1. High Speed Tapered Roller Bearing Optimization
Brady Walker
3/11/08

2. Background
The intent of this project is to determine the optimal cup, cone and rib angle for various speeds.
Historically, tapered roller bearings have not been used for high speed applications however they have shown promise if designed properly.

3. Approach Determine Force Balance/Internal Loading
Determine Cage Speed & Centrifugal Loading
Determine Contact Stress for line contact
Determine Contact Stress for point contact
Write program to analyze tapered bearing with varying geometry
Results/Conclusion

4. Force Balance/Internal Loading

5. Cage Speed and Centrifugal Loading
Centrifugal Loading is derived from:
Cage Speed is derived from:

6. Contact Stress for Line Contact

7. Contact Stress for Point Contact

8. Contact Stress for Point Contact
90-af
D1/2
df/2
rII2 h af L2

9. FORTRAN CODE COMPLETE Program Output theta= 1.57079637050629
v= E-002
L2=
d3a=
phia= E-003
h= E-002
d3=
Dmean=
omega=
Fc=
Qi=
Qo=
Qf=
rI1=
rI2=
rII2=
rhoI E-002
rhoI E-002
rhoII E+000
rhoII E-002
rhosum E-002
Program Input
ENTER CUP ANGLE (DEG) 15
d1= r=
dm=
lt=
leff= z=
ENTER SHAFT SPEED (RPM)
8000
speed=
Thrust=
Rx=
Ry=
astar=
bstar= a=
b= E-002
Qf=
max sigma=
delta= E-004
max subsurface shear=
depth to max shear= E-002
Qimax
Qomax=

10. Hertzian Contact Stress Profile for Rib- Roller End Contact
Results
An example bearing was analyzed with the FORTRAN program and the Hertzian contact stress for the cup, cone and rib were determined:
s (psi)
_____ Cone Contact Stress
_____ Cup Contact Stress
x (in)
y (in)
s (psi)
y (in)
Hertzian Contact Stress Profile for Cup and Cone
Hertzian Contact Stress Profile for Rib- Roller End Contact

11. Results
Optimum cup angles were determined based on bearing speeds (DN).
DN (million)
Cup Angle (deg)
0.25 40
0.50
0.75 30
1.00 25
1.50 20
2.00 15
3.00 10