Example - Contact Stresses in a Steel Ball Bearing


A steel ball bearing consisting of an inner race, an outer race, and 12 balls is shown in the following Figure. (Material properties of balls and race E=210 GPa, v=0.29) A rated load of P0=3600 N is given in the manufacturer's data sheet for this ball bearing when operated at 2500 rpm. An empirical relation [Ref-1] is used to determine the load P on the topmost ball that bears the largest portion of the load; P = 5P0/n = 1500 N in which n is the number of balls.

At the region of contact between the inner race and topmost ball, determine the maximum shear stress, maximum Hertzian contact pressure and dimensions of the area of contact.

An example about Contact Stresses in a Steel Ball Bearing
Solution:

Step 1 : Write down input parameters (including material properties) which are defined in the sample example.


INPUT PROPERTIES SUMMARY
Parameter Symbol Value Unit
Poisson's ratio of ball v1 0.29 ---
Poisson's ratio of race v2 0.29 ---
Elastic modulus of ball E1 210 GPa
Elastic modulus of race E2 210 GPa
Radius of ball R1 4.90 mm
Inner race radius   R2 5 mm
Inner race radius R3 25 mm
Maximum load on a bearing ball P 1500 N




Step 2 : Visit "Contact Calculations of Sphere in Circular Race" page and solve the problem. Results generated by the calculator are as follows.


RESULTS
Parameter Symbol Object-1 Object-2 Unit
Maximum Hertzian contact pressure pmax 2193.6 MPa
Maximum shear stress τmax 684.9
Rigid distance of approach of contacting bodies d 0.012 mm
Semimajor axis of contact ellipse a 2.101
Semiminor axis of contact ellipse b 0.156

Conclusion:

Contact stresses of steel ball bearing have been calculated. The maximum Hertzian contact pressure and shear stress are calculated as 2193.6 MPa and 684.9 MPa respectively.



Reference: