zones 2 ׉ 7cassandra://Qde_o2XsqgD_v3uOxgEc1Rc1EF5VQx_pNnBXbWOsAME`̵ay=!!׉EsAdvanced Geometrical Tolerancing 1.3 surface condITIon Surface condition Material properties of boundary layer Chemical Chemical composition Inhomogeneities Physical Hardness Residual stress Graint Geometrical properties Size deviation Geometrical deviation Roughess, waviness Edge deviation Surface, discontinuities (cracks, pores, laps etc.) Process specific deviation (welding, casting etc.) Figure 1.4 Workpiece surface conditions The geometrical characteristics are defined as deviations from geometrical ideal integral or derived features of a workpiece. Integral features are surfaces which have geometrical, unique and nominal form like. planes, cylinders, spheres, and cones. Derived are axes, midpoints media planes. In general features of size (FOS) Location deviation Orientational deviation Form deviation Datum Figure 1.5 Form, locational and orientational deviation 3 ׉ 7cassandra://9h5jjcXmaBcOrheLT7F9U8XW39KyJjmQGZEQPrE_bzU`̵ay=!"ay=!!{בCט{u׉׉ 7cassandra://e5hJAhSGSpjBOWMyn_RT-IsYQavpgj3QtqLK4GWtKdUb` ׉ 7cassandra://nx5GpZzkiABqeHQohIe_tMftFprIGv2jFXNhNg1vXwcC`S׉ 7cassandra://GY0KZPygjBGj3JiR3ekeXN3Xfv_xxHO3koJdnNfG9Lw"`̵׉ 7cassandra://9YMYPzvIvaK5lNjRGFEyUu6ZTORvTsEsZaqyGGgDLbk;n͠ay=!ט{u׉׉ 7cassandra://iI_MdKWSzV6MyvP4iOWDn8iuuDX99-SalUzru-aDRCY ` ׉ 7cassandra://9Ocj7aYkmAdfahX-7UbN0o9qolw_EgB7t9-3mIpaYEoG`S׉ 7cassandra://MY8Byo15l7ONEvW6gzZX8piz2A7MtE83Bo2JKhf3GP0`̵׉ 7cassandra://abYCD9xbEJAwqXMtXGw7mOON1xd6J2TePXeo6eB143g͇͠ay=!׉EAdvanced Geometrical Tolerancing Geometrical deviationS are: • size deviations • form deviations • orientation deviations • locational deviations • run out • waviness • roughness • surface discontinuities • edge deviations Size deviation is the difference between actual size and nominal size. Form deviation is the deviation of a feature (geometrical element, surface or line) from its nominal form. orientational deviation is the deviation of a feature from its nominal form and orientation. The orientation is related to one or more datum features. The orientation deviation includes indirect the form deviation. locational deviation is the deviation of a feature (surface, line, point) from its nominal location. The location is related to none, one or more (other) datum feature(s). The locational deviation includes indirect also the form deviation and the orientation deviation (of the surface, axis, or median face). Waviness, roughness, surface discontinuities and edge deviations are not part of this document. Only complete and correct tolerated drawings or 3D models enable the production of workpieces to be as precise as necessary and as economic as possible. When all tolerances necessary to define a workpiece are indicated individually the drawing or model becomes overloaded with indications and will be hard to read. Therefore general tolerances can be applied according ISO 22081. General tolerances shall be applied by an indication in or near the title block of the drawing or annotation plane in a CAD model. When there is no appropriate ISO Standard or National Standard available a company standard should be elaborated. . 4 ׉ 7cassandra://GY0KZPygjBGj3JiR3ekeXN3Xfv_xxHO3koJdnNfG9Lw"`̵ay=!#׉E>60 ±0,5 17 ±0,2 10 ±0,2 20 ±0,2 20 ±0,2 6 ±0,2 17 ±0,2 10 60 ±0,5 20 20 6 0,4 A 3x 10 0,3 0,5 M A C B Advanced Geometrical Tolerancing 1.4 dImensIonInG meTHod C 3x 10 ±0,2 B 30 ±0,3 30 ±0,3 20 ±0,2 10 8 ±0,2 8 0,4 Figure 1.6 Coordinate dimensioning A Figure 1.7 Geometrical dimensioning Coordinate tolerancing is an over simplification of part definition leaving out important pieces of information. Major shortcomings are: • Undefined measurement setup • No indication of measurement origin • Rectangular tolerances zones • Accumulation of tolerances • Fixed size tolerance zones • Exact start point of dimensions undefined Avoiding these shortcomings GPS gives the several benefits: • Improved communication • Better ‘functional’ product design • Increased tolerances • Lower costs; 0,4 C 5 ׉ 7cassandra://MY8Byo15l7ONEvW6gzZX8piz2A7MtE83Bo2JKhf3GP0`̵ay=!$ay=!#{בCט{u׉׉ 7cassandra://oHX6ME3HyVhAYkDTJb4FXWAIe3_sHe5Gx6FNXc7B_h4R` ׉ 7cassandra://dHGM6L055r48jue2qjgjQEOuJPAaGGXaa-JD-YSUz2Q+`S׉ 7cassandra://CtRdJAMXeSgEadKZGq-StEU6du6tws64dXgAOJKAfDgi`̵׉ 7cassandra://VLGKC-9TIemgo6wg6A6zd6Afe2jz4cwcZgwLj9ogknw](f͠ay=!ט{u׉׉ 7cassandra://yvbogSgd1VjRSwM9SYM8NSEmpnGcAiQQtyzUxneKDHIs` ׉ 7cassandra://bLUuCnH4_iKGSlbJ9PgHR7UmLaPgdaHf57-bedPv5WEN`S׉ 7cassandra://B9k_lZQhEd7jAS_rDvLuoOWKCnMqKeXdLcQ3g6-X7NYQ`̵׉ 7cassandra://ndWnqTea4CzTgYiwRePpap-8ebAYf628c1GVZYMZZ8MV N͠ay=!נay=!P99ׁHhttp://e.g.ISׁ ׁ Јנay=!ʁ̓9ׁHhttp://2.1.coׁ ׁ Ј׉EAdvanced Geometrical Tolerancing Figure 1.8 Step dimensions vs GD&T on a surface Figure 1.8 Step dimensions vs GD&T on a derived feature Plus/minus dimensions, which are two point local sizes, and tolerances are still used but their use should be limited to defining features of size and the depth or length of features such as holes and pins. For many reasons, ± dimensions and tolerances should not be used to locate features. 6 ׉ 7cassandra://CtRdJAMXeSgEadKZGq-StEU6du6tws64dXgAOJKAfDgi`̵ay=!%׉EAdvanced Geometrical Tolerancing 2 concePTs, Terms and symbols 2.1.concePTs and Terms The fundamentals, concepts, principles and rules of the Geometric Dimensioning and Tolerancing (GD&T) are specified in ISO 8015. Geometric tolerances shall be specified in accordance with functional and economical requirements. Manufacturing and inspection can also influence the geometrical tolerancing. A geometrical tolerance applied to a feature defines the allowed deviation from nominal surface or position. 2.1.1 InvocaTIon Once a portion of the ISO GPS system is invoked in a mechanical engineering product documentation, the entire ISO GPS system is invoked, unless otherwise indicated on the documentation. The ISO GPS system is defined in a hierarchy of standards including the following types Symbols of standards: Fundamental standards e.g. ISO 8015 General standards e.g.ISO 1101 Additional standards e.g. ISO 22081 Normative standards applicable for Geometric Tolerancing are summarized in ISO 1101. 2.1.2 feaTures and feaTure PrIncIPle Feature A feature is a physical portion of the workpiece, such as a point, hole, pin or a surface. These features can be integral features being surfaces or surfaces lines or derived features (e.g. a median line or median plane). Definitions of features are taken from ISO 14660-1 and ISO 14660-2 ww Axis Sphere Cylinder Circumscribed line Torus Cone Circumscribed line Plane Figure 2.1 Workpiece features 7 ׉ 7cassandra://B9k_lZQhEd7jAS_rDvLuoOWKCnMqKeXdLcQ3g6-X7NYQ`̵ay=!&ay=!%{בCט{u׉׉ 7cassandra://yRlm3ostM0X8aincSf351ioXA3zlBHFUFAj28Y05qbAK` ׉ 7cassandra://vkLsVh1gVzK2GNnzNhHX6Bbh23H0W1fxYVBAhRCDvI8E`S׉ 7cassandra://kNjtNBBRS20YnMXRWg0bKMSziLerDCxoe6qhk7F5gJkv`̵׉ 7cassandra://cgmwCfn-D2Q4I06g7XUkgqsrc6HqMtIBUjWRzkRkCyMm>8͠ay=!ט{u׉׉ 7cassandra://iFNIYf0OYLR5_V6HfqRJWrGM_7DO8bij4c2KHLgJ6TAu` ׉ 7cassandra://wWEKCnLMGUswzynIjvcyfsYxi1__HygbsX_AtMxN0JMO``S׉ 7cassandra://zg7P3bZ-GpbLTTWzpi-JEvkjbU4gcUwJjtgg2qN-z4s+`̵׉ 7cassandra://B0YZIqP4MtPNex29lLzTh6-J5mieIaZZNzAEV52d41w f͠ay=!׉E20 32 Advanced Geometrical Tolerancing Feature oF Size is a geometrical shape defined by a linear or angular dimension that is a size. The size of a future of size is always obtained by a two point measurement. Typically, a feature of size is a cylinder, a sphere, two opposite parallel surfaces, a cone or wedge. (ISO 14660-1) inteGral Feature is a surface or a surface line derived Feature is a mid point, center line, or media plane A workpiece shall be considered as made up of a number of features limited by natural boundaries. By default, every GPS specification for a feature or relation between features applies to the entire feature or features; and each GPS specification applies only to one feature or one relation 2.1.3 THeoreTIcal exacT dImensIon Theoretically Exact Dimension (TED) also known true dimension, is a theoretical exact location of a feature of size defined by nominal dimensions. The TED is shown in a rectangular frame and has no tolerance. Theoretically exact dimensions may only vary by the theoretical tolerance that is stated in the associated tolerance frame. TED are used to dimension the theoretical exact location of position, angularity, line profile and surface profile. 4x 10 + 0,4 - 0,2 n\w0œ4Ç\A\B\C] 0,4 A B C C 15 32 B Figure 2.2 Theoretical exact dimension A 8 ׉ 7cassandra://kNjtNBBRS20YnMXRWg0bKMSziLerDCxoe6qhk7F5gJkv`̵ay=!'׉EAdvanced Geometrical Tolerancing 2.1.4 rIGId work PIece PrIncIPle By default, a work piece shall be considered as having infinite stiffness and all GPS specifications apply in the free state, undeformed by any external forces including the force of gravity. Requirements that apply to non rigid work pieces shall be defined in the drawing according to ISO 10579. 2.1.5 PrIncIPle of IndePendency By default, every GPS specification for a feature or relation between features shall be fulfilled independent of other specifications except when it is stated in a standard or by special indication (e.g. m modifiers according to ISO 2692, CZ according to ISO 1101 or ¬ modifiers according to ISO 14405-1) as part of the actual specification. maximum circularity deviation maximum straightness deviation maximum limit of size Figure 2.3 Principle of indendency An altered default specification operator is applied when non ISO standards are used. and shall be defined in a relevant document. The altered default specification operator shall be thorough, unambiguous and completely defined in order to be regarded as a complete specification operator. Figure 2.4 Drawing footer or annotation plane 9 ׉ 7cassandra://zg7P3bZ-GpbLTTWzpi-JEvkjbU4gcUwJjtgg2qN-z4s+`̵ay=!(ay=!'{בCט{u׉׉ 7cassandra://tSEUfrxCBugDLdRrvORo8H1h2VoLM34esGQkBWZgvS0s` ׉ 7cassandra://6iAm6S-nGsMYBytnmov45P2xA20DqMtWTFF-WVdrTTk=`S׉ 7cassandra://cIJMg5sreJo3YY_miXymctpjqVAcVLd82x1EHJrD4GI`̵׉ 7cassandra://1mMP2KW8ikR_efckKfyc6E6IOUir_vKrAiebQpCn5Cwͭ ͠ay=!ט{u׉׉ 7cassandra://sGX5s_IwayC-K8sJSZ6JiHtL5yQeoy0ltqN4JiXt_D4M` ׉ 7cassandra://HAsyeL7GSADtzsJ4-pLLkfxmHRn06jwxUg1D3V0bgiML`S׉ 7cassandra://REzjnhkui7IUqb3Wvc2T_EQykGp02i2bNXNXDIWtAAo`̵׉ 7cassandra://xCT5mNhnTFRfieB19A9pbO-neoPsg3yBJEmNmsgV9r0` ͠ay=!׉EAdvanced Geometrical Tolerancing 2.1.6. enveloPe requIremenT The envelope requirement according to ISO 14405 specifies that the surface of a single feature of size should not violate the imaginary envelope of perfect form at maximum material size. An envelope requirement makes sense with e.g. fittings. In most cases an envelope requirement may not be needed. A survey in several countries showed that an envelope requirement makes sense in only in 10% of the cases. The envelope requirement may be specified either: • by indication of the symbol ‘E’ placed after the linear (size) tolerance • by indication in the drawing title box “ISO 2768 .... E” • by a company standard The envelope requirement cannot be applied to features for which a straightness or flatness tolerance is specified that is larger than the size tolerance. The envelope may also be indicated as a form tolerance with ‘0 m‘ in the feature frame. Envelope requirement over a restricted lenght is indicated as: ø 20 ± 0,03 ¬ / 10 Tolerancing principle ISO 8015 d1, d2 and d3 actual local diameters Envelope at MMC Actual local diameters Envelope at MMC Perfect form at MMC Actual local Actual local diameter diameters 149,96 Figure 2.5 Envelope requirement 10 ׉ 7cassandra://cIJMg5sreJo3YY_miXymctpjqVAcVLd82x1EHJrD4GI`̵ay=!)׉EAdvanced Geometrical Tolerancing 2.2 Gd&T symbols The symbols on indications of geometrical tolerances according to ISO 1101 Geometric tolerances can be applied to three kinds of features: • Integral feature, surfaces or surface lines • Derived features, midpoints,center lines, media planes, features of size • Patterns 2.2.1 GeomeTrIc cHaracTerIsTIc symbols The geometric characteristic symbols are 14 symbols used to describe the geometry attribute of a part. The symbols are divided into four types: form, orientation, location and run-out. Notice that profile any line and profile any surface can define form, orientation and location. Based on the type they may have never, always or sometimes reference to a datum. Tolerances Characteristics Form Straightness Flatness Roundness Cylindricity Line profile Orientation Surface profile Parallelism Perpendicularity Angularity Line profile Location Surface profile Position Concentricity (for centre points) Coaxiality (for axes) Symmetry Line profile Run-out Surface profile Circular run-out Total run-out Table 2.1 Geometric characteristics symbols 11 Symbol a b d e g h k j i g h ( o o q g h u v Datum needed no no no no no no yes yes yes yes yes yes or no yes yes yes yes yes yes yes ׉ 7cassandra://REzjnhkui7IUqb3Wvc2T_EQykGp02i2bNXNXDIWtAAo`̵ay=!*ay=!){בCט{u׉׉ 7cassandra://BHDGs_nD1Jnyw_bv2mZ9C6jRU0ZOvo2x-W0USHOjqbs` ׉ 7cassandra://YUg-QKwwP4u5XL_8r7SvFf1JFJ2HM8dXzJkM2pQEO9kA`S׉ 7cassandra://R_A88SCDp5u3A0Lnp1dNsjm5_BQoeCc-hhD_XOcRP5k`̵׉ 7cassandra://L1a8auSxd8vVC8BEqBMrYYuTbDiGRu7atJUKmqRV-rISA :͠ay=!ט{u׉׉ 7cassandra://9A8XOWqfE8iYQ9pkgyEgO9yUCkDnypHzusVcSS02R78` ׉ 7cassandra://h3ZUJdq6RFlyPN3FJGnhnjICIbHsh7uwbzz9emxeVtk/`S׉ 7cassandra://LaYJGJoCpZfifNQpdjtNqCNEUFzr3s1v9GcCAQqFITc`̵׉ 7cassandra://G2M0aMg1-DCaPfygi5xUg_vU1d_r_CD0d6Ko1z47iaE_r͠ay=!׉EAdvanced Geometrical Tolerancing Form tolerance Form tolerances limit the deviations of a feature from its geometrical ideal line or surface form. orientation tolerance Orientation tolerances limit the deviations of a feature from its geometrical ideal orientation with respect to the datum (s). location tolerance The location tolerance zone is the geometrical ideal location, orientation and distance, with respect to the datum(s). Location also limits the orientation and the form tolerance.of the toleranced feature. run-out Run-out tolerances are partly orientation tolerances (axial circular run-out, axial total runout) and partly location tolerances(radial cirular run-out, radial total run-out). Geometrical tolerances and tolerance symbols Unrelated geometrical tolerances (form tolerances) Profile (form) of lines (line profile) g a d Profile (form) of surfaces (surface profile) Flatness Cylindricity Related geometrical tolerances i k j ( Symmetry Run-out Circular run-out Total run-out Table 2.2 Geometric tolerances and tolerance symbols 12 Circular radial run-out Circular axial run-out Total radial run-out Total axial run-out u v o q h b e ׉ 7cassandra://R_A88SCDp5u3A0Lnp1dNsjm5_BQoeCc-hhD_XOcRP5k`̵ay=!+׉EIAdvanced Geometrical Tolerancing 2.3 THe Tolerance frame 2.3.1 Tolerance frame Interpretation Number of occurrences Datum letters Modifier symbol Size tolerance zone Symbol for tolerance zone Symbol for tolerance characteristic Figure 2.6 Tolerance frame composition nw0œ02mÇ] [R\Sm\T] Figure 2.7 Tolerance and datum frames 13 ׉ 7cassandra://LaYJGJoCpZfifNQpdjtNqCNEUFzr3s1v9GcCAQqFITc`̵ay=!,ay=!+{בCט{u׉׉ 7cassandra://AE5TICYm_6_l113cCvhOT8T7JMXB_gMVBmI9xuHaqIY` ׉ 7cassandra://KtLnDfAyxm1WEFGlmjFH1uWVKfxgaBykrDIf5CAf6Ak#`S׉ 7cassandra://cuk-Sn_ij30yMgJZb5ojVouyoPNQnAxX5vZ81t7koyw ;`̵׉ 7cassandra://qcUGaQFg4ave7tyV4V-sFCRpx54UBVPj6w5tPekhe3Y^͠ay=!ט{u׉׉ 7cassandra://3N1mi9NiwhZ1WnIDTvBirFuZyMsWw7yRO7mMHWEBgU4@` ׉ 7cassandra://beAGtU8im8I7LTCogNPpNi8LhJ5FKobGFp49VeusTNE' `S׉ 7cassandra://Pq-61mVkgJgKFxo3ZU8wr6C-dKBHwZaXv8PCBhD_Hr8 ?`̵׉ 7cassandra://4cmzKVtQpJfvdlq12NQ2mFyLsTcIt0k0YzpzhI2YKBsX ͠ay=!׉EHAdvanced Geometrical Tolerancing Figure 2.8 Complete tolerance frame 14 ׉ 7cassandra://cuk-Sn_ij30yMgJZb5ojVouyoPNQnAxX5vZ81t7koyw ;`̵ay=!-׉EBAdvanced Geometrical Tolerancing 0,2 A-B Datum established by two features. n\w0œ2Ç\R\S\T] n\Sw0œ3Ç\R\S\T] 0, A2 C B S 0, C BA2 0, A2 Cylindrical tolerance zone, three datums. Spherical tolerance zone, three datums. Tolerance zone space between two parallel planes, one datum. 0,2 Form requirement, no datum. 6x 0,1 Requirement applies to more features. n\w0œ1Ç\R\S\T] 8x 12 0,05 0,2 0,1 NC Figure 2.9 Tolerance frames Requirement applies to more features, dimension over tolerance frame. Indication qualifying the form “Non Convex” (obsolete since ISO 1101:2017). 15 ׉ 7cassandra://Pq-61mVkgJgKFxo3ZU8wr6C-dKBHwZaXv8PCBhD_Hr8 ?`̵ay=!.ay=!-{בCט{u׉׉ 7cassandra://rzRDPWMdnAM_VbNFIa2G_yFY87GhWfI7n4JBbilTrDkG` ׉ 7cassandra://6XCnPYHGLsLfF8498Qy56wNqB4C03D1Lv1rZ37qC-eE* `S׉ 7cassandra://wWhLVJ64ut5_8F7vQy0sKEuRsEng81OqJe3t7vk5a583`̵׉ 7cassandra://zWXfE6HzyenaEovCj96NFiyioqAFtcsrIQV5NT1hnGAo͠ay=!ט{u׉׉ 7cassandra://bqtNedju39sbdNg7yP-gpOTOh3HbybT_skhm9ACCZ1gY` ׉ 7cassandra://daCYYOgIYOpa82vB_gD5Fv5kCdvt97vM0iHTgrYEaws%`S׉ 7cassandra://xnXp1_pQEPqd7Bh23-lgA1a4IoyLOVgiEqpgO-zJODc `̵׉ 7cassandra://d0CkKEHigLVCDL5lGRvlkbCd5tH_M_2BZ3ZA_5k2TJU͠X \͠ay=!׉E Advanced Geometrical Tolerancing 0,5 A B C 0,1 A Superposition, different type geometric requirements 0,5 M A B C 0,1 M A B Superposition, same type geometric requiremenst 0,02 M A M B Datum reference attached to tolerance frame D E Open or closed datum reference traingle Figure 2.10 Tolerantce frame and datum reference 2.3.2 feaTure IndIcaTIon Symbols Interpretation Axis or media plane as toleranced feature or datum feature Surface or section line as toleranced feature or datum feature Figure 2.11 Derived feature 16 ׉ 7cassandra://wWhLVJ64ut5_8F7vQy0sKEuRsEng81OqJe3t7vk5a583`̵ay=!/׉EAdvanced Geometrical Tolerancing Figure 2.10 Indication on surface or extensionl ine Axis or media plane common datum established by two features Figure 2.12 Common datum from A and B Top side as datum feature with form tolerance Figure 2.13 Position of the arrow and datum indicator depreciated and Former practiceS On deprecated and former practices consult ISO 1101. For detailed information on datums see ISO 5459 17 ׉ 7cassandra://xnXp1_pQEPqd7Bh23-lgA1a4IoyLOVgiEqpgO-zJODc `̵ay=!0ay=!/{בCט{u׉׉ 7cassandra://-44AXW4FI_RF-jiJqLsrgHec6L44JKLXz4bWdLUWZXEsN` ׉ 7cassandra://lDPVS2TFzLVF4knScJUT7HrPxLBhSXx-zUrerTYGFaMO`S׉ 7cassandra://0NAxmZoFhpq1BVxhhW8JChUF1g-dX-4sip-4KXgcgaI+`̵׉ 7cassandra://ahA9BDjfpQzkxetnaO4nYuOJah5vHPk8pwzgdPWnKVo͓͠ay=!ט{u׉׉ 7cassandra://_OZ6Lxez-jiH4HKvx-Fn4pbUVN84VbACv63Ljdjxf5wE` ׉ 7cassandra://6bD3vR3i4-TSXpm9vNtADavBz2KDbURYYNKpRtCqvvs8`S׉ 7cassandra://XsIa3L4puE6Gb33MXH9rz8DB49QocynjdkwU6ho9Lf0`̵׉ 7cassandra://AWEcqUWjv11vMP7AXOLZXCeOeOmudXV_BoXzvaujv-k͠ay=!׉E Advanced Geometrical Tolerancing 2.3 wIdTH and dIrecTIon of THe Tolerance zone Tolerance zones have limiting lines or surfaces that are equidistant from the nominal (geometrical ideal) form. The shape of the tolerance zone is independent of the size of the feature(s). Exceptions are tolerance zones of line profile or surface profile where the nominal (geometrical ideal) form is defined by theoretical exact dimensions (TEDs). The width of the tolerance zone is equal to the tolerance value, and is directed according to ISO 1101 in the direction of the leader line arrow: • with tolerances of axes and median faces perpendicular to the toleranced axis or median face; • with tolerances of surfaces or lines perpendicular to the surface. Drawing Tolerance zone Figure 2.14 Arrow perpendicular to surface Figure 2.15 Arrow perpendicular to surface In the figure the width of the tolerance zone is in the direction of the leader line arrow perpendicular to the surface. Below when the width of the tolerance zone is not perpendicular to the surface or the axis or the median face, the direction of the width of the tolerance zone shall be indicated as shown Figure 2.16 Arrow not perpendicular to surface but under given angle Figure 2.17 Tolerance zone not perpendicular to surface 18 ׉ 7cassandra://0NAxmZoFhpq1BVxhhW8JChUF1g-dX-4sip-4KXgcgaI+`̵ay=!1׉EAdvanced Geometrical Tolerancing 2.4 sHaPe of THe Tolerance zone Depending on the toleranced characteristic and depending on the drawing indication the tolerance zone is one of the following. • area within a circle • area between two concentric circles • are between two equidistant curved lines or between two parallel lines • the space between two equidistant curved surfaces or two parallel planes • the space between two coaxial cylinders • space within a sphere • space within a cylinder Drawing Tolerance zone Figure 2.18 Position tolerance Figure 2.19 Cylindrical tolerance zone 0,02 Figure 2.20 Roundness Figure 2.21 Tolerance zone of two concentric circles 0,02 Figure 2.22 Flatness Figure 2.23 Space between two equidistant planes 19 ׉ 7cassandra://XsIa3L4puE6Gb33MXH9rz8DB49QocynjdkwU6ho9Lf0`̵ay=!2ay=!1{בCט{u׉׉ 7cassandra://gI_GmVSOCY33AxXIGpYTkapwnlkYKTUZMo1ndkuNoxA=` ׉ 7cassandra://g1OFRSBd2kal-pwNRODKgyBIrUE13piQRJ3hKTRzZ8Y+t`S׉ 7cassandra://J-qBo2olgrDs6420SEh_qfXhT72bbWAuf8uKl0Qrc6g `̵׉ 7cassandra://lrajgzQoQT_oIY1StPLOFihpl3CQICeU9p4VrIee_7gL#͠ay=! ט{u׉׉ 7cassandra://-3HREdDCS3e1m7sRvhT3FLYPNCd-rxL9kcHIg3-ibZo{` ׉ 7cassandra://gdtEdi5T1s6ASaIdJ8jCBGF1N4_tEsAyv7W9Tkdd9Yc0`S׉ 7cassandra://bQ7COXBYIoqvFlFeCXE21ozqStJdXdX-OUsakqlDElw 8`̵׉ 7cassandra://W_0BGoRHNKBHWDSvQx_2zNfHeKovbn-dlqruweyhBP0Qr͠ay=! ׉EZAdvanced Geometrical Tolerancing Drawing S 10 0,2 S 0,1 A A 24 Figure 2.24 Position of a sphere Figure 2.25 Spherical tolerance zone Tolerance zone 0,1 Figure 2.26 Straightness Figure 2.27 Tolerance zone of wo parallel lines A 0,05 A ! Figure 2.28 Total run-out Figure 2.29 Tolerance zone of two coaxial cylinders with respect to a datum axis 20 ׉ 7cassandra://J-qBo2olgrDs6420SEh_qfXhT72bbWAuf8uKl0Qrc6g `̵ay=!3׉EAdvanced Geometrical Tolerancing 2.4.1 lImITed Tolerance zone If not otherwise indicated, the geometrical tolerance (tolerance zone) applies to the entire length or surface of the feature. When the leader line arrow points to a thick chain line or area within a thick chain line, the tolerance applies to this region. 0,01 0,02 21 5 Figure 2.30 Requirement over a restricted length or surface 13 0,1 Figure 2.31 Requirement over a restricted length or surface When the tolerance value is followed by an oblique stroke and another value (e.g. 0,1/50), the second value (50 here for the straightness requirement) indicates the length within which the tolerance (0,1) applies. The tolerance zone (of 0,1 width) of the specified length (50) applies to all possible locations on the feature. 21 4 10 ׉ 7cassandra://bQ7COXBYIoqvFlFeCXE21ozqStJdXdX-OUsakqlDElw 8`̵ay=!4ay=!3{בCט{u׉׉ 7cassandra://JT1xSzaEXahsOCYryhI64sSEd1Vt8yvvxU4ZufGqsuc` ׉ 7cassandra://4SLnVgMGSz5aS0z_JKEMdzxMWf5Y2_E4_gTtzaEmECU8`S׉ 7cassandra://RzXjip0nvAa35FrauBxqOBIUWlqO7nL1uvugrNdLwp0`̵׉ 7cassandra://xdf2czMC4JaxQJcqcOADqfx0rBjIhnNphPS8q4dKakU$ez͠ay=! ט{u׉׉ 7cassandra://CCQ8MekKB3FVEc7Uv5sOW18H9ULN8bephBqwdAF8d3w!` ׉ 7cassandra://BtwqfH8ndFMN1gzB1ixvPYUPExgHJqnWMCBS_S8RDkc6v`S׉ 7cassandra://rXC_aBM6IlTL1LstVWTgN2lgL_Y6mUfWVRl25-xEy5U`̵׉ 7cassandra://3_4OAqCc4j3uUagmB9HSLFaSqiUWB1GlFUSK4WH94NE ͠ay=!׉EwAdvanced Geometrical Tolerancing 2.5 auxIlIary Planes 2.5.1 InTersecTIon Plane Figure 2.32 Line profile, lines perpendicular to axis A Figure 2.33 Straightness, lines parallel to datum A Figure 2.34 Line profile, 0,3 parallel to parallel to datum A and 0,1 parallel to datum C. Datum B for orientation only. Figure 2.35 Lines parallel to D orientation parallel to datum C 22 ׉ 7cassandra://RzXjip0nvAa35FrauBxqOBIUWlqO7nL1uvugrNdLwp0`̵ay=!5׉ExAdvanced Geometrical Tolerancing 2.5.2 orIenTaTIon Plane In the case of a median feature (center point, median line, median surface) tolerated in one direction: In 2D view, when the direction of the width of a tolerance zone is at 0° or 90° relative to the datum or relative to the pattern of the theoretically exact dimensions, the arrow of the leader line gives this direction. Figure 2.36 The direction of the arrows make up the planes for the tolerance zone The way having the leader lines defining the direction of the tolerance zone plane is deprecated. Figure 2.37 Centerline between two planes perpendicular to datum B 23 ׉ 7cassandra://rXC_aBM6IlTL1LstVWTgN2lgL_Y6mUfWVRl25-xEy5U`̵ay=!6ay=!5{בCט{u׉׉ 7cassandra://GMpV2RAX-r8fDjCdE2Rr1jlQUDofGLGrksWAcPtTknE/` ׉ 7cassandra://N67ldWehNy8AoaMWbTgVpb7YNv1CSiL7j2IC-xzp-4w/ `S׉ 7cassandra://2VlY7Y9LOUat6KRXK5wnZDihchxOLEB2j2jOpk9qf_s `̵׉ 7cassandra://RefFDHLnW0AHkrNZNOalAlskCrOApbicnqPbi1a3qys >f͠ay=!ט{u׉׉ 7cassandra://QMxssowVc65qKxAIDn3zkDFqf2FF1o4WaEf-AW0NIXEo%` ׉ 7cassandra://yrx3uv_Z0woMrfo32FYW4AyVYbkbxoPI2kdNLPKXgaA)`S׉ 7cassandra://DDDu3ATdalODVOC8nHZTlH-sUdpnPeCrbch8gvKY01w!`̵׉ 7cassandra://fh713QBC5yvWRTXqRH4Hch1ZRV69SQMslTKAnCq7lz8"j͠ay=!׉EAdvanced Geometrical Tolerancing Figure 2.38 Centerline between two planes parallel to datum B Figure 2.39 Centerline between four planes. 24 ׉ 7cassandra://2VlY7Y9LOUat6KRXK5wnZDihchxOLEB2j2jOpk9qf_s `̵ay=!7׉E>Advanced Geometrical Tolerancing 2.5.3 dIrecTIon feaTure Figure 2.40 Circular run-out, orientation of the tolerance zone direct implied Figure 2.41 Circular run-out, orientation of the tolerance zone indicated by direction feature Figure 2.42 Tolerance zone for roundness of the cone perpendicular to the cone axis 25 ׉ 7cassandra://DDDu3ATdalODVOC8nHZTlH-sUdpnPeCrbch8gvKY01w!`̵ay=!8ay=!7{בCט{u׉׉ 7cassandra://8yWqR2x7JEtx9KpMdMITw7C0n8BKP36Yr7jgf8RemMA(` ׉ 7cassandra://r22Q5aHo-cCrysPPnLibcf_UjyN0DokP2bW9XWgZi5A%`S׉ 7cassandra://YQtw60PR2--2njPieV1XgT6gwYP98Bu0i4QlhEaSUO8 Y`̵׉ 7cassandra://i8WFRD0bYbgDh34fDAc0i5Mw9pMoIoC8Mfjufb3OqnA͏w^͠ay=!ט{u׉׉ 7cassandra://kQzazPY0HI60u1vu34lRMNgU7Jf7otXw4LkpXEET-nM` ׉ 7cassandra://PSUNVhCtYR-9dzonb7FhnXWU6e0KbDeg2k-8YXgkarEHv`S׉ 7cassandra://nOdmXTNdNgPxL_C_CHpdtHoTsVqvN9ku2lXB6gUpdGI#`̵׉ 7cassandra://MvXwY3FF944zrmRlX7Lu3uvvshw4gmx2EIXTmyUvwTEteX͠ay=!׉EAdvanced Geometrical Tolerancing 2.5.4 collecTIon Plane A collection plane shall be indicated when the “around” symbol is used:to identify that a specification applies to a collection of features. A collection plane identifies:a set of single features whose intersection with any plane parallel to the collection plane is a line or a point Figure 2.43 Tolerance zone for a set of lines on the closed compound continuous surface 26 ׉ 7cassandra://YQtw60PR2--2njPieV1XgT6gwYP98Bu0i4QlhEaSUO8 Y`̵ay=!9׉EAdvanced Geometrical Tolerancing 2.6 General Tolerances Figure 2.45 All tolerances stated All features of a workspiece have a form and dimension. Therefore all elements need to be dimensioned and need a geometric tolerance. The use of ISO 2768 simplifies the drawing or model and makes sure all elements are tolerated. ISO 2768-1 ISO 2768-2 Tolerances for linear dimensions and angles Geometric tolerances (obsolete from the introduction of ISO 22081 in 2021) The general tolerances use classes. When this standard is used the classes need to be stated. For example ISO 2768 mK ISO 2768 mH Figure 2.46w General tolerances according ISO 2768 27 ׉ 7cassandra://nOdmXTNdNgPxL_C_CHpdtHoTsVqvN9ku2lXB6gUpdGI#`̵ay=!:ay=!9{בCט{u׉׉ 7cassandra://m486jy6AAXKo5jDJTN6LsV4-9k7h5i-9G17D96L_HMI` ׉ 7cassandra://-brrD8XLhJ_8fPl_O38wUcePjD0HwWH1Zf0-Fxcs0N8O`S׉ 7cassandra://nKAWgGI6TznV6v3eeJa4KSaJbAezJmDnFKsOXu-ajKM,`̵׉ 7cassandra://K7wZZQQ4zweRnuuooxQDd9zehSq0B_H_b8BoGOVo2wg]> ͠ay=!ט{u׉׉ 7cassandra://JaDzAWvKcJWifoz-Rw7TRHCVwsxPD_tS948WxJqaw74[` ׉ 7cassandra://8pt42hnYUyrZHILQsA9n-Phfgeuf6sALTKLS-x0WCkg y`S׉ 7cassandra://BHa3a9NUsLItZx5MlYauTU6ZUbi-7AhEb2PC9jGoTPA `̵׉ 7cassandra://QymAP6tMhE7AziXb4A8hhwjEDu0v6LEgTq-thidvw8c5-^͠ay=!׉EiAdvanced Geometrical Tolerancing Limits in mm for nominal sizes in mm Tolerance class f (fine) m (medium) c (coarse) v (very coarse) - Table 2.4 General lineair tolerances The table is an example of the limits for nominal sizes as stated in ISO 2768-1. Tolerances for dimensions smaller the 0,5 mm need to be stated on the drawing. This standard includes linear standard tolerances, Tolerances for fillets and chamfers and angular tolerances. The angular tolerances define the global orientation of the line of line piece in degrees. Form deviation is not included in angular general tolerance. ISO 2768-2, obselote for new design from 2021, is on the geometrical deviations. On form there are general tolerances on straightness and flatness. There are no general standards on roundness and cylindricity. On the related tolerances there are symmetry, parallelism, perpendicularity and circular run-out. There are no general tolerances on cylindricity, total runout and profile. 0,5 to 3 above above above above above above above 3 to 6 6 to 30 ± 0,05 ± 0,05 ± 0,1 ± 0,15 ± 0,1 ± 0,2 ± 0,5 ± 0,1 ± 0,2 ± 0,5 ± 1 30 to 120 ± 0,15 ± 0,3 ± 0,8 ± 1,5 120 to 400 ± 0,2 ± 0,5 ± 1,2 ± 2,5 400 to 1000 ± 0,3 ± 0,8 ± 2 ± 4 1000 to 2000 ± 0,5 ± 1,2 ± 3 ± 6 2000 to 4000 - ± 2 ± 4 ± 8 straightness and flatness tolerances for nominal lenghts larger than Tolerance class H K L t/m 10 10 to 30 0,02 0,05 0,1 0,05 0,1 0,2 Tabel 2.5 General tolerances for straightness and flatness larger than 30 to 100 0,1 0,2 0,4 larger than 100 to 300 0,2 0,4 0,8 larger than 300 to 1000 0,3 0,6 1,2 larger than 1000 to 3000 0,4 0,8 1,6 28 ׉ 7cassandra://nKAWgGI6TznV6v3eeJa4KSaJbAezJmDnFKsOXu-ajKM,`̵ay=!;׉EmAdvanced Geometrical Tolerancing Unless otherwise stated workpieces exceeding the general tolerances can not merely rejected when the workpieces is meeting it’s function. General tolerances apply to all form tolerances except: • Cylindricity (fittings might use the envelope requirement) • Parallelism ( • Angularity • Coaxiality • Profile any line and any surface • Position • Total run-out other General toleranceS • ISO 3302: Rubber dimensional tolerances • ISO 8062: Dimensional en geometrical tolerances for molded part • ISO 13920: General tolerances for welded constructions • …...... 29 ׉ 7cassandra://BHa3a9NUsLItZx5MlYauTU6ZUbi-7AhEb2PC9jGoTPA `̵ay=!<ay=!;{בCט{u׉׉ 7cassandra://bpRjHUFmUFyNCfZEEuH3gO2T2rolg-9joIW5aiynPlQ` ׉ 7cassandra://ELeNraeVsAqXLeaYt4ogUYya09l-tc7fsRFLclZ-HVACB`S׉ 7cassandra://9OUox1R4H0qDRhWfLhzpC1SmFA5bxm4_dxV7Z5ZyedM`̵׉ 7cassandra://YiRtxK-jJwS4daodMPebEMQYKEPFY4c5yty0tAXMODQ͕͠ay=!ט{u׉׉ 7cassandra://AFVbV0pjcER1MIPALfDcL7qd7mDG4oWNdCBYdIA8WfAG` ׉ 7cassandra://MhQiKgLuNWxllAlAQ6dwIkACqvcmzQzWdW3dGfNznKM+`S׉ 7cassandra://14Z-xqRAHhz5TOpIKbcgRw6A8RdFHL6Ymg5UhPNC4ko`̵׉ 7cassandra://skVJqyYD-v1QQwu_Z78Yfxd_99pstHiLYx3kYVxysEEͬ D͠ay=!׉EAdvanced Geometrical Tolerancing 3 modIfyInG symbols Description Toleranced feature indication Datum feature indication Datum target indication Theoretically exact dimension Median feature Unequel tolerance zone (offset) Between From ... to Projected tolerance zone Maximum material requirement Least material requirement Free state condition (non-rigid parts) All around (profile) Envelope requirement Common zone Minor diameter Major diameter Pitch diameter Line element Not convex Any cross-section Direction feature Collection plane Intersection plane Orientation Plane Table 3.1 Geometric modifying symbols 31 Symbol å UZ ) ç p m l f “ ¬ CZ LD MD PD LE NC ACS (obsolete 2017) (obsolete 2017) (obsolete 2017) ׉ 7cassandra://9OUox1R4H0qDRhWfLhzpC1SmFA5bxm4_dxV7Z5ZyedM`̵ay=!=׉E*Advanced Geometrical Tolerancing 3.1 combIned zone Modifying symbols are symbols that communicate additional information about the tolerancing of a part.or datum. Individual tolerance zones having the same value applied to different features may be indicated as show. 0,05 Figure 3.1 Individual tolerance zones When the features are to be contained in a combined tolerance zone, this is to be indicated by “CZ” after the tolerance value in the tolerance frame. 0,05 CZ Figure 3.2 Combined zone tolerance 0,05 CZ Figure 3.3 Combined zone tolerance 32 ׉ 7cassandra://14Z-xqRAHhz5TOpIKbcgRw6A8RdFHL6Ymg5UhPNC4ko`̵ay=!>ay=!={בCט{u׉׉ 7cassandra://nLzsWUk2j0lGuD2d6Y4Tv5zLxzrJdvjCqgWW7yqWmoA`` ׉ 7cassandra://NLDDh6lDfYTHBFmMRKPIXpoSgGMUDW141jSvv1hfLmw1i`S׉ 7cassandra://AnjgLRLPoIN_QtYhr17DQ-4yNkWwABeaZs4OwAXLE3g`̵׉ 7cassandra://UQ8XBjhgY6_qGbVm2kqDtTY9E6ANUuCxgFuhvVEKx00r78͠ay=!!ט{u׉׉ 7cassandra://oBsxx0S654rVk81acu1sRXkc9TxunnhdzdZhsgoDthsI` ׉ 7cassandra://RoaVEG9ttIHWEd7jmz8XiMDJ0sgZb1kkNruUhQJZ3cQ;`S׉ 7cassandra://LA4cZR8eUidKfM5nlo8tGJAQIGZOP8vz2L0HkLV-aHIJ`̵׉ 7cassandra://jJpd_n7hAXuwaTvpopnZa48RoLQyAeEmd58i-dkYlrwΣf͠ay=!"נay=!&ˁ>9ׁHhttp://part.Thׁ ׁ Ј׉EAdvanced Geometrical Tolerancing Where CZ is indicated in the tolerance frame, all the related individual tolerance zones shall be constrained in location and in orientation. Surfaces are considered one surface and axises as combined axis. Figure 3.4 Combined zone tolerance 0,1 CZ Figure 3.5 Combined zone tolerance A 0,02 CZ B 10 0,1 0,05 M A - B Figure 3.6 Datum with combined zone straightness tolerance 33 10h6 8h6 ׉ 7cassandra://AnjgLRLPoIN_QtYhr17DQ-4yNkWwABeaZs4OwAXLE3g`̵ay=!?׉EAdvanced Geometrical Tolerancing 3.2 ProjecTed Tolerance feaTure Projected zone tolerance is used to assure that there will be no interference between a screw, stud or dowel pin and the mating part.The projected zone, a orientation (angularity) and position tolerance applies to the virtual external projection of the feature indicated by the symbol p. Figure 3.7 Projected tolerance zone 34 ׉ 7cassandra://LA4cZR8eUidKfM5nlo8tGJAQIGZOP8vz2L0HkLV-aHIJ`̵ay=!@ay=!?{בCט{u׉׉ 7cassandra://XevBfaZDYPXnuBtktAFPvguSaF4W4D7OkrWRZ0Y_1ak~` ׉ 7cassandra://0uQ08sAxESF_h71l27aOZWKu5cfGnHkcoaRegzRUDwY6`S׉ 7cassandra://XCYkCcSkvGNSiDYki6Hda1hLkVY9kScWwXttEqjawUo`̵׉ 7cassandra://wncpC4v7QvBm_3LY9czOKMy_MJmQv5ZBCSocoppty24f͠ay=!%ט{u׉׉ 7cassandra://g9LdZPZZqQC2svnXuAY0J2VY7ZwNPLi2X824fEBf1ZQ2` ׉ 7cassandra://hMrquia6-zcPSJ7ulYUH4zp7el-X_BZ-0nIXbpP_H7s3N`S׉ 7cassandra://6X_4NsKvcqjkZ2qAnSXffWLfykfxcCVS8u1Ee777JdM$`̵׉ 7cassandra://t0Q9JqXcA-l6NpAqn4mz9bAevkP_3ZGtzpb5_YJntpwzL͠ay=!'׉ElAdvanced Geometrical Tolerancing Figure 3.8 Projected tolerance zone Figure 3.9 Projected tolerance zone 35 ׉ 7cassandra://XCYkCcSkvGNSiDYki6Hda1hLkVY9kScWwXttEqjawUo`̵ay=!A׉EAdvanced Geometrical Tolerancing 0,2 P 8 0,2 P 15 Figure 3.10 Indirect identification of the tolerance zone Figure 3.11 Direct identification of the tolerance zone The external projection is to be indicated by a long-dashed double dotted narrow line. The length of the external projection shall be indicated by a Theoretical Exact Dimension (TED) or might be places in the second compartment of the tolerance control frame after the symbol p. 0,2 P 0,2 P 15 - 5 Figure 3.12 Tolerance zone with offset Figure 3.13 Tolerance zone with offset When indirectly indicated the first value after the modifier indicates to the farest limit of the extended feature the second value indicates the nearest limit. The lenght of the extended feature is the difference between the values. 36 P 10 5 P 15 ׉ 7cassandra://6X_4NsKvcqjkZ2qAnSXffWLfykfxcCVS8u1Ee777JdM$`̵ay=!Bay=!A{בCט{u׉׉ 7cassandra://W-EnL3CIpNJrJ-_Lg2iME6--A6Wl3VuN9isiN7UVkWo6` ׉ 7cassandra://zcWHI1FDnF3yCr_AKDr_63kfMeUASj4Zg3dBtnhAelI+`S׉ 7cassandra://P7HyHnrRN6V_uOtHQ4nYW35CSXxkgAatQN-g3nIEMDA l`̵׉ 7cassandra://MrYN0j1DeKfMTpNrol0h85W1e23Sx4xTK7BFctzKt7Q͜j͠ay=!)ט{u׉׉ 7cassandra://8mLMtCR9UjOn9_V7wT8XFdbCxgE4BZBdFy_-LG4DiJU%` ׉ 7cassandra://9nO3-wa5KcUTN8XLoME0U9esV6vhCl7ekFYwjxr8uWY=+`S׉ 7cassandra://PgJikpCtehVM-YDGVaMEADV24TpBQozINLskHaCv6A4 `̵׉ 7cassandra://ICCBS_jHidSnMfrdXfUHGKDnTy7INQDkraiAQ1dHTD0͜͠ay=!*׉EAdvanced Geometrical Tolerancing 3.3 free sTaTe condITIon Tolerancing a non-rigd part needs to be done according ISO 10579. All dimensions and tolerances are to be met in restrained condition. A note is required stating how the part is to be restrained. Only tolerances modified with the modifier f apply when the parts is in the free state condition, free of applied forces. iso 10579 restrained condition: dimensions and tolerances apply with part restrained to datum feature B with 10n applies to each datum target c Figure 3.14 Free state Here the only tolerance that applies in the free state is the profile of a surface tolerance on the two surfaces established by datum B. All other tolerances apply in the restrained condition. 37 ׉ 7cassandra://P7HyHnrRN6V_uOtHQ4nYW35CSXxkgAatQN-g3nIEMDA l`̵ay=!C׉EAdvanced Geometrical Tolerancing 3.4 medIan feaTure Axis or media plane as toleranced feature or datum feature Figure 3.15 Media plane or axis 3.5 unequal zone The profile surface shall be contained between two equidistant surfaces enveloping spheres of defined diameter equal to the tolerance value. The centres of the spheres have an offset from the theoretical surface. The direction and value of the offset is given between brackets. A “+” sign indicates“out of the material” and the “-” sign “into the material”. Figure 3.16 Unequal zone 1. theoretical profile in this example, the material is below the profile 2. sphere to define the offset theoretical profile 3. sphere to define the tolerance zone 4. limits of the tolerance zone 38 ׉ 7cassandra://PgJikpCtehVM-YDGVaMEADV24TpBQozINLskHaCv6A4 `̵ay=!Day=!C{בCט{u׉׉ 7cassandra://oemYUcTos-Wha-vO-kE09wPJWJSK4hBVLF9Lu9i4hYYM` ׉ 7cassandra://p6TgTjXZTe0MVirWa4L0PrYNmp-pEgS7Mm9-hXSXKEg*`S׉ 7cassandra://a0t935sNZ1PYc0jOVorGU55mEzAhgSW7GSWTU2MQ5iQ"`̵׉ 7cassandra://vIIumc5oQrY8OlOZLd_Z06fVn6ocxSKqxBiMELFaWaY͡j͠ay=!,ט{u׉׉ 7cassandra://JWDFdb7r0W-TrOoiC-S1NO-yvMCUNi9QK1V9uhh-K-I` ׉ 7cassandra://wKAU5PuaVPFdERinqdbAAd-mNoGg8mzpSY-hV5Jd9pU-`S׉ 7cassandra://vx3W3heSohAtIg4vhXlAetF-WP3TCxRzHUS1NygMaSA`̵׉ 7cassandra://mqum2lyPlmSUUEzZNgusg4aOjbV2xRKlpeCXjvor8tYͮB ~͠ay=!-נay=!/*9ׁHhttp://2.atׁ ׁ Ј׉EAdvanced Geometrical Tolerancing 3.6 all around The all around symbol in figure 3.16 is used to extend the tolerance zone to include all the features in the view shown. Figure 3.17 All around and all over symbol 3.7 beTween Figure 3.17 shows the between symbol used to indicate that the tolerance applies to the features between two points. Indicated by the TED dimension is the minimal syrface. Minimal surface results that de TED of 8 kan only get smaller. Figure 3.18 Between symbol 39 ׉ 7cassandra://a0t935sNZ1PYc0jOVorGU55mEzAhgSW7GSWTU2MQ5iQ"`̵ay=!E׉EAdvanced Geometrical Tolerancing Figure 3.19 Between symbol The diameter of the shaft is ø 18h7. This is size only. Between H and K is the additional envelope requirement. The keyway also needs an envelope requiremnet to avoid it to be a banana shape. The keyway is positioned symmytical to the shaft centerline. P Q 0,05 - 0,2 Q The tolerance zone value is variable along the considered feature. Here at ‘P’ the tolerance is 0,05 and increases proportional till 0,2.at ‘Q’. P 20 Figure 3.20 Variable tolerance zone 40 ׉ 7cassandra://vx3W3heSohAtIg4vhXlAetF-WP3TCxRzHUS1NygMaSA`̵ay=!Fay=!E{בCט{u׉׉ 7cassandra://nNVIMOV4G_a3iSVHl0B1uoGdZQOgtsZmEXB4g_uHw_0` ׉ 7cassandra://YrPIqeK3FSJBTj-leXRmj2appvRRa3rQgCj3rFuzwtE4`S׉ 7cassandra://eBznv_CoASRXiYMcOyuBozRGKEW8uIEQVRY31tJMu1Y0`̵׉ 7cassandra://z4xr66eCtqBXsSpxrXz46P-7Oomgy4DcBDsl8FmR55Yf͠ay=!0ט{u׉׉ 7cassandra://DaGwCDK4jqHD9utGMdHxfqLHfja-iE3v_iClawZK6gY(` ׉ 7cassandra://UuG2cvo0tzNnztf9EL0awE-DIB0Qhylz9XjCeFwcALYN`S׉ 7cassandra://UfK6Z9hFu0hhdF6CAfcJjzGFtBdJDKZNL1yKS4F3epc`̵׉ 7cassandra://gNd4e2x-eYTzAkeFPBBZj7ijga-1T2krTpotOGHu_sYͩ ͠ay=!1נay=!3̈ 9ׁHhttp://maximum.maׁ ׁ Ј׉EAdvanced Geometrical Tolerancing 2x [K 0,2 L L] K Figure 3.21 More surfaces To extend the profile tolerance to include more surfaces in this case the notation ‘2x’ is used. The letters indentifying the start and end need to be placed between brackets. 3.8 screw THreads, mulTIPle sPlInes and Gears Figure 3.22 Screw threads, multiple splines and gears Tolerances and datums specified for screw threads apply to the axis derived from the pitch cylinder, unless otherwise specified, e.g. “MD” for major diameter and “LD” for minor diameter. Tolerances and datums specified for muliple splines and gears shall designate the specific feature to which they apply, i.e. “PD ” for pitch diameter, “MD ” for major diameter or “LD ” for minor diameter. 41 ׉ 7cassandra://eBznv_CoASRXiYMcOyuBozRGKEW8uIEQVRY31tJMu1Y0`̵ay=!G׉EAdvanced Geometrical Tolerancing 3.9 maxImal maTerIal requIremenT The Maximum Material Requirement (MMR) and the Least Material Requirement (LMR), indicated by m or l in the feature control frame datum frame or both, take into account the mutual relationship of the size and the geometrical tolerance of interrelated features. When MMR or LMR is specified size and geometrical tolerance are transformed into one collective requirement. A to the m or l additional modifier is the Reciprocity Requirement (RPR) modifier indicated by t. MMR, LMR and RPR are standardized in ISO 2692. Figure 3.23 Relations between size and GD&T characteristics The MMR can be applied when there is a functional relation between size and form or between size and GD&T characteristics. Definition Maximum Material Condition Abbreviation Meaning The state of a feature where the feature is everywhere at its maximum of material MMC • For a shaft this is the maximum diameter • For a hole this is the minimum diameter Maximum Material Size The limit of size where the material of a feature is at its maximum.material condition MMS • Shaft: maximum limit of size • Hole: minimum limit of size The collective effect of the maximal material size and the geometrical tolerance followed by m Maximum Material Virtual Size MMVS • Shaft: MMVS = MMS + geometrical tolerance • Hole: MMVS = MMS - geometrical tolerance Maximum Material Vitual Condition Table 3.2 MMR definitions 42 MMVC A feature limiting boundery of perfect form and of MMVS. ׉ 7cassandra://UfK6Z9hFu0hhdF6CAfcJjzGFtBdJDKZNL1yKS4F3epc`̵ay=!Hay=!G{בCט{u׉׉ 7cassandra://2HHE30kK3qCZr45LCrk4pvp7oEmwqK99MVbRAYrB2Y0"l` ׉ 7cassandra://MCCGY5z2ExHcmGe3nKSiaxPRVXOOab7qyriualSYNg0I`S׉ 7cassandra://IAOy9R3SP9Btc4bUCsczJU3yRJSHmYJB5zn6eS9Lq-w`̵׉ 7cassandra://Z8d0yEQNH8pbWW2rBcNuzFRQnMS2ts8B-b0LYNtiJXwd͠ay=!4ט{u׉׉ 7cassandra://ls-uacpODgO1cACdlZMGl6fuJpW7nAij33mfFW9twW4` ׉ 7cassandra://9V40iazzGosXN3yIuLxs4i7Zj3gtqhBSTbSMgHt1d7Uנay=!@ȁ̅9ׁHhttp://4mm.deׁ ׁ Ј׉EAdvanced Geometrical Tolerancing 3.9.2 mmr on a daTum feaTure For the pattern of the 6 holes, indicated as CZ, a MMR applies. The allowed position deviation is the range between 0,2mm to 0,4mm.depending on the size of the holes of ø 5mm. The MMVS for the 6 holes: MMVS = MMS - GD&T = 4,9 - 0,2 = 4,7. Since datum A constrains two rotations datum feature B is used to constrain the translations only. There is no MMR for the datum in the position tolerance frame. Therefor the requirement for the 6 holes is Regardless Feature Size (RFS) of datum B. Independent of the size of B. Datum feature B has a straightness requirement at MMC. P Figure 3.30 Position tolerance for the 6 holes RFS of datum B. In the tolerance frame for the 6 holes in figure 3.31 also the datum feature B is at MMR. This allows a float of the pattern 6 holes (CZ) with respect to the theoretical center of datum B. The float is 0,1mm from the datum size. The straightness is not included for the float. Figure 3.31 Straightness to be disregarded. 47 ׉ 7cassandra://Ktcoz9yzcLqp7aR_VEaUh6_6bb3r0mzisefbTdI-Oc4-`̵ay=!M׉ERAdvanced Geometrical Tolerancing The straightness tolerance on datum feature B has a MMR. the straightness needs to be included in the float. The maximal allowed float is 0,1 + 0,03 = 0,13mm. The MMVS which is not to be violated for the datum is : MMVS = MMS - geometrical tolerance MMVS = 9,9 - 0,03 = 9,87 Figure 3.32 Straightness to be regarded, pattern of holes seven pin caliber. 3.9.3 maxImal maTerIal requIremenT 0 When the tolerance is not distributed on size and position but is provided for both for random distribution this is indicated by 0 m. Here also the MMVS must not be violated. Postion tolerance is ø 0,3 at LMS and is ø 0 at MMS. MMS equals MMVS. The use of 0 m allows to freely choose were the tolerance is applied to.either size, geometrical tolerance or any ratio between these tolrances. Figure 3.33 MMC with 0 tolerance 48 ׉ 7cassandra://o9zhXJvt224CNE1QyTOgT0wsYQrnxAjjXTUQBJGAI3cW`̵ay=!Nay=!M{בCט{u׉׉ 7cassandra://yMxNyM-bygokRLmefW2nvmV_VsWY4-eqgwsg2e3SI38 ` ׉ 7cassandra://x-CrXRhbz2s1wkLkML2U3LGq2WOAifJBisHY-4BWXO8>`S׉ 7cassandra://cyzgBMW3CzO9Hbrdj9tjUTYL6yNhD5Rgm9mPd4rLfoE`̵׉ 7cassandra://08h_77zRjbBKs03nOBe2dou2l-_jFcX7jxKopAUws2Mf͠ay=!Aט{u׉׉ 7cassandra://hy6T92WwRIn1seyKi-URP6yKuG7wEaWEax9_M_CKTLM3+` ׉ 7cassandra://j-7EoGXm5zeyc8MWmWnV0fW1iIbFevM3SLjoq2pebtoD`S׉ 7cassandra://H7kXIWtnF9vLdJY6S-ce8C31tTL3dhpdRfAMW-kILwM`̵׉ 7cassandra://PGjeYGMgegAQxirN10qBSc4WlUnsLwFIyucRh2RBzRs^͠ay=!B׉E Advanced Geometrical Tolerancing 3.9.4 GauGInG cz and sz On the left the 6 holes make up a pattern size de modifier CZ is used. A functional gauge includes 7 pins. of : MMVS = MMS - GD&T = 7,9 - 0 = 7,9mm. Datum A is defined at MMC. A center pin of 9,9mm completes the gauge. Figure 3.34 Pattern of holes and datum feature at MMC The lower illustration states the 6 independent, holes. The gauge is an indexing gauge one pin of 7,9mm and one pin of 9.9mm. Figure 3.35 Requirement on the individual holes (SZ), holes and datum feature at MMC 49 ׉ 7cassandra://cyzgBMW3CzO9Hbrdj9tjUTYL6yNhD5Rgm9mPd4rLfoE`̵ay=!O׉EQAdvanced Geometrical Tolerancing Figure 3.36 Gauging CZ and SZ The top illustration concerns the relation of two features, 2 holes of ø 6mm, to each other and to a single datum. Tolerance frame a) has a CZ requirement. Both holes of ø 6 need to meet the requirement with respect to the datum simultaneously. Tolerance frame b) has a SZ requirement Both holes of ø 6 need to meet the requirement with respect to the datum independently. The lower two illustrations show realised positions of the holes. When gauging simultaneously, a gauge with three pins, the two holes have a position to the datum simultaneously then the gauging results in a reject. When the gauging is from the datum to each hole separate, a gauge with two pins gauging from the datum to one hole and a second gauging to the other hole, then the holes are accepted. 50 Figure ׉ 7cassandra://H7kXIWtnF9vLdJY6S-ce8C31tTL3dhpdRfAMW-kILwM`̵ay=!Pay=!O{בCט{u׉׉ 7cassandra://Mrc4_qaYxU0NBlilfxWwTHaF34Fm04QcA6t2te-iPzc` ׉ 7cassandra://jaeGAMzBJsZNHddk6T-GL6vcrRmXPS__jT9-1Tqhpgs=o`S׉ 7cassandra://zRWWaMcDFAjaHEan8hzKyUk-fCr8GbDqFFV383FtWSk`̵׉ 7cassandra://_8RU355XLxWAlT2ZWsNRZ_nz7hkMEV4PIXYmqSLaqfAob͠ay=!Dט{u׉׉ 7cassandra://lRc_n2RS3GmTfPAsvXXj_KfsqyerqE8B1ZTBv-MpVBYͺ` ׉ 7cassandra://fVRgf7O-VIsMH_ImQBhLOI4dJDxBtB8zZ_8tIXP2ml0`S׉ 7cassandra://Y64eTMbyS4xvWupcO0Y7h3BQ-8ScQVAFoo7oStR7L3Q `̵׉ 7cassandra://1KLSkCX7EYszoDxQ1y24JETDXLcOwlAN9u2beQ3-t4kͿ&͠ay=!E׉EAdvanced Geometrical Tolerancing Figure 3.37 MMR for location and the datum feature creating mobility / float • Allows BONUS TOLERANCE Max. allowable tolerances promotes LOWEST MANUFACTURING COSTS • Allows FUNCTIONAL GAUGING • Allows DATUM FEATURE SHIFT (float / mobility) • Common Usage: 100% INTERCHANGEABILILTY Parts assembled with clearance fit • Must apply to FEATURE OF SIZE Figure 3.38 Benefits using MMR 51 ׉ 7cassandra://zRWWaMcDFAjaHEan8hzKyUk-fCr8GbDqFFV383FtWSk`̵ay=!Q׉EhAdvanced Geometrical Tolerancing Figure 3.39 Block with MMR on toleranced features and datum feature 52 ׉ 7cassandra://Y64eTMbyS4xvWupcO0Y7h3BQ-8ScQVAFoo7oStR7L3Q `̵ay=!Ray=!Q{בCט{u׉׉ 7cassandra://P4mu_LfjO3Wgi0SGrRqMm-2iX0x_4zS4z01h5Uhcn90!` ׉ 7cassandra://m3CC1ZSziL9DxTZ--v_5qTmWaK-UQqGBN4dqv25SvMA?_`S׉ 7cassandra://XZpMYxcEmCHNfpA_eYmiy-cWQ7NtzoMrdaM0M7RnnZE`̵׉ 7cassandra://PGBERJC6lg-OfqJcvSd-_wJsWVbwTuh4AcoXn-JT4-Áj͠ay=!Hט{u׉׉ 7cassandra://KWCqPhe91IpFc8ldSYkbq7H-eBVyp9VOCqxc6oUGuos?i` ׉ 7cassandra://XM111HfdaZ0seNMfyKDVuUlkF_IRuws2pulG9KUqffUD`S׉ 7cassandra://BC1lD3m5gQR4FG5zZX_jhnKgEqZFVgbg_HK995AcyOgo`̵׉ 7cassandra://8wcjUDqkc3awCEYEiO0bMpMkDbqyxyIexh8Juj6r6eAv4͠ay=!K׉E>Advanced Geometrical Tolerancing 3.9.5 aPPlIcaTIons of maxImal maTerIal requIremenT Toleranced feature Datum feature Tolerance Line profile Straightness Roundness Surface profile Flatness Cylindricity Line profile, datum Surface profile, datum Angularity Parallelism Perpendicularity Position Coaxiality / Concentricity Symmetry Circular run-out Total run-out m Max. Mat. Requirement Table 3.5 Possible applications of MMR and LMR g a d h b e g h i k j ( o q u v l Least Mat. Requirement x x x x x x x x x x x x x x x x x x x x x x x x the preciSe Functional requirement can oFten only be indicated uSinG the maximal material requirement. only then the larGeSt poSSible toleranceS appear reSultinG in the moSt economic produced part. 53 Related tolerance Unrelated tolerance Symbol Axis Media face Surface Axis Media face Surface ׉ 7cassandra://XZpMYxcEmCHNfpA_eYmiy-cWQ7NtzoMrdaM0M7RnnZE`̵ay=!S׉EnAdvanced Geometrical Tolerancing 3.10 leasT maTerIal condITIon The least material condition (LMC) is the condition where the feature of size has the least amount of material. Definition wLeast Material Condition Abbreviation Meaning The state of a feature where the feature is everywhere at its minimum material LMC • For a shaft the minimum diameter • For a hole the maximal diameter Least Material Size The limit of size where the material of a feature is at its minimum. LMS • Shaft: minimum limit of size • Hole: maximum limit. Least Material Virtual Size Least Material Virtual Condition The minimum material size plus or minus the geometrical tolerance. LMVS • • LMVC Table 3.6 Least Material Condition Shaft: LMVS = LMS - geometrical tolerance Hole: LMVS = LMS + geometrical tolerance A feature limiting boundery of form and LMVS 0 12 -0,5 A 9 Figure 3.46 Coaxiality with LMR 0 m + 0,5 0 0 L A L The LMVC of the cylinders may not be abused. The result is a minimal wall thickness. In the example above, the minimum wall thickness of 1 mm has been achieved when the workpiece has been manufactured to LMC at 0 l. 54 ׉ 7cassandra://BC1lD3m5gQR4FG5zZX_jhnKgEqZFVgbg_HK995AcyOgo`̵ay=!Tay=!S{בCט{u׉׉ 7cassandra://pE813QrhHbriT-4a9LIfc7zU0B_H-hLedeL7psa50nsA` ׉ 7cassandra://Pv3MZFs9XHWw5koTmAly4wNOpvzn0n2iVkvv_jTQEL4"`S׉ 7cassandra://DMoEy1nxzH--qKkntGfyn4HJgh3rc6EeOd2BJA514U0 `̵׉ 7cassandra://TUHu2v3i6WuzV85qZRg5YlX8lKQbgSf_iRMvTCAxmeU b͠ay=!Mט{u׉׉ 7cassandra://NLbl_7G7vgMWbwYgqzRAOZ13eaznaqLOZ8ONLcz7cro` ׉ 7cassandra://-Fd7MLKZEZ0TpPvIMyuT4vVZlv0eoxsHcb_R91c08JcT`S׉ 7cassandra://CP9XjNm8Zq9Fxcx-zdZ5BPYpt9-cmTECIzZoR5KGsMgk`̵׉ 7cassandra://SGT_HHkCQstE0rRD9Oz-8PajasINmK9IzPfk_Ec32N8br͠ay=!N׉EAdvanced Geometrical Tolerancing Figure 3.47 Controlling minimum wall thickness between the hole ø 4 and the bottom of datum hole B 55 ׉ 7cassandra://DMoEy1nxzH--qKkntGfyn4HJgh3rc6EeOd2BJA514U0 `̵ay=!U׉EAdvanced Geometrical Tolerancing 3.11 recIProcITy requIremenT When MMR, m, or LMR, l, is specified, size and geometrical tolerance are transformed into one collective requirement. where the geometric tolerance will be enlarged by the size tolerance not vice versa. A to the m or l additional modifier is the reciprocity requirement indicated by t to indicate that the size tolerance is allowed to increase by the difference the between the geometrical tolerance and the geometrical deviation. Reciprocity requirement is indicated on drawings as an additional requirement to MMR or LMR by the symbol t placed after the symbol m, or the symbol t placed after the symbol l. Reciprocity requirement is only applicable for tolerated features not for datums. Figure 3.48 Reprocity requirement with MMR The same MMVC applies to the requirements a) and b). In both cases MMVS is ø 40. The difference is the size tolerance. In case b) the size tolerance can not be enlarged by the non utilized coaxiality tolerance. In case c) the RPR has the same effect as 0 m. The total tolerance may be used for deviations of size, form, orientation and location in an arbitrary way. However the RPR requirement is a recommendation for the tolerance distribution. 56 ׉ 7cassandra://CP9XjNm8Zq9Fxcx-zdZ5BPYpt9-cmTECIzZoR5KGsMgk`̵ay=!Vay=!U{בCט{u׉׉ 7cassandra://9tYRShjxAtzDZu1hLl0jnyXUNo0xaRk_-fsf4igrgnE$X` ׉ 7cassandra://RSaPyjwV8As5XX-QEViYi839yxLntXHnTIz9KEo8f3kOS`S׉ 7cassandra://xP88VztGDF059spUzjuQROn02w1hRfI4fIiu5FQk45wH`̵׉ 7cassandra://bWF-YL2SNhpwIGxICsPKfUNBCH2txfWeNy3GxhcNGqohF͠ay=!Pט{u׉׉ 7cassandra://QxbKCWjqXdzb1uuM0nu-81JWr8cS5_wvr_ud5M84RrYT(` ׉ 7cassandra://nv3uZ5z4pgKE9lJuJVY4tTZsryHli3_5WZSvR0Ce8yQCg`S׉ 7cassandra://wz-qAl80XLXRRGN_dT1_pk5V6vpd6BD7pK_pYlH1-64p`̵׉ 7cassandra://e0NA3tWarejQ_7cr0oP15pxT7i2PKEJk8uvSYs2sh70ͨ ͠ay=!Q׉E730 ±0,2 0,1 Advanced Geometrical Tolerancing module II 4 Tolerances of form 4.1 flaTness Flatness is one of the four form tolerances. A flatness tolerance in general limits the flatness of a planar surface. Flatness tolerances are often used to ensure an good joint. Applications are sealings, load disdribution, appearance, assembly mating surfaces. Flatness tolerance can also be used to define the flatness of a media plane of a feature of size. It is important to be able to determine whether a flatness applies to a surface or to a feature of size dimension because the interpretation for each is different. 4.1.1 flaTness aPPlIed To a surface type oF Symbol tolerance b Form Flatness tolerance zone Space between parallel planes Table 4.1 Flatness applied to a surface reFerence None datum allowable tolerance modiFierS f allowable datum modiFierS N/A 0,1 Figure 4.1 Flatness applied to a surface Figure 4.2 Interpretation 0,1 / 10 x 10 The requirement is that every random area of 10 x10 mm. has to be flat within 0,1 mm. 30 150 Figure 4.3 Flatness of restricted area 57 ׉ 7cassandra://xP88VztGDF059spUzjuQROn02w1hRfI4fIiu5FQk45wH`̵ay=!W׉EAdvanced Geometrical Tolerancing The requirement is that the top surface has to be flat within a tolerance of 0,1 mm. The tolerance zone for flatness tolerance is the space between two parallel planes. The distance between the planes is equal to the flatness tolerance value. Possible form deviations and their acceptance: Reject Accept Figuur 4.4 Possible deviations 4.1.2 assesmenT of flaTness devIaTIons of a surface The deviations of form of a surface are measured with respect to an ideal plane. The flatness deviation is difference between the largest and smallest value. Flatness is a form requirement and has no location or orientation. Therefor three adjustable support are used to correct for orienational effects. Figure 4.5 Verifying flatness In the example the requirement is a flatness of 1 mm. The left measurments would give a reject. After an orientational correction the part is accepted. Reject - 0,8 0 + 0,2 - 0,5 + 0,5 + 0,1 Figure 4.6 Rejects and accepts 58 0 + 0,2 0 - 0,4 0 + 0,2 Accept - 0,5 + 0,5 + 0,1 0 + 0,2 + 0,4 ׉ 7cassandra://wz-qAl80XLXRRGN_dT1_pk5V6vpd6BD7pK_pYlH1-64p`̵ay=!Xay=!W{בCט{u׉׉ 7cassandra://Gy08JeEQ551azha-PiicPij0LRMr7Bo3eegQMfZ4vOMٷ` ׉ 7cassandra://c1sqLHnXpiUEzZ96eDZt39D5lhk-rJw_B1TOZRoEmoc8`S׉ 7cassandra://XwXssY43zfLvQQUVw8Hdc8JVzf0Ir2dNqWHAru9zIpI`̵׉ 7cassandra://J_VTMBQIERAMsPQ2nUwQAqk86BwD33s4UP_yV-l3XRsx͠ay=!Sט{u׉׉ 7cassandra://xJbT4iWZyLb0JRUarJK5_waQ_CskgrwZrzYf82QN9Xo'` ׉ 7cassandra://9i78Zxauyr2GR1buelIc8tWa2sVEhfOXy5rVKF7o-jE`S׉ 7cassandra://T24sGH2tmuHKFil6Hol36lLhItAdIwEH7IFmMUW-Gko &`̵׉ 7cassandra://froBGhKr7wCogJJ3PodiRKqJKZhwpf7vhGiokV59x5k͝F͠ay=!T׉Eh30 ±0,2 Advanced Geometrical Tolerancing 4.1.3 flaTness aPPlIed To a feaTure of sIze aT mmc type oF Symbol tolerance b Form Flatness tolerance zone Space between parallel planes Figure 4.2 Flatness applied to a feature of size Virtual Condition MMVS 0,4 M reFerence None datum allowable tolerance modiFierS f m l allowable datum modiFierS N/A Figure 4.7 Flatness to a feature of sizes Figure 4.8 Interpretation Size If the flatness is applied to a feature of size the media plane must be within the tolerance zone. The part has to be within the limit of size but using the m (or l) modifier allows a bonus tolerenace. The part has to meet the MMVC. The tolerance may be larger than the size tolerance. tolerance zone width 30,2 30,0 29,8 Table 4.3 Virtual condition at MMC 0,4 0,6 0,8 Assesment of the flatness of a feature of size at MMR can be done using a caliber. 59 ׉ 7cassandra://XwXssY43zfLvQQUVw8Hdc8JVzf0Ir2dNqWHAru9zIpI`̵ay=!Y׉EAdvanced Geometrical Tolerancing exerciSe Figure 4.9 Exercise • Where does the flatness tolerance apply to? • What is the shape and size of the flatness tolerance zone? • Are there more form requirements? 60 ׉ 7cassandra://T24sGH2tmuHKFil6Hol36lLhItAdIwEH7IFmMUW-Gko &`̵ay=!Zay=!Y{בCט{u׉׉ 7cassandra://cr2nMQeIsqmY5PM8mF7q6OORySrJjX6A6GRlByQVTVQ` ׉ 7cassandra://lCZuj72NcvKjGonJsIoKGCmTSkxcDHS-Jp4LR526LzA7`S׉ 7cassandra://GfT2F_pRD8DB9RtJG20U79G7uU0AO-f_VHtoOh9n73Y`̵׉ 7cassandra://tEvZ42WkzE0q91WreCDd-8wkk9z22-P45cDRBkYmco8h͠ay=!Vט{u׉׉ 7cassandra://VkwnD9h6J0ljb_wZv6vjunv4bb8eQm9leX2NIyXA50k` ׉ 7cassandra://-m4pjjV82doGhSCy-QOKf9Z_75xE-yuxiPW-pbDuHEo4`S׉ 7cassandra://O_-3Y8SpCQlYvKBJaeOhWM98tuhOlsuIwMvfAqy_Ur0`̵׉ 7cassandra://YUVb0ntmrIQ5cVGUwsy6NS3HN8lILBouvWYdkqGpctAͼT ͠ay=!W׉E0 12 -0,4 0.2 Advanced Geometrical Tolerancing 4.2 sTraIGHTness Straightness tolerance is one of the four form tolerances. Straightness tolerances are important to ensure good joint design by defining the allowable straightness deviation of a surface line element. Straightness can also be used to define the allowed straightness deviation of a axis to ensure assembly. It is important to be able to determine whether a straightness applies to a surface or to a feature of size dimension because the interpretation for each is different. 4.2.1 sTraIGHTness aPPlIed To a surface type oF Symbol tolerance a Form Straightness tolerance zone Two parallel lines. Table 4.4 Straightness 0,2 reFerence No datum allowable tolerance modiFierS f allowable datum modiFierS None Figure 4.10 Straightness of a line element Figure 4.11 Interpretation 0,1 / 50 The requirement is that every random length of 50 mm. has to be straight within 0,1 mm. 150 Figure 4.12 Straightness over a restricted length 61 ׉ 7cassandra://GfT2F_pRD8DB9RtJG20U79G7uU0AO-f_VHtoOh9n73Y`̵ay=![׉EAdvanced Geometrical Tolerancing The requirement is that each line element has to be within a tolerance of 0,2 mm. The tolerance zone for the straightness tolerance is the space between two parallel lines. The distance between the lines is equal to the straightness tolerance value. Possible form deviations and their acceptance: Rejects Accepts Figure 4.13 Possible deviations 4.2.2 assesemenT of sTraIGHTness of a surface Figure 4.14 Assesment of straightness of a surface The deviations of the line of the workpiece surface from a geometrical ideal reference are measured. The workpiece is leveled using the adjustment at B creating a reference line. The difference between the largest and smallest measurement is the straightness deviation. 62 ׉ 7cassandra://O_-3Y8SpCQlYvKBJaeOhWM98tuhOlsuIwMvfAqy_Ur0`̵ay=!\ay=![{בCט{u׉׉ 7cassandra://UiD8LeaXQ_s6JPCbelEZ-wbOyeRV5cdRrqdEgnVEVAs` ׉ 7cassandra://EOGcP5vEDaBxlTQ2u2594T-xtdeiq1GSMi4vU_B677w9m`S׉ 7cassandra://j3l-dyHhh6hj5ehuAFdEbhlwcEkfcywNZrVeX8_Qrx8`̵׉ 7cassandra://FyyWQ3ldX-SLDAcRQKTx12HTfeuEHM7zM5uOE0OkCLAͧ ͠ay=!Yט{u׉׉ 7cassandra://MFl49Zit_DWjJ3UeqGEFqAvyxFHO97VD5ewbKtfYQKQI` ׉ 7cassandra://jRJQ8WE3NYp3K5AVB-1OPvbNy2NwPTmbQSLwQs6ND0c;`S׉ 7cassandra://tbggbGAINgPEyQLtDcn1_vhMdAF4CDB8YKPF5_6Gx20`̵׉ 7cassandra://yJPEWnbHTQagVLqMFxrRagCRLgI-mdG9AsUG_Qq8FuA͏͠ay=!Z׉ER0 12 -0,4 0.2 Advanced Geometrical Tolerancing 4.2.3 sTraIGHTness aPPlIed To a feaTuse of sIze Symbol type oF tolerance a Form Straightness tolerance zone Cylinder Table 4.5 Straighness of a feature of size datum reFerence No allowable tolerance modiFierS f l m allowable datum modiFierS None 0,2 Figure 4.15 Straightness of a feaure of sizet Figure 4.16 Interpretation The requirement is that the straightness tolerance of the axis has to be within a cylindrical tolerancezone of ø 0,2 mm. Possible form deviations and their acceptance: Rejects Accepts Figure 4.17 Straightness deviations 63 ׉ 7cassandra://j3l-dyHhh6hj5ehuAFdEbhlwcEkfcywNZrVeX8_Qrx8`̵ay=!]׉EAdvanced Geometrical Tolerancing 4.2.4 sTraIGHTness aT mmc MMVS Virtual condition 0,2 M Figure 4.18 Straightness of a feature of size Figure 4.19 Virtual condition at MMC When straightness is applied to a feature of size the axis must be within the tolerance zone. The part has to be within the limit of size but using the m (or l) modifier allows a bonus tolerenace. The part has to meet the virtual condition of ø 12,2. The geometric tolerance may be larger than the size tolerance. Size tolerance zone diameter 12 11,8 11,6 Table 4.6 Virtual condition at MMC 4.2.5 sTraIGHTness and commen zone requIremenT 0,2 0,4 0,6 4x 20g7 0,01 CZ Figure 4.20 Straightness and CZ 64 0 12 -0,4 ׉ 7cassandra://tbggbGAINgPEyQLtDcn1_vhMdAF4CDB8YKPF5_6Gx20`̵ay=!^ay=!]{בCט{u׉׉ 7cassandra://8eicbPHgmBF8Z3fsBqFVxXKPQnFPitfbgbGIIRSV9VUr` ׉ 7cassandra://CZZdXCJ92WZ41d4HetwjLkOrVgSAf-NTt3xSv2H25vg4T`S׉ 7cassandra://WZlCHpBhoWax4Tqy9l74eB7nuAf8gAkmwzydmeP2HM8Y`̵׉ 7cassandra://lDS5aLOLjcajbldsKR2TQV_aGau8PyaiK_G3faXY01cr͠ay=!\ט{u׉׉ 7cassandra://xnik2yp8ADa3XRHxWO4Tr-Ha-hR_qCK5lxoizZOBAtwf` ׉ 7cassandra://oRSDrr8NxrbbyvU0dtguKXiiF2Tjwm3Zcv1uGJOljHo1q`S׉ 7cassandra://VuJU__EjBNoM1iap30hY2SSOsDcEpuYeFdbIIeGEXr0`̵׉ 7cassandra://BvBbGlc03VDFXj9_rWq3D63dbrrsF2P5dLux1wjGxVUr ,͠ay=!]׉E0 8 -0,05 12 ±0,2 Advanced Geometrical Tolerancing 4.2.6 assesmenT of sTraIGHTness devIaTIon of a feaTure of sIze A simple approximation method for assing the straightness deviation of an axis is using two dial indicators. The values have to be determinated at several, at least three, measuring positions. Figure 4.21 Assesment of straightness deviation of an axis exerciSe 0,05 M A 0,4 M A M Figure 4.22 Exercise 65 ׉ 7cassandra://WZlCHpBhoWax4Tqy9l74eB7nuAf8gAkmwzydmeP2HM8Y`̵ay=!_׉E=12 h6 Advanced Geometrical Tolerancing 4.3 roundness Roundness is one of the four form tolerances. The roundness tolerance is used to limit deviations of circular elements. A roundness tolerance is often used to ensure a good seal, rolling characteristics, bearing support or appearance. 4.3.1 roundness aPPlIed To a surface type oF Symbol tolerance d Form Roundness tolerance zone Two concentric circles Table 4.7 Roundness reFerence None datum allowable tolerance modiFierS f allowable datum modiFierS None 0,002 0,002 Figure 4.23 Roundness Figure 4.24 interpretation 66 ׉ 7cassandra://VuJU__EjBNoM1iap30hY2SSOsDcEpuYeFdbIIeGEXr0`̵ay=!`ay=!_{בCט{u׉׉ 7cassandra://Ne-uH58PwAkO9PqTRqW96t9TWRWdF_lmu0mbIRAdwKU ` ׉ 7cassandra://xQFLtSce050x4OL3t0gDZ90J5uSffESb18FwpQadJJ4 `S׉ 7cassandra://Y3TYIubryTF7jBWa1eLVtj76E2MKS0XOTXLV7VC207k `̵׉ 7cassandra://PQ7OUAu7cUz3AOMGjZBVKRJ6p0RDfVZKxFzsjy62Jq0l^͠ay=!`ט{u׉׉ 7cassandra://Cona9P8ApfQlBNv_hi4Tw8ST-88BXgkQ0cm06pVxkak` ׉ 7cassandra://UcEcUIRpYPNNq6djxhuowbv7tPl8_LSLAl3Wmyqn1EY@U`S׉ 7cassandra://Ert6XqfORgLrK2hdyayLMkjLoRjtqqlDO_CUQ6tRTXod`̵׉ 7cassandra://vWQqpHpdQeZsI299d5MlllIV-Tc4d-cV2kGql5snN1kͦ" ^͠ay=!aנay=!c̊.9ׁHhttp://mm.atׁ ׁ Ј׉ERAdvanced Geometrical Tolerancing The requirement is that the roundness has to be within a tolerance of 0,002 mm.at any cross section. The tolerance zone for roundness is de distance between two concentric circles. The difference between the radii is equal to the roundness tolererance. Rejects Accepts Figure 4.25 Roundness deviations 67 ׉ 7cassandra://Y3TYIubryTF7jBWa1eLVtj76E2MKS0XOTXLV7VC207k `̵ay=!a׉EAdvanced Geometrical Tolerancing 4.3.2 assesmenT of roundness devIaTIons A diameter measurement does just what the word implies; it measures the diameter. It does not check the shape of the surface which is what roundness and cylindricity control. Since the roundness or cylindricity tolerance is a radial distance between concentric boundaries, a radial method of checking the surface w.r.t. an ideal reference circle is necessary. . Figure 4.26 Oval and lobbed forms However, rotating a part between centers is not an acceptable method since it relates the part surface to an axis, which technically is a check of another geometric tolerance called runout. With three point measurements (V-blocks) is is possible to detect different types of lobbed forms. (e.g. centreless grinding, reaming). Figure 4.27 Assessment of lobed forms in V-blocks Figure 4.28 Three point measurement shaft and hole 68 ׉ 7cassandra://Ert6XqfORgLrK2hdyayLMkjLoRjtqqlDO_CUQ6tRTXod`̵ay=!bay=!a{בCט{u׉׉ 7cassandra://XezrZ83USfc1toNf925eOW4JtrI5k9PF-4MKt9WYx-Ub` ׉ 7cassandra://cC5MtZwHnqhSj9q1XqTydJA_GxDF4RvtaVM_TESHc9c6`S׉ 7cassandra://yCE9m6W4De0Sn0xG6EQ67stJpVbQDq0Nxq0Ny99LtP0`̵׉ 7cassandra://wCKSoar5qKjq3hsXMro24PEKkBTt-dsCAHmTkU2pKbQD ͠ay=!gט{u׉׉ 7cassandra://LIUknxhpYHIM1fuIJi_PIm5DvznVKGJTYorJ7Ru-5bk` ׉ 7cassandra://3kzClKXsYqFjWJKdlBa6M8BYngB-5eMkHrJXGf5MNfs7`S׉ 7cassandra://kzCEfcFKijjKNofCAKk6NZ_QmiuIHCKY4p5yow7gJDg`̵׉ 7cassandra://ab34kwLtnytZ-IVYH_LLepJeVTvcCueDLnBnvFPouHk͠ͅay=!i׉E@Advanced Geometrical Tolerancing V-Block angle 2 lobs 3 lobs 4 lobs 5 lobs 30º 2,3 3,7 2,9 2,7 60º 0 3 0 0 90º 1 2 0,4 2 108º 1,4 1,4 0,4 2,2 Figure 4.8 Correction values k for measurement of roundness deviations The number of lobs may be detected by counting the maximums during one revolution of the workpiece in the V-block. With regular lobs the unroudness tolerance can be found by dividing the reading by the corrections in the table. δr = Δ / k = (Amax - Amin ) / k When there is a superposition of harmonics the selection of the proper correction is practically impossible. To truly check for the roundness or cylindricity of a surface without regard to the axis of the part, the part must be rotated about the ultra-precision spindle of a specialized roundness measuring machine. A probe contacts the surface and transcribes an enlarged profile of the surface onto a polar graph. The profile is then checked against a clear overlay of concentric circles to determine if it falls within the allowable tolerance zone. 120º 1,6 1 0,4 2 150º 1,9 0,3 1,5 0,7 180º 2 0 2 0 69 ׉ 7cassandra://yCE9m6W4De0Sn0xG6EQ67stJpVbQDq0Nxq0Ny99LtP0`̵ay=!c׉EW12 h6 Advanced Geometrical Tolerancing 4.4 cylIndrIcITy Cylindricity is one of the form tolerances and is one of the most common shapes across all industries. A few examples where cylindricity tolerances are used are seals around shafts, lip seal applications and bearing applications. 4.4.1 cylIndrIcITy aPPlIed To a feaTure Symbol type oF tolerance e Form Cylindricity tolerance zone Space between two coaxial cilinders Table 4.9 Cylindricity 0,01 0,05 datum reFerence None allowable tolerance modiFierS f allowable datum modiFierS None Figure 4.29 Cylindricity Figure 4.30 Interpretation 0,05 70 ׉ 7cassandra://kzCEfcFKijjKNofCAKk6NZ_QmiuIHCKY4p5yow7gJDg`̵ay=!day=!c{בCט{u׉׉ 7cassandra://7H3YxGDDOX7qA0WESDDvkiR8qJ3cOUI0kiwJkutEsOce`` ׉ 7cassandra://U2bH4nNBCYvj7wwl_CcfcdkIPfRFLJ5gXP_rAAA9MxQ7$`S׉ 7cassandra://b2qbO_W5XR6TGDAGXcltX6vAzWXm3AoSIeOJ_van3uE`̵׉ 7cassandra://4GebSfkMGRZDXP-et6wY2dI2FWVLX_aWfX5Rr2TogNU; ͠ay=!lט{u׉׉ 7cassandra://54WK_vd7jdOCdvy5lGIjs6Egi5KEB6EDxDqxMKI_Sgg` ׉ 7cassandra://0xCHSvYiwUveWsT-Z1gP06fX4j20V9AGa95maHR3LygHP`S׉ 7cassandra://yuiujUAOMYegqtZVoNvr0mz7S0VGGh0Djr31M8Qg1po"`̵׉ 7cassandra://QKSDD2R9-ZZj_yXeaDjPfZATxP6FqHunAct6SGO06zYBg~͠ay=!mנay=!oE9ׁHhttp://zone.anׁ ׁ Ј׉EAdvanced Geometrical Tolerancing Possible form deviations and their acceptance: Rejects Accepts Figure 4.31 Possible deviations 4.4.2 assesmenT of cylIndrIcITy devIaTIons Deviations of the workpiece surface from an almost ideal reference cylinder are measured. There are several strategies to verify cylindrical tolerance. With the radial selection method profile lines of several cross-sections perpendicular to the axis of measurement are plotted and evaluated according to the requirement. The maximum measuring difference of all measurement divided by two gives the deviation δr for cylindricity. Figure 4.32 Verifying a cylindricity tolerance 71 ׉ 7cassandra://b2qbO_W5XR6TGDAGXcltX6vAzWXm3AoSIeOJ_van3uE`̵ay=!e׉EAdvanced Geometrical Tolerancing 5 daTum sysTem A datum is theoretical exact point, axis or plane derived from a true geometric counter part of the specified datum feature. The datum system defines functional relationships between part features. Datums define the orientation and/or location of the tolerance zone.and provide the origin for part measurement. The datums can be seen as a means to lock degrees of freedom (DOF’s) of a tolerance zone. The number of degrees of freedom of the tolerance zone which are locked depends on the nominal shape of the datum features and the degrees of freedom which have been locked by preceding datums. Fixed deGreeS oF Freedom: Surface, 3 DOF’s one translation, two rotations Cylinder, 4 DOF’s two translations, two rotations Sphere, 3 DOF’s three translations Figure 5.1 Degrees Of Freedam (DOF) 5.1 sImulaTed daTum feaTure Datums are based on datum features. datum: A theoretical exact point, axis or plane derived from a true geometric counter part of the specified datum feature. datum Feature: Real feature of a workpiece such as an edge, a plane or hole, used to establish the location of the datum. Simulated datum Feature: Real surface of sufficiently precise form contacting the datum features and used to establish the datum. Datum Datum feature Datum feature simulator largest inscribed cylinder real surface axis of the hole Figure 5.2 Datum feature simulators datum 72 ׉ 7cassandra://yuiujUAOMYegqtZVoNvr0mz7S0VGGh0Djr31M8Qg1po"`̵ay=!fay=!e{בCט{u׉׉ 7cassandra://mIDCAyJSQd41e18FCo3a5RspY08pcGBACWwfy_QGZDA(` ׉ 7cassandra://R-DVICKIc0B6zzHxnIJikC_1S6laCWMuHaxxu8eWejc=`S׉ 7cassandra://siGawG5ummBwliPnc1_RG5fitB-95wQNTdQC2N6t46Ul`̵׉ 7cassandra://z4J4xKE7GFjQqFQRMg-V54OWArr0N1Ry4Ck4u49oOEgAf͠ay=!qט{u׉׉ 7cassandra://p9jxVtZvkcG1gnyHFPJeb4qrLpePi0isthRzr04czk4V` ׉ 7cassandra://CvaRki9L9fRBD-sNnT65h-OgHuVWXIoxCgRLclNLpco<$`S׉ 7cassandra://uotBJGM3oGnQSWkbHGdWaB0vxdDmByVij72qlk4ExXck`̵׉ 7cassandra://Vwe8qG0-V8oan9jy9KKSWkTvKauxwPZuDO6t5g-mDB8ͭ8 ͠ay=!r׉EVAdvanced Geometrical Tolerancing Datum Datum feature Datum feature simulator smallest real surface circumscribed cylinder axis of a shaft datum datum surface of a part real surface surface plate real surface media plane surface plates datum real surface datum Figure 5.3 Datum feature simulators four contact points 73 Center point of sphere ׉ 7cassandra://siGawG5ummBwliPnc1_RG5fitB-95wQNTdQC2N6t46Ul`̵ay=!g׉EAdvanced Geometrical Tolerancing 5.2 mInImum rock requIremenT When a datum feature is not stable relative to the simulated datum feature it shall be arranged so that the possible movement in any direction is equalized. In other words the datum feature shall be aligned relative to the simulated datum feature into a median position. Extreme positions Figure 5.4 Minimum rock requirement for a surface Datum Extreme positions Datum Figure 5.5 Minimum rock requirement for a shafts When the datum feature is the common axis of two coaxial cylinders with different diameters the datum is the common axis established by the smallest circumscribed cylinders. Datum Datum feature and datum feature simulator real surface A B Figure 5.6 Two different diameters smallest pair of circumscribed cylinders It is good pratice to have form requirements on datum features. This by tolerancing the feature or by using a general standard like ISO 22081. 74 datum ׉ 7cassandra://uotBJGM3oGnQSWkbHGdWaB0vxdDmByVij72qlk4ExXck`̵ay=!hay=!g{בCט{u׉׉ 7cassandra://Jh-HueKY4ZAvm-qKaP4ulVZJU0LxcTFfCzrfMjoMfHMK>` ׉ 7cassandra://soL1O1eCPr4yT7DUzjdOmQuUlTrSfW2nRb9mwveeEug1v`S׉ 7cassandra://mkgyax-iwnxTV7Ty9hCMo1l8efBDin2JFfFlSA4NtYA`̵׉ 7cassandra://BNjvtNZIPPT1PQaZA3kFIaDCWHtgTaB-wBT-NGZSRzc͋j͠ay=!tט{u׉׉ 7cassandra://Coc-WNUw0vLUbU7SGBs-FK85L8Q_NCMLSyAXGJlh498aj` ׉ 7cassandra://lQrtMt6j785CrN-Rz253nJojLNh9MM2VPQ73eTP8Oqo0b`S׉ 7cassandra://k7ln-rTbvSrOIejr-1xawbJRK9s7pfjm6eyW7r2qSaQ`̵׉ 7cassandra://f-C2Z0VgmbxlBUXJJQPCSGfajAlKsHn9A8BCIk56SQgK͠ay=!u׉EAdvanced Geometrical Tolerancing 5.3 IndIcaTIon of daTums on THe drawInG Figure 5.7 Indication of a datum reference plane Figuur 5.8 Indication of a datum axis 75 ׉ 7cassandra://mkgyax-iwnxTV7Ty9hCMo1l8efBDin2JFfFlSA4NtYA`̵ay=!i׉EAdvanced Geometrical Tolerancing Figuur 5.9 One datum feature from more (two) elements 6x 50 0,3 0,3 A C-C n\w0œ5Ç\A\B] C 0,5 A B A 300 ±0.5 B Figure 5.10 Pattern of holes used as datum 76 100 0,1 200 ׉ 7cassandra://k7ln-rTbvSrOIejr-1xawbJRK9s7pfjm6eyW7r2qSaQ`̵ay=!jay=!i{בCט{u׉׉ 7cassandra://Kds1F9ZZCeKbsUGIUXjLhSlkVn250V6xXEsj1pXGNTo` ׉ 7cassandra://DjybKZydvzIz_2SVQPFzDDIkU2f4uNbseWj-yZVTPXA`S׉ 7cassandra://rX3tMy7OYXssXgiDV2zI7tiQKr9KtA3QZlkox8ZQoSM `̵׉ 7cassandra://JELGho4kDmZkJ8yWFQyHzepXN0FT-9zBdlbqnB7RFYw]b͠ay=!wט{u׉׉ 7cassandra://38WY-RfZquo8a-6gC9akYi1rSGpxE8rKY22Mcm_BOjAt` ׉ 7cassandra://KzoU_vOf48dQDEppV0sjl9NKX4r5O96hu8d7hlZg8D03`S׉ 7cassandra://w4WtNXXBnRpUr8xNEJsS_8Hb9crbocEB-K_q0I6CJ-s`̵׉ 7cassandra://2ICFLcE4VdkOKrZ2CSmNVx5Qsg5okAXwfIUvL9xXJKcU ͠ay=!x׉ErAdvanced Geometrical Tolerancing Datums limit the Degrees Of Freedom. The number of DOF’s restricted depends on the feature type and the DOF’s restricted by preceding datums. Figure 5.11 Degrees Of Freedom Surface limits 3 DOF’s Cylinder limits 4 DOF’s Bol limits 3 DOF’s One translation, two rotations. Two translations, two rotations. Three translations. 77 ׉ 7cassandra://rX3tMy7OYXssXgiDV2zI7tiQKr9KtA3QZlkox8ZQoSM `̵ay=!k׉EAdvanced Geometrical Tolerancing 5.4 daTum sysTem 5.4.1 Necessity for datums aNd datums systems Where one or more datum systems are established each by two or more datum features only those DOF’s can be locked which not have been locked by preceding datums. The sequence of the datums influences the result obtained. A 0,2 A B A 0,2 B A 12 B Figure 5.12 Datum system of two datums 12 B Figure 5.13 Effects of the sequence of the datums 78 12 12 ׉ 7cassandra://w4WtNXXBnRpUr8xNEJsS_8Hb9crbocEB-K_q0I6CJ-s`̵ay=!lay=!k{בCט{u׉׉ 7cassandra://Qjs5EPDrYNrftbS_BBHgGPHuLvrpEILdrn085DDS1ko` ׉ 7cassandra://TLrqwrf9vQyRx4GrN-bTmt_4na5aF58H87z26O_XB_c/`S׉ 7cassandra://_K8PckUfh7ZicI_MI4M9HVsHX-HBoZxlLi6u76lZAqM`̵׉ 7cassandra://Qei-UUvI6nSdfI37sp0TDwqVln6Ah_nXkdjxRl8wafk|0͠ay=!zט{u׉׉ 7cassandra://GUth3QrxLL9WrcVfqG_6NLj1PkF0qX8FJv4iIT4FoOo<` ׉ 7cassandra://dsVNmz-pRUkrbKGVY147Uo2Kck9s7JtI-DZN2399e5Q+ `S׉ 7cassandra://Zw57balmrePJra017zHsTQ-6FsGRg80A-QG8ndJ3QsAv`̵׉ 7cassandra://HBPRpeVQb3GuTrbid5fA0AqIlfZvzRW_SUxsXAGt1Bsep ͠ay=!{׉E23 23 Advanced Geometrical Tolerancing 5.4.2 datum system aNd dof 0,2 D E 16 0,2 D E F 16 D 28 28 E F D E X D - E x Y - - Z x - Rx Ry Rz x x - - o x X D - E - F x Figure 5.14 Effect of choosing datums Y x - - Z - Rx Ry Rz x - x o x - Figure 5.15 Effect of choosing datums x - - o o 79 ׉ 7cassandra://_K8PckUfh7ZicI_MI4M9HVsHX-HBoZxlLi6u76lZAqM`̵ay=!m׉E40 80 40 80 Advanced Geometrical Tolerancing 0,05 A B 0,05 A B A A X A - Y x Z x Rx Ry Rz x - x X A x B - Y - x Z - x Rx Ry Rz x - x - o o Figure 5.16 Effect of choosing datums Figure 5.17 Effect of choosing datums 80 ׉ 7cassandra://Zw57balmrePJra017zHsTQ-6FsGRg80A-QG8ndJ3QsAv`̵ay=!nay=!m{בCט{u׉׉ 7cassandra://r1jx0dY19WvzQLZW0oAcnwzMiYzoZW3PyG_AwL4nXK4` ׉ 7cassandra://7g5xx7xfyK8VdTo4HXSn4jDFrUJRkbiCZsr9_ynHI3I!`S׉ 7cassandra://TeKcPpQP27IbeJz7B_xAnFb6qJb009xbeiYRdhcinYU X`̵׉ 7cassandra://XAlTrHRjM2GccrJlRh5iGRXNgQI97dQc_zpzjbrmxMM`͠ay=!}ט{u׉׉ 7cassandra://owfT01S5Geir-Z9BcY7ZnzpoQF7N0vz0lXd56Pbwxso` ׉ 7cassandra://U7kR5_jcH0g8RjPPkjOo0LIx23hEnCk5ISrc5rVwT50E`S׉ 7cassandra://Q32nlMu632mcECU-HpeQuMfgx4tJyKZx1WWX2nAdqqw`̵׉ 7cassandra://WxMyNptCGYhpQyVj2Gp6heGS34TNGo2D5F-dJ-ifRXY͒&H͠ay=!~נay=!2́E9ׁHhttp://used.Thׁ ׁ Ј׉EAdvanced Geometrical Tolerancing 0,1 D E F E 10,5 F 10,5 D X D - E x Y - x Z x Rx Ry Rz x x - - o o - F o o o o o x! Figure 5.18 Effect of choosing datums The degree of freedom Rz is contrained by using both datum E and datum F. 81 ׉ 7cassandra://TeKcPpQP27IbeJz7B_xAnFb6qJb009xbeiYRdhcinYU X`̵ay=!o׉EDAdvanced Geometrical Tolerancing 5.4.3 datum at mmc When a datum feature is applied on a MMC bases a fixed sized datum simulator (gage) at MMVC must be used.The size of the MMVC depends on the MMS and the geometrical tolerance applied to the datum feature. 4 + 0,2 0 0,2 M A B M 0,05 B Figure 5.19 MMVC for datum B is ø 16 A 4 + 0,2 0 0,2 M A B M 0,05 Figure 5.20 MMVC for datum B is ø 16, straightness to be disregarded B A 4x 4 + 0,2 0 n\w0œ2mÇ\A\Bm] 0,2 M A B M 0,05 M B Figure 5.21 MMVC for datum B is ø 16,05, straightness to regarded A 82 0 16 -0,1 0 16 -0,1 0 16 -0,1 ׉ 7cassandra://Q32nlMu632mcECU-HpeQuMfgx4tJyKZx1WWX2nAdqqw`̵ay=!pay=!o{בCט{u׉׉ 7cassandra://vzmxWTn9BqKF23BQqMFIeHP5v4kDKiqMQ025irrww50` ׉ 7cassandra://-WCjWJW6HsX3EQLCVUJmQYnJhZpVb3IXqgmrFtOUSQU?`S׉ 7cassandra://eyFj5zzSNVD4T9AisIg9jHvBxuQSV6orbYKrQXgevGw`̵׉ 7cassandra://5OSsWeRD7Q3IWfGtM6CSR-XMnQPsPsmCIOfhIFAXxKErJ͠ay=!ט{u׉׉ 7cassandra://7QhRx5lXxcedvgTFbtJSUd80DWajceqqwEA65dSgL1cDd` ׉ 7cassandra://2cEZh6PypjWrhbnBt7--tjOhjlF1jP6F66vqmmkQyIQ.d`S׉ 7cassandra://vajkIVQOXHFKLs7VgG2JAMB8cOjqYehPVnESyptMwaA`̵׉ 7cassandra://iGMvnLKr-CeIBBEKtJLeU4-ys5cjEHgt-zy4xY71JRsp͠ay=!׉EAdvanced Geometrical Tolerancing 5.5 daTum TarGeTs Figure 5.22 Only a restricted are of the element is used as datum Datum A is not the total surface but only a single restricted area is used as datum. A datum target frame is a circle, divided into two compartments by a horizontal line. The lower compartment is reserved for the datum feature identifier followed by a digit corresponding to the datum target number. The upper compartment is reserved for additional information, such as dimensions of the target area. The target dimension can be in or next to the circle. Datum targets enable repeatable targets to be established from uneven or warped surface and from partial surfaces. Using datum targets can make the workpiece cheaper. Datum D is determined by three areas. Two rectangular datum targets and a circular datum taget. The target dimensions of the rectangles are places next to the datum target circles. 20 x 10 D1 25 50 D2 20 x 10 20 50 Figure 5.23 Three surfaces as datum targets 83 D3 70 25 ׉ 7cassandra://eyFj5zzSNVD4T9AisIg9jHvBxuQSV6orbYKrQXgevGw`̵ay=!q׉EAdvanced Geometrical Tolerancing Datum A is determined by three points. The TED dimensions indication the location of the points have no tolerance. 100 ±0,2 60 20 A1 A2 50 A3 A Figure 5.24 Datum target A is determined by three points Figure 5.25 Datum targets a point, line and surface 15 15 x 20 C1 C1 Figure 5.26 Datum target size in circle and target dimensioned using TED’s 84 80 20 10 ±0,05 120 ±0,2 20 ׉ 7cassandra://vajkIVQOXHFKLs7VgG2JAMB8cOjqYehPVnESyptMwaA`̵ay=!ray=!q{בCט{u׉׉ 7cassandra://RFUP0fiyebBSaymGi03mLUuKzNK6aSjxh9Tbth5_MBA&m` ׉ 7cassandra://HsqMfaeLvqGmpUEtOtB8WeTHfY5tQlDCPb0zyooywfs?`S׉ 7cassandra://VopDcn_myKTF4nTKtu7dA610JFAOrcqj-5ZHUohYXno`̵׉ 7cassandra://kSMfI1ogVA7qBlGXAcXl3eaErkrpkaj8CRq3IXppznk'?f͠ay=!ט{u׉׉ 7cassandra://IyBEALsrxFLjbkYe9_knNcgrufPbyABOXHE5BTWUUxEQ` ׉ 7cassandra://yQkX3aZu29mzO_csV2C_2Dm_wuuFPX7tnklHfksgkgA#`S׉ 7cassandra://KyqUOosuNVk3CH7UlhQQKlXg5NUNy1X0qWiTu7_wz2g `̵׉ 7cassandra://ehgr0UE_pSKs9D4WuAXKkgSPW7c3neZEN7nuNw8loXs&b͠ay=!׉EAdvanced Geometrical Tolerancing Datum A is determined by the line connecting the centers of the cross section A1 and A2. Datum A is determined by the shared center lines of the sections A1 and A2. Datum A is determined by the centerline connecting the center of the circle created by A1, A2, en A3 and the center of the circle created by A4, A5 and A6. Datum A is determined by the point A1 to A4 defining the center of the sphere. The points need to be equidistant. Figure 5.27 Datum targets 85 ׉ 7cassandra://VopDcn_myKTF4nTKtu7dA610JFAOrcqj-5ZHUohYXno`̵ay=!s׉EAdvanced Geometrical Tolerancing exampleS datum tarGetS Figure 5.28 Datum targets • Area’s as datum targets • Lines as datum targets • Points as datum targets : A1, A2 : B1, B2 : C1 Primary datum A Secondary datum B Tertiary datum C 86 ׉ 7cassandra://KyqUOosuNVk3CH7UlhQQKlXg5NUNy1X0qWiTu7_wz2g `̵ay=!tay=!s{בCט{u׉׉ 7cassandra://WPysl0B06ZmiTtNSsLr_-ijG3Lhl7NHBazk9AmsVT9c` ׉ 7cassandra://lE3WiMJLeNp0NUnczSW1NznqQMtrRG6u9XIwcuNp-qY0o`S׉ 7cassandra://lll5V5M5SMftM4W6gxgncLDkEgpvQKtKCbzHRc1UVdA`̵׉ 7cassandra://li7nqmTw4G_bAgvE1WzVDIhY_QyF2pQfAsLpf58aQRY͙ ͠ay=!ט{u׉׉ 7cassandra://PjSy0GzfHLlOs_pKM2J5qMD40TQwLn8Ex9RzcS-goQ4|)` ׉ 7cassandra://yYzD_FA3MFQgXmPlm77bjVa15j2I1T3FFF2svXRD9NI5`S׉ 7cassandra://yCHAkZqpYkhfPwKNy2IezMpbqpFb7Nt3Z_TOa7JYBcQ`̵׉ 7cassandra://kCzbvu_LsWFPOjOKVbzoXELd_6OkTPu47Kv10bhnsAQċj͠ay=!׉EAdvanced Geometrical Tolerancing There is no over constraining when using only points as datum targets .Each of the six DOF is only constrained once. C 1 D 1 A 1,2,3 B 1,2,3 Figure 5.29 Datum targets on cylindrical surface 87 ׉ 7cassandra://lll5V5M5SMftM4W6gxgncLDkEgpvQKtKCbzHRc1UVdA`̵ay=!u׉E[Advanced Geometrical Tolerancing A surface contains 3 DOF’s being one translation an two rotations. By using the symbol >< a surface only contrains the two orientations. Figure 5.30 Rotation only Number of degrees of freedom contrained: 1. Point 2. Orientation only 3. Surface 4. Cylinder 5. Cone 6. All DOF’s Figure 5.31 6 DOF constrained 88 ׉ 7cassandra://yCHAkZqpYkhfPwKNy2IezMpbqpFb7Nt3Z_TOa7JYBcQ`̵ay=!vay=!u{בCט{u׉׉ 7cassandra://MAXXpdDGK_9LikZ-dKOdI9jdUZelGHrLmZErulU2Hhk` ׉ 7cassandra://Yux8hxxmzq_da84ssE5hWjPU-kHf82vInx3rQzNJitg;`S׉ 7cassandra://lKK3eAC4GeYIUqF76zJwa_c_kdEYgTT97t5hQ0ac3-8c`̵׉ 7cassandra://wxFDAIwTT1KMYu9Qb46ZXMbWAT1G_galukU38kbsG3o]b ͠ay=!ט{u׉׉ 7cassandra://tvXuUUO81NEd9tdJ31yEvqfU7yfEAWxUy_wZAlmX4d0k` ׉ 7cassandra://ADvgtiBsX2JohOxjuSFOO1naBFUHPkVli3wtGogN2kE:.`S׉ 7cassandra://fUirSbcvl6sSH4AofA5OeD7iSxW4hcWWt4w-kX_R3_o`̵׉ 7cassandra://go58gW84zdXk12zhdPte5W6ZyaXmpFl2BqUThfkf9W0 ͠ay=!נay=!2k9ׁHhttp://measured.Thׁ ׁ Ј׉EAdvanced Geometrical Tolerancing 6 Tolerances of orIenTaTIon Orientation tolerances define angular deviations of surfaces or features of size but cannot control location. 6.1 PerPendIcularITy A perpendicularity tolerance limits the perpendicular deviation of a planar surface or feature of size relative to a datum reference. A perpendicularity tolerance can only constrain rotational deviations. A perpendicular tolerance always uses a datum. It can control form and orientation. Perpendicular tolerances are used in assemblies, appearance, establish the relation between datum features or supports (guides and stops). 6.1.1 PerPendIcularITy aPPlIed To a surface type oF Symbol tolerance j Orientation Perpendicularity tolerance zone Space between parallel planes Space between two parallel lines Table 6.1 Perpendicularity applied to a surface reFerence Required datum allowable tolerance modiFierS f allowable datum modiFierS f l m 0,02 A A 0,02 Figure 6.1 Perpendicularity applied to a surface Figure 6.2 Interpretation 89 ׉ 7cassandra://lKK3eAC4GeYIUqF76zJwa_c_kdEYgTT97t5hQ0ac3-8c`̵ay=!w׉EAdvanced Geometrical Tolerancing The functional requirement is that the righthand surface of the workpiece has to be within a tolerance zone of 0,02 mm. perpendicular to datum A. Reject Accept Figure 6.3 Possible deviations 6.1.2 assesmenT of PerPendIcularITy aPPlIed To a surface he deviations of the workpiece surface from a reference element are measured.The reference element needs to be aligned according to the datum (perpendicular, parallel or under a specified angel). The orientation deviation δd smallest distance Amin is the difference between the largest distance Amax . and the Figure 6.4 Assessment of perpendicularity Figure 6.5 Assessment of the orientation deviation δd here perpendicularity, of a surface ,, The dial indicator is set to zero in the lefthand site corner in the front. The orientation deviation δd is : 0,003 + 0,005 = 0,008 mm. Figure 6.6 Assessment of orientation 90 ׉ 7cassandra://fUirSbcvl6sSH4AofA5OeD7iSxW4hcWWt4w-kX_R3_o`̵ay=!xay=!w{בCט{u׉׉ 7cassandra://I9h-xPR5REls5vB_c94PXzBGwSeiQoBwbuAZYDro-j0H` ׉ 7cassandra://vvwCGOW2KnEjDQzCPARVu-2zJ0naTs0HbYgEgXtYX089`S׉ 7cassandra://lfEqevFqopgRjXmQC1KKK9T5dcgLR5VUJRRHAlyYlec`̵׉ 7cassandra://tlUVmlCsPIjwEpC8tSwdTqZ8NJ4kAVGYrqd5o3591Tk_& f͠ay=!ט{u׉׉ 7cassandra://XeMhQettEwFnf4DZtFAl86QXnqzDeubWYLLaQ-PjUK4}c` ׉ 7cassandra://MioQ7IEo1mR4W2_Cfqc9o88-Y52LVQCRD3sTdIB-vOA:`S׉ 7cassandra://b5ZEVRVC9RY9rsOdLtzSkKITVYnAJcdOvfyeA8A61TU~`̵׉ 7cassandra://n9cMGNhNsGmqn83cUohaA9yGoRYCDvW-7TyoRXasWd4y-͠ay=!׉E8 ±0,1 Advanced Geometrical Tolerancing 6.1.3 PerPendIcularITy of a medIa Plane aT mmc 7,7 A 0,2 M A Figure 6.7 Perpendicularity of a media plane at MMC MMVS = MMS - geometric tolerance Figure 6.8 Virtual condition boundary width Slot perpendicularity tolerance 7,9 8,0 8,1 Table 6.2 Bonus tolerances 0,2 0,2 0,2 bonuS tolerance total tolerance 0 0,2 0,1 0,2 0,3 0,4 There are several ways a perpendicularity tolerance at MMC can be verified. A common method is the use of a gage. The gage verifies that the feature of size fits into its MMVC. The part must rest on the datum and the feature must fit into or over its MMVC (acceptance boundary). The size and location needs to be verified separately. 91 ׉ 7cassandra://lfEqevFqopgRjXmQC1KKK9T5dcgLR5VUJRRHAlyYlec`̵ay=!y׉E.Advanced Geometrical Tolerancing 6.1.4 PerPendIcularITy aPPlIed To a cylIndrIcal feaTure of sIze type oF Symbol tolerance j Orientation reFerence datum allowable tolerance modiFierS Required f l m p Perpendicularity tolerance zone Space between two parallel planes Space within a cylinder (when ø is used) Table 6.3 Perpendicularity applied to a feature of size allowable datum modiFierS f l m 2x ø 20 20 0,02 A 60 ±0,3 A Figure 6.9 Perpendicularity applied to a feature of size 2 cylinders Ø 0,02 perpendiculair to datum A Figure 6.10 Interpretation 92 ׉ 7cassandra://b5ZEVRVC9RY9rsOdLtzSkKITVYnAJcdOvfyeA8A61TU~`̵ay=!zay=!y{בCט{u׉׉ 7cassandra://60rNZzFXE5PJ0F2A8k2rMleS9ERfN3XkZiiVTuk7Rcw4w` ׉ 7cassandra://XXExkqwdgRuTU3RcTHW9_4fnmagiY-Mqq5Fn_Ij2pn88`S׉ 7cassandra://8z7jIojDIA_-PtLJ4nkvtwCkPodbm2aV5GWCA03jGB0`̵׉ 7cassandra://CjmHtAl2eDbxLo_uJz1i60qnbLxVvuDPFhZcXDAZssQͳ\ ͠ay=!ט{u׉׉ 7cassandra://90TB0Ch6Ej8ggJl1BwnaK-2pcUoICOaEUKjeBQHAP7I` ׉ 7cassandra://pDIOh0JgG4jgYbGiwbR8v3wDvbwACWiPDXXezBUxOKU8`S׉ 7cassandra://jvED61ZJVaOoqTeJiOHXB9YVsgayxgrZCtWBs3XE5wU|`̵׉ 7cassandra://g_0lAG71Nu9mW_Wged_ZkmIAJ7AvHHQU7EQwpAufcpE ͠ay=!נay=!k9ׁHhttp://measured.Thׁ ׁ Ј׉EAdvanced Geometrical Tolerancing The requirement is that the axis of the two holes are perpendicular to the datum. Reject Accept Figure 6.11 Possible deviations 6.1.5 assesmenT of orIenTaTIon aPPlIed To a feaTure of sIze The deviations of the workpiece feature of size, either being hole, slot, parallel planes, shaft or bar, from a reference element are measured.The reference element needs to be aligned according to the datum (perpendicular, parallel or under a specified angel). For the measuring method below the distances from a measuring plate are measured. The orientation deviation δnx is calculated from the deviation in x being δnx and the deviation in y being δny.. Figure 6.12 Assesment of perpendicularity of a feature of size 93 ׉ 7cassandra://8z7jIojDIA_-PtLJ4nkvtwCkPodbm2aV5GWCA03jGB0`̵ay=!{׉EBAdvanced Geometrical Tolerancing 6.1.6 PerPendIcularITy To a cylIndrIcal feaTure of sIze aT mmc 0 16 - 0,02 0,04 M A A Figure 6.13 Penpedicularity at MMC Figure 6.14 Interpretation MMVS = MMS + geometric tolerance MMVS = ø 16 + 0,04 = ø 16,04 diameter boSe perpendicularity tolerance 16,00 15,99 15,98 Table 6.4 Bonus tolerances There are several ways a perpendicularity tolerance at MMC can be verified. A common method is the use of a gage. The gage verifies that the feature of size fits into its virtual condition. The part must rest on the datum and the feature must fit into or over its virtual condition (acceptance boundary). location needs to be verified separately. 94 0,04 0,04 0,04 bonuS tolerance total tolerance 0 0,04 0,01 0,02 0,05 0,06 In the example the maximal material virtual size equals 16,04 mm. The size and ׉ 7cassandra://jvED61ZJVaOoqTeJiOHXB9YVsgayxgrZCtWBs3XE5wU|`̵ay=!|ay=!{{בCט{u׉׉ 7cassandra://7r2_bpGb1XmfEE2q7tupo7VonTWxWIHRZn2-e1Hvwn8` ׉ 7cassandra://Z3XlIgDoOndBA6A8OFRw74fbZD9a505WHgyYPWrbrJw8 `S׉ 7cassandra://zCmHnPBp_9uEnmkUYbl270O72_BH1ZSZulGcyI4NwWA`̵׉ 7cassandra://Ofc8P6ybqTLZyt43hDeO3E66NN5RJaU_D8_8AzDpQNIe ͠ay=!ט{u׉׉ 7cassandra://9cjfoPXlXmZWhzLxH5cWDZkKN7Lty2zQsuYnH11ducY` ׉ 7cassandra://HjCksIhNRGF9ZOv6UCxvmXuvdaR_yFx4c7BS11kr2lQ+e`S׉ 7cassandra://uO6a77pq0iqAKhhvcECEyuD1kEorwMk2uKxbCdFutSA`̵׉ 7cassandra://_OQk9pcjSkCKdjN9x9_guTcjgpwtAxx83E7urt6zUC4t ͠ay=!׉E 30 ±0,2 0,1 Advanced Geometrical Tolerancing 6.2 ParallelIsm A parallelism tolerance limits the amount a surface, axis or center plane is allowed to deviate from parallelism relative to a datum reference. Parallelism is an orientation tolerance and does not control the location of the feature. Only rotational degrees of freedom are constrained. An orientation tolerance can translate relative to the datum but not rotate. A parallelism tolerance always uses a datum. It can control form and orientation. Parallelism tolerances are used in assemblies (maintain uniform gap), supports (distribute load and reduce wear) and performance (lineair motion). 6.2.1 ParallelIsm aPPlIed To a surface type oF Symbol tolerance k Orientation Parallelism tolerance zone Space between parallel planes Space between two parallel lines Table 6.5 Parallelism applied to a surface reFerence Required datum allowable tolerance modiFierS f allowable datum modiFierS f l m 0,1 A A Figure 6.15 Parallelism applied to a surface Figure 6.16 Interpretation 95 ׉ 7cassandra://zCmHnPBp_9uEnmkUYbl270O72_BH1ZSZulGcyI4NwWA`̵ay=!}׉E[Advanced Geometrical Tolerancing The requirement is that the top surface is parallel to the datum. Reject Accept Figure 6.17 Possible deviations 6.2.2 assesmenT of ParallelIsm aPPlIed To a surface The deviations of the workpiece surface from a reference element are measured. The reference element needs to be aligned according to the parallel or under a specified angel). The orientation deviation δd between the largest distance Amax smallest distance Amin . Figure 6.18 Assessment of the orientation deviation δd here parallelism, of a surface ,, datum (perpendicular, is the difference and the 96 ׉ 7cassandra://uO6a77pq0iqAKhhvcECEyuD1kEorwMk2uKxbCdFutSA`̵ay=!~ay=!}{בCט{u׉׉ 7cassandra://cVgKeHKd_CLXk1tTFHcIm6k1xNfm1XGboIVw5qzakOQ8` ׉ 7cassandra://FG7Lmx8LV75bedxlg9VFNm2cl6o6Bzk9fgxnIbi-jwU8`S׉ 7cassandra://ua5ZcpzhIfhCTW1tz8x-iU47Hj_a7yIoeO1tMMbR8ocX`̵׉ 7cassandra://lk38q7W6yIfx-VO7Fg0xAKMxx_TYe8evDaxSysGizmI @͠ay=!ט{u׉׉ 7cassandra://iYAfOEVXIFok-A1cdOibb3nDzZMbatShqdlk0tmkJr01` ׉ 7cassandra://LE8cSxYHr9M6vsoo7o5XeZMRhMShF9yP0pA0Kwq3daI!`S׉ 7cassandra://op8o162FjRZgbl9Uy1iHOL_RdI3f7fQa_YFpoeh0PQA `̵׉ 7cassandra://CrEKRQGf9YMcn8mzz5KWbJahH4wxZ4XKzQeMUfJftAoWu ~͠ay=!׉E220 G7 0,02 Advanced Geometrical Tolerancing 6.2.3 ParallelIsm aPPlIed To a cylIndrIcal feaTure of sIze type oF Symbol tolerance k Orientation reFerence Required Parallelism tolerance zone Space between parallel planes Space within a cylinder (when ø is used) Table 6.6 Parallelism applied to a feature of size datum allowable tolerance modiFierS f l m p w allowable datum modiFierS f l m 0,02 A Tolerance zone two parallel planes A Figure 6.19 Parallelism applied to a feature of size Figure 6.20 Interpretation Reject Accept Figure 6.21 Possible deviations 97 ׉ 7cassandra://ua5ZcpzhIfhCTW1tz8x-iU47Hj_a7yIoeO1tMMbR8ocX`̵ay=!׉EAdvanced Geometrical Tolerancing 6.2.4 assessmenT of ParallelIsm aPPlIed To a feaTure of sIze The differences of the distance from a measuring plate are to be measured. Figure 6.22 Assesment of the parallelism deviation δp , of a feature of size 98 ׉ 7cassandra://op8o162FjRZgbl9Uy1iHOL_RdI3f7fQa_YFpoeh0PQA `̵ay=!ay=!{בCט{u׉׉ 7cassandra://SGSkQ5dXQaED2ZSQbj3ekoIWZR3113UsW1Go_0yfhEs` ׉ 7cassandra://E8k8oH4C6liQCt7E5GqYwoRlulj0uaTtJFhTnpOvBoA`S׉ 7cassandra://7JIkCo6zyEAYQ364j4bIt_QM66moU8iiawDZQlNckwQ`̵׉ 7cassandra://WfxsYdlpg8SrpLvcIb77DYXx65TWQ37806w5jJnrWIMͬ0$͠ay=!׉E)Advanced Geometrical Tolerancing module III 7 Tolerances of locaTIon In previous chapter position was discussed being the most common tolerance for location. Coaxiality / Concenytricity and symmetry are two more geometric tolerances controlling location. All location tolerances also indirect control orientation and form. 7.1 coaxIalITy / concenTrIcITy 7.1.1 coaxIalITy The coaxiality tolerance is a geometric tolerance that defines the permissible deviation of the axis of a surface of revolution from a datum axis. type oF Symbol tolerance o Location Coaxiality tolerance zone Space within a cylinder Table 7.1 Coaxiality reFerence datum allowable tolerance modiFierS allowable datum modiFierS Required f m l w* f m l * Required datum axis 0,05 A Figure 7.1 Coaxiality A Figure 7.2 Interpretation 105 0,05 ׉ 7cassandra://0CgPCxOMpUBHqE0nsF5iOeGemPNcoyOY042VjQYnuxQ`̵ay=!׉EAdvanced Geometrical Tolerancing Reject Accept Figure 7.3 Possible deviations poSSibilitieS For indicatinG coaxiality 25 H8 E 0,01 A ø 25 H8 = ø 25 + 0,033 A 25 H8 E 0,01 M A 25 H8 0,01 M A M 25 H8 0 M A M Figure 7.4 Possibiities of indicating coaxiality From top to bottom: 1. Each hole must respect the envelope requirement separately The axis of the right hole must be contained in a cylinder of ø 0,01 coaxial to datum A. 2. Each hole must respect the envelope requirement separately The right hole must be must respect a the MMVS (= ø 25 - 0,01 =ø 24,99) that is coaxial to the datum 3. A stepped caliber must fit in which has on the right the MMVS (ø 24,99) and the left the MMS (ø 25) 4. A caliber at MMS must fit both holes 106 ׉ 7cassandra://7JIkCo6zyEAYQ364j4bIt_QM66moU8iiawDZQlNckwQ`̵ay=!ay=!{בCט{u׉׉ 7cassandra://1eF7DWWEowyvSHC4ElN6AKvDndDPFbPaZMywP7w3IXwr` ׉ 7cassandra://T0NUadaN23taT7Sh4tlMjVuqEAfX8rmQwLWRm1V_NlM+`S׉ 7cassandra://IiDG6CafHDIEOgElXN_7ybWb_t0TodT-rh-2ngqJwVIj`̵׉ 7cassandra://7onEGIsjXpsrJrylWmzDANV6vHl-ZNEx5rPNscKOUx8m4͠ay=!ט{u׉׉ 7cassandra://Cu9ZSYrz8YKDdlZH4ysDiM7i9OUF4PxmbtWeDKsRpGk_` ׉ 7cassandra://2uFmKdwu-whdgL0SgeZLHa7e8RLhR6uscvdn1qFmUew@`S׉ 7cassandra://2GXFxInko5_DtS1NC7ux0OX9ZfMYgMYyT_NCa5VoDDA`̵׉ 7cassandra://4o0TVAztAxU6l66No5bJRX7e6vyjgjsqXx62pEI9gAA͑R͠ay=!׉EIAdvanced Geometrical Tolerancing 7.1.2 concenTrIcITy The concentricity tolerance is geometric tolerance that defines the permissible deviation of the media points of a surface of revolution from a datum center point. type oF Symbol tolerance o Location Concentricity tolerance zone Space within a circle Table 7.2 Concentricity reFerence datum allowable tolerance modiFierS allowable datum modiFierS Required f m l w* f m l * Required A B A ACS 0,03 B Tolerance for centricity is a circle at any cross section. Figure 7.5 Concentricity and the interpretation of concentricity 0,03 107 ׉ 7cassandra://IiDG6CafHDIEOgElXN_7ybWb_t0TodT-rh-2ngqJwVIj`̵ay=!׉EpAdvanced Geometrical Tolerancing 7.1.3 mmr and coaxIalITy 0 16 -0,1 0,05 A Tolerance zone for concentricity is a cylinder of Ø 0,05 regardless feature size. 0 10 -0,02 A Figure 7.6 Concentricity without MMR 0 MMR applied to the toleranced feature 16 -0,1 0,05 M A The tolerance is Ø 0,05 and as much more as the MMS of the toleranced feature of Ø 16 falls short. 0 10 -0,02 A Figure 7.7 MMR on the toleranced feature Examples for the coaxiality tolerance: Ø 16,00 >> 0,05 + 0 = Ø 0,05 Ø 15,95 >> 0,05 + 0,05 = Ø 0,10 Ø 15,90 >> 0,05 + 0,10 = Ø 0,15 When the MMR is applied to a feature the MMVC of the toleranced feature shall not be violated when applied to a datum the related MMVC of the datum feature shall not be violated. 16 -0,1 0 0,05 MA The modifier m at the datum makes the tolerance for coaxiality dependent on the dimension of the datum. The coaxiality tolerance is Ø 0,05 and as much more as the MMS of Ø 10 falls short. 0 10 -0,02 A Figure 7.8 MMR on the datum feature Examples for the coaxiality tolerance: Ø 10,00 >> 0,05 + 0 = Ø 0,05 Ø 9,99 >> 0,05 + 0,01 = Ø 0,06 Ø 9,98 >> 0,05 + 0,02 = Ø 0,07 . 108 ׉ 7cassandra://2GXFxInko5_DtS1NC7ux0OX9ZfMYgMYyT_NCa5VoDDA`̵ay=!ay=!{בCט{u׉׉ 7cassandra://oRyLUma_rsPfDljM9-Pp6OKInM33o7tjSitFt_gkcME` ׉ 7cassandra://akhU2xAbKgow4pyWIblpdtlI-cH-dFzHLWv0SZio0XM# `S׉ 7cassandra://8S1Cyb4FenVUmWIfQrIecQdbhBQpVzgigOcdoT2vsB4 `̵׉ 7cassandra://P7HPBuNH1chF-fX0xS7mfzmQ70jHops1ZWRO3HGaUSwM͠ay=!ט{u׉׉ 7cassandra://ZyfyQ6DSm7du0p1FYY10ZlkFu6sPjMJPdiWVa7WY6Hkz` ׉ 7cassandra://Xj7T63MYbyKFJLQzDDatygcyhBmlhriqKgX4IC37XWk<`S׉ 7cassandra://qEZrSrN-9sTiH_RTxmTMnOC071N8W5VNAIa8A9VdYS4`̵׉ 7cassandra://kh4eUD8RizezRw2DcFvVobUWsLkJsN5fYArOeEwJJ2k_e ͠ay=!נay=!u̍9ׁHhttp://coaxiality.toׁ ׁ Ј׉E8Advanced Geometrical Tolerancing 0 16 -0,1 0,05 M A M The modifier m at the toleranced feature and the datum feature makes the tolerance for coaxiality dependent on both the dimension of the toleranced feature and the datum feature. The coaxiality tolerance is Ø 0,05 and as much more as the dimensions Ø 16 of the toleranced feature and the dimension of the datum feature are smaller then the MMS. 0 10 -0,02 A Figure 7.9 MMR both on toleranced and datum feature Example for the maximal coaxiality.tolerance Ø 15,90 and Ø 9,98 >> 0,05 + 0,10 + 0,02 = Ø 0,17 109 ׉ 7cassandra://8S1Cyb4FenVUmWIfQrIecQdbhBQpVzgigOcdoT2vsB4 `̵ay=!׉E(Advanced Geometrical Tolerancing 7.2.1 symmmeTry Tolerance 7.2 symmeTry Symmetry defines the symmetry deviation of a with feature of size to a datum center plane or datum axis. One of the features can be symmetrical and the other cylindrical. When dimensioning symmetrical relationships several geometrical tolerances may be used. The choices are position, profile and symmetry. The use of symmetry is rare. Both position and symmetry have the same shape of tolerance zone and both limit deviations in location and orientation. type oF datum Symbol tolerance q Location Symmetry tolerance zone Space between parallel planes Table 7.3 Symmetry reFerence Required allowable tolerance modiFierS allowable datum modiFierS f m l f m l 0,05 A A Figure 7.10 Symmetry Figure 7.11 Interpretation datum plane 110 0,05 ׉ 7cassandra://qEZrSrN-9sTiH_RTxmTMnOC071N8W5VNAIa8A9VdYS4`̵ay=!ay=!{בCט{u׉׉ 7cassandra://KLF-9G2p90G3a95Ku9PdlIVGi0ZBIKh0XOJ6EdFCSfQ` ׉ 7cassandra://vAAZP-XtTHc-goAUsGjwxhgQX7CU4RfbO_sHr2Y7TXo/`S׉ 7cassandra://f1vF10N0RiXefUSjXL3joziI0-_pIIa-0vOgorwpHfYk`̵׉ 7cassandra://VF_txCqWAFqSlRBSCbW30dIUPYiT_14jDG9y5RVRxXA͜|͠ay=!ט{u׉׉ 7cassandra://wRPCSliKCe5lL0gXtdpNhULd6JNNwNbHhbsORZnXHL4` ׉ 7cassandra://teiEnj9loIEGZh-TWNCqzCVEl6Y-iVGOF81DyRGLPEQ7`S׉ 7cassandra://IP2UKakK_5AQsrQsDp0t87pckzB2RPpq86vxfjDt4Ls`̵׉ 7cassandra://E0rJYbeBFR3UrSH4krSuh2bI84bJOHIMQ_mN44Oi6Ys}D͠ay=!׉EAdvanced Geometrical Tolerancing Reject Accept Figure 7.12 Possible deviations 7.2.2 InTercHanGInG Toleranced feaTure and daTum feaTure A 0,2 B - C 0,2 A B C In the example to the left the perpendicularity deviation of the plane through the holes is not limited in relation to the datum media plane. Making the holes the datum features the perpendicularity is also limited. Figure 7.13 Interchanging toleranced feature and datum feature 111 ׉ 7cassandra://f1vF10N0RiXefUSjXL3joziI0-_pIIa-0vOgorwpHfYk`̵ay=!׉EAdvanced Geometrical Tolerancing exerciSe 0,005 C 20 ±0.05 0,03 M A M A 20 60 80 0,1 B B 0,1 B 12 F8 0,05 A B 0,05 C Figure 7.14 Exercise ISO 2768 mK • What is the shapes and size of the form tolerance zone? • Where is the envelope requirement used for? • Which orientation tolerances are stated and what are the the and size of the tolerance zones? • Which location tolerances are stated and what are the the and size of the tolerance zones? 112 40 h6 E 8 ±0.05 0 10 -0.05 0,05 M C 0,05 M A ׉ 7cassandra://IP2UKakK_5AQsrQsDp0t87pckzB2RPpq86vxfjDt4Ls`̵ay=!ay=!{בCט{u׉׉ 7cassandra://RzJndlyWe8tq1f-GT7wCD1m2wbhRAfymeQS8obZBKRgM` ׉ 7cassandra://-u9qu3-8CjDTFd9PaPqLlcsoYDF2IDYRJQsaqNy0R6AEg`S׉ 7cassandra://A8Gdz6WUemCxij-8QrG08QA8yY7PBlSjgQCblzzk9po`̵׉ 7cassandra://wXi05TbR0XDeG5zzNOUroRZH9zgIPSIPwQJfHRI7fFY͝f͠ay=!ט{u׉׉ 7cassandra://uZwVL-5fFd4AVjMac6zVUEUsxiMTRbIbmu3_EjAuy28e7` ׉ 7cassandra://TIUuLvRLjPSJJNtP3sBLXE29-HqfiZNokCVKY8-uRDI(?`S׉ 7cassandra://D7h3q7lcQSxLpAG5bMfe2UTyAsvoiQJPpApbFy6TcFw C`̵׉ 7cassandra://D0X8V_qmk1pSeG_b1bLlSgzQHNL25Z1rUPqSlwvZzfg]b \͠ay=!׉EAdvanced Geometrical Tolerancing 7.3 PosITIon Tolerance A position tolerances is a tolerance of location that directly controls location and indirectly controls form and orientation of a feature of size. It’s among the most common used tolerances. A position tolerance limits the amount a center point, axis or center plane of a feature is permitted to deviate from nominal position defined by theoretical exact dimensions. A datum may or may not be used In comparison to coordinate tolerancing postion tolerances offer several advantages. • Provides 57% larger tolerance zone • Permits bonus tolerances (MMC and LMC) • Prevents tolerance accumulation • Permits use of function gage (MMC and LMC) • Lowers manufacturing and inspection costs Figure 7.15 Comparison of zones with round and square cross-section 7.3.1 THeoreaTIcal exacT dImensIon A Theoretcical Exact Dimension (TED) is the theoretical exact location of a feature of size as esthablished by nominal dimensions. TED’s also known as boxed dimensions must not be toleranced. The dimension is shown in a rectangular frame. Theoretically exact dimensions may only vary by the geometric tolerance that is stated in the tolerance frame associated with them. Theoretically exact dimensions should be used when dimensioning the theoretically exact location of features for tolerances of Angularity, Position, Profile of a line and Profile of a surface. 113 ׉ 7cassandra://A8Gdz6WUemCxij-8QrG08QA8yY7PBlSjgQCblzzk9po`̵ay=!׉E10 0,03 Advanced Geometrical Tolerancing poStion applied to a SurFace The requirement is that the toleranced feature is positioned with a tolerance of 0,03 mm with respect to datum feature A. The tolerance zone location is located and orientated by the TED. The deviations of form, orientation and location are controlled. A 0,03 A Figure 7.16 Position applied to a surface Rejects Accepts Figure 7.17 Position deviations 114 ׉ 7cassandra://D7h3q7lcQSxLpAG5bMfe2UTyAsvoiQJPpApbFy6TcFw C`̵ay=!ay=!{בCט{u׉׉ 7cassandra://buDhy0KRwgD2sDwUtwFNsQOcL2OODP_JSGbjTMgomyk` ׉ 7cassandra://XfpvSnJ32DrNab1ECe6damRf7AIwWxwahuULd6RW2BYG`S׉ 7cassandra://w1KvGnpQDzG16BSXtkT63DrLwhx5Y3rvxNQRFOVlEKY`̵׉ 7cassandra://DMAS4kph55RD1HU1KmAwEgG6qLg_gxbQn3pNLL9HDOoq ͠ay=!ט{u׉׉ 7cassandra://UCm1U1udwkqkXi_3UZA-m1z6yJ5LvQKYS8ezW-OE21cs|` ׉ 7cassandra://EsMKZrDO88d56hE1XQaqhm_n4cHuUtPmKc6xo1pduDs.`S׉ 7cassandra://LtdbH-VDMzUKMwYXKxJhuDP8NEQ4WWD65QBGnDlEoG0`̵׉ 7cassandra://5D3aQdg0yPwN1VOYuLCWuC9URhyrJmb4W9PMtHoG1cM*B͠ay=!׉EAdvanced Geometrical Tolerancing poSition applied to a hole Position tolerances are commonly used to control : • Distance between features of size • The location of a pattern of features of size • The coaxiality between features of size • A symmetrical relation between features of size type oF datum Symbol tolerance reFerence allowable tolerance modiFierS ( Location Position tolerance zone Spaced between two parallel planes Space within a cylinder (when ø is shown) Table 7.4 Interpretation Required m l p f w allowable datum modiFierS m l f 6 B 12 + 0,4 0 0,2 A B C 0,2 A C Figure 7.17 Position applied to a hole Figure 7.18 Interpretation The default tolerance zone is two parallel planes. Where the diameter symbol is specified in the feature control frame the tolerance zone shape is a cylinder. A position tolerance zone is located and oriented by the specified TED’s. In most cases datum reference features are used in the feature control frame. Here the tolerance zone is perpendicular to datum A. 115 16 ׉ 7cassandra://w1KvGnpQDzG16BSXtkT63DrLwhx5Y3rvxNQRFOVlEKY`̵ay=!׉EVAdvanced Geometrical Tolerancing poSition, beSt Fit The requirement is that the centerlines of the 4 holes have to be with a cylindrical tolerance zones. The postion of the tolerance zones is determinted by the TED’s. When there are no datums then the requirement is ‘Best fit’ ‘Best fit’: The workpiece is to be rotated and translated in all directions for smallest deviations of the position tolerance related features. Orientation and location of the side, top and bottom surfaces is random. Figure 7.19 Positioning of a pattern of holes 4x 0,4 top view Figure 7.20 Interpretation 116 ׉ 7cassandra://LtdbH-VDMzUKMwYXKxJhuDP8NEQ4WWD65QBGnDlEoG0`̵ay=!ay=!{בCט{u׉׉ 7cassandra://n7b1ayGqWSMZ7_cyQacEWqyitZJn3qIFlcI5V8_pmrcr*` ׉ 7cassandra://57TZ3lb1uHiLESauXl0I8x7SJufGBhCUv--doRW1J1M0`S׉ 7cassandra://ubPYk7sXBtLwPZn72QKJg-ZEfKBAz9UwSEcDH07ORFk`̵׉ 7cassandra://xvv-JPt_JNR302OD_OjLf7ABRIdiu48ZhwJorlESKrIw: ͠ay=!ט{u׉׉ 7cassandra://pc9_QCotqnwc3QdyZgBqUXNLS2bmSTn4aB3RsBsO6OgJ` ׉ 7cassandra://9-Nd1nQDcoD_ddtIgTWJEed5Bfyu2SG6eatSjUgDaoo=`S׉ 7cassandra://jH9d9SoUPHkT1bEEJpEJp8nS_XV9MsmE7l9MdmvFlj8`̵׉ 7cassandra://hPo5quw8ICIsNfg_VAClpNAxLPD7iYNmPb9UkTtbhCg-p4͠ay=!׉EAdvanced Geometrical Tolerancing Coordinate dimensions are used to position the pattern of the with respect to the workpiece surfaces. Position tolerances are used to define the pattern. n\w0œ2Ç\A\B\C] 20.3 Figure 7.21 Positioning a pattern of holes 117 ׉ 7cassandra://ubPYk7sXBtLwPZn72QKJg-ZEfKBAz9UwSEcDH07ORFk`̵ay=!׉E-20 32 Advanced Geometrical Tolerancing SuperpoSition oF poSitional toleranceS n\w0œ6Ç\A\Y\Z] n\w0œ2Ç\A] 4x 10 0,2 0,6 A Y Z 0,2 A Y 15 32 Z A Figure 7.22 Superposition of position tolerances The axis of the four holes shall be within a cylindrical tolerance zone of ø 0,2 perpendicular to datum A. The actual axis of each hole shall be within a cylindrical tolerance zone of ø 0,6. The positional tolerance zones are located to their theoretical exact positions in relation to the datums A, Y and Z. Figure 7.23 Superposition tolerances explained 118 ׉ 7cassandra://jH9d9SoUPHkT1bEEJpEJp8nS_XV9MsmE7l9MdmvFlj8`̵ay=!ay=!{בCט{u׉׉ 7cassandra://-clYvjhVj6wJdJ0dcT6ihjm-P-vuzWUz9dEGz4YRVko` ׉ 7cassandra://aLY83T554XCQ3N8V5AdW2okcATpRrX80m2gBkxXOFfw2`S׉ 7cassandra://PwvvPChR8yGGV4c3OFZvgJOsHN9DfPAFZnWhR8Q3BlQ`̵׉ 7cassandra://cbFgIX_8y2ZXIoXH1Jw9nE9oZThOp5qBlzAW4L2klncf*j͠ay=!ט{u׉׉ 7cassandra://J_QuUHbs_vtU0sPCoUyXpS6KjRsv3Pk6QuqyBh0orXsJ` ׉ 7cassandra://E8WQ-Jou1X-Kvu7qUJ-fstyx2IJhn5x3feTMVJr5iJ80]`S׉ 7cassandra://SVOMNZNZ0MKcrVU5dmCFpjlPUYe6A5t8q2rNe4DAGHUo`̵׉ 7cassandra://TTS3jvRluiZsTRNidNoOGOnVi_tTdR-ZRcVm6fUyUKshf͠ay=!׉EAdvanced Geometrical Tolerancing Figure 7.24 Superposition, example from ASME Figure 7.25 Superposition tolerances explained 119 ׉ 7cassandra://PwvvPChR8yGGV4c3OFZvgJOsHN9DfPAFZnWhR8Q3BlQ`̵ay=!׉EAdvanced Geometrical Tolerancing 7.4 assessmenT of True PosITIon of Holes The center line of a hole to the center line of another hole or with respect to a surface can be assessed using a center line caliper. What is measured however are coordinate dimensions. These coordinate dimensions can be translated towards position tolerances. Figure 7.26 Centerline caliber Figure 7.27 True position 120 ׉ 7cassandra://SVOMNZNZ0MKcrVU5dmCFpjlPUYe6A5t8q2rNe4DAGHUo`̵ay=!ay=!{בCט{u׉׉ 7cassandra://dJxNVE5Up5nDbKMBvGWtkmSitQsm0j_dZldbB6N6Bko` ׉ 7cassandra://3dQ6DHxv7xqCkFzUcqZcu3uk6Gh3cq1cNuPM7DVJO6E6`S׉ 7cassandra://nsk2yvjpVKXUjLD0xKIe0vnECDoM9UPKfOmH3cAEQ5Q`̵׉ 7cassandra://-nXvedKmuPwiQbo5FKOeY3I_XTnay_k2leO8RkPFkyY͆͠ay=!ט{u׉׉ 7cassandra://qzRHMqKZfX5In2Qam6ylvz0bE33lj2inFLZYDHRVx3A` ׉ 7cassandra://0tovaXLwsvRXLibrLNGOE3BKWkwbUt6qk_JJaSISiJg$X`S׉ 7cassandra://fmS2xwwi1MFRdQ6rxBYm4QEov1xEwUhdzvrsxA-9hLo `̵׉ 7cassandra://a9pxOPpZcNdfKhjySXqqEy05w9Arpi0DpNWViIbftoY'b͠ay=!׉EAdvanced Geometrical Tolerancing 7.5 PosITIon aT mmc Where a position tolerance applies at MMC the tolerance zone is a virtual condition acceptance boundary located (VBC = MMVC) at true position which the surface of the tolerance feature of size must not violate. MMC for a hole is when the hole is at its smallest size. MMVC = MMS - geometrical tolerance = 6 - 0,4 = 5,6 6 B 12 + 0,4 0 0,4 M A B C VBC = ø 5,6 A C Figure 7.28 Position MMC applied to a hole Figure 7.29 Interpretation diameter hole poStion ø tolerance 6,0 MMC 6,2 6,4 LMC Table 7.5 Position MMC applied to a hole 0,4 0,4 0,4 bonuS tolerance total location tolerance ø 0 0,2 0,4 0,4 0,6 0,8 121 16 ׉ 7cassandra://nsk2yvjpVKXUjLD0xKIe0vnECDoM9UPKfOmH3cAEQ5Q`̵ay=!׉EAdvanced Geometrical Tolerancing 7.6 assessmenT of True PosITIon of PaTTern of Holes When true position is applied to a pattern of holes the tolerance is the virtual boundary or MMVC shall not be violated. Figure 7.30 Pattern of holes in MMC 122 ׉ 7cassandra://fmS2xwwi1MFRdQ6rxBYm4QEov1xEwUhdzvrsxA-9hLo `̵ay=!ay=!{בCט{u׉׉ 7cassandra://lWe1WI5sNQu6EdjL-k_GoOnX4OEwiS8XW6-Fjxoj0TcC` ׉ 7cassandra://fVqHt4N1YXFGhjhvOrj1XLOOcr_wKXRpjDAnmQdNrH0#v`S׉ 7cassandra://aDxonGBp-ahoFT3xLKS_TkHjKXSUXB4yaWbVihKQcII (`̵׉ 7cassandra://8d19GAsFwhu0jCq3Oyd-f48YSytOmwk_W5b8eEOURkUYR͠ay=!ט{u׉׉ 7cassandra://hhDfeiUtuzeIapIuW7P5AOisT5UTKjvzuL73-WuxUeU` ׉ 7cassandra://OjjZBydh7yfQopOz4xxmDTdWUndPFb6tXqKv0u9U7wQ8`S׉ 7cassandra://SJkgGdLYtRwTWZ-156-O-dYA-SRTvzzJlZ0teWweWMA`̵׉ 7cassandra://18qW3bv5Sj-l5psZlPRUXa0Tbh0vKfDAaCr30RTVhv0ee^͠ay=!׉EAdvanced Geometrical Tolerancing The MMS for the holes is 9,9 MMVC = MMS - geometric tolerance = 9,9 - 0,1 = 9,8 MMVS 9,8 Figure 7.31 Caliber for the pattern of holes Figure 7.32 Possible position of the holes 123 ׉ 7cassandra://aDxonGBp-ahoFT3xLKS_TkHjKXSUXB4yaWbVihKQcII (`̵ay=!׉E3Advanced Geometrical Tolerancing 7.6 GrouP of Holes as daTum The four hole group is related to datum D, A and B. The MMVC (ø 11,85) of this group together establish the datum C of the positional tolerance ø 0,15 of the three hole group. The MMVC of the four holes (ø 11,85) together with the MMVC of the three holes (ø 7,75) must fit into the holes. In addition perpendicular to D the MMVC (ø7,85) for the positional tolerance ø 0,05 of the three holes must fit together into the three holes. Figure 7.33 Super position and a group of features as datum 124 ׉ 7cassandra://SJkgGdLYtRwTWZ-156-O-dYA-SRTvzzJlZ0teWweWMA`̵ay=!ay=!{בCט{u׉׉ 7cassandra://9_fWGZ-wnX3ST1YF51Iwum1bPVn7dI_lnWbBUbtOssoE` ׉ 7cassandra://c9UYWXKtT7n6IACrC5K7-EH4g7ZH8mBAtJHxGvPVFuM)`S׉ 7cassandra://DUZVebL1jcmpMwCwzXpEwZrj7kS1DnIeEpvse_7Tg7E `̵׉ 7cassandra://lmwExbZ8Jd3zKwCG8mj9_gct8llalmQ8nEJFiGvE3pUb͠ay=!ט{u׉׉ 7cassandra://6KdEDW3VQ_uvmtiTxaUzrfd1XmgIbefv5tYRjAYYrFU` ׉ 7cassandra://YBJ4EyK0CkLzOCNwltAG57X9hOicMEAjcyoiH8twLyoCU`S׉ 7cassandra://QMAnlhT5qJrJbAVtQuC68Fb8kgC1UuwmJjPud9PjrxkB`̵׉ 7cassandra://tl_utW_3-1dBf5b6Sgxd22oe01pe9k5qsTAx-c64lag͌S^͠ay=!׉EaAdvanced Geometrical Tolerancing Figure 7.34 Super position and a group of features as datum 125 ׉ 7cassandra://DUZVebL1jcmpMwCwzXpEwZrj7kS1DnIeEpvse_7Tg7E `̵ay=!׉EAdvanced Geometrical Tolerancing 7.7 maxImal maTerIal requIremenT aT 0 How tolerances are specified affects the part function and manufacturing costs. Tight tolerances do not guarantee a quality part only an expensive one. “Zero tolerance at MMC” protects the parts function and reduces costs by offering maximal flexibility for manufacturing. “Zero tolerance at MMC” is indicated by 0 m and states that the functional tolerance is not distributed on size and position but provided for both. 2x 10,5 0,4 0 n\w0œ3mÇ\A\B\C] C 0,3 M A B C 10 60 B 10 0,4 2x 10,5 - 0,3 n\w0mÇ\A\B\C] C 0 M A B C 60 B A A Figure 7.35 Conventional tolerancing Figure 7.36 Zero tolerance at MMC Position tolerance: Bonus tolerance Total tolerance 0,3 0,4 0,7 MMC hole Position tolerance Virtual condition 10,5 - 0,3 10,2 Position tolerance: Bonus tolerance Total tolerance MMC hole Position tolerance Virtual condition 0 0,7 0,7 10,2 - 0,0 10,2 126 10 10 ׉ 7cassandra://QMAnlhT5qJrJbAVtQuC68Fb8kgC1UuwmJjPud9PjrxkB`̵ay=!ay=!{בCט{u׉׉ 7cassandra://FrXGCLbqprBD1S4giWEthZvtbyB0qnLzTYU6qUOlm3Q}` ׉ 7cassandra://l9aIJqny-Hb30J5KoEA-Q7zTD4obLc-snG84bFuI2Vk?o`S׉ 7cassandra://9nn8WAWDAVnRxcX8UJ3Gx1eNU6Vx1ZVlpvjkpwDWocE`̵׉ 7cassandra://F7tKNiYvZRqAfmfnbGRXznwAnPtS_IWYhDkn7rrX0ss|f͠ay=!ט{u׉׉ 7cassandra://wBKk5D8cVcOIVc33vSxMJwB95s0oGaVUxEGyj7hHgi4` ׉ 7cassandra://O-pxtZNjjSzYZ2eqg3GLBfRx21zjvlCxZcveHcRl55o,D`S׉ 7cassandra://E85qMVglw7UeAqR0Sl1_f4W6QKLPFByAoHR7bQPi0r4`̵׉ 7cassandra://R9NAgtELaElQ-Es5oCDfHHmNSz_UERFEKqt0kNuaB2Ej' ͠ay=!׉EAdvanced Geometrical Tolerancing 7.8 fIxed and floaTInG fasTners When in an assembly two or more parts are held together using fastners the position tolerance ‘T’ for the holes can be calculated One part can be threaded then this is called “fixed fasteners”. When both holes have clearance and bolts are used this is called “floating fasteners” T = Total position tolerance H = MMC of the clearance hole F = MMC of the fastner Figure 7.37 “Floating fastners” T =H - F MMS of a M12 bolt is considered 12 Figure 7.38 “Fixed fastners” Position tolerance: T = (H - F)/2 MMS of a M12 bolt is considered 12 The height of the part is 16mm 127 ׉ 7cassandra://9nn8WAWDAVnRxcX8UJ3Gx1eNU6Vx1ZVlpvjkpwDWocE`̵ay=!׉EAdvanced Geometrical Tolerancing 7.9 assesmenT of locaTIon Tolerances Figure 7.39 Assesment of the location deviation δo On the cylindrical surface the values Ai sections perpendicular to each other Aix location tolerance. and Au and Aiy δo must be accessed in each axial location in is half the is calculated using Pythagoras. δo Location deviations of a surface is verified w.r.t. a surface like the flatness assessment. Figure 7.40 Assessment of location deviation 128 ׉ 7cassandra://E85qMVglw7UeAqR0Sl1_f4W6QKLPFByAoHR7bQPi0r4`̵ay=!ay=!{בCט{u׉׉ 7cassandra://X1DCYmP0kbIbNAwDCVlOh055xgBm420xn1ftzT33sSIC` ׉ 7cassandra://2kn-HbB1HTvsIdmfrwPEnFSOTKoqb4q2dQ3AoNSYfHc<`S׉ 7cassandra://BcBh7jtG-L63aSDeMMHL5T5OwYE2mvuqRsjPfw0XPVI`̵׉ 7cassandra://k8mGCY6zlEghU1NTcpiRVLNQNZI-dDIzz7QUF8As8tYf͠ay=!ט{u׉׉ 7cassandra://Leb7U4ctM7sgeNIojeL6wirri2oENVxHpUv2SKSTs7sD*` ׉ 7cassandra://ef7hX3H_pIMePDWU8XQQFNv-b1DJD4YeanBGwhZhOIM*`S׉ 7cassandra://kLdXT6G9KFMaFscPsNdCoaUiAosHnUkSaiOC_aF5xoE,`̵׉ 7cassandra://9HsqzrfY_NbSOePP_whWR5LNbnqnBxHoS70Rrjounjcʹ:b͠ay=!׉EcAdvanced Geometrical Tolerancing 7.10 PaTTerns and combIned sPecIfIcaTIons The left hand site examples are equal in ISO 5458:1998 and ISO 1101: 2017. However in 1998 standard the two small holes are considered one feature with respect to datum hole A. The holes were on one 180º line. ISO 5458: 1998 In 2017 the same example had a different interpretation due to the focus on the indendency principle. The position requirement only states the location of the holes as indicated y the TED’s. The holes are no longer a group of holes with respect to the datum Figure 7.41 Ambigeous indication for patterns 129 ׉ 7cassandra://BcBh7jtG-L63aSDeMMHL5T5OwYE2mvuqRsjPfw0XPVI`̵ay=!׉EAdvanced Geometrical Tolerancing ISO 5458: 1998 ISO 5458: 2018 en ISO 1101: 2017 Figure 7.42 Ambigeous indication for patterns 130 ׉ 7cassandra://kLdXT6G9KFMaFscPsNdCoaUiAosHnUkSaiOC_aF5xoE,`̵ay=!ay=!{בCט{u׉׉ 7cassandra://XE9sm8RZDnSyu5dVpRiA8mEUOUbmRXqXevq1sz1wxNY1` ׉ 7cassandra://tnoo2NNDrMHVp5IaX9YrW9c4FPizDpFZuGjHnvzvj2g)`S׉ 7cassandra://DToHKezeulGdrahFx6tPkErkBWg1dkahqXCyM-Tza6w`̵׉ 7cassandra://p0Clu18WL68Y9jvi8dbFHexgdwOY2PxtqBWsuewuPTwͺf͠ay=!ט{u׉׉ 7cassandra://gOmGwDfdAv-oqrP0k0mrbRoSuteWqo-SwwEQrHwARBc` ׉ 7cassandra://p1N5u3lJgMhLDgOLdIie3BZNTV5K_UYEVm418TzNC7U?B`S׉ 7cassandra://HqGt19MS7a_loihs_oxgmz_4-uX-yr__SNvJOnkhEk4`̵׉ 7cassandra://VarKRjgkSZGhFfjJ8StleQD1KBWfKG6_eiKiScUhaKgg1b͠ay=!׉EqAdvanced Geometrical Tolerancing ISO 1101: 2017 ISO 5458: 2018 Figure 7.43 Ambigeous indication for patterns 131 ׉ 7cassandra://DToHKezeulGdrahFx6tPkErkBWg1dkahqXCyM-Tza6w`̵ay=!׉EAdvanced Geometrical Tolerancing Figure 7.44 Ambigeous indication for patterns Figure 7.45 Unambigeous indication for patterns 132 ׉ 7cassandra://HqGt19MS7a_loihs_oxgmz_4-uX-yr__SNvJOnkhEk4`̵ay=!ay=!{בCט{u׉׉ 7cassandra://sELsmCc4g8omm9zxjAPtwpmIJi0Osr0-WQPDhDXTHHQ` ׉ 7cassandra://QEgc2NP55SZFrdkD4yVYpl41w_YkLZdZevBnHP4rjKcC`S׉ 7cassandra://cyMc6sFC3PlBSFMlomgm_9GrqdvaXrfNGhLuBa1A6w0d`̵׉ 7cassandra://0RobQfUDWF67NuORH661dkAObeYwQsfcze3qGyQuRW0j͠ay=!ט{u׉׉ 7cassandra://n-gvSwFAL_8OjhaUHM-2_ve3OBIaOvWOWYM_HfqqR_U"]` ׉ 7cassandra://8X4VKDm5qfBEnTb28e_o1LuM4d-OYyk_Kg9s27cAnFc:`S׉ 7cassandra://BURqjkuyu9zCWL2lIFXY4_wkqdzrlzszbOkv8veOPbs`̵׉ 7cassandra://sXLt99nR8hMjMN8JtaO9KwcquohuihW2sxyKuji3IXAjf͠ay=!׉EAdvanced Geometrical Tolerancing Figure 7.46 Ambigeous indication for patterns Figure 7.47 Unambigeous indication for patterns 133 ׉ 7cassandra://cyMc6sFC3PlBSFMlomgm_9GrqdvaXrfNGhLuBa1A6w0d`̵ay=!׉EAdvanced Geometrical Tolerancing Figure 7.48 Unambigeous indication for patterns Figure 7.49 Ambigeous indication for patterns 134 ׉ 7cassandra://BURqjkuyu9zCWL2lIFXY4_wkqdzrlzszbOkv8veOPbs`̵ay=!ay=!{בCט{u׉׉ 7cassandra://dAZv2TAmxl-ymFkmxxcjG3OuNYtgll0TZ70Ijc2At1U3` ׉ 7cassandra://2j2jbLrmkoWKNF73DQcgDRKSzXCzF4BDxhmGrB--vuw9t`S׉ 7cassandra://TgPC3F_QeU35kV7LTSv3eGRSgyEcqzZe3xiP8zV79iA`̵׉ 7cassandra://lDqNpa0Ok5ICBlg6_IwAK1Uxi7m1ORXFNTp81MYeljs1j͠ay=!ט{u׉׉ 7cassandra://zovFYref7P23wHFk1KUVIE79f6yVyOE6-aVR8JsIwxUi` ׉ 7cassandra://S8UjhWz-Daj1r_zz3cKiS562f9lYhFOsAdlZgBpIveM4v`S׉ 7cassandra://8hJfnqo_lU3CNDgXbkrlsQ2Ot8e5foxOwjGfxzLksmI`̵׉ 7cassandra://nUvhyreVo4r6bDdnweZ17Ur46uqocxxQCEr8gCtQ_9Af͠ay=!׉EAdvanced Geometrical Tolerancing 3.9.5 maximal material requiremeNt 2021 Figure 3.39 Till 2021 considered as definiotion of a pattern Figure 3.40 Interpretation for the pattern 135 ׉ 7cassandra://TgPC3F_QeU35kV7LTSv3eGRSgyEcqzZe3xiP8zV79iA`̵ay=!׉EAdvanced Geometrical Tolerancing Figure 3.41 Two patterns defined by the modifier CZ Figure 3.42 Interpretation for the two patterns 136 ׉ 7cassandra://8hJfnqo_lU3CNDgXbkrlsQ2Ot8e5foxOwjGfxzLksmI`̵ay=!ay=!{בCט{u׉׉ 7cassandra://LJDCDHoW83-Yd-TKPh6EF32t19-bx4bx73b_25KjTTgZ` ׉ 7cassandra://DYLHy0BX6GAjl0Mo2AqmoTnneQUJ7Iai2p56OYcAQHA4q`S׉ 7cassandra://-UOGnvePyDK4sno0TpZvLiBuqmwi3VbmgBzTzIVr2hUj`̵׉ 7cassandra://iB7xeZ-3G4VkuKZkoIUlITdfqqsRJ-M_oHx0Yx1Hjng<b͠ay=!ט{u׉׉ 7cassandra://dkeyxQFrJocK70t9s1YaLeWbpgLH6txebguoR9NkUI4;t` ׉ 7cassandra://vC5RIIEAsUc7h9zZKRsDfjRWoej6NYMzt-koALYj6JA<`S׉ 7cassandra://rRWMzd0-ZHJdBk2FttnUeiLwiEh2r9EeeHRCQTpf7z0X`̵׉ 7cassandra://EEMOn3-PfxinQsTavJbzFMPo6kh1SyPM56pBuPECRbÄ́t ͠ay=!׉EAdvanced Geometrical Tolerancing Figure 3.43 Three patterns defined by the modifier CZ and the simultaneous requirement for the two middle,patterns Figure 3.44 Interpretation for the three patterns 137 ׉ 7cassandra://-UOGnvePyDK4sno0TpZvLiBuqmwi3VbmgBzTzIVr2hUj`̵ay=!׉E 30 16 Advanced Geometrical Tolerancing 8 Tolerances of run-ouT Run-out tolerances are used to control the functional relation of a surface or surface element relative to a datum axis. Run-out is the high to low point deviation of the surface elements realative to the datum axis. A few applications for circular and total run-out are clearance between rotating parts, gear mesh, balance rotating parts and reduce vibrations. 8.1 cIrcular runouT Circular run-out limits the high to low point deviation of circular elements of any surface of revolution. The tolerance zone applies independently at each circular element of the toleranced surface. Circular run-out controls roundness and axis offset 8.1.1 radIal cIrcular run-ouT type oF Symbol tolerance u Location Radial circular run-out tolerance zone Radial space between two coaxial circles Table 8.1 Radial circular run-out reFerence Required datum allowable tolerance modiFierS f allowable datum modiFierS f 0,05 A A Figure 8.1 Radial circilar run-out Figure 8.2 Interpretation 138 ׉ 7cassandra://rRWMzd0-ZHJdBk2FttnUeiLwiEh2r9EeeHRCQTpf7z0X`̵ay=!ay=!{בCט{u׉׉ 7cassandra://pGnAZVjWRf4DOCUxUJXhOOh73A06ES4NSsO-AGMm_0E` ׉ 7cassandra://rTpzM-Tky3LmsG7LpKAXgwu7_cmAhskoIEv4nUmy4-k-`S׉ 7cassandra://DrKxXa5a7XGSQ4coqwHwTtFErK7L_n7eOD6jxwU3sIQ +`̵׉ 7cassandra://nXJKwRvjQxxrA0QhXTYOooqn53viP7nDFlWvhLtvGz0Pb͠ay=!ט{u׉׉ 7cassandra://yvlO6q8O16OLyMdwSkECZ289D0sqCLLf19Obg35KUHcF` ׉ 7cassandra://xNuerzByiM3CI-WlsukdweUmJmDjJJQywxkkhXBrY9Q-`S׉ 7cassandra://ED_ARg-ibVzvBcWPTGP_mpDtaJD1fYqRuDt_6d8YQ8w`̵׉ 7cassandra://W08tXGL8J2Qa44XNf5EZz9OV-GZJ-pQEzLFbyqv616M͝ ͠ay=!׉ERAdvanced Geometrical Tolerancing Reject Accept Figure 8.3 Possible deviations 139 ׉ 7cassandra://DrKxXa5a7XGSQ4coqwHwTtFErK7L_n7eOD6jxwU3sIQ +`̵ay=!׉E30 16 Advanced Geometrical Tolerancing 8.1.2 axIal cIrcular run-ouT type oF Symbol tolerance u Location reFerence Required Axial circular runout tolerance zone Axial space between two coaxial circles (offset axially) Table 8.2 Axial circular run-out datum allowable tolerance modiFierS f allowable datum modiFierS f 0,05 A A Figure 8.4 Axial circular run-out Figure 8.5 Interpretation Reject Accept Figure 8.6 Possible deviations 140 ׉ 7cassandra://ED_ARg-ibVzvBcWPTGP_mpDtaJD1fYqRuDt_6d8YQ8w`̵ay=!ay=!{בCט{u׉׉ 7cassandra://x4bYIeDwBsSgcqQj-HN8XSi27Sk8eAHupto9gMUPQn8ت` ׉ 7cassandra://hhA-fsrmaNivTmvqTw1nChcJD-lkjX5Q4Ax8omplMBM7`S׉ 7cassandra://nfMSXmgc3oM5QSwwET2XpTvaga_uoj5k23wjpgPwxhs`̵׉ 7cassandra://UMs66I9KEq3A9TkvsMYWiIApCFZlq9PU7gpCUshRq1M͵[ ͠ay=!ט{u׉׉ 7cassandra://Jw2xy7kuSz9iAmlHDvDP9zsfEGwWeLOnKWHzHyB3sOcw ` ׉ 7cassandra://ZSQkyh-Gu9p8J1nnJrtQNK61kLj6ml8RwHE_ZEJ8-0Q,`S׉ 7cassandra://wHUYzQIzmupMg4bHorRSnF6QnNOMB1kzdHaltfigHps`̵׉ 7cassandra://6d9yPF5mxFUHkOzHM-uHsmOfU10Zx2OvWtL-e5WcKmg͆ ͠ay=!׉E32 16 16 Advanced Geometrical Tolerancing 8.2 ToTal runouT Total run-out limits the high to low point deviation of all surface elements of any surface of revolution. Total run-out controls straightness, roundness, cylindricity, taper and axis offset. 8.2.1 radIal ToTal runouT type oF Symbol tolerance v Location reFerence Required Radial total run-out tolerance zone Radial space between two coaxial cylinders Table 8.3 Radial total runout datum allowable tolerance modiFierS f allowable datum modiFierS f 0,003 A - B 0,003 Datum axis A B Figure 8.7 Radial total run-out Figure 8.8 Interpretation Reject Accept Figure 8.9 Possible deviations 141 ׉ 7cassandra://nfMSXmgc3oM5QSwwET2XpTvaga_uoj5k23wjpgPwxhs`̵ay=!׉E16 30 Advanced Geometrical Tolerancing 8.2.2 axIal ToTal run-ouT type oF Symbol tolerance v Location reFerence Required Axial total run-out tolerance zone Axial space between two planes (offset axially) Table 8.4 Axial total runout datum allowable tolerance modiFierS f allowable datum modiFierS f 0,02 C C Figure 8.10 Axial total run-out Figure 8.11 Interpretation Reject Accept Figure 8.12 Possible deviations 142 ׉ 7cassandra://wHUYzQIzmupMg4bHorRSnF6QnNOMB1kzdHaltfigHps`̵ay=!ay=!{בCט{u׉׉ 7cassandra://IceBj8wa3FRd6Z1Xp7QK9f2nJgxBm83hHGLFiiS8lfoS` ׉ 7cassandra://E1TNgmtckqvI_fmR0m4WYfGYpBcIatnjPkIxHaTip8Y?`S׉ 7cassandra://HoZLuhfIl2V7JEFGBKryhfMnFuKeNYsZ9oM6BmlyUw0 ]`̵׉ 7cassandra://GSz_xNj8Mxk67zYwjnGHYvhMIBvm86TCihcPpK5-hB4n%b͠ay=!ט{u׉׉ 7cassandra://J7UasAd9KPK9oZHlOVP3T9s1sAJgAmq6OEGqBRz40nY8` ׉ 7cassandra://cnzQQ-NdoZD-yD9PMVPEL9pDmAlAQfPo-vz8vDbyRvI8`S׉ 7cassandra://pEKbW2TaXWdTFALTKdN8kTcFgtJOq1YfrxnZ76z8EKo`̵׉ 7cassandra://ouPmHws8135sIjG2Ix1MfiMYVVY3yqm_viZ-VafNLAE͉p͠ay=!׉EYAdvanced Geometrical Tolerancing exampleS oF run-out Figure 8.13 Examples of run-out 143 ׉ 7cassandra://HoZLuhfIl2V7JEFGBKryhfMnFuKeNYsZ9oM6BmlyUw0 ]`̵ay=!׉E10 G7 12 0,1 A 17 Advanced Geometrical Tolerancing exerciSe 36 + 0,5 0 1,3 B C 0,05 A B A 20 ISO 2768 mK 0,1 B C Figure 8.14v Exercise • Describe the shapes and sizes of each of the tolerance zones? • What is the roundness of diameter ø 20 limited to? • What is the maximal boundary of diameter ø 36? • What DOF’s are taken by the datums B and C for the radial circular run-out tolerance on diameter ø 36? Figure 8.15 Exercise 144 ׉ 7cassandra://pEKbW2TaXWdTFALTKdN8kTcFgtJOq1YfrxnZ76z8EKo`̵ay=!ay=!{בCט{u׉׉ 7cassandra://Wzo7rkyUcFOlKe9SmTGoRE5xFfRtC_3CKs4w-4QHWno` ׉ 7cassandra://s-wUkyPJ1xcMU2YiWMuBxB7Ora-AllHbd5a2FR_RCTU5`S׉ 7cassandra://ivzpZwZQGkHexnJf2mzoLa0FOdcw65FpwNWNgbxUo_8`̵׉ 7cassandra://2XjBL-a9Uz-aoqS0IT4t8_5lpEvy4IlCw3lcIngIjlwh[ :͠ay=!ט{u׉׉ 7cassandra://Lym-pv4poC9UQm4_klN6WbLCuq5mDBV-ti6i9GVD91U\` ׉ 7cassandra://SdRIN0PRJ8TtpMoHOVrB0WElzTAnu9egdjbbuNvfuKQ7`S׉ 7cassandra://44M1x48kHqy7Aoi8fsNRPJQjzXsY6s4K_8IOfITisrIu`̵׉ 7cassandra://mU6FdzVttskZ_DUt0UMWzrvjGSULYqGGypD_esiEyPQÇ^͠ay=!׉EQAdvanced Geometrical Tolerancing 8.3 assesmenT of runouT When verifying the radial run-out the datum axis has to be esthablished. For circular run-out the high (Amax ) to low points (Amin Run-out deviation: δl = Amax - Amin ) of each individual circular element need to be verified. Verifying total run-out requires the measurement of the high to low points of all surface elements. Figure 8.16 Assesment radial run-out with revolving workpiece During measuring of axial run-out deviations the workpiece and indicator must be fixed in axial direction. Figure 8.17 Assesment axial run-out 145 ׉ 7cassandra://ivzpZwZQGkHexnJf2mzoLa0FOdcw65FpwNWNgbxUo_8`̵ay=!׉EAdvanced Geometrical Tolerancing 9 Tolerances of ProfIle A profile is an outline of a surface, a shape, made up of one or more features. With profile tolerancing a distinction needs to be made between tolerancing lines or surfaces. The nominal profile is to be defined by TED’s or mathematical data. The tolerance zone is default equally disposed on either site of the nominal profile. A profile tolerance can be used to limit deviations of line elements or a surface. A profile tolerance, depending on how it’s applied, can affect four types of geometric characteristics: Size, form, orientation and location. When datums are used profile tolerances often control orientation and location. A profile tolerance without a datum maybe a size and/or form control. A profile tolerance can limit: • Form: • Orientation: • Location: Tolerance used without a datum Datum added, indirect limitation of form Datum and TED added, indirect limitation of orientation and form Figure 9.1 Use of profile requirements 146 ׉ 7cassandra://44M1x48kHqy7Aoi8fsNRPJQjzXsY6s4K_8IOfITisrIu`̵ay=!ay=!{בCט{u׉׉ 7cassandra://0z9yDXCIlTasMvtpqQ59eKHFqvSp_hRiABahBQuGKz0$t` ׉ 7cassandra://CXcXTFi65zwtO4RtYfLuqQazPrEGk9_3xE-TYayZnPUH`S׉ 7cassandra://eUQ6o-gCUiUDIde2tS0jeLegxrDOCXC3UN7561HZd2I`̵׉ 7cassandra://QcErpwPhCANkBvSCZPniRqHdzle42eDQi6HYtCVd46sF͠ay=!ט{u׉׉ 7cassandra://oKuAnZMu5JdO5_iSuLQpd9WI2-o67TzYb20SZ6cfQ6Q` ׉ 7cassandra://4VrUyQ28-eTze_M1zW0adlWarFfslKJJ3jGTUIw4QyU4`S׉ 7cassandra://4d0uIqCWRb7AKHsc1TV4Be3hJ2kxsTsFXuf9YFbQi9c`̵׉ 7cassandra://wrP65a2Ui00i5tRmobke88i2y6gd3wUMcfmn0AAw91gp^͠ay=!׉ERAdvanced Geometrical Tolerancing 9.1 lIne ProfIle A line profile tolerance is a geometric tolerance that establishes a two dimensional tolerance zone that is normal to the nominal profile at each line element. The shape of the tolerance zone is the same as the nominal profile of the feature. type oF Symbol tolerance g Location Tolerance zone line profile The profile line shall be contained between two equidistant lines enveloping circles the centers of which are situated on the nominal profile *) profile any line without a datum is a form tolerance Table 9.2 Line profile reFerence Required *) datum allowable tolerance modiFierS f UZ allowable datum modiFierS m l f Figure 9.1 Line profile as form requirement ISO 1660:1987 Figure 9.3 Interpretation Figure 9.4 Line profile as location requirement ISO 1660::1987 Figure 9.5 Interpretation 147 ׉ 7cassandra://eUQ6o-gCUiUDIde2tS0jeLegxrDOCXC3UN7561HZd2I`̵ay=!׉E[Advanced Geometrical Tolerancing Line characteristics have an orientation so profile any line too. In older standards the orientation was given by the view holding the requirement. This has been changed with the introduction of the intersection plane. Also was it not clear if the requirement was on one feature (ISO 8015) or on several feature and when does this combination stop. This was also not defined in previous standards. With the introduction of ISO 1101: 2013 and ISO 1660: 2017 these ambigeous situation is solved. Unit Feature (UF) is used to make several feature into one feature. The between requirement defines the limits for the requirement and finaly the intersection plane defines the orientation of the requirement. Figure 9.6 Line profile as location requirement ISO 1101: 2017 Profile any line is commonly used for sheet metal work. 148 ׉ 7cassandra://4d0uIqCWRb7AKHsc1TV4Be3hJ2kxsTsFXuf9YFbQi9c`̵ay=!ay=!{בCט{u׉׉ 7cassandra://cbhgDRonvGdbXwdPMyRjwJBU90xSr3uHISP7xh7eK7U ` ׉ 7cassandra://0i00gPsJVMb-poStHYa5J9MblgbOOUBAxlL1sudAgBE=`S׉ 7cassandra://j1Hf__6PCp6x_lL507JJmupanS98c2PB1MukcObWEAs`̵׉ 7cassandra://B6_d3vbBSjtUfJ_30O-23hT4HDisGVYNJfp0xKgunX8ͻ p͠ay=!ט{u׉׉ 7cassandra://sjuCE5oBbE8EEIN1gGJurZthT_bdTNMGrj3UGLUHHkUn` ׉ 7cassandra://PCy98_t7ptda0i30DFu_UXgEY-dO7_JNGXKBk69SISY8`S׉ 7cassandra://uudYjtK2OTh2nXnPidhZ8lCrlelDqtblQ2_73_0kDms`̵׉ 7cassandra://Hc7h1uk8gu01Wtgdyq-_ZQd3ZQ8dH8A-zyWR11WDIcwn͠ay=!׉E8Advanced Geometrical Tolerancing 9.2 surface ProfIle A profile of a surface tolerance is a geometric tolerance that establishes a three dimensional tolerance zone that is normal to the nominal profile at each surface element. The shape of the tolerance zone is the same as the nominal profile of the feature. type oF Symbol tolerance h Location Tolerance zone surface profile The surface profile shall be contained between two equidistant surfaces enveloping spheres the centers of which are situated on the nominal profile Tabel 8.2 Profile any surface reFerence Required datum allowable tolerance modiFierS f UZ allowable datum modiFierS f Figure 9.7 Surface profile as form requirement ISO 1660: 1987 Figure 9.8 Interpretation Figure 9.9 Surface profile, location requirement ISO 1660:1987 Figure 9.10 Interpretation 149 ׉ 7cassandra://j1Hf__6PCp6x_lL507JJmupanS98c2PB1MukcObWEAs`̵ay=!׉E~Advanced Geometrical Tolerancing United Feature (UF) builds an one compound feature out of several singel features. Combined Zone (CZ) combines tolerance zones. Figure 9.11 Surface profile Unit Feature Figure 9.12 Interpretation With ISO all requirements are independent by default and the symbol SZ (Separate Zone) is optional. Only the position characteristic needs the SZ for independency. The all around symbol is used stating that te requirement applies to all the four features around. When the the requirement is ‘all around’ a collection plane is used. Figure 9.13 Surface profile Separate Zone Figure 9.14 Interpretation 150 ׉ 7cassandra://uudYjtK2OTh2nXnPidhZ8lCrlelDqtblQ2_73_0kDms`̵ay=!ay=!{בCט{u׉׉ 7cassandra://bQCpZJER0LyWjJIrjDhlGcf_k2qaKe6tMedKjU-0Ev8` ׉ 7cassandra://ms7MP4l8pU5g_vXMxaCv3CZZbrCBAFIYeXGKSkTvH9k< symbol. Datum D only constrains only the rotations and not the translation. Datums E and F are hidden features and indicated using dashed leader lines Figure 9.17 Surface profile Figure 9.18 Interpretation 151 ׉ 7cassandra://dhhG6Gfjx3f8V0OcBa2JQfGRGeHquk53F6h6uiyK6IM`̵ay=!׉EAdvanced Geometrical Tolerancing 9.5 ProfIle any surface aPlIed To a conIcal surface Figure 9.19 Surface profile, form requirement Figure 9.20 Interpretation Figure 9.21 Radial position of the cone using profile Figure 9.22 Radial position of the cone using coaxiality 152 ׉ 7cassandra://YkmIv-klcntGsjtLCF0AuA3rLr5xwe7ggpuqHxLsusg[`̵ay=!ay=!{בCט{u׉׉ 7cassandra://eiZIHuZsNRzz5WbtKvZ_y3J9ETCPhASpz4iKjZ4DGuk` ׉ 7cassandra://W0cQn6ix8EdFEMk4kgfsq3VLvwqtjIO2DLae8TQfnWs*`S׉ 7cassandra://pmD3tyIKy3cnacMbwNy0C2ks6STdJ5kAhpZ9TLOl4y8`̵׉ 7cassandra://z6qW5EHd_3_UuoCocDits-brMhCD-IxEHo-eVVEzWIcun͠ay=!ט{u׉׉ 7cassandra://VEb0JqWjan_9_1vgBsHCvdpPBxT7OVNDqPcbvxuJv8QC` ׉ 7cassandra://tmngAMJapzFnioaZGCyNmqwKEU9MPcDfXxkiE4Memt0$`S׉ 7cassandra://5wTpwq1ECNCZSfrtnVw5kjT2e6hXDRLtySfRFk8i_Cs `̵׉ 7cassandra://AqeDw12itevArqsoU3COZiNdxASxYSKlwc89AqkbGn8j͠ay=!׉EAdvanced Geometrical Tolerancing Figure 9.23 Radial and axial position of the cone Figure 9.24 Interpretation Figure 9.25 Axial position of 0,15 and radial and form requirement of 0,05 Figure 9.26 Using profile for the cone a position of the two flat surface 153 ׉ 7cassandra://pmD3tyIKy3cnacMbwNy0C2ks6STdJ5kAhpZ9TLOl4y8`̵ay=!׉EAdvanced Geometrical Tolerancing Figure 9.27 Radial position using coaxiality, axial requirement 0,2 and a form requirement of 0,1 Flat surfaces are position using profile. Figure 9.28 Centerline of the cone a datum feature 154 ׉ 7cassandra://5wTpwq1ECNCZSfrtnVw5kjT2e6hXDRLtySfRFk8i_Cs `̵ay=!ay=!{בCט{u׉׉ 7cassandra://gRO-BdTgQxmwCz-vrR1INAkZWz29jFthK-cinEJupkQx` ׉ 7cassandra://wwfWdCXCPLM9iav9eu6JTNv3ydUh71h3k9gkH-vLHE4`S׉ 7cassandra://RZodHqlfNVRSvqQjYYHAlKZuVW6VQQN50j2VdO4Mixk `̵׉ 7cassandra://qGpDVUntWQay8rtGlOHac1ctwNbnF9BHv8M1eGpi_Ss@f͠ay=!ט{u׉׉ 7cassandra://uEmeG8wQtZ8I3pJUDdBPDobgfzXKCyU6oLK5kmAYZToG` ׉ 7cassandra://tJRT83AQQ4X0FCjA2Hsm5idfZ5_EvJzCVMbiQgbuMpI:e`S׉ 7cassandra://VYZpVe4RlqjtDfQGVkGQ-dIk9Hgs6BIT7APEo79fa4g^`̵׉ 7cassandra://CE427K0V9e3gQ36nupDKhqJwsYxN-zCfaQFujcUIwrU^͠ay=!׉EnAdvanced Geometrical Tolerancing 9.6 sPecIfyInG a wedGe ( Figure 9.29 Specifying a wedge using angularity 155 ׉ 7cassandra://RZodHqlfNVRSvqQjYYHAlKZuVW6VQQN50j2VdO4Mixk `̵ay=!׉E1Advanced Geometrical Tolerancing 10 3d PmI mbd 10.1 InTroducTIon To PmI Concerning GD&T there is no difference between specifying the workpiece requirements on a 2D drawing or 3D MBD. when working according the latest ISO standards as stated in tier 1. ISO 16792:2021 is the standard on MBD. It’s merely is stating ‘how’ to put the GD&T on the model and has requirement on the CAD system. This chapter wil give a few examples. The out of the design is merely a model with the GD&T requirements as a native file or STEP 242 file completed with several views. Table 10.1 PMI tiers 10.2 way of annoTaTInG SYMANTIC: GD&T annotation on the model according ISO >> Software readable (CAM / CAI). GRAPHICAL Manual added info >> Human interface required. Note: All examples in this chapter are taken from ISO 16792. 156 ׉ 7cassandra://VYZpVe4RlqjtDfQGVkGQ-dIk9Hgs6BIT7APEo79fa4g^`̵ay=!ay=!{בCט{u׉׉ 7cassandra://M9lc4Uv7ljyzwiF-J55Nb-XkSEWady5f2zn_q0N-N2Ak` ׉ 7cassandra://BauqmBDvA-G_9Qhb2FhrXRT6B5b6Eh1e1ge0JD0vjiI;`S׉ 7cassandra://3SDmr7P-Tgr8D-Gx-g7YbktZytIc1aFI3Bf9H_eB7UQ`̵׉ 7cassandra://AWvHMXdbVQ4m8sSn_K_b_t2p_p1x9Vbhty4v3ZNxmcU-Cj͠ay=!ט{u׉׉ 7cassandra://69lVdWUKj1SC9sxceyM8uZ8otOZ4ijJwzI1c3jUMXzE` ׉ 7cassandra://yz1fjku35ix8EoXkjN-UvpxTSoboXu3orDYPYTtUmyY,`S׉ 7cassandra://EC1cOr5C420OUW4DWMNJ-35NLYkkLEl9POOZmbGPxII`̵׉ 7cassandra://xC5oszK9vLQCy_Z-xGdwVr2mbNRCjaxSo4YvamIrpE0b͠ay=!׉EAdvanced Geometrical Tolerancing 10.3 model coordInaTe sysTem Design shall have one or more coordinate systems depicted by three mutual perpendicular line segments with the origine at the intersecetion. Model coordinate system shall be right handed unless otherwise specified. Figure 10.1 Model coordinate system 10.4 model requIremensT ISO 16792 states display requirements, requirements on associativity between the GD&T annotation frames and the toleranced features, placement of the GD&T annotation symbols as well as placement of welding symbols and roughness symbols. 10.4.1 dIsPlay manaGemenT Figure 10.2 All annotation displayed 157 ׉ 7cassandra://3SDmr7P-Tgr8D-Gx-g7YbktZytIc1aFI3Bf9H_eB7UQ`̵ay=!׉E|Advanced Geometrical Tolerancing Figure 10.3 One type of annotation displayed Figure 10.4 Selected annotation displayed 158 ׉ 7cassandra://EC1cOr5C420OUW4DWMNJ-35NLYkkLEl9POOZmbGPxII`̵ay=!ay=!{בCט{u׉׉ 7cassandra://0CDtb-A7YHoY2ElVGV7cd6gMWKubPqOA5vpFqzO2IPw` ׉ 7cassandra://bAaKTBcOvQ5YxNgdvlDYblTjpj5djPI1XOQbJwTtsIs-/`S׉ 7cassandra://NL8KcXAcR_mQasHjh7eYIbESJaS6c4bU-IfkkySjvfc`̵׉ 7cassandra://BzHCppmWdAgDhvdZUfgCyEJOEERtJFFWJSD_l80C_68j͠ay=! ט{u׉׉ 7cassandra://ZeGKxOKAB-CUkG4Irdfgz9XGttiy4bnBqbyFJOgRDNwUD` ׉ 7cassandra://OJkwWRwmmVMSye5Q_AdmuV8LgqQNp_Uq2OymUQZh4HI$~`S׉ 7cassandra://eC5wo9jHetbTx-Q7NIYWmqSJMj_AjlBd4tMQvfLn9Do <`̵׉ 7cassandra://pkERXWLiPz39U65neX3VIXmkgAHZaUYBPzrvVtddN5s2^͠ay=! ׉EAdvanced Geometrical Tolerancing 10.4.2 assocIaTIvITy querIes Figure 10.5 Size query Figure 10.6 Geometric tolerance query Figure 10.7 Surface query 159 ׉ 7cassandra://NL8KcXAcR_mQasHjh7eYIbESJaS6c4bU-IfkkySjvfc`̵ay=!׉EwAdvanced Geometrical Tolerancing 10.4.3 rePresenTInG aTTrIbuTes, querIes Figure 10.8 Representing simplyfied holes 160 ׉ 7cassandra://eC5wo9jHetbTx-Q7NIYWmqSJMj_AjlBd4tMQvfLn9Do <`̵ay=!ay=!{בCט{u׉׉ 7cassandra://1oMCUL2-Xk-F9ajkjbhum69LlGtklfNxGIcXUJLhIsM9` ׉ 7cassandra://SmKYb5jcjbMkXSzaJ4rOX39IIL_SwkUpUGdoNakoAa43&`S׉ 7cassandra://emTnwd6U2aNNi4Xq4BuRiUwVDXSxD02CQHxSof6AdPoT`̵׉ 7cassandra://N4wrdko6rFOiEM8vjPpm4opTpQT72L-DD845Lhx98fw]b͠ay=!ט{u׉׉ 7cassandra://P2it-04JANQJV6d_LCI4FfWXHNU2knXCKO6_ulwfarQ)` ׉ 7cassandra://Hd1SgBzYgwcWgFmhtDhqTrX46mRzoN40nJ2SadHgqsM$Z`S׉ 7cassandra://sN6b-rSC-5nm1sTe7lGyH_8YQ50h8nbKLZPwij9OePI Q`̵׉ 7cassandra://TESF6YiTloR5L0UOvqViSmlGtE-kgb6KABIQj5UVqUošb͠ay=!׉E?Advanced Geometrical Tolerancing Figure 10.9 Pattern query 161 ׉ 7cassandra://emTnwd6U2aNNi4Xq4BuRiUwVDXSxD02CQHxSof6AdPoT`̵ay=!׉EAdvanced Geometrical Tolerancing 10.4.4 resTrIcTed area Figure 10.10 Restricted area using shading Figure 10.11 Restricted area using supplemental geometry 162 ׉ 7cassandra://sN6b-rSC-5nm1sTe7lGyH_8YQ50h8nbKLZPwij9OePI Q`̵ay=!ay=!{בCט{u׉׉ 7cassandra://ldDsO9L1M79YgA_QSvyG13RIcQbBaUKRnC1Zz1FFchgC` ׉ 7cassandra://PuagtDAL0Hzz4MX8zkD7J7OPjkc5O3WcTfhmaJpUUmU0P`S׉ 7cassandra://LWtSWn_zG48McY-B_DRa3ijFkH6Rii3zMFu1OiTV7zI `̵׉ 7cassandra://KKGebG2qSwrLxos3aWPHxYHHwoFliZWCt8phTDLSEiAͽj͠ay=!ט{u׉׉ 7cassandra://TCjdpV3GGbH1oW6i-_R9j0Q2mnGo9tZ-TmXo6AtmksM0` ׉ 7cassandra://CaBmZS_LqrHve-s3RDzQcEkJQsFl8eH0s6L9JFJiIb0%`S׉ 7cassandra://w_dzy1GkW5foT7YFPNuPgVeIALyYAS-oKPFiBGrMnPI `̵׉ 7cassandra://C0Ca2hUDqoh4N5AKWL61tHMIgl9WuyI2MnRlOAs8L-U͛f͠ay=!׉EAdvanced Geometrical Tolerancing 10.4.5 resTrIcTed area Figure 10.12 Partial surface as a datum Figure 10.13 Datum targets 163 ׉ 7cassandra://LWtSWn_zG48McY-B_DRa3ijFkH6Rii3zMFu1OiTV7zI `̵ay=!׉EAdvanced Geometrical Tolerancing 10.4.6 dIrecTIon dePendanT Tolerances Figure 10.14 Straightness parallel to datum A Figure 10.15 Direction dependent straightness 164 ׉ 7cassandra://w_dzy1GkW5foT7YFPNuPgVeIALyYAS-oKPFiBGrMnPI `̵ay=!ay=!{בCט{u׉׉ 7cassandra://qz2Fh0of04eCs_1vmOXHImRiQVtrEDWK4vZCZ349UW4Y6` ׉ 7cassandra://e3n0Uqb5LdOhgyyDql6bskX4IWd-TAFz9UtRbTAHJkI&`S׉ 7cassandra://hkpPKNxamLE7Ts0EscXT9QvNq0UfBBGOLMNlHpbXt6Q `̵׉ 7cassandra://w-PdvrEWrwHoujvuRdluLe6jtrfLOTMMxrMMbpmvU1kGf͠ay=!ט{u׉׉ 7cassandra://c4H3DxAPzVOXTd1wjcXG4yajkWuqHlawQPQgQ0VEP1Uc` ׉ 7cassandra://Kx4FsMS9FMgHnVcpdLUBzNsWUHGGQzdLsicykriRfRA'`S׉ 7cassandra://-_7kBlUSnjkopbFXpFOw6dmUkW_TQHz6YBQZA1ybHP8 &`̵׉ 7cassandra://474TcgnKQI0hIim5Vdqt7qlr1pRs_q9rtB59fCVMUB8^͠ay=!׉E|Advanced Geometrical Tolerancing 10.5 daTums Figure 10.16 Indication of datum features Figure 10.17 Indication datum CZ 165 ׉ 7cassandra://hkpPKNxamLE7Ts0EscXT9QvNq0UfBBGOLMNlHpbXt6Q `̵ay=!׉EFAdvanced Geometrical Tolerancing Figure 10.18 User defined datums 166 ׉ 7cassandra://-_7kBlUSnjkopbFXpFOw6dmUkW_TQHz6YBQZA1ybHP8 &`̵ay=!āay=!Á{בCט{u׉׉ 7cassandra://dKJs6rQJy86vYLMd-qpSpk11n_Ow0md0AKREZWenVz4<` ׉ 7cassandra://DVewPbEijWUTuwzZxpYZzNFOMXHNX5yA0aVLygyJj08=`S׉ 7cassandra://nd-1OwHb7ZOrqihQPYU2PgAXGcXMYgsui7EX4ak4Dlc)`̵׉ 7cassandra://q0sI7zwTdgRQxD684r72NGMORVqXW_xRInpJEV_4PR0̢j͠ay=!ט{u׉׉ 7cassandra://tGPfm9wiBALX5auVR_7Y4fy3gKlgGLX1i_jTatuivJI.n` ׉ 7cassandra://Crv9kH1-TKWi6wbCD2c1G4gv2Zqpbc7dhDZSEqosge4'`S׉ 7cassandra://1HHyeYZwQZFknE1LCAsV0Ygq6r498QTqgt2tLkE7k0g w`̵׉ 7cassandra://wc4YCYueSbCvzm_gs5c5B2Xp-_mtWnTckxfCy_-BFcE qb͠ay=!׉EAdvanced Geometrical Tolerancing 10.6 dImensIons Table 10.2 Resolved dimensions Figure 10.19 Coutersink holes Figure 10.20 Counterbore hole 167 ׉ 7cassandra://nd-1OwHb7ZOrqihQPYU2PgAXGcXMYgsui7EX4ak4Dlc)`̵ay=!׉EyAdvanced Geometrical Tolerancing 10.7 rouGHness Figure 10.21 Surface texture Figure 10.2 Orientation surface texture 168 ׉ 7cassandra://1HHyeYZwQZFknE1LCAsV0Ygq6r498QTqgt2tLkE7k0g w`̵ay=!Ɓay=!Ł{בCט{u׉׉ 7cassandra://vvKME42H5Bv0v-6cpSjTq39CQ7n1H2NzNyV5hlSsloIl` ׉ 7cassandra://Id6l4OUX0H9EJIrbE0WUEvi6ydzUAWUrFpK7PnA74WA7`S׉ 7cassandra://7ZicO1bikagk65K2xPW3CDz-YQwMPy1KD-P90BtJU0Y`̵׉ 7cassandra://XSg4aM7teQufcQvTtefx6hWuaTCDvKvTer0OyDO86FgN_Z͠ay=!ט{u׉׉ 7cassandra://yrjRyLpBUlHRaB-w-ckm87AQTTyl4s9S9lz_3TcvwAAZ` ׉ 7cassandra://3TaHxZlv729KQkBAtHacAiB_mmWvjwUAxOMFX97ai5o(`S׉ 7cassandra://GC6SxleLSRyGfzFQczjEchu1xjfT8prZGZr2XBsubrM Q`̵׉ 7cassandra://Q4aA9QUlWgG1wY_b1lYL2MZO7DtSQl3LqPMnUvJM_aw6RZ͠ay=!׉EAdvanced Geometrical Tolerancing 11 references InTernaTIonal orGanIzaTIon for sTandardIzaTIon (Iso) Georg Henzold, Geometrical Dimensioning and Tolerancing for Design, Manufacturing and Inspection, 3nd edition, ISBN 9 780 128 240 618 Walter Jorden, Wolfgang Schütte Form- und Lagetoleranzen: Handbuch für Studium und Praxis 10 Auflage, ISBN 9 783 446 458 475 Bernd Klein, Toleranz Design im Maschinen- und Fahrzeugbau 4 Auflage, ISBN 9 783 110 555 103 Alex Krulikowski ISO Geometrical Tolerancing (ISO 2004) Alex Krulikowski ISO GPS The Ultimated Pocket Guide (ISO 2012) amerIcan socIeTy of mecHanIcal enGIneers (asme) Don Day The GD&T Hierarchy Pocket Guide Y14.5-2009 Paul J. Drake, Jr. Dimensioning and Tolerancing Handbook, ISBN 9 780 070 181 311 Alex Krulikowski Fundamentals of Geometric Dimensioning and Tolerancing 3rd Edition ISBN 9 781 111 129 828 Alex Krulikowski The Ultimated GD&T Pocket Guide 169 ׉ 7cassandra://7ZicO1bikagk65K2xPW3CDz-YQwMPy1KD-P90BtJU0Y`̵ay=!׉EAdvanced Geometrical Tolerancing mosT relevanT Iso sTandards ISO 286 ISO 1101 ISO 1660 ISO 2692 ISO 5458 ISO 5459 ISO 8015 ISO 10579 ISO 14405-1 ISO 14405-2 ISO 14405-3 ISO 14638 ISO 16792 ISO code system for tolerances on linear sizes - Part 1: Basis of tolerances, deviations and fits Tolerances of form,orientation, location and run-out Profile tolerancing Maximum material requirement, least material requirement, reciprocity requirement Pattern and combined geometrical specification Datum and datum systems Fundamentals, Concepts principles and rules Non-rigid parts Dimensional tolerancing — Part 1: Linear sizes Dimensions other than linear or angular sizes Angular sizes Matrix Model Digital product definition data practices 170 ׉ 7cassandra://GC6SxleLSRyGfzFQczjEchu1xjfT8prZGZr2XBsubrM Q`̵ay=!ȁay=!ǁ{,ׁ2GDT adv 1.01afrJ®W