1. Geometry

Ball: diameter 8mm Disc: inner-outer diameter: 20 – 40mm Material: Structural Steel (E=200 GPa, m=0.3) Force applied on the ball: 16p (N) Consider problem in 2 load steps. First step: the applied force is increase Second step: keep force as constant 2 cases: 1st case: without Archard wear model 2nd case: included Archard wear model in second step

Figue 1: The geometry of ball and disc

2. Theoretical analysis

Use this link with all parameters about the geometry and material properties: https://amesweb.info/HertzianContact/HertzianContact.aspx

Results about Contact pressure and Maximum Shear stress

Figure 2: the results about Contact pressure and Maximum shear stress

3. FEM analysis and comparion

a. Contact Pressure

 
Figure 3: Contact pressure and graphic

b. Maximum shear stress

Figure 4: Maximum shear stress respect to the depth from contact surface (left: theoretical, right: ansys)

Figure 5: Maximum shear stress

The results between theoretical calculations and software are the same

4. Hertz contact with Archard wear model

Define Archard wear model parameters

Figure 6: define Archard Wear parameters

Results

 

Figure 7: Contact pressure after included Archard wear model

In first load step: the result as previous case.

In second load step: contact pressure is reduced due to wear

Figure 8: wear thickness