1. Geometric Dimensioning & Tolerancing
Creating better communications
Presented by
J.C.Kalra
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2. Definitions and Rules
Many of the industry’s problems stem from faulty communications. In today’s competitive market, it is not enough to make drawings that can be understood. We must make drawings that cannot possibly be MISUNDERSTOOD.
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3. What is GT&D?
Geometric Dimensioning and Tolerancing (GDT) is a method for precisely defining the geometry of mechanical parts.
It introduces tools which allow mechanical designers, fabricators, and inspectors to effectively communicate complex geometrical descriptions which are not otherwise able to be described in a defined language.
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4. GD&T a vast subject
Geometric Dimensioning and Tolerancing is a vast language of which there are many facets.
However, we will discuss is a small subset of the total. This subset is based on concepts which MUST be learned in order to progress further. Without a solid understanding of these fundamentals, one cannot gain a firm grasp of later topics.
We will present the most essential (and often misinterpreted) topics in a step-by-step fashion, starting with a simple two-dimensional case.
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5. A 2D Datum Example in detail
We will describe in detail an example of use of GDT in the area of sizing and positioning of holes which must mate with shafts.
We will start with a two-dimensional geometry of a component in the next slide.
This might be a sheet metal part which is inch thick with a length and width of about 10 inch.
Figure 1 shows the part with possible ways to define the location of the hole.
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6. Figure 2.1                                                              dimensional part. The
Pictured in Figure 1 is a two-dimensional part. The roughness of its edges has been greatly exaggerated in order to clarify the discussion.
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7. A 2D Datum Example in detail
As has been made apparent, the linear dimensions originate from the sides of the part, but it is not clear from where on the sides the dimensions should begin. (We consider where the center of the hole is later.)
The method of fixturing the part for measurement of its features is critical since many different groups of people will be measuring the part: design, fabrication, fabrication inspection, purchasing inspection, etc.
Without a common agreement as to how the part will be measured, measurements become meaningless.
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8. Figure 2
One way to define where the dimensions should originate is shown in Figure 2.
A steel straight edge can be used to define a line for the two edges.
Figure                                           
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9. Problem with conventional dimensioning
One problem with this method is that the two defined lines are not necessarily perpendicular, as shown in the figure. Without perpendicularity, the part dimensions do not agree with print dimensions, since print dimensions are assumed to be perpendicular.
We can force the two defined lines to be perpendicular to each other by using a right-angle straight edge, as shown in Figure 3. Now when the part is pushed against these two edges so that it cannot move (rock), the two edges can be used as mutually perpendicular datums.
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10. Fig 3
Fig 4
Figures 2.3 and 2.4
However, as Figure 3 and 4 show, the part position with respect to these two datums is ambiguous. The final orientation of the part depends upon which side contacts first.
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11. Figure 5 illustrates an ordered datum scheme that prevents confusion.
The first side that is pressed against one of the edges – primary datum - will contact at the two highest points of the part edge.
The part now only has one degree of freedom left: it can slide back and forth against the straight edge.
Figure 5
                                                                     
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12. Two Datums for fixing orientation for 2 D part
Once we butt the primary side of the part against the corresponding straight edge, we will have completely constrained the orientation of the part in 2D space, as shown in Figure 5.
This second side contacts its straight edge at one high point since it is not able to rotate to contact more than one high point. It fixes the position of the 2 D part.
Figure 5 labels the datums as A and B, in the order of fixturing hierarchy.
These datums are referred to as "functional datums" since they contact the part and are physical hardware used, for example, on a factory floor.
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13. 2D Hole Positioning
                                                                          
Now that we have rigorously defined how we fixture the part for dimensioning features, we can define where the hole is.
Figure 6 shows two dimensions which show where the hole is with respect to datums A and B.
Fig 6
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14. 2D Hole Positioning
Plus/minus tolerances  0.25 are also shown. This results in a square tolerance zone within which the center of the circle must lie.
It can easily be realized that a square tolerance zone is typically not what is needed for defining the position of a hole with respect to a mating shaft, as shown in Figure 7.
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15.                                           
Fig. 7
In addition, a square tolerance zone is typically not what is needed for defining the position of a hole with respect to a mating shaft, as shown in Figure 7.
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16. GDT Position Tolerancing
Fig. 8
GDT Position Tolerancing
Figure 2.7 : GDT of the Same Hole                                                                                        
Figure 8 illustrates the equivalent GDT tolerancing of the hole position. The tolerance zone within which the center of the circle must lie is circular rather than rectangular.
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17. Advantages with Circular Tolerance Z0ne
The largest deviation from true position occurs on the diagonals of a square, and the circle meets this, while providing 40% more possible deviation along the vertical and horizontal.
This circular tolerance zone contains 57% more area than an equivalent square tolerance zone.
Therefore, more parts can be accepted by inspection. With the square tolerance zone, parts that can fit are rejected since typically only the vertical and horizontal location deviations are checked.
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18. Basic Dimensions
The 7.5 and 3.0 dimensions in Figure 8 (2 slides earlier) for the hole location do not have attached tolerances for a reason. They are called basic dimensions and represent the exact position of the center of the circular tolerance zone within which the center of the circle must lie.
Basic dimensions are usually specified in one of three ways:
Enclosing the numerical value in a rectangle,
Placing the word “basic” after the dimension,
Use of general note.
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19. Feature Control Frame
In figure 8 (3 slides earlier), the diameter of the circular tolerance zone comes from the feature control frame which is below the 2.5 hole diameter dimension.
Geometric tolerances and modifiers are applied to drawings with the help of a feature control frame.
A feature control frame is a rectangle which is divided into compartments within which the geometric characteristic symbol, tolerance value, modifiers and datum references are placed.
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20. Modifiers for Features-of-size
Maximum Material Condition (MMC):
When feature-of-size contains the maximum amount of material.
REMEMBER
An external feature-of-size (e.g.a shaft) is at MMC when it is at largest size limit.
An internal feature-of-size (e.g.a hole) is at MMC when it is at smallest size limit.
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21. Modifiers for Features-of-size
Least Material Condition (LMC):
When a feature-of-size contains the minimum amount of material.
REMEMBER
An external feature-of-size (e.g.a shaft) is at LMC when it is at smallest size limit.
An internal feature-of-size (e.g.a hole) is at LMC when it is at largest size limit.
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22. Modifiers for Features-of-size
Regardless of feature size (RFS);
RFS applies when a geometric tolerance (or a datum) applies independent of the feature size. The geometric tolerance is limited to the stated amount regardless of the size of the feature-of-size.
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23. Modifying Symbols
In addition to geometric characteristic symbols, there are five modifying symbols used in GD&T. These are:
TERM
ABBREVATION
SYMBOLS
Maximum Material Condition
MMC
Least Material Condition
LMC
Regardless of Feature Size
RFS
Diameter
Dia M L S Ø
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24. Features, Feature-of-size & Location Dimension
A feature is a general term applied to a physical portion of a part, such as a surface, hole or a slot.
Feature-of-size:
A feature-of-size is one cylindrical or surface or a set of parallel surfaces, each of which is associated with a size of dimensions
Location Dimension
Location dimension is a dimension which locates the centreline or centre plane of a part feature relative to another part feature.
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25. RULE # 1 ESTABLISHED BY ASME Y14.5M-2000
Size limits control surface forms. Unless otherwise specified, for rigid features, the LMC is measured for violation of every set of diametrically opposing points and MMC is measured to verify compliance with envelop of perfect form of MMC.
Explanation : For features-of-size, where only a size dimension is specified, the surface shall not extend beyond a boundary (envelop) of PERFECT FORM AT MMC.
REMEMBER
Rule # 1 applies to all features-of-size on a drawing. It is like an invisible control that applies to all features-of-size unless it is overridden by a geometric dimension.
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26. RULE # 1 ESTABLISHED BY ASME Y14.5M-2000
Perfect “form” in Rule # 1 means perfect flatness, straightness, roundness, and cylindricity.
For an external feature of size 10.6 – 10.8, if produced between MMC and LMC, let’s say 10.7, then a form error equal to amount of departure from MMC (10.8 – 10.7 = 0.1) would be permissible.
If it is produced at LMC, a form error equal to amount of departure (0.2) would be permissible.
Rule # 1 applies to individual features-of-size only.
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27. RULE # 1 ESTABLISHED BY ASME Y14.5M-2000
Exceptions:
Rule # 1 does not apply to parts which are not rigid, i,.e. those which are subject free state variation. Another standard applies.
Bar stock, tubing, sheets or structural shapes which have their own standards.
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28. RULE # 2 & 3 ESTABLISHED BY AMSE Y14.5M-2000
Second and third rules are simply conventions for expressing geometric tolerances in feature control frames.
Rule # 2:For all geometric characteristics symbols used, where no MMC (M) or LMC (L) symbol is specified in the feature control frame, the regardless of feature size concept (RFS) is implied for geometric tolerance and any datum feature-of-size specified.
Rule # 3: For tolerance of position, the RFS symbol (S) may be specified as a clarifying redundancy. As stated in Rule # 2, when no material condition (modifier) is specified, RFS concept is implied.
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29. Bonus Tolerances
Whenever a geometric tolerance is applied to a feature-of-size, and it contains an MMC modifier in the tolerance portion of the feature control frame, a bonus tolerance is possible.
When the MMC modifier is used in this fashion, it means that the stated tolerance applies when the feature-of-size is at maximum material condition.
When the actual feature-of-size departs from MMC, an increase in the stated tolerance, equal to the amount of departure, is permitted. This increase or extra tolerance is called the bonus tolerance.
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30. Bonus Tolerance Actual Size Bonus Tol. Tol. Zone  40.5 0.4 40.3 0.2
 40±0.5
Actual Size
Bonus Tol.
Tol. Zone 
40.5
0.4
40.3
0.2
0.6
40.1
0.8
40.0
0.5
0.9
39.5
1.0
39.7
1.2
1.4 
0.4 M A A
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31. No Bonus Tolerance Actual Size Bonus Tol. Tol. Zone  40.5 0.4 40.3
 40±0.5
Actual Size
Bonus Tol.
Tol. Zone 
40.5
0.4
40.3
0.2
40.1
40.0
0.5
39.5
0.6
39.7
0.8
1.0 
0.4 S A A
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32. Virtual Condition
When analyzing parts that assemble with other parts, or when designing gauges, it is essential to be able to calculate a theoretical extreme boundary.
Virtual condition is the theoretical extreme boundary of a feature-of- size generated by the collective effects of MMC and any applicable geometric tolerances.
When a feature-of-size has no geometric tolerance, the virtual condition is decided by Rule 1.
When a feature-of-size has a geometric tolerance which overrules Rule 1, then its effect must be considered on virtual condition.
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33. Figure VC1.1
For the shaft in Figure 17, the diameter of the virtual condition is the diameter of the MMC shaft plus the diameter of the position tolerance zone.
Fig. 17
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34. Figure VC1.2
Fig 18
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35. Figure 19 shows the shaft and hole virtual conditions superimposed
Figure 19 shows the shaft and hole virtual conditions superimposed. Since the shaft virtual condition is smaller than the hole virtual condition, the two parts will always mate
Figure VC1.3
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36. How to Define Virtual Condition
In summary, the way to calculate virtual condition (VC) for a shaft and hole is: SHAFT VC = MMC diameter + Position Tolerance Zone Diameter HOLE VC = MMC diameter - Position Tolerance Zone Diameter
Virtual condition is extremely useful in the design of functional gauges. A functional gauge made to virtual condition will ensure that a part will always mate with its counterpart.
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37. Form Controls
Form Controls refine or expand the shape of a feature or feature-of-size, whenever the limits established by Rule # 1 are not functionally satisfactory or applicable.
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38. Form control never use a datum feature
General Information
Form is defined on engineering drawings by following four symbols :
Flatness
Straightness
Circularity
Cylindricity
Form control never use a datum feature
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39. Flatness
A flat surface has all its points falling into a single plane.
A flatness tolerance is the amount which surface elements are permitted to vary from the true plane. A flatness tolerance zone is the distance between two planes.
Flatness as well as other form tolerances are measured in relation to its own true counterpart.
A theoretical plane is established by the three high points of the considered surface, a second plane is parallel to the first, but offset by the flatness tolerance value. All points of the considered surface must lie between these two planes.
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40. Rule # 1 & Flatness
Whenever Rule # 1 applies to a planer surface-of-size, an automatic flatness exists for both surfaces.
This automatic control is the result of interpretation of Rule # 1 (perfect form at MMC) and the size dimension.
When the feature of size is at MMC, both surfaces must be perfectly flat.
As the feature of size departs from MMC, a flatness error, equal to the amount of departure is allowed.
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41. Application of Flatness Controls
When the automatic flatness control from Rule # 1 is not sufficient to satisfy the functional requirements of a part, a flatness control may be added.
A flatness control never overrides Rule # 1, it refines the maximum allowable flatness error of the surface.
The flatness control limits the surface flatness only when the part departs from MMC by more than the flatness tolerance value.
The Flatness control does not override Rule # 1.
The Flatness control does not affect the virtual condition.
The flatness tolerance value should be less than the size tolerance.
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42. Straightness of feature
Straightness is a condition where each line element of a feature is a theoretical straight line. A straightness tolerance of a feature, is the amount a surface element is permitted to vary from a theoretically straight line.
The shape of a surface element straightness tolerance zone is two parallel lines. The distance between lines is the tolerance value specified in the feature control frame.
The tolerance zone applies only in the view that the straightness symbol is shown on the drawing – in effect, it offers no control in the other view.
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43. Straightness of Feature-Of-Size
Straightness is the only form tolerance that can be applied to either a feature or a feature of size. A straightness control has a different tolerance zone depending upon its application to a feature or to a feature of size.
When straightness is used on a feature-of-size, the following apply:
The tolerance zone applies to the axis of a feature-of-size.
Rule # 1 is overridden.
The virtual condition for the feature-of-size is affected.
Modifiers may be used in the feature control frame.
The tolerance value specified may be greater than the size tolerance.
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44. Circularity
CIRCULARITY is a condition at any radial section, perpendicular to the common axis, the surface of a cylinder (sphere or a cone) is a perfect theoretical circle.
A CIRCULARITY TOLERANCE is the amount by which surface elements of a diameter may vary from theoretical circle mentioned above.
A CIRCULARITY TOLERANCE defines a tolerance zone bounded by two circles spaced apart a radial distance equal to the circularity tolerance, within which each circular element of the surface must lie. This tolerance applies independently at any plane at all axis.
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45. Cylindricity
A Cylindricity tolerance is the amount which surface of a cylinder may be allowed to vary from a theoretically perfect cylinder.
A cylindricity tolerance zone is bounded by two concentric cylinders within which the surface must lie.
Applied to an external cylindrical feature, one tolerance cylinder zone circumscribes the high points of the diameter and the second is radially smaller by the cylindricity tolerance value.
Applied to an internal cylindrical feature, one tolerance cylinder zone cylinder contacts the high points of the diameter and the second is radially larger by the tolerance value.
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46. Cylindricity
The cylindricity tolerance must be less than the half the size tolerance.
Cylindricity can only be applied to a feature itself) diametrical surface elements), therefore, it cannot use MMC or LMC modifier. A geometric control can use these modifiers only when it is applied to a feature-of-size.
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47. Datums
This chapter introduces the terminology and concepts which relate dimensional measurements to theoretical planes (or axes) called datums. This information is essential in order to understand how dimensions and their tolerances should be measured.
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48. Datums – General information
What is a Datum?
We have already seen why datums are necessary in slides 11 and 13.
A datum is a theoretical point, line, axis, or a plane which indicates the origin of a specified dimensional relationship between a toleranced feature and a designated feature on a part. A designated part feature serves as a datum feature, whereas, its true counterpart (the gauge) establishes the datum plane or axis.
For practical purposes, a datum is assumed to exist and be simulated by processing or inspection equipment, such as machine tables, surface plates, collets, gauge surfaces.
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49. Datums – General information
What is the purpose of a datum?
Datums are used to locate parts in a repeatable manner for checking geometric tolerances related to datum features.
In addition, datums communicate functional information about the part. For example
datum features on a drawing show the drawing user, which part mount and locate the part in its assembly.
Also, the primary datum feature is the part feature which establishes the attitude (orientation) of the part in its assembly.
What is a datum Feature: A datum feature is a part feature which contacts or is used to establish a datum.
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50. Datums – General information
How are Datums Specified and Referenced?
The symbol for specifying datum feature, is a rectangle containing the datum identifying letter preceded and followed by a dash.
Datums are referenced in a feature control frames. In a feature control frame, the compartment next to the tolerance value compartment references a primary datum. Secondary and tertiary datum references follow.
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51. How are Datum Features Selected?
Datum features are selected on the basis of the functional design requirements of a part. Datum features are the surfaces which locate and mount the part in its assembly. For example:
For example if a part mounts on surface A and diameter B is used for locating the part.
Surface A and diameter B are designated as datum features and the bolt holes are dimensioned relative to datums A and B through geometric tolerances.
Since the part is clamped against surface A, this surface will establish the attitude (orientation) of the part and is referenced as primary datum . Pilot diameter locates the part and is referenced as the secondary datum, in the dimensioning of the bolt holes.
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52. Planer Feature Datums
In some cases, for the measurements required, a single reference is sufficient., the datum reference is considered a primary datum.
A primary datum always establishes the attitude (orientation) of the part for measurement.
A datum plane is a theoretical plane which contacts three high points of the datum feature.
Measurements from a datum plane, are always made perpendicular to the datum plane.
When measuring geometric tolerances, which refer the datum, the three high points of the datum feature must be contacting the datum plane.
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53. Datum Reference Frame
When more than one datum is required for repeatable measurements,a datum reference frame is used.
A datum reference frame is a set of three mutually perpendicular planes. (See figure 14).
These planes provide direction as well as an origin for measurements. For specified measurements, the part datum features contact the datum planes.
When making part measurements, the part must be brought into contact with the datum reference frame in a prescribed manner. The part feature contacting the datum reference frame first is the primary datum. The part feature contacting the datum reference frame second is the secondary datum and the part feature contacting third is tertiary datum.
Feature control symbols specify primary, secondary and tertiary datums.
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54. Figure 3.1                                                                                                            The 3D part is also shown, its
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55. Datum Precedence
In order to position a part on a datum reference frame, in a repeatable manner, datums must be referenced in order of preference.
Datum precedence refers to the order in which part features come in contact with the datum reference frame (1st, 2nd and 3rd).
Figure 19 is an example where the datum features are planer. The intended datum precedence is indicated by the order of the datum reference letters in the feature control frame viz. A, B and C. These surfaces are the functional locating surfaces of the part. When checking the location of the holes, datum A is primary, datum B is secondary, and datum C is tertiary.
Only dimensions which are referred to the datum reference frame through geometric tolerances or special notes should be measured from datum reference frame.
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56. 3-2-1 Rule
The rule defines the minimum number of points of contact for the primary datum as 3, the secondary datum as 2 and tertiary as 1.
The rule applies to planer datums only.
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57. Features-of-Size Datums
When a reference is made to a feature-of-size as a datum, it is necessary to specify which way the datum is to be simulated, that is: LMC, RFS or MMC. This is accomplished by use of modifiers that appear in a feature control frame immediately after the datum reference.
Note: A datum feature may be referenced in several conditions in different feature control frames on the same drawing.
As per Rule # 2, unless otherwise specified, RFS is assumed.
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58. Features-of-Size Datums
When a planer surface is specified as datum feature, it is used to establish a datum plane.
When a feature of size is specified as a datum feature, the surface or surfaces of that features-of-size are used to establish a datum axis or centreplane.
REMEMBER
Whenever a datum feature-of-size is referenced, it must be specified MMC or LMC whichever is appropriate; otherwise RFS applies by default.
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59. Datum Targets
Datum targets are designated points, lines or areas of contact used to locate a part in a datum reference frame.Datum targets are shown on the part surfaces on a product drawing.
Datum targets should be considered whenever the whole surface may introduce uncertainties of obtaining repeatable measurements. Typical examples are castings, forgings, warped or bowed surfaces.
Datum target points, lines and areas are identified by using datum target symbols. A datum target point is specified by an “X” symbol. When it is desired to use a line contact, a datum target line is specified. When a specific area or areas contact a datum plane, target areas of desired shape and size are specified.
A dashed line from the datum target symbol indicates that the datum target is on the far side (hidden) surface.
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60. Datum Targets
Datum targets areas describe the shape, size and location of gauge features which are used to establish datum planes.
Basic dimensions are used to locate the datum target points relative to each other and other datums on the part.
When it is desired to use a line contact between the datum feature and the datum plane. A datum target line is specified. A datum target line is specified in three ways:
A phantom line on the plan view of the surface.
An “X” symbol on the edge view of the surface.
A combination of both.
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61. Datum Targets
When it is desired to use a specific area or areas to contact a datum plan, a target area or areas of the desired shape and size is specified.
A datum target area is designated by section lines within a phantom outline of the target area with the necessary basic dimensions added to describe shape and location. See figure 3-14A.
If the target area is circular, the diameter may be specified in the upper half of the datum target symbol. See figure 3-14B.
When it is impractical to show the circular target area, the method shown in 3-14C may be used.
Figure 3-15 illustrates an application of datum target areas.
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62. Co-Datums
When two datums features of equal importance are used to establish a single plane or axis, they are called co-datums.
A co-datum is designated by placing the appropriate datum reference letters, separated by a dash, into the datum reference frame compartment of the feature control frame.
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63. Orientation Controls
This chapter is about controlling the orientation (attitude) of a part features relative to each other. Every part feature must have some orientation relative to rest of the part. Sometimes a general note like “Unless Otherwise Specified All 90 degree angles to be XX” will suffice. In many cases, a direct oriental control, like parallelism, angularity or perpendicularity is required to meet the functional requirements of the part
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64. General Information
Orientation Controls define the angularity, squareness, and parallelism of a features relative to one another. These are sometimes called attitude controls.
The symbols which designate these controls are shown below:
PERPENDUCULARITY
ANGULARITY
PARALLELISM
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65. Orientation Tolerance Zones
Orientation tolerance zones are total in value. This means that an axis, or centreplane, or all elements of a surface must fall within the tolerance zone specified by the orientation control.
There are three types of orientation control tolerance zones:
Two parallel planes
Two parallel lines
Cylindrical
When perpendicularity, angularity and parallelism are applied to plane surfaces, the flatness of the surface is controlled to within the orientation tolerance zone. Naturally flatness cannot exceed the orientation tolerance.
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66. Perpendicularity
Perpendicularity is the condition of a surface, or centreplane, or axis being exactly 90 degree to a datum.
A perpendicularity tolerance is the amount which a surface, or axis, or a centreplane is permitted to vary from being perpendicular to the datum.
Most perpendicularity applications fall into one of the four types of general cases: (
Perpendicularity applied to a surface or a planer feature-of-size.
Perpendicularity applied to a diameter (in one direction only)
Perpendicularity applied to the axis of a diameter..
Perpendicularity applied to a surface line element.
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67. Angularity
Angularity is the condition of a surface, or centreplane, or axis being exactly at a specified angle from a datum.
An angularity tolerance is the amount which a surface, or axis, or a centreplane is permitted to vary from its specified exact angle to the datum.
Angularity establishes a tolerance zone for a surface, centreplane or an axis which is at a specified basic angle (other than 90 degrees) from a datum plane or axis.
An angularity tolerance zone is always two parallel planes.
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68. Parallelism
Parallelism is the condition of all points on a surface, centreplane, or axis are at equal distance from a datum plane or a datum axis.
A parallelism tolerance is the amount which a surface, axis, or a centreplane is permitted to vary from the parallel state.
A parallelism control establishes a tolerance zone of two parallel planes or a cylinder within which all points of a controlled surface , centreplane or an axis must lie.
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69. Location Controls
Location controls are a very powerful engineering tools for defining, producing and inspecting parts economically.
Much confusion exists about location controls. This comes from a weak foundation in basic geometric concepts like Rule #1, MMC, bonus, shift etc.
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70. General Information Location tolerance consists of:
Tolerance of position and
Concentricity.
The symbols for these are shown below:
Positional Tolerance
Concentricity
Location Tolerances deal with features-of-size only. Therefore all modifies MMC, LMC and RFS apply.
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71. General Information
Location tolerances are used to control three types of relationships:
Centre distance between features-of-size.
Location of a feature-of-size, or a group of features-of-size, relative to a datum or datums.
Coaxiality or symmetry of feature-of-size.
REMEMBER
Location controls should always be applied to features-of-size
Location controls always require a datum reference.
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72. Tolerance of Position
Tolerance of position is the most widely accepted location control used on engineering drawings today.
This is because of its ability to describe the requirements of interchangeable components.
One of the primary application of tolerance of position is related to bolt hole pattern location, because no other method so accurately describes the functional requirements of the mating hole pattern.
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73. Advantages of Tolerance of Position
A number of advantages can be cited (these will become evident as we go further) :
Round tolerance zones – 57% larger.
Permits additional tolerances:
Bonus
Shift
Permits use of fixed gauges.
Overcomes tolerance accumulation
Protects part functions
Lowers production costs.
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74. Fundamentals of Tolerance of Position
A tolerance of position is specified in a feature control frame by:
The position symbol
A tolerance value
Modifiers, and
Appropriate datum references
(See slide 16).
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75. Fundamentals of Tolerance of Position
Two definitions regarding tolerance of position are:
True position :
The exact (perfect) location of a point, or plane (normally the centre) of the feature-of-size in relationship with a datum reference frame and /or other features-of-size. Basic dimensions are used to establish the true position of the feature-of-size on drawings.
Tolerance of position:
The total permissible variation in the location of a feature-of-size about its true position.
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76. Requirements of Tolerance of Position
Much of the confusion about tolerance of position comes from the numerous bad examples that exist on the drawings. The following four basic requirements of a tolerance of position application are given below. Drawing users may use this information for checking the drawings.
Tolerance of position must be applied to a feature of size.
Datum references are required.
Basic dimensions are used to establish true location of the feature-of-size from the specified datum and between inter- related features-of-size.
LMC or MMC modifiers are specified if required. Rule # 3 applies.
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77. Visualization of Tolerance of Position
If any of the above conditions are not fulfilled, the tolerance of position cannot be interpreted...
Tolerance of Position Visualized in Two Ways:
As a boundary limiting the movement of the surface of feature.
As tolerance zone limiting the movement of the axis of a feature.
Both concepts are useful and equivalent. However boundary concept is used extensively, because it represents functional requirements of mating parts and is more flexible of the two systems.
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78. Boundary Concept of Tolerance of Position
The specified tolerance of position applies when the hole is at MMC.
The hole must be maintained within its specified limits of size and its location must be such that no surface element infringes the virtual condition. It is referred as gauge pin diameter.
The boundary is three dimensional in nature. The height of boundary is equal to height of the feature-of-size.
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79. Boundary Concept of Tolerance of Position
Tolerance of Position as an Indirect Orientation Control. The attitude of theoretical boundary produced is either perpendicular or parallel to the primary datum in the feature control frame and the orientation of the feature-of-size is controlled by this boundary.
Rule #1 overridden: Virtual condition overrides MMC. The straightness of the feature-of-size is also controlled by the boundary.
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80. Axis Concept of Tolerance of Position
For Internal Holes:
When the hole is at MMC (smallest diameter) its axis must fall within a cylindrical tolerance zone located at the true position.
This tolerance zone also defines the attitude of the hole at MMC.
Straightness is also limited by this zone.
When we read diameter symbol against positional tolerance in feature control frame, it means “the axis may be out position by”.
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81. Boundary and Axis Concepts Equivalent
The manner of converting a tolerance of position from boundary concept to an axis tolerance zone is shown.
This can be accomplished by studying the effects of moving the hole until it contacts the boundary. This causes the centre of the hole to generate a diametral tolerance zone about its true position. This zone is the equivalent axis tolerance zone derived from the boundary concept.
Axis concept is useful for inspection purposes. Boundary concept explains how mating of various parts takes place.
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82. Boundary Concept Used for Elongated Holes.
The “Boundary” note, below feature control frame, clarifies the fact that this a specific type of positional requirement that is not to be assessed for compliance other than whether the controlled feature surface violates the boundary generated by MMC of the contour minus the geometric positional tolerance.
The surface of this internal contour (hole) must lie outside of the boundary generated.
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83. Composite Positional Tolerance vs. Two Single Segment ControlsB C
Ø 0.5 (M)
Ø 2 (M) A B C
Ø 0.5 (M)
Composite Positional Tolerance
Two Single Segment Positional Tolerance
The essential element of holding the positional relationship between the features within a pattern is kept by both.
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84. Composite Positional Tolerance vs. Two Single Segment Controls
The smaller tolerance between the two levels of control is the one that refines the positional tolerance with respect to each other (hole to hole tolerance for example).
If no datums are included in in the lower level control or if the only datum included happens to be the primary datum used in upper level control and that datum is used to control is for perpendicularity, then there is no difference.
However, If datums are used in the lower level control for location control that is used in the upper level control or is used in a different order, or datum not not used at all in the upper level control is used, the meaning becomes different.
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85. Composite Positional Tolerance vs. Two Single Segment Controls
In composite positional Tolerance:
Upper Level - Pattern locating tolerance zone framework : PLTZF Lower level - Feature relating tolerance zone framework : FRTZF
Tolerances in FRTZF (lower level) refine the tolerances in PLTZF (upper level).
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86. Concentricity
Concentricity tolerance is indicated by the concentricity symbol, a tolerance value and an appropriate datum reference placed in a feature control frame.
Concentricity: The condition where the axis of a cylinder, cone, square, hexagonal etc. are common to the axis of a datum feature.
Concentricity Tolerance : Total amount of allowable variation of a feature-of- size axis to a datum axis. This is a cylindrical tolerance zone whose axis is coincident with the datum axis, within which the axis of the considered feature-of-size must lie.
A concentricity tolerance zone and its datum reference can only be on RFS basis. The size tolerance of a feature-of-size is independent of the concentricity tolerance.
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87. Runout controls consist of Circular runout and Total runout.
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88. General Information
Following information applies to both Circular and Total runout controls. (See Symbols)
Runout is a composite control affecting both the form and location of a part feature relative to a datum axis.
Whenever a runout control is specified, a datum reference is required.
Terms like FIM (Full Indicator Movement), TIR (Total Indicator Reading) and TIM ( Total Indicator Movement) all mean runout tolerances.
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89. General Information
A runout tolerance can be applied to any diameter shape that is around the datum axis, or to a surface that is perpendicular to the datum axis. Examples:
diameter around the datum axis,
a conical surface around the datum axis.
Or a surface perpendicular to the datum axis.
A runout tolerance value specified in a feature control indicates the maximum permissible indicator reading of the considered feature when the part is rotated 360 degrees about its datum axis.
The most common application is the location of coaxial features relative to a datum axis. Less common are indirect benefits viz. controlling circularity, wobble, angularity and perpendicularity.
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90. Circular Runout
Circular Runout is a composite control affecting both the form and location of circular elements of a part feature. It is composite as affects both form and location simultaneously.
Circular runout is frequently used to control the location of a circular elements of a diameter.
When applied to diameter, it controls both circularity and coaxiality of the diameter to the datum axis.
When applied to a surface 90 degrees to a datum axis, it controls the attitude (orientation) of the circular elements.
Circular runout applies each circular element of a surface independent from one another.
Tolerance zone of the circular runout is easily visualized. It can be thought of as two coaxial circles whose centres on the datum axis.
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91. Total Runout
Total Runout is a composite control affecting the form and location of ALL surface elements simultaneously.
When total runout is applied to a surface around a datum axis ( such as a diameter or a cone), it controls cumulative variation of :
Circularity
Straightness
Location
Angularity
Taper
Profile of a surface.
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92. Total Runout
When a total runout is applied to a diameter, the tolerance zone is easily visualized. It consists of two coaxial cylinders whose centres are located on the datum axis.
The radial distance between these cylinders is equal to the runout tolerance value. The size of the larger cylinder is determined by the radius of the surface element which is farthest from the datum axis. (See Figure 6-9). Note: The diameter must meet its size requirement.
When a total runout is applied to a surface that is 90 degrees to the datum axis, it controls variation of:
Perpendicularity
Flatness
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93. Profile Controls
A lack of understanding of profile controls has resulted in their limited use.
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94. General Information
There are two types of profile control: profile of a line and profile of a surface. The symbols are at figure 7-1.
Profile controls can be used to limit the
Size, Form or Orientation of a part feature.
The outline of an object in a given plane is referred to as its profile.
A true profile is the exact profile of a geometric shape as described by basic dimensions.
A profile tolerance specifies a uniform boundary along the true profile within which all the elements of the considered surface element or elements must lie.
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95. General Information
Profile tolerance can be applied to all surface elements simultaneously (as in the profile of a surface) or to individual surface elements (as in profile of a line) taken at various cross sections through the part.
Profile control are unique because they are the only geometric tolerance which can be used as a form control (without a datum) or as related feature tolerance (with a datum).
REMEMBER
Profile tolerance can be used as a form control or a datum related tolerance.
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96. General Information ADVANTAGES OF PROFILE TOLERANCES
Clear definition of the tolerance zone
Communicates datums and datum sequence (in feature related tolerance).
Eliminates accumulation of tolerances.
A profile tolerance can be applied to any type of part feature (that is surface, irregular shape, cylindrical etc.), but the true profile of the feature must be defined with basic dimensions.
Profile controls can specified either unilaterally (when shown as such by dotted lines) or bilaterally (when no dotted lines are shown on the drawing.
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97. Profile of a Surface
When a profile of a surface is specified, the tolerance zone is three dimensional. It extends along the entire length, width, and depth of the toleranced feature simultaneously.
The toleranced zone is two parallel boundaries; offset from the true profile by a specified amount.
The following rules apply
Profile (of a surface) control applies RFS.
Bonus tolerance concepts are not applicable.
Shape of tolerance zone is two parallel boundaries offset an equal distance (above or below) from the true profile.
Profile control limits the size of the part as well as the orientation and form of the toleranced feature..
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98. Composite Profile vs. Two Single Segment Profile Controls
0.5 A B C
0.25
0.5 A B C
0.25
Even in the above case, when primary datum A appears in lower level control, the meaning remains the same with respect to each other. The addition of datum A in each lower level control simply means that the job of refining the perpendicularity tolerance of the line elements of the oddly configured profile now falls to the lower level control.
Since the tolerance in the lower level of each control is smaller, it is the one that more closely controls the size limitation and the size/ form/ profile tolerance. Since datums B and C have not been brought down into lower level control (with tighter tolerance), the relationship to B and C is controlled by the upper level control that include B and C (with looser tolerance)
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99. Composite Profile vs. Two Single Segment Profile Controls
0.5 A B C
0.25
0.5 A B C
0.25
In the example above, the differences in meanings arise when the datums used for location (B and C) in the upper level control are brought into lower level as shown.
In the feature control frame on the left, the datums have to be in the same order as in the upper level, whereas in two segment the refinement of the oddly configured profile is permitted to be refined by datums in the same order as the upper level or in a different order.
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100. Composite Profile vs. Two Single Segment Profile Controls
0.5 A B C
0.25
0.5 A B C
0.25 D E
In addition to the versatility of being able to use the same datums in different order, the lower level control in two segment profile, tolerances may use entirely different datums than the upper level control.
At any rate the datums used in lower level control for two segment profile retain their full implications and are not limited to angular tolerance refinement.
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101. Composite Profile vs. Two Single Segment Profile Controls
0.5 A B C
0.25
In the example shown, the upper level control creates a stationary, total wide, all around tolerance zone that controls the movement of the controlled feature surface. The surface of the controlled feature must reside within the 0.5 tolerance zone located as shown by the basic dimensions from datums B and C and perpendicular to datum plane A.
The smaller lower level, total-wide, all around tolerance zone of 0.25 may float in its location to datum B and C but must maintain its perpendicularity to datum A and its location to datum B. The actual surface of the controlled feature must reside within both 0.5 and the refining 0.25 tolerance zone.
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102. Composite Profile vs. Two Single Segment Profile Controls
If, on the other hand, there were two separate segments, as shown now, the upper level control would create 0.5 tolerance zone located by datums Band C and perpendicular to datum A.
The smaller lower level, would create a tolerance zone 0.25 wide , but it can float only in relation to datum C only, I.e. location with respect to datum B and perpendicularity with respect to datum A are decided by the lower level segment. float only in relation to datum C only, I.e. location with respect to datum B and
0.5 A B C
0.25
perpendicularity with respect to datum A are decided by the lower level segment.
This a more restrictive control than the composite control. See Figure 5-40.
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103. Profile of a Line
When a profile of a line control is specified, it limits the boundaries of individual line elements of a surface.
The tolerance zone is two dimensional. It extends for the entire length of the true profile.The tolerance zone is two parallel lines, offset from the true profile by the specified amount.
The following rules apply
Basic dimensions are used to define the true profile.
Profile control applies RFS.
The shape of the tolerance zone is two parallel boundaries (line elements) offset an equal distance above and below the true profile.
The profile control limits the orientation and form of the toleranced feature.
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104. SUMMARY We have discussed today:
What is Geometric Dimensioning & Tolerancing, its advantages.
GD&T for two dimensional drawing:
Why datums? How decided? How determined?
Positional Tolerance – advantages
Maximum Material Condition (MMC) – Bonus Tolerance
Regardless of Feature Size (RFS) and Least Material Condition (LMC).
Virtual Condition
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105. SUMMARY
ASME Y14.5M-2000 Rules
Other Geometric Dimensioning Symbols and their meanings
As mentioned in the beginning, this was an introductory course. I hope you have benefited and are now eager to learn more.
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106. Thank You
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