1. Modeling Static Friction of Rubber-Metal Contact
MANE 6960
Friction & Wear of Materials
Katie Sherrick

2. Introduction Most laws of friction are based on metal-metal contact
Elastomer-metal contacts do not have the same friction properties as traditional friction laws would indicate
Differences in elastomer-metal contact friction are due primarily to the viscoelastic nature of the elastomer

3. Single-Asperity Contact

4. Contact Pressure: Elastic-Rigid
Hertzian Contact P δ
G = shear modulus (sphere)
a = contact radius

5. Viscoelasticity
Rubber and elastomeric materials are viscoelastic in behavior  exhibit both viscous and elastic properties when undergoing deformation
Time-dependent strain

6. SLS Model Standard Linear Solid (Zener)
More accurate than the Kelvin or Maxwell models for elastomeric materials
Accounts for both creep and stress relaxation

7. Normal Viscoelastic-Rigid Single Asperity Contact
Correspondence principle  elastic solution is used to obtain viscoelastic

8. Tangential Loading
If tangential load Q is applied to the normally-loaded asperity couple, the distribution of shear stresses is per Mindlin: P δ
c is radius of the stick zone Q
Limiting displacement for an asperity couple: Q = μP

9. Static Friction Force Dark annulus = slip region, light = stick region
Friction force = integral over the contact radius a of the shear stresses in the contact  max friction force happens when the contact area is in full slip, so c=0 (stick zone is gone). Method: calculate q for a given asperity couple

10. Static Friction Force as a function of Normal Approach (δn)
Model Validation
Static Friction Force as a function of Normal Approach (δn)

11. Multi-Asperity Contact Mechanics
Contact between rubber-like material and metal is simulated for the load-controlled case
The asperity interactions depend on surface roughness parameters (Greenwood & Williamson)
Average summit radius β
Standard deviation of summit heights σ
Summit density ηs

12. Multi-Asperity Modeling
Depending on compression of each asperity couple, each individual couple is either:
Partial slip
Full slide
A critical asperity height is calculated:
d = surface separation
σ= std. dev of summit heights
δt = tangential displacement

13. Multi-Asperity Modeling
All contacts with a height larger than scr are in partial slip regime
The total friction force is a summation of the full slide and partial slip regimes:
Friction force for viscoelastic contact are calculated by substituting the appropriate operator for G in this equation
Φ(s) is the normalized Gaussian asperity height distribution

14. Multi-Asperity Modeling
When Fpartially-slip = 0, all asperities in contact are in full slide  max friction force is reached
Calculated using either the load-controlled or displacement-controlled single-asperity contact models

15. Multi-Asperity Results
Material Properties
Effect of Surface Roughness
Material properties: limiting displacement is smaller for stiffer material (Fibroflex 80 Shore A vs. Fibroflex 95 Shore A)
Surface roughness: limiting displacement and static friction force are larger for rougher surfaces (std dev of summit heights is larger)
Model results are comparable to experimental values at low pressures

16. Questions?