Machinery's Handbook, 31st Edition
2348 Involute Splines Shear Stress at the Pitch Diameter of Teeth: The shear stress at the pitch line of the teeth for a transmitted torque T is: (3) The factor of 4 in (3) assumes that only half the teeth will carry the load because of spac ing errors. For poor manufacturing accuracies, change the factor to 6. The computed stress should not exceed the values in Table 11. Compressive Stresses on Sides of Spline Teeth: Allowable compressive stresses on splines are very much lower than for gear teeth since non-uniform load distribution and misalignment result in unequal load sharing and end loading of the teeth. (4) (5) In these formulas, h is the depth of engagement of the teeth, which for flat root splines is 0.9/ P and for fillet root splines is 1/ P , approximately. The stresses computed from Formulas (4) and (5) should not exceed the values in Table 11. = , S DNL hK TK K 9 2 Bursting Stresses on Splines: Internal splines may burst due to three kinds of tensile stress: 1) tensile stress due to the radial component of the transmitted load; 2) centrifugal tensile stress; and 3) tensile stress due to the tangential force at the pitch line causing bend- ing of the teeth. (6) where t w = wall thickness of internal spline = outside diameter of spline sleeve minus spline major diameter, all divided by 2. L = full length of spline. (7) where D oi = outside diameter of spline sleeve. (8) In Equation (8), Y is the Lewis form factor obtained from a tooth layout. For internal splines of 30-deg. pressure angle a value of Y = 1.5 is a satisfactory estimate. The factor 4 in (8) assumes that only half the teeth are carrying the load. The total tensile stress tending to burst the rim of the external member is: S t = [ K a K m ( S 1 + S 3 ) + S 2 ]/ K f ; and should be less than those in Table 11. , S D L Y T 4 Beam loading tensile stress e 3 2 = Crowned Splines for Large Misalignments.— As mentioned on page 2347 , crowned splines can accommodate misalignments of up to about 5 degrees. Crowned splines have considerably less capacity than straight splines of the same size if both are operating with precise alignment. However, when large misalignments exist, the crowned spline has greater capacity. American Standard tooth forms may be used for crowned external members so that they may be mated with straight internal members of Standard form. S DNL tK TK K 4 s e f a m = , S DNL hK TK K 2 e w m a For flexiblesplines c For fixed splines c e f m a = , tan S Dt L T Radial load tensile stress w 1 π φ = , Centrifugal tensile stress . 1656 . 0212 S D 2 2 oi D 1,000,000 rpm ri 2 2 # = + ^ h ^ h
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