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Shafts and Shaft Components 395
Failure by shear across the area ab will create a stress of τ = F/tl. Substituting the
strength divided by the factor of safety for τ gives

S sy F 37.5(10) 3 5850
= or =
n tl 2.80 0.375l
or l = 1.16 in. To resist crushing, the area of one-half the face of the key is used:

S y F 65(10) 3 5850
= or =
n tl/2 2.80 0.375l/2
and l = 1.34 in. The hub length of a gear is usually greater than the shaft diameter, for
stability. If the key, in this example, is made equal in length to the hub, it would there-
fore have ample strength, since it would probably be 1 7 in or longer.
16

7–8 Limits and Fits

The designer is free to adopt any geometry of fit for shafts and holes that will ensure the
intended function. There is sufficient accumulated experience with commonly recurring
situations to make standards useful. There are two standards for limits and fits in the
10
United States, one based on inch units and the other based on metric units. These differ
in nomenclature, definitions, and organization. No point would be served by separately
studying each of the two systems. The metric version is the newer of the two and is well
organized, and so here we present only the metric version but include a set of inch con-
versions to enable the same system to be used with either system of units.
In using the standard, capital letters always refer to the hole; lowercase letters are
used for the shaft.
The definitions illustrated in Fig. 7–20 are explained as follows:
• Basic size is the size to which limits or deviations are assigned and is the same for
both members of the fit.
• Deviation is the algebraic difference between a size and the corresponding basic size.
• Upper deviation is the algebraic difference between the maximum limit and the
corresponding basic size.
• Lower deviation is the algebraic difference between the minimum limit and the
corresponding basic size.
• Fundamental deviation is either the upper or the lower deviation, depending on
which is closer to the basic size.
• Tolerance is the difference between the maximum and minimum size limits of a part.
• International tolerance grade numbers (IT) designate groups of tolerances such that
the tolerances for a particular IT number have the same relative level of accuracy but
vary depending on the basic size.
• Hole basis represents a system of fits corresponding to a basic hole size. The funda-
mental deviation is H.

10 Preferred Limits and Fits for Cylindrical Parts, ANSI B4.1-1967. Preferred Metric Limits and Fits, ANSI
B4.2-1978.