Machinery's Handbook, 31st Edition
Involute Splines
2345
30 25 20 15 10
A B Aircraft flexible or single-key commercial Single-key, high-capacity C High-capacity fixed
7.0 5.0 3.0 2.0 1.5 1.0 0.7 0.5 0.3
D E
Aircraft fixed Limit of spline design (65,000-psi solid shaft)
100
1,000
10,000
100,000
1,000,000
Torque, lb-inches
Fig. 3. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships Curve B represents high-capacity single keys used as fixed couplings for stresses of 9500 pounds per square inch, neglecting stress concentration. Key-length is one to one and one-quarter times shaft diameter and both shaft and key are of moderately hard heat-treated steel. This type of connection is commonly used to key commercial flexible couplings to motor or generator shafts. Curve C is for multiple-key fixed splines with lengths of three-quarters to one and one- quarter times pitch diameter and shaft hardness of 200–300 BHN. Curve D is for high-capacity splines with lengths one-half to one times the pitch diame ter. Hardnesses up to 58 RC (Rockwell C scale) are common and in aircraft applications the shaft is generally hollow to reduce weight. Curve E represents a solid shaft with 65,000 pounds per square inch shear stress. For hollow shafts with inside diameter equal to three-quarters of the outside diameter the shear stress would be 95,000 pounds per square inch. Length of Splines: Fixed splines with lengths of one-third the pitch diameter will have the same shear strength as the shaft, assuming uniform loading of the teeth; however, errors in spacing of teeth result in only half the teeth being fully loaded. Therefore, for balanced strength of teeth and shaft the length should be two-thirds the pitch diameter. If weight is not important, however, this may be increased to equal the pitch diameter. In the case of flexible splines, long lengths do not contribute to load carrying capacity when there is misalignment to be accommodated. Maximum effective length for flexible splines may be approximated from Fig. 4. Formulas for Torque Capacity of Involute Splines.— The formulas for torque capacity of 30-degree involute splines given in the following paragraphs are derived largely from an article “When Splines Need Stress Control” by D. W. Dudley, Product Engineering , Dec. 23, 1957.
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