TOLERANCE ANALYSIS AND ASSIGNMENT Tolerance Analysis and Assignment Machinery's Handbook, 31st Edition
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All parts are produced with some amount of variation, or difference, between the intended geometry and features of the part produced. While variation is unavoidable and expected, the challenge is determining an acceptable amount. The amount and type of variation is called tolerance . Part feature tolerances are not assigned arbitrarily, but rather are specified by designers with good understanding of manufacturing process capabilities, cost limita- tions, and assembly and functional requirements. Good design allows for the broadest toler- ances possible that meet all requirements, resulting in parts that are easier and less costly to produce. Overly restrictive tolerances limit manufacturers to unnecessarily precise meth- ods, driving up costs, which can be impacted dramatically by small differences in tolerances. Tolerance analysis and tolerance assignment are bottom-up and top-down approaches, respectively, to calculating tolerances, and typically they are used in iterative fashion. Tolerance assignment is done at the design stage, to meet assembly and functional re- quirements. Tolerance analysis is performed later, on preliminary or final part tolerances, to detect any needed design improvements and changes in tolerance assignments. Pre- dicting the results of variations may be an end in itself, but more often, the goal is to select the best tolerances throughout an assembly to meet design requirements. The Tolerance Stack-Up Chain.— Tolerance stack-up calculations analyze the effects that tolerances have on function and guide tolerance assignment. A tolerance stack-up chain diagram is created first to clearly identify the assembly dimension to be solved and each part dimension contributing to the stack-up, as is shown in Fig. 5.
Standard Deviation (σ) (from mfg. data)
G
Mean (μ) (from mfg. data)
A
F
Dim Max Min
0.376 0.375 0.375464 0.000106 0.5906 0.5858 0.588126 0.001004 1.751 1.749 1.750128 0.000203 0.1875 0.1825 0.185147 0.000874 1.755 1.745 1.750748 0.001200
B C D E F G
E
B
D
C
0.9395 0.9355 0.937331 0.000517 Fig. 5. Tolerance Stack-Up Chain Diagram, Related Specifications, and Dimension Data From the diagram, a tolerance stack-up equation is derived. In dimension labeling, a sign convention denotes direction: positive for up or right; negative for down or left. The assem - bly dimension can then be solved, as in the following example, written in general form: (1) Clear, unambiguous part definition, as provided by geometric dimensioning and toler - ancing, is required for accurate tolerance analysis. Care must be taken to ensure the effects of geometric variation are included in dimensions expressed numerically. Any sources of variation allowed by referenced drawings must be included in the stack-up equation. Tolerance Analysis Calculation Methods.— For solving analysis or assignment prob- lems, four methods of tolerance stack-up calculation are common. Worst-Case: During analysis, the worst-case method predicts the largest variation in the assembly dimension and requires the smallest tolerances be assigned. Worst-case calculations are appropriate when every feature is inspected to screen from use any out-of-specification parts, and/or when there are few (approximately seven or fewer) di - mensions in the chain. Benefits of this analytical method are its simplicity and speed. A tolerance stack-up calculation is performed twice, resulting in the maximum value on the first pass and the minimum value on the second pass. Thus, the general stack-up equation is expressed as two separate equations, with each dimension represented by its maximum and minimum values. The default is to put maximum values on the first line and minimum on the second; this is reversed for contributing dimensions with negative signs. A = – B – C – D + E + F + G
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