1. Embodiment Design: Dimensions and Tolerances
Chapter 8, Section 8.7
Part III
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

2. Dimensions
Dimensions are used on engineering drawing to specify size, location, and orientation of features of components.
Dimensions are as important as the geometric information that is conveyed by the drawing.
Each drawing must contain the following information:
The size of each feature
The relative position between features
The required precision(tolerance) of sizing and positioning features
The type of material, and how it should be processed to obtain its expected mechanical properties.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

3. Definition of Tolerance
Total amount a dimension may vary. It is the difference between the maximum and minimum limits.
There is no such thing as an “exact size”.
Tolerance is key to interchangeable parts.
A tolerances is the acceptable variation in the dimension.
Tolerances must be placed on a dimension or geometric feature of a part to limit the permissible variations in size because it is impossible to repeatedly manufacture a part exactly to a given dimension.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

4. Ways to Express Tolerances
Direct limits or as tolerance limits applied to a dimension.
Geometric tolerances.
Notes referring to specific conditions.
A general tolerance note in title block.
Tight Tolerance
Greater ease of interchangeability of parts
Less play or chance of vibration
Increased cost of manufacture
Loose
Tolerance
Poorer system performance
Easier to assemble components
Reduced cost of manufacture
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

5. Proper Way of Dimensioning
Proper way to give dimensions for size and features
Proper way to give dimensions for location and orientation of features
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

6. Use of Section View
Courtesy of Professor Guangming Zhang, University of Maryland.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

7. Eliminating of Redundant Dimension
Courtesy of Professor Guangming Zhang, University of Maryland.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

8. Expressing Tolerances
Bilateral tolerance:
Balanced bilateral tolerance: 2.500±0.005
Unbalanced bilateral tolerance: −
Unilateral tolerance:
Variation is in only one direction:
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

9. Quality Control Chart
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

10. Issues with Parametric Design
There are generally TWO classes of issues in parametric design associated with tolerances on parts when they must be assembled together:
Fit: How closely the tolerances should be held when two components fit together in an assembly.
Stackup: The situation where several parts must be assembled together and interference occurs because the tolerances of the individual parts overlap.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

11. Fit Clearance fits: Interference fits: Transition fits:
Both the maximum and minimum clearances are positive.
ANSI has established nine classes of clearance fits form RC1 to RC9.
Interference fits:
The shaft diameter is always larger than the hole diameter, so that both the maximum and minimum clearance are negative.
ANSI has established five classes of interference fits from FN1 to FN5.
Transition fits:
The maximum clearance is positive and the minimum clearance is negative.
ANSI has established three classes of transition fits: LC, LT, LN.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

12. Bearing and Shaft Assembly
Maximum clearance = Amax - Bmin = – = 0.07mm
Minimum clearance = Amin - Bmax = – = 0.2mm
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

13. Stackup
Tolerance stackup occurs when two or more parts must be assembled in contact.
Stackup occurs from the cumulative effects of multiple tolerances.
A stackup analysis typically is used to properly tolerance a dimension that has not been given a tolerance or to find the limits on a clearance (or interference) gap.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

14. Finding Tolerance Stack Up
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15. Worst-Case Tolerance Design
In the worst-case tolerance design scenario the assumption is made that the dimension of each component is at either its maximum or minimum limit of the tolerance.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

16. Determination of Basic Gap Dimension and Its Tolerance
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

17. Statistical Tolerance Design
An important method used to determine assembly tolerances is based on statistical interchangeability.
The method is based on the following additional assumptions:
The manufacturing process for making the components is in control, with no parts going outside of the statistical control limits.
The dimensions of the components produced by the manufacturing process follow a normal or Gaussian frequency distribution.
The components are randomly selected for the assembly process.
The product manufacturing system must be able to accept that a small percentage of parts produced will not be able to be easily assembled into the product.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

18. Process Capability Index ( 𝐶 𝑝 )
The process capability index, ( 𝐶 𝑝 ), is commonly used to express the relationship between the tolerance range specified for the component and the variability(standard deviation) of the process that will make it.
𝐶 𝑝 = 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑠𝑝𝑟𝑒𝑎𝑑 𝑎𝑐𝑡𝑢𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑠𝑝𝑟𝑒𝑎𝑑 = 𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 3𝜎+3𝜎 = 𝑈𝑆𝐿−𝐿𝑆𝐿 6𝜎
The relationship between the standard deviation of a dimension in an assembly of components and the standard deviation of the dimensions in separate components is:
𝜎 𝑎𝑠𝑠𝑒𝑚𝑏𝑙𝑦 2 = 𝑖=1 𝑛 𝜎 𝑖 2
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

19. Determination of Gap and Its Tolerance Using Statistical Method
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20. Determination of Variation Contribution of Each Part in Assembly
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21. Normal Distribution 𝑧= 𝑥−𝜇 𝜎
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22. Advanced Tolerance Analysis
When many dimensions are involved, and the mechanism is definitely three-dimensional, a system of tolerance charts has been developed.
For tolerance analysis on three-dimensional problems, specialized computer programs are almost mandatory.
Some of these are standalone software applications, but most major CAD systems have backages to perform tolerance analysis.
They also typically support the Geometric Dimensioning and Tolerancing (GD&T) system.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

23. Geometric Dimensioning and Tolerancing
In engineering practice this and many other tolerance issues are described and specified by a system of Geometric Dimensioning and Tolerancing (GD&T) based on ASME standard Y14.5–2009.
GD&T is a universal design language to precisely convey design intent. (Refer to Figure 8.25)
Two important pieces of information in an engineering drawing brought by GD&T:
it clearly defines the datum surfaces from which dimensions are measured
it specifies a tolerance zone that must contain all points of a geometric feature
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

24. Datum
Datums are theoretically perfect points, lines, and planes that establish the origin from which the location of geometric features of a part is determined.
A part has six degrees of freedom in space.
Depending on the complexity of the part shape there may be up to three datums.
The primary datum, A, is usually a flat surface that predominates in the attachment of the part with other parts in the assembly.
One of the other datums, B or C, must be perpendicular to the primary datum.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

25. Datum Feature Identifiers
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26. Geometric Tolerances
Geometric tolerances can be defined for the following characteristics of geometric features:
Form:
Flatness, straightness, circularity, cylindricity
Profile:
Line, surface
Orientation:
Parallelism, angularity
Location:
Position, concentricity
Runout:
Circular runout, total runout
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

27. Material Condition Modifiers
Maximum material condition (MMC) is the condition in which an external feature like a shaft is at its largest allowable by the size tolerance.
Least material condition (LMC) is the opposite of MMC, that is, a shaft that is its smallest allowed by the size tolerance or a hole at its largest allowable size.
Regardless of feature size (RFS) means that the tolerance zone is the same no matter what the size of the feature.
BONUS TOELRANCE: The increase in the tolerance zone with size of the feature is usually called a bonus tolerance because it allows extra flexibility in manufacturing.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies

28. Guidelines for Tolerance Design
Focus on the critical-to-quality dimensions that most affect fit and function.
For the noncritical dimensions, use a commercial tolerance recommended for the production process of the components.
A possible alternative for handling a difficult tolerance problem might be to redesign a component to move it to the noncritical classification.
A difficult problem with tolerance stackup often indicates that the design is over constrained to cause undesirable interactions between the assembled components.
If tolerance stackup cannot be avoided, it often is possible to minimize its impact by careful design of assembly fixtures.
Another approach is to use selective assembly where critical components are sorted into narrow dimensional ranges before assembling mating components.
Make sure that you have the agreement from manufacturing that the product is receiving components from a well-controlled process with the appropriate level of process capability.
Consider carefully the establishment of the datum surfaces.
Dieter/Schmidt, Engineering Design 5e. ©2013. The McGraw-Hill Companies