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

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

Single-Asperity Contact

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

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

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

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

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

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

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

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

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

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

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

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

Questions?