Machinery's Handbook, 31st Edition
Involute Splines
2347
Table 9. Fatigue-Life Factors, K f , for Splines
Fatigue-Life Factor, K f
No. of Torque Cycles a
Unidirectional
Fully-reversed
1,000 10,000 100,000 1,000,000
1.8 1.0 0.5 0.4 0.3
1.8 1.0 0.4 0.3
10,000,000 0.2 a A torque cycle consists of one start and one stop, not the number of revolutions. Table 10. Wear Life Factors, K w , for Flexible Splines Number of Revolutions of Spline Life Factor, K w Number of Revolutions of Spline Life Factor, K w 10,000 4.0 100,000,000 1.0 100,000 2.8 1,000,000,000 0.7 1,000,000 2.0 10,000,000,000 0.5 10,000,000 1.4 … … Wear life factors, unlike fatigue life factors given in Table 9, are based on the total number of rev olutions of the spline, since each revolution of a flexible spline results in a complete cycle of rocking motion which contributes to spline wear. Definitions: A fixed spline is one which is either shrink fitted or loosely fitted but piloted with rings at each end to prevent rocking of the spline which results in small axial move ments that cause wear. A flexible spline permits some rocking motion such as occurs when the shafts are not perfectly aligned. This flexing or rocking motion causes axial movement and consequently wear of the teeth. Straight-toothed flexible splines can accommodate only small angular misalignments (less than 1 deg.) before wear becomes a serious prob lem. For greater amounts of misalignment (up to about 5 deg.), crowned splines are prefer able to reduce wear and end-loading of the teeth. Shear Stress Under Roots of External Teeth: For a transmitted torque T , the torsional shear stress induced in the shaft under the root diameter of an external spline is: (1) S D K TK 16 re f a s 3 π = for a solid shaft
D D K TD K 16 re h f re a 4 4 − h
π =
for a hollow shaft
S
(2)
s
^
The computed stress should not exceed the values in Table 11. Table 11. Allowable Shear, Compressive, and Tensile Stresses for Splines
Max. Allowable Stress
Hardness
Compressive Stress, psi Tensile Stress, psi Straight Crowned
Shear Stress, psi
Material
Brinell 160-200 230-260 302-351
Rockwell C
22,000 32,000 45,000 45,000 55,000 50,000
— 20,000 — 30,000
1,500 2,000 3,000 4,000 5,000
6,000 8,000 12,000 16,000 20,000
Steel
33-38
40,000 40,000 50,000 45,000
Surface-hardened Steel Case-hardened Steel Through-hardened Steel (Aircraft Quality)
— 48-53 — 58-63 — 42-46
— —
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