PRODUCT DESIGN: Dimensions and Tolerances

The following terms are used generally in dimensioning:

• Nominal size.

The size we use in speaking of an element. For example, we may specify a 1 1/2 -in pipe or a 1/2 -in bolt. Either the theoretical size or the actual measured size may be quite different. The theoretical size of a 1 1/2 -in pipe is 1.900 in for the outside diameter. And the diameter of the 1/2 -in bolt, say, may actually measure 0.492 in.

• Limits.

The stated maximum and minimum dimensions.

• Tolerance.

The difference between the two limits.

• Bilateral tolerance.

The variation in both directions from the basic dimension. That

is, the basic size is between the two limits, for example, 1.005 ± 0.002 in. The two

parts of the tolerance need not be equal.

• Unilateral tolerance.

The basic dimension is taken as one of the limits, and variation is permitted in only one direction, for example,

• Clearance.

A general term that refers to the mating of cylindrical parts such as a bolt and a hole. The word clearance is used only when the internal member is smaller than the external member. The diametral clearance is the measured difference in the two diameters. The radial clearance is the difference in the two radii.

• Interference.

The opposite of clearance, for mating cylindrical parts in which the internal member is larger than the external member.

• Allowance.

The minimum stated clearance or the maximum stated interference for mating parts.

When several parts are assembled, the gap (or interference) depends on the dimensions and tolerances of the individual parts.

The previous example represented an absolute tolerance system. Statistically, gap

dimensions near the gap limits are rare events. Using a statistical tolerance system, the probability that the gap falls within a given limit is determined.10 This probability deals with the statistical distributions of the individual dimensions. For example, if the distributions of the dimensions in the previous example were normal and the tolerances, t, were given in terms of standard deviations of the dimension distribution, the standard deviation of the gap w¯ would be

However, this assumes a normal distribution for the individual dimensions, a rare occurrence. To find the distribution of w and/or the probability of observing values of w within certain limits requires a computer simulation in most cases. Monte Carlo computer simulations are used to determine the distribution of w by the following approach:

1 Generate an instance for each dimension in the problem by selecting the value of

each dimension based on its probability distribution.

2 Calculate w using the values of the dimensions obtained in step 1.

3 Repeat steps 1 and 2 N times to generate the distribution of w. As the number of

trials increases, the reliability of the distribution increases.