Spline stress calculation. Tables I-VII.
Based on article: “When Splines Need Stress Control” by Darle W. Dudley.
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Table I. Allowable Shear Stress for Splines.
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Material |
Hardness |
Max Allowable Shear Stress, Ss (PSI) |
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Brinell |
Rockwell C |
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Steel |
160 - 200 |
- |
20,000 |
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Steel |
230 – 260 |
- |
30,000 |
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Steel |
302 - 351 |
33 - 38 |
40,000 |
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Surface - hardened steel |
- |
48 - 53 |
40,000 |
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Case - hardened steel |
- |
58 - 63 |
50,000 |
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Aerospace thru – hardened steel. |
- |
42 - 46 |
45,000 |
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Table II. Spline Application Factors, Ka.
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Power source |
Type of load |
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Uniform (generator, fan) |
Light Shock (oscillating pump) |
Intermittent Shock (actuating pump) |
Heavy Shock (punchers, shears) |
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Uniform (turbine, motor) |
1.0 |
1.2 |
1.5 |
1.8 |
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Light shock (hydraulic motor) |
1.2 |
1.3 |
1.8 |
2.1 |
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Medium shock (internal combustion engine) |
2.0 |
2.2 |
2.4 |
2.8 |
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Table III. Fatigue – Life Factor for Splines.
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Number of torque cycles. (number of ON/OFF cycles) |
Life Factor, Lf |
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Unidirectional |
Fully - reversed |
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1,000 |
1.8 |
1.8 |
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10,000 |
1.0 |
1.0 |
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100,000 |
0.5 |
0.4 |
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1,000,000 |
0.4 |
0.3 |
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10,000,000 |
0.3 |
0.2 |
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Table IV. Load Distribution Factor for Splines.
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Misalignment |
Factor, Km |
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½-in. Face Width. |
1-in. Face Width. |
2-in. Face Width. |
4-in. Face Width. |
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0.001 in. / in. |
1 |
1 |
1 |
1 ½ |
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0.002 in. / in. |
1 |
1 |
1 ½ |
2 |
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0.004 in. / in. |
1 |
1 ½ |
2 |
2 ½ |
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0.008 in. / in. |
1 ½ |
2 |
2 ½ |
3 |
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Table V. Allowable Compressive Stress for Splines.
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Material |
Hardness |
Max Allowable Compressive Stress, Sc, (PSI) |
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Brinell |
Rockwell C |
Straight |
Crowned |
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Steel |
160 – 200 |
- |
1,500 |
6,000 |
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Steel |
230 – 260 |
- |
2,000 |
8,000 |
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Steel |
302 – 351 |
33 – 38 |
3,000 |
12,000 |
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Surface - hardened steel |
- |
48 – 53 |
4,000 |
16,000 |
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Case - hardened steel |
- |
58 – 63 |
5,000 |
20,000 |
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Table VI. Wear Life of Flexible Splines.
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No. of Revolutions. |
Life Factor, Lw. |
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10,000 |
4.0 |
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100,000 |
2.8 |
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1 million |
2.0 |
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10 million |
1.4 |
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100 million |
1.0 |
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1 billion |
0.7 |
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10 billion |
0.5 |
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Table VII. Allowable Tensile Stress for Splines
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Material |
Hardness |
Max Allowable Stress St, (PSI) |
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Brinell |
Rockwell C |
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Steel |
160 – 200 |
- |
22,000 |
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Steel |
230 – 260 |
- |
32,000 |
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Steel |
302 – 351 |
33 – 38 |
45,000 |
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Surface – hardened steel |
- |
48 – 53 |
45,000 |
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Case – hardened steel |
- |
58 – 63 |
55,000 |
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Thru – hardened steel |
- |
42 – 46 |
50,000 |