shaft_torsion.xls

Spreadsheet to help design shafts in torsion

Written 10/9/2002 by Alex Slocum

Large diameter, D 14

Small diameter, d 8

Motor Power (W) 20

Motor speed (rpm, rad/sec) 100 10.47 With radius between diameters

Shaft torque (N-m) 1.910 radius r (mm) Kt

Major shaft diameter 14 0.1 2.29

transition radius (mm) 0.5 0.2 1.82

Fillet stress concentration factor, Kt 1.45 0.3 1.63

Undercut stress concentration factor, Kt 1.52 0.4 1.52

Shaft length (mm) 50 0.5 1.45

Shaft modulus, E (GPa) 2.00E+11 0.6 1.40

Shaft Poisson ratio 0.29 0.7 1.36

Shear modulus, G (GPa) 7.75E+10 0.8 1.33

Polar I at fillet shaft diameter (mm^4) 402 0.9 1.31

Polar I at undercut shaft diameter (mm^4) 236 1 1.29

Fillet design torsion stress (MPa) 27.6

Undercut design torsion stress (MPa) 43.0

Shaft twist along minor diameter (deg, rad) 0.18 3.06E-03

Hole d (mm) Kt

1 3.47

2 3.16

3 2.99

4 2.88

5 2.80

6 2.74

shaft_torsion.xls Radius transition or undercut between diameters? D

Dd

With radius between diameters With radius undercut between diameters

Shaft min d Kt

22.8 7.80 2.02 21.67

18.1 7.60 1.76 20.40

16.2 7.40 1.64 20.59

15.2 7.20 1.57 21.37

14.4 7.00 1.52 22.52

13.9 6.80 1.48 23.98

13.6 6.60 1.45 25.73

13.3 6.40 1.43 27.78

13.0 6.20 1.41 30.16

12.8 6.00 1.40 32.91

radius r (mm) Kt

6.86 1.5 1.50 2.78

6.67

6.79

7.06

7.46

7.98

Stress (Mpa) t/G Stress (Mpa) t/G

Stress (Mpa) t/G Stress (Mpa) t/G

dr

Dr

d

d r

DCorner rWidth bDepth t

B=D/4, t=D/8