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- 1. Imperial Automotive IndustriesGeometric Dimensioningand Tolerancing Mark A. Morris
- 2. Contact Information John Lindland (734) 369-3120 President – Consultant – Seminar Leader QualSAT, Inc. JLindland@qualsat.com Mark A. Morris (734) 878-6569 Representing QualSAT, Inc. mark@MandMconsulting.com 2
- 3. Geometric Characteristic Symbols Form Tolerances Profile Tolerances Orientation Tolerances Runout Tolerances Location Tolerances 3
- 4. Section 1Background, History, and the Importance of GD&T 4
- 5. Engineering Drawings Engineering drawings are the vehicle used to communicate requirements for manufactured parts. Graphic Representations Words Numbers Symbols Engineering drawings are used to communicate contractual requirements. 5
- 6. We Need Operational Definitions “Without an operational definition, investigations of a problem will be costly and ineffective, almost certain to lead to endless bickering and controversy.” W. Edwards Deming, Ph.D.Operational definitions provide three components: 1. Specify Test to determine Compliance 2. Set Criteria for Judgment 3. Make Decisions based on the Criteria 6
- 7. Orthographic andIsometric Projection 7
- 8. Orthographic andIsometric Projection 8
- 9. 1st vs. 3rd Angle Projection First Angle Projection Third Angle ProjectionNote: Third angle projection is more common in theUSA, first angle projection is more common in Europe. 9
- 10. ISO vs. ASME Comparing the ISO and the ASME Approaches to GD&T Issue or Topic ISO ASME Approach Theoretical Functional Explanation Graphical, Few Words Comprehensive Cost of Standards 700 – 1000 USD < 100 USD Number of Standards 10 - 16 1Based on the work of Alex Kulikowski, 1998 10
- 11. ASME Y14.5M – 1994 Structure Scope, Definitions, and General Dimensioning General Tolerancing and Related Principles Symbology Datum Referencing Tolerances of Location Tolerances of Form, Profile, Orientation, and Runout 11
- 12. History of the Standard Stanley Parker has been credited with bringing to light the problems that existed with limit dimensioning while working at the Royal Torpedo Factory in Scotland. ANSI Y14.5M1964 ANSI Y14.5M-1973 ANSI Y14.5M-1982 ASME Y14.5M-1994 Dimensioning and Tolerancing ASME Y14.5.1M-1994 Mathematical Definitions 12
- 13. Identify the Standard Used ASME Y14.5M-1994 requires the standard be identified on the drawing when it is applied. Methods change as standards evolve. For example: A -A- ANSI Y14.5-1982 ASME Y14.5-1994 13
- 14. General Information International System of Units (SI) have been used. U.S. Customary Units could have been used. Figures are intended as illustrations to aid in understanding. They show one possible solution. Capital letters on figures are intended to appear on finished drawings. 14
- 15. Foundations of Mechanical Accuracy The Four Mechanical Arts Geometry Standards of Length Dividing the Circle Roundness Wayne R. Moore 15
- 16. Development of Flatness Step 1 – Alternate between plates 1 and 2 until a relative match is achieved. Plate 1 agrees with plate 2 None are known to be flat Step 2 – Consider plate 1 as the master plate and work plate 3 to plate 1. Plate 1 agrees with plate 2 Plate 1 agrees with plate 3 None are known to be flat Based on the work of Sir Joseph Whitworth 16
- 17. Development of Flatness Step 3 – Alternate between plates 2 and 3 until a relative match is achieved. Plate 2 agrees with plate 3 Plates 2 and 3 are known to be flatter that plate 1 None are known to be flat Step 4 – Consider plate 2 as the master plate and work plate 1 to plate 2. Plate 1 agrees with plate 2 Plate 3 agrees with plate 2 None are known to be flat All are of nearly equal flatness 17
- 18. Development of Flatness Step 5 – Alternate between plates 1 and 3 until a relative match is achieved. Plate 1 agrees with plate 3 Plates 1 and 3 are known to be flatter that plate 2 None are known to be flat Step 6 – Consider plate 3 as the master plate and work plate 2 to plate 3. Plate 1 agrees with plate 3 Plate 2 agrees with plate 3 None are known to be flat All are of nearly equal flatness Continue reducing the error until all three plates agree. 18
- 19. 3 Documents for Product Quality Product Drawing Process Definition Quality Control Plan 19
- 20. Section 2Definitions, Rules, and Symbols 20
- 21. Key Definitions Datum – Theoretically exact point, axis, or plane derived from the true geometric counterpart. Datum Feature – Actual feature on a real part used to establish a datum. Datum Feature Simulator – A surface of sufficient precision to establish a simulated datum. Simulated Datum – A point, axis, or plane established by processing or inspection equipment. Datum Target – A specified point, line, or area on a part used to establish the datum scheme. 21
- 22. Key Definitions Feature of Size – A cylindrical or spherical surface, or two opposing elements or parallel surfaces. Least Material Condition – This occurs where a feature of size contains the least material allowed by the stated limits of size. Maximum Material Condition – This occurs where a feature of size contains the most material allowed by the stated limits of size. Regardless of Feature Size – A term that indicates that a geometric tolerance or datum reference applies for any increment of size within its size tolerance. 22
- 23. Key Definitions Tolerance – The total permissible variation in size for a specified dimension. Bilateral Tolerance – A tolerance zone where the boundary conditions contain the specified dimension. Geometric Tolerance – A general term that refers any of the 14 symbols used to control form, orientation, profile, runout, or location. Unilateral Tolerance – A tolerance zone that only exists on one side of the specified dimension. True Geometric Counterpart – The theoretically perfect boundary or best fit (tangent) plane of a specified datum feature. 23
- 24. Fundamental Rules Each dimension shall have a tolerance. (except for those dimensions specifically identified as reference, maximum, minimum, or stock) Ensure full understanding of each feature. Show the detail needed and no more. Serve function needs, no misinterpretation. Manufacturing methods are not specified. Non-mandatory dimensions are OK. Designed of optimal readability. 24
- 25. Fundamental Rules Dimension materials made to gage numbers. 90o apply when features are shown as . 90o apply when centerlines are shown . Dimensions apply at 20oC (68oF). Dimensions apply in a free state. Tolerances apply for full size of feature. Dimensions and tolerances only apply at the drawing level where they were specified. 25
- 26. Limits of Size Actual Size is a general term for the size of a feature as produced. It has two interpretations. Actual Local Size is the value of the individual distance at any cross section of any feature of size. Actual Mating Size is the dimensional value of the actual mating envelope. Limits of Size are the specified minimum and maximum values for a feature of size. 26
- 27. Rule #1 – The Taylor Principle “Where only a tolerance of size is specified, the limits of size of an individual feature prescribe the extent to which variations in its geometric form, as well as size, are allowed.” ASME Y14.5M-1994Simply put: Limits of size for an individual feature control the allowable variation to its form and its size. 27
- 28. Size Controls Form This on a drawing According to Rule #1, a true geometric counterpart at MMC 25.4 must pass through the hole. 25.0 Allows this Or this 25.0 25.4 (LMC) (MMC) 25.4 (LMC) 25.4 (LMC) 25.0 (MMC) 28
- 29. Size Controls Form This on a drawing 12.2 12.0 According to Rule #1, a true geometric counterpart at MMC must pass over the pin. Allows this Or this 12.0 (LMC) 12.0 (LMC) 12.2 (MMC) 12.2 (MMC) 29
- 30. Features with and without Size Definition: A feature is a physical portion of a part such as a surface, hole, tab, slot, pin, etc. Features Without Size: Any Plane Surface Features With Size: Cylindrical Surface Spherical Surface A Set of 2 Opposing Elements or Parallel Planes 30
- 31. Features With & Without Size 31
- 32. MMC & LMC Workshop Determine MMC and LMC for each feature of size below. +.001 .752 .375 -.000 .750 .375 +.0002 -.0002 2.742 2.748 32
- 33. Rule #2 RFS applies to geometric tolerances defining individual tolerance, datum reference, or both, where no modifying symbol has been specified. MMC and LMC must be specified where required. 33
- 34. Angular Units Angular Dimensioning 25o 30’ 45” Either degrees, minutes, and seconds or decimal degrees or may be used. 25.5125o Precede small angles with zeros for degrees and 0o 0’ 55’’ minutes as place holders. 34
- 35. Millimeter Dimensioning +0 Use a single 0 to describe 25 -0.25 unilateral tolerances where the intended value is nil. For bilateral tolerances, use + 0.10 the same number of significant 25 -0.25 digits in both limits of size. For limit dimensioning, use the same number of significant 25.10 digits both limits of size. 24.75 For basic dimensions, tolerance control is accomplished by the 25 feature control frame. Follow rules for millimeter dimensions. 35
- 36. Decimal Inch Dimensioning For unilateral tolerances, use + .000 the same number of zeros when 1.000 - .010 the intended value is nil. For bilateral tolerances, use the same number of significant + .004 digits in dimension and limits. 1.000 - .010 For limit dimensioning, use the same number of significant 1.004 digits both limits of size. .990 For basic dimensions, use the same number of significant 1.000 digits as in the feature control frame. 36
- 37. Location of Features Rectangular Coordinate Dimensioning Rectangular Coordinates w/o Dimension Lines Tabular Dimensioning Polar Coordinate Dimensioning Repetitive Features or Dimensions Use of “X” to indicate “by” 37
- 38. Tolerancing and Related Principles General Practices Direct Tolerancing Methods Tolerance Expression Interpretation of Limits Single Limits Tolerance Accumulation Chain Dimensioning Base Line Dimensioning Direct Dimensioning 38
- 39. Chain Dimensioning 10.05 7.55 12.55 13.35 What are the min and 9.95 7.45 12.45 13.25 max values between surfaces X and Y? Y X - + +/- Tol Description Totals 39
- 40. Base Line Dimensioning What are the min and 43.35 43.25 max values between 30.05 29.95 surfaces X and Y? 17.55 17.45 10.05 9.95 Y X - + +/- Tol Description Totals 40
- 41. Direct Dimensioning 30.05 29.95 What are the min and max values 17.55 17.45 between surfaces X and Y? 10.05 9.95 Y X 23.35 23.25 - + +/- Tol Description Totals 41
- 42. Use of Basic Dimensions Basic dimensions define the perfect location of features with respect to the datum reference frame. Basic dimensions define the theoretical exact size and location for features. Feature control frames define the intended tolerance for features. 42
- 43. Understand Perfect Geometry Perhaps the best way to comprehend GD&T is first to envision the geometry of the perfect part defined by basic dimensions. Then we can apply the tolerances given in the feature control frames to define the allowable variation from the perfect part. 43
- 44. Using Tables toDefine Basic Dimensions Paragraph 1.9 discusses locations of features. Paragraph 1.9.3 allows the use of tables that list the location of features as rectangular coordinates from mutually perpendicular planes. Tables may be prepared in any suitable manner that adequately locates features. 44
- 45. Feature Control Frame Symbols Description SymbolFeature Control Frame .010 A B CDiameterSpherical Diameter SMaximum Material Condition MLeast Material Condition LProjected Tolerance Zone PFree State FTangent Plane TStatistical Tolerance ST 45
- 46. Feature Control Frame Elements Label the elements of the feature control frame using the following terms: Datum Modifier Geometric Characteristic Diameter Symbol Primary Datum Feature Modifier Secondary Datum Feature Tolerance Tertiary Datum .014 M A B M C 46
- 47. Feature Control Frames Example C B A 47
- 48. Feature Control Frames Example .005 A .005 A B .005 A .005 A .005 B A 48
- 49. Feature Control Frame Placement Locate the Feature Control Frame below or attached to the leader-directed dimension or callout. Run the leader from the frame to the feature. Attach a side or an end of the frame to an extension line from the feature. Attach a side or an end of the frame to an extension of the dimension line related to the feature in question. 49
- 50. Other Common Symbols Description SymbolRadius RSpherical Radius SRControlled Radius CRReference ( )BetweenAll AroundNumber of Places 8XCounter Bore or Spot FaceCountersinkDepth or Deep 50
- 51. Feature Control Frames Example 1.010 .010 M A B C 1.000 2.000 .020 A B C A A B o 30 3.000 1.500 B .005 A 1.750 .005 5.000 B .005 A B A C 51
- 52. Geometric Characteristic Symbols Type of Application Tolerance Characteristic Symbol 2D or 3D Flatness Individual Straightness Features Circularity Cylindricity Perpendicularity Parallelism Angularity Related Position Features Symmetry Concentricity Circular Runout Total Runout Either Individual or Profile of a Line Related Features Profile of a Surface 52
- 53. Some Other General Rules Statistical Tolerancing – Assignment of component tolerances to meet assembly needs of statistical stacks. Radius and Diameter Callouts – R, CR, SR, , and S . Non-Rigid Parts – Method of restraint must be specified. Screw Threads, Gears and Splines – Screw threads are evaluated at their pitch diameter unless otherwise specified. Gears and splines must be specified. 53
- 54. Section 3Applications of Tolerance Zones 54
- 55. Form Tolerances Flatness Straightness Circularity Cylindricity 55
- 56. Form Tolerances Datum references are never made for form tolerances. Rule #1 says that limits of size control variation in form. Generally, form tolerances are only necessary to refine (require a tighter tolerance) limits of size. Form tolerances are often applied to features to qualify them as acceptable datum features. 56
- 57. FlatnessDefinition Flatness exists when a surface has all of its elements in one plane.Tolerance Zone Two parallel planes within which the surface must lie. 57
- 58. Checking for Flatness 58
- 59. Proper Application of Flatness No datum is referenced. It is applied to a single planar feature. No modifiers are specified. Tolerance value is a refinement of other geometric tolerances or Rule #1. 59
- 60. StraightnessDefinition Straightness exists when an element of a surface or an axis is a straight line.Tolerance Zone Two parallel lines in the same plane for two-dimensional applications. A cylindrical tolerance zone that contains an axis for three-dimensional applications. 60
- 61. Checking for Straightness 61
- 62. Proper Application of Straightnessapplied to a Surface Element No datum is referenced. It is applied to a surface element. It is applied in a view where the element to be controlled is shown as a line. No modifiers are specified. Tolerance value is a refinement of other geometric tolerances or Rule #1. 62
- 63. Straightness of a Feature of Size When straightness is applied to a feature of size: Tolerance zone applies to the axis or centerplane. Rule #1 does not apply. The tolerance value may be larger that the limits of size for the feature of size. 63
- 64. Proper Application of Straightnessapplied to a Feature of Size No datum is referenced. It is applied to a planar or cylindrical feature of size. If a planar feature of size, the diameter symbol is not used. If a cylindrical feature of size, the diameter symbol is used. P , T , and L modifiers are not specified. Tolerance value is a refinement of other geometric tolerances. 64
- 65. Circularity (roundness)Definition Circularity exists when all of the points on a perpendicular cross section of a cylinder or a cone are equidistant to its axis.Tolerance Zone Two concentric circles that contain each circular element of the surface.Note: Circularity also applies to spheres. 65
- 66. Checking for Circularity 66
- 67. Proper Application of Circularity No datum is referenced. It is applied to a circular feature. No modifiers are specified. Tolerance value is a refinement of limits of size on the diameter or of other specified geometric tolerances. 67
- 68. CylindricityDefinition Cylindricity exists when all of the points on the surface of a cylinder are equidistant to a common axis.Tolerance Zone Two concentric cylinders that contain the entire cylindrical surface. 68
- 69. Checking for Cylindricity 69
- 70. Proper Application of Cylindricity No datum is referenced. It is applied to a cylindrical feature. No modifiers are specified. Tolerance value is a refinement of limits of size on the diameter or of other specified geometric tolerances. 70
- 71. Decisions for Form Tolerances Form Tolerances Consider Limits of Size Flatness Straightness Circularity Cylindricity Surface Axis or Elements Center Plane Consider Material Condition RFS MMC 71
- 72. Orientation Tolerances Angularity Perpendicularity Parallelism 72
- 73. Orientation Tolerances Datum references are always used for orientation tolerances. Orientation tolerances applied to a surface control the form of toleranced surface. Only a tangent plane may need control. Orientation tolerances may be applied to control both features of size and features without size. Orientation tolerances do not control size or location. Generally, profile tolerances are used to locate features without size and position tolerances are used to locate features of size. 73
- 74. AngularityDefinition Angularity exists when all of the points on a surface create a plane or a feature axis is at the specified angle, when compared to a reference plane or axis.Tolerance Zone Two parallel planes at the true angle to a reference plane and contain the entire surface surface. Datum Feature Datum PlaneNote: Applies to median planes and axes too. 74
- 75. Checking for Angularity 75
- 76. Proper Application of Angularity Datum reference is specified. Surface applications may use tangent plane modifier. Feature of size applications may use MMC, LMC, diameter, of projected tolerance zone modifiers. Basic angle defines perfect geometry between the datum reference and the toleranced feature. Specified tolerance is a refinement of other geometric tolerances that control angularity of the toleranced feature. 76
- 77. PerpendicularityDefinition Perpendicularity exists when all of the points on a surface, median plane, or axis are at a right angle to a reference plane or axis.Tolerance Zone Two parallel planes that are perpendicular to a reference plane and contain the entire surface surface. Datum Feature Datum PlaneNote: Applies to median planes and axes too. 77
- 78. Checking for Perpendicularity 78
- 79. Proper Application ofPerpendicularity Datum reference is specified. Surface applications may use tangent plane modifier. Feature of size applications may use MMC, LMC, diameter, of projected tolerance zone modifiers. Basic angle defines perfect geometry between the datum reference and the toleranced feature. Specified tolerance is a refinement of other geometric tolerances that control the perpendicularity of the toleranced feature. 79
- 80. ParallelismDefinition Parallelism exists when all of the points on a surface, median plane, or axis are equidistant to a reference plane or axis.Tolerance Zone Two parallel planes that are parallel to a reference plane and contain the entire surface surface. Datum Feature Datum PlaneNote: Applies to median planes and axes too. 80
- 81. Checking for Parallelism 81
- 82. Proper Application of Parallelism Datum reference is specified. Surface applications may use tangent plane modifier. Feature of size applications may use MMC, LMC, diameter, of projected tolerance zone modifiers. Basic angle defines perfect geometry between the datum reference and the toleranced feature. Specified tolerance is a refinement of other geometric tolerances that control parallelism of the toleranced feature. 82
- 83. Decisions for Orientation Tolerances Orientation Tolerances Angularity Parallelism Perpendicularity Consider Limits of Size Feature Consider Limits Plane of Size Of Location Surface Consider Material Condition RFS MMC LMC 83
- 84. Location Tolerances True Position Symmetry Concentricity 84
- 85. Location Tolerances Datum references are always used for location tolerances. Location tolerances are reserved for tolerancing applications on features of size. They are always located by basic dimensions back to the datum scheme. Location tolerances shown on the same centerline are assumed to have a basic dimension of zero. Symmetry and concentricity application are centered about the datum scheme specified for the controlled feature. 85
- 86. True PositionDefinition True position is the exact intended location of a feature relative to a specified datum scheme.Tolerance Zone Most frequently, the tolerance zone is a cylinder of specified diameter within which the true axis of the feature must lie.Note: True position can also be applied to median planes relative to specified datums. 86
- 87. Positional Tolerancing Traditional tolerancing (say + .005”) consist of 2-D rectangular boundaries. A circular boundary with the same worst-case conditions increases the area of the tolerance zone by 57%, prior to any bonus tolerance. 87
- 88. Traditional Fastener Tolerances Threaded Fastener 3/8 – 16 Clearance Hole 13/32 1/64 = .0156 .0015 Clearance Perfect Condition Worst-Case Condition 88
- 89. Bonus Tolerances When tolerancing features of size, bonus tolerances may be applicable. With MMC, as the size of a hole increases, so does the acceptable tolerance zone, provided the hole does not exceed its limits of size. Larger Larger Hole at Hole Hole MMC Larger Original Tolerance Tolerance Zone 89 Zone
- 90. Maximum Material Condition (MMC) Largest permissible external feature. Outside Diameter External Feature Size Key Smallest permissible internal feature. Holes Slots Key Way 90
- 91. Maximum Material Condition .760 4X .750 .014 M A B C Size Tolerance MMC C B Note: Datum feature A is the back surface. 91
- 92. Least Material Condition (LMC) Smallest permissible external feature. Outside Diameter External Feature Size Key Largest permissible internal feature. Holes Slots Key Way 92
- 93. Least Material Condition .760 4X .750 .014 L A B C Size Tolerance LMC C B Note: Datum feature A is the back surface. 93
- 94. Regardless of Feature Size (RFS) RFS is no longer documented except in rare cases where it is required for clarity. RFS is assumed for features of size when neither MMC nor LMC are specified. 94
- 95. Regardless of Feature Size .760 4X .750 .014 A B C Size Tolerance C B Note: Datum feature A is the back surface. 95
- 96. Applications ofMaterial Condition Modifiers Maximum Material Condition M Used for clearance application. Least Material Condition L Used for location applications. Used to protect wall thickness. Regardless of Feature Size Used when size and location do not interact. 96
- 97. Applications forLeast Material Condition .503 The purpose of the hole is to .501 .002 L locate the PLP pin below. Worst Case Scenario Hole diameter at .503 (LMC) Pin diameter at .499 (LMC) Clearance is .004 .500 Pin can shift .002 in any direction .499 Tolerance for hole location is Ø .002 at LMC Hole can be off location .001 in any direction Pin can be off location .003 in any direction 97
- 98. Applications forLeast Material Condition .503 The purpose of the hole is to .501 .002 L locate the PLP pin below. Hole at MMC – Pin at LMC Hole diameter at .501 (MMC) Pin diameter at .499 (LMC) Clearance is .002 .500 Pin can shift .001 in any direction .499 Tolerance for hole location is Ø .004 at MMC Hole can be off location .002 in any direction Pin can be off location .003 in any direction 98
- 99. Applications forLeast Material Condition .503 The purpose of the hole is to .501 .002 L locate the PLP pin below. Hole at MMC – Pin at MMC Hole diameter at .501 (MMC) Pin diameter at .500 (MMC) Clearance is .001 .500 Pin can shift .0005 in any direction .499 Tolerance for hole location is Ø .004 at MMC Hole can be off location .002 in any direction Pin can be off location .0025 in any direction 99
- 100. Virtual and Resultant Conditions Virtual Condition is the constant boundary generated by the collective effects of a feature’s specified MMC or LMC and the geometric tolerance for that material condition (i.e, the premise for functional gaging). Resultant Condition is the variable boundary generated by the collective effects of a feature’s specified MMC or LMC, its geometric tolerance for that material condition, the size tolerance, and any additional geometric tolerance derived from the feature’s departure from its specified material condition (e.g., extreme boundary allowed for a given situation). 100
- 101. Virtual and Resultant ConditionsGiven MMC Ø 25.5 25.1 Internal Feature of Size Ø 0.1 M Virtual Resultant Condition Condition Constant Variable Value Value Ø Hole Ø Tol V Cond R Cond Inner Outer 25.1 0.1 25.2 Boundary Boundary 25.2 0.2 25.4 25.3 0.3 25.0 25.6 25.4 0.4 25.8 25.5 0.5 26.0 101
- 102. Inner and OuterBoundary Conditions Ø 25.5 25.1 Ø 0.1 M Virtual Condition Size Inner Boundary Tolerance Zone At MMC Outer Hole at LMC Boundary Bonus Tolerance At LMC 102
- 103. Virtual and Resultant ConditionsGiven MMC Ø 24.9 24.5 External Feature of Size Ø 0.1 M Virtual Resultant Condition Condition Constant Variable Value Value Ø Pin Ø Tol V Cond R Cond Outer Inner 24.9 0.1 24.8 Boundary Boundary 24.8 0.2 24.6 24.7 0.3 25.0 24.4 24.6 0.4 24.2 24.5 0.5 24.0 103
- 104. Virtual and Resultant ConditionsGiven LMC Ø 25.5 25.1 Internal Feature of Size Ø 0.1 L Virtual Resultant Condition Condition Constant Variable Value Value Ø Hole Ø Tol V Cond R Cond Outer Inner 25.1 0.5 24.6 Boundary Boundary 25.2 0.4 24.8 25.3 0.3 25.6 25.0 25.4 0.2 25.2 25.5 0.1 25.4 104
- 105. Virtual and Resultant ConditionsGiven LMC Ø 24.9 24.5 External Feature of Size Ø 0.1 L Virtual Resultant Condition Condition Constant Variable Value Value Ø Pin Ø Tol V Cond R Cond Inner Outer 24.9 0.5 25.4 Boundary Boundary 24.8 0.4 25.2 24.7 0.3 24.4 25.0 24.6 0.2 24.8 24.5 0.1 24.6 105
- 106. Inner and Outer BoundariesGiven RFS Ø 25.5 25.1 Internal Feature of Size Ø 0.1 Variable Variable Value Value Ø Hole Ø Tol I. B. O. B. Inner Outer 25.1 0.1 25.0 Boundary Boundary 25.2 0.1 25.3 0.1 25.4 0.1 25.5 0.1 25.6 106
- 107. Inner and Outer BoundariesGiven MMC Ø 24.9 24.5 External Feature of Size Ø 0.1 Variable Variable Value Value Ø Pin Ø Tol O. B. I. B. Outer Inner 24.9 0.1 25.0 Boundary Boundary 24.8 0.2 24.7 0.3 24.6 0.4 24.5 0.5 24.4 107
- 108. Zero Tolerance at MMC Where zero tolerance is specified at MMC, the tolerance is totally based on the actual mating size of the feature specified. Location and orientation must be perfect when the feature is at MMC. As the feature departs from MMC the allowable tolerance is based on the size the feature compared to its MMC. 108
- 109. Logic for Zero Tolerance at MMC Ø 1.006 + .003 Ø .004 M A B Ø .514 + .003Ø .005 M A B M A Ø .994 + .003 Ø .002 M AØ .500 + .001 B Ø .005 M A B M A 109
- 110. Logic for Zero Tolerance at MMC Ø .999 Ø .506 Virtual Virtual Condition Condition Boundary Boundary Functional Extremes are Ø .991 and Ø .999 110
- 111. Logic for Zero Tolerance at MMC Ø .994 + .003 Ø .002 M A B Based on assumptions about process variation, we may have arbitrarily divided the total tolerance of Ø .008 into Ø .006 for size and Ø .002 for orientation. We could have divided the tolerance into Ø .004 + Ø.004, or Ø .002 + Ø .006, or even Ø .008 + Ø .000. 111
- 112. Logic for Zero Tolerance at MMC Ø .995 + .004 Ø .000 M A B Why not give the entire tolerance to the manufacturing process and let the process divide it up as needed? This is what happens when we specify zero tolerance at MMC. 112
- 113. Verification of Position at MMC Determine tolerance at MMC. Determine actual mating size. Calculate positional tolerance allowed. Determine positional error in location. Compare positional error in location to positional tolerance allowed. Decide to accept or reject. 113
- 114. Specification of Position at MMC .760 .750 .010 M A B C C 2.000 1.000 1.250 3.000 B 114
- 115. Verification of Position at MMC Hole #1 Hole #2 Hole #3 Hole #4Hole Size at MMCActual Mating Size of Hole .752 .756 .758 .762Positional Tolerance Allowed Actual Location in the X Axis 1.255 4.248 4.249 1.252 Actual Location in the Y Axis .996 1.007 3.010 3.003 Actual Positional Tolerance Accept or Reject 115
- 116. Verification of Position at LMC Determine tolerance at LMC. Determine actual mating size. Calculate positional tolerance allowed. Determine positional error in location. Compare positional error in location to positional tolerance allowed. Decide to accept or reject. 116
- 117. Specification of Position at LMC .760 .750 .010 L A B C C 2.000 1.000 1.250 3.000 B 117
- 118. Verification of Position at LMC Hole #1 Hole #2 Hole #3 Hole #4Hole Size at LMC Actual Mating Size of Hole .752 .756 .758 .760Positional Tolerance Allowed Actual Location in the X Axis 1.255 4.248 4.249 1.252 Actual Location in the Y Axis .996 1.007 3.010 3.003 Actual Positional Tolerance Accept or Reject 118
- 119. Proper Application of Position Position control is applied to a feature of size. Datum references are specified and logical for the application. Basic dimensions establish the desired true position of the feature of size. Tangent plane modifier is not used. Diameter symbol is used to specify axis control. Diameter symbol is not used to specify center plane control. MMC, LMC, or RFS may be specified. 119
- 120. SymmetryDefinition Symmetry defines the location of non-cylindrical features about a derived median plane.Tolerance Zone The tolerance zone is defined by two planes, equidistant to a datum center plane. The derived median points must fall A within these two planes. 120
- 121. Set Up for Symmetry 121
- 122. Proper Application of Symmetry A planar feature of size to be controlled uses the same center plane as the datum scheme. Diameter symbol is never used to specify the symmetry tolerance. MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified. 122
- 123. ConcentricityDefinition Concentricity defines the location of cylindrical features about an axis of rotation.Tolerance Zone The tolerance zone is defined as a cylinder about the datum axis that must contain the median points of diametrically opposed elements of a feature. A 123
- 124. Checking for Concentricity 124
- 125. Proper Application of Concentricity The surface of revolution to be controlled is coaxial to the axis of the datum scheme. Diameter symbol is used to specify the concentricity tolerance. MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified. 125
- 126. Decision Matrix for Coaxial Features Position Total Runout Concentricity (RFS) Cost to $ $$$ $$ Produce Cost to $ $$ $$$ Inspect Characteristics Location Location Location under and Orientation and Control Orientation and Form Orientation 126
- 127. Decisions for Location Tolerances Location Tolerances Concentricity Position Symmetry Center Axis Plane Determine Tolerance For Position Only Consider Material Condition RFS MMC LMC 127
- 128. Profile Tolerances Profile of a Line 2-D Application Profile of a Surface 3-D Application 128
- 129. Profile Tolerances Profile tolerances are used to control multiple coplanar surfaces. Perfect geometry must be defined via basic dimensions. The default interpretation for the tolerance zone is bilateral and equal about the true perfect geometry. Profile tolerances are not used to control features of size so MMC, LMC, and RFS do not apply. Profile features can be used as datum features or they must be related to a defined datum scheme. 129
- 130. Profile 3-D Application 2-D ApplicationDefinition Profile defines the theoretically exact position of a surface (3-D) or the cross section of a surface (2-D).Tolerance Zone A uniform boundary on either side of the true profile that must contain either the surface or line. 130
- 131. Profile for Cam Application 131
- 132. Functional Gaging of Profile 132
- 133. Proper Applicationof Profile Tolerances Profile features are used as datum features or related to a defined datum scheme. and Basic dimensions relate the true profile back to the datum scheme. or The profile tolerance value must be a refinement of dimensions used to locate the true profile. 133
- 134. Decisions for Profile Tolerances Profile Tolerances Consider Limits of Size Profile of a Profile of a Line Surface Consider Tolerance Zone Unilateral Bilateral Inside Outside Equal Unequal 134
- 135. Runout Tolerances Circular Runout 2-D Application Total Runout 3-D Application 135
- 136. Runout 3-D Application 2-D ApplicationDefinition Runout is a composite control used to specify functional relationships between part features and a datum axis.Tolerance Zone Circular runout is a 2-D application that evaluates full indicator movement on a perpendicular cross section rotating about a datum axis. Total runout evaluates full indicator movement of the full surface rotating about a datum axis. 136
- 137. Checking for Runout 137
- 138. Proper Application of Runout The surface to be controlled is either coaxial or perpendicular to the axis of the datum scheme. Diameter symbol is never used to specify a runout tolerance. MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified for a runout tolerance. 138
- 139. Decisions for Runout Tolerances Runout Tolerances Consider Limits of Size Circular Total Runout Runout 139
- 140. Geometric Characteristicsfor Round Features Circularity (roundness) Evaluates cross section of surface to its own axis Cylindricity Evaluates entire surface to its own axis Runout Evaluates cross section of surface to a defined axis Total Runout Evaluates entire surface to a defined axis Concentricity Evaluates best fit axis of feature to a defined axis 140
- 141. Tolerance Design Flow Chart Design Requirements Establish Datums Individual Features Related Individual or Features Related Features Form Tolerances Profile Tolerances Location Orientation Runout Tolerances Tolerances Tolerances 141
- 142. Section 4Datums and Datum Schemes 142
- 143. Reference Planes(The Point of Known Return) Ted Busch, 1962 Define the datum reference frame. Use of mutually perpendicular planes. The goal is the replication of measurements. Immobilize the part in up to six degrees of freedom. 143
- 144. Theoretically PerfectGeometry Three mutually perpendicular planes.3 Datum Planesdefine the Origin Datumof Measurement Point 144
- 145. Criteria for Selecting Datum Features Geometric Relationship to Toleranced Feature Geometric Relationship to Design Requirements Accessibility of the Feature Sufficient in Size to be Useful Readily Discernable on the Part 145
- 146. Designating Precedence of Datums Alphabetical order is not relevant. Order of precedence is shown in the feature control frame. Consider function first. Then, consider the process next. Finally, consider measurement processes. 146
- 147. Datum Features of Size MMC callouts on a datum features of size can allow a datum shift on the exact location of the datum feature. This applies to: Cylindrical Surfaces (internal or external) Spherical Surfaces A Set of 2 Opposing Elements or Parallel Planes A Pattern of Features such as a Bolt Hole Pattern 147
- 148. Decisions for Datum Selection Select Datum Feature Feature Surface of Size Center Axis Plane Consider Material Condition RFS MMC LMC Are Other Datums Required? 148
- 149. Rational Strategyfor Datum SelectionIt is reasonable to prioritize the datum selectionprocess as follows: 1. Functional Requirements 1. Production Requirements • Measurement Requirements 149
- 150. What Are We Really Interested In? • Error in Geometric Forms • Size for Features of Size • Location of Features 150
- 151. Introduction to Datum Workshop Select datums based on function. Some features are leaders, others are followers. Sequence of considerations: Establish the datum reference frame (DRF). Qualify the datum features to the DRF. Relate remaining features to the DRF. For consistency, assume .005” tolerance zones unless otherwise specified. Select and qualify the datum features and identify the datum point as specified in the following examples. 151
- 152. Locate the part on the back surface first, then the bottomDatum Workshop edge, then the left side. 152
- 153. Locate the part on the back surface first, then the bottomDatum Workshop edge, then the right hand side of the bottom slot. 153
- 154. Locate the part on the back surface first, then the bottomDatum Workshop edge, then centrally to the bottom slot with a .998 virtual size key. 1.000 1.005 154
- 155. Locate the part on the front surface first, then by a 1.504Datum Workshop virtual size hole for the large boss, then by a .996 virtual size key for the right hand slot. 1.500 1.502 1.000 1.004 155
- 156. Locate the part on the front surface first, then by a 1.502Datum Workshop virtual size hole for the large boss, then by the bottom edge. The bottom edge must lie in a tolerance zone from 2.490 to 1.500 1.502 2.510 from the large boss. 2.500 156
- 157. Section 5Tolerancing Strategies 157
- 158. Process for Tolerance Analysis Establish Performance Requirements Develop a Loop Diagram Convert Dimensional Requirements to Target Values with Equal Bilateral Tolerances Determine the Target Value for Requirement Select the Method of Analysis Calculate Variation for Performance Requirement 158
- 159. Statement of the Problem A problem well defined is half solved. John Dewey Thorough problem definition may lead directly to its solution. Hans Bajaria The formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. Albert Einstein 159
- 160. Assembly Stack-Up Analysis End Start - + +/- Tol Description Totals What is the minimum and maximum gap between the bottom of the collar and the upper bearing? 160
- 161. Component Tolerances .055 .045 .227 .217 .070 .060 2.906 2.805 2.896 2.795 3.116 3.096 .080 .077 .050 .045 161
- 162. Stack Analysis Result End Start - + +/- Tol Description .0785 .0015 Bottom of Bearing .050 .005 Hub Upper Lip 2.800 .005 Hub Lower Lip .0475 .0025 Top of Lower Bearing .0785 .0015 Datum A of Valve 3.106 .010 Top of Valve .222 .005 Bottom of Collar 3.179 3.2035 .0305 Totals What is the minimum and maximum gap between the bottom of the collar and the upper bearing? 162
- 163. Worst Case Evaluation Assembly Length A B C 1.000 .500 2.000 + .002 + .001 + .004Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500Tolerance of Assembly Length = .002 + .001 + .004 = + .007While this approach of adding component tolerances is mathematically correct, in practical application it is often too conservative. 163
- 164. Worst Case Pros and Cons Pros No risk of components not interacting properly. 100% interchangeability of components. Cons Method is conservative. Underutilization of full tolerance range. Tolerances for interacting dimensions are smaller than necessary, which may increase cost. 164
- 165. Statistical Method ofLinear Evaluation Assembly Length A B C 1.000 .500 2.000 + .002 + .001 + .004 Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500 Tolerance of Assembly Length = .0022 + .0012 + .0042 = + .0046 To statistically calculate the tolerance we take the root of the sum of the squared values of the individual tolerances (RSS). 165
- 166. Some Critical Assumptions Component dimensions are independent. Components are assembled randomly. Component should be normally distributed. The actual average value for each component is equal to the nominal value specified for that component. (Otherwise, the nominal value for the assembly will not be met and the tolerances will not be realistic.) Process control is needed. 166
- 167. From Part Tolerances to anAssembly Tolerance Variances are additive while A standard deviations are not. B Assembly C 167
- 168. Statistical TolerancingPros and Cons Pros Larger tolerances on interacting dimensions. Cons Small percent of final assemblies fall outside limits. Special Considerations Averages of interacting dimensions must be controlled via variables measurements. Interacting dimensions must be independent and normally distributed. Lot size should be moderately large. 168
- 169. From an Assembly Toleranceback to Component Tolerances A B Assembly CIn practice, we are often required to begin with a defined end result and determine appropriate tolerances for the components. 169
- 170. Two Theorems of Relevance Two theorems hold great importance in the interrelationship of tolerances. The first is similar to the Pythagorean Theorem σ sum = (σ12 +σ 2 +σ 3 +...+σ n ) 2 2 2 The second theorem appears less obvious: σ1−2 = (σ12 +σ 2 ) 2 B A 170
- 171. Composite Tolerances andSingle Segment Tolerances .030 M A B C .030 M A B C .010 M A There are times when it .030 M A B C is more important to control the relationships .010 M A B between features than to control their locations .030 M A B C to the datums. .010 M A B 171
- 172. Standard Positional Tolerance .760 4X .750 .030 M A B C C 2.000 1.000 1.250 3.000 B A 172
- 173. Functional Gage for VirtualCondition of Holes to Datums 4X .720 Datum Surface A C 2.000 1.250 3.000 1.000 B 173
- 174. Composite Tolerance with OneDatum in the Lower Segment .760 4X .750 .030 M A B C .010 M A C 2.000 1.000 1.250 3.000 B A 174
- 175. Composite ToleranceFeature Control Frame Pattern Locating Tolerance Zone PLTZF locates and orients Framework features to the specified One Tolerance datums via basic dimensions. (PLTZF) Zone Symbol FRTZF locates the features within the pattern via basic .030 M A B C dimensions to each other and controls their orientation .010 M A relative to the specified datum(s). FRTZF releases the pattern Feature Relating from the requirements given Tolerance Zone by basic dimensions to their Framework datum features. (FRTZF) 175
- 176. Two Functional Gagesfor the Composite Tolerance .030 M A B C .010 M A 4X .720 4X .740 Datum Surface A Datum Surface AC 2.000 2.000 1.250 3.000 3.000 1.000 B 176
- 177. Composite Tolerance with TwoDatums in the Lower Segment .760 4X .750 .030 M A B C .010 M A B C 2.000 1.000 1.250 3.000 B A 177
- 178. Two Functional Gagesfor the Composite Tolerance .030 M A B C .010 M A B 4X .720 4X .740 Datum Surface A Datum Surface A C 2.000 2.000 1.250 3.000 3.000 1.000 Orientation of Datum B remains parallel to the hole pattern as it moves up or down on two rails. B B 178
- 179. Two Single Segments with TwoDatums in the Lower Segment .760 4X .750 .030 M A B C .010 M A B C 2.000 1.000 1.250 3.000 B A 179
- 180. Two Functional Gages for theTwo Single Segment Tolerances .030 M A B C .010 M A B 4X .720 4X .740 Datum Surface A Datum Surface AC 2.000 2.000 1.250 3.000 3.000 1.000 1.000 B B 180
- 181. Fixed and FloatingFastener Calculations Floating Fastener scenario exists when the fastener must pass through two clearance holes in mating parts. Fixed Fastener scenario exists when one of the parts has threaded holes and the other part has clearance holes. Projected Tolerance Zone should be used to specify the height out of the threaded hole that the tolerance zone applies. 181
- 182. Threaded Holes “Threaded holes aren’t really holes. They are a vehicle to locate and orientate mating parts.” Carl Lance Nubs on a shower head behave the same as a threaded hole. 182
- 183. Two Clearance Holes –Floating Formula Application Two Pieces Required What should we use as the + .007 4X .406 positional tolerance for each - .002 .XXX M A B C of these two mating parts? C .029 M A B C .502 .500 Assuming a 3/8 – 16 threaded fastener… .404 2.000 - .375 .029 1.000 1.250 3.000 B AMMC of clearance holes minus MMC of fastener is given to the positionaltolerance of both pieces. 183
- 184. Threaded Hole with Clearance Hole –Fixed Fastener Application .404 What tolerances should we use for positional -.375 tolerances for these two mating parts? .029 4X + .007 4X .406 3/8 - 16 2B UNC thru - .002 .XXX M P .502 A B C .XXX M A B C .502 C .015 M P .502 A B C .502 C .014 M A B C .500 .500 2.000 2.000 1.000 1.000 1.250 3.000 B A 1.250 3.000 B AMMC of clearance hole minus MMC of fastener must be shared between thetwo positional tolerance of the two pieces. 184
- 185. Topics Worthy of Discussion Definition of Functional Requirements Failure Mode and Effects Analysis Consistent Tooling and Gaging Locators Communication with Suppliers Developing Optimal Specifications 185
- 186. Sources of Variation The following primary contributors to body-in-white variability were identified as part of the Auto Body Consortium’s 2mm Program for Variation Reduction: Locator Pins 28.4% Incoming Material 21.3% Welding 19.1% Clamping 13.5% Robot Programming 5.0% Carriers 3.5% Rough Locators 2.8% NC Blocks 2.8% 186
- 187. Sources of Variation A summary of the sources of locator pin problems: Size 22.5% Pin Interference with Panel 17.5% Loose Pins 12.5% Pin Too Short 7.5% PLP Quantity 7.5% Pin PLP Selection 7.5% Pins Needed Rotating 5.0% Worn Pins 5.0% Missing Pins 5.0% Pin Shape 2.5% Pin Too Long 2.5% 187
- 188. Other Sources of Variation Gravity Material Clamp Sequence Methods Equipment Tool Interference People Environment Tool Repeatability Measurement Error Incoming Part Quality Uncoordinated Datum Scheme Clearance from Clamp Finger to Net Block 188
- 189. Section 6Functional Gaging 189
- 190. Merits of Functional Gaging Simple Functional Checks for Conformity Takes Advantage of Bonus Tolerances Checks Parts for their Virtual Condition Allows for Best-Fit Solutions Rejects Less Functionally Good Parts 190
- 191. Functional GagingPros and Cons Pros Reduces risk of shipping bad product. Reduces risk of scrapping good product. Reduces inspection costs. Provides attribute data. Cons Doesn’t provide variables data. Usually won’t qualify for PPAP submission. May not correlate with CMM data. 191
- 192. Functional Gaging of Profile 192
- 193. What to Do About Design Errors… The first thing you want to do about design error is to find them early. As human nature would have it, most designers seem to want to focus on the next design, rather than spending their time on past mistakes. If you can identify design errors early in the design review process, the potential of actually getting the drawings corrected is often much greater. 193
- 194. Some things to Lookfor in Design Reviews Datum schemes that don’t make sense. Datum schemes that don’t match the physics of assembly. Datum schemes that are in conflict with themselves. Datum schemes that will be difficult to manufacture. Datum schemes that will be difficult to inspect. 194
- 195. Some things to Lookfor in Design Reviews Geometric tolerances that aren’t referenced to a datum scheme when they should be. Geometric tolerances that are referenced to a datum scheme when they shouldn’t be. Diameter symbols used where they shouldn’t be used. Diameter symbols not used where they should be. 195
- 196. Some things to Lookfor in Design Reviews Use of geometric tolerances that don’t refine either the limits of size or other tolerances. Patterns of holes where the quantity of holes has not been specified. Dimensional requirements that can’t be made. Dimensional requirements that can’t be checked. 196
- 197. Process for Design Change Quality management systems require a defined process for design changes within the scope of design control. Designers need explicit and accurate feedback to improve both current and future designs. If drawings aren’t updated to eliminate design flaws, the odds are pretty good that you’ll see that problem again in the future. 197

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