Modeling Static Friction of
Rubber-Metal Contact
MANE 6960
Friction & Wear of Materials
Katie Sherrick
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• Most laws of friction are based on metalmetal 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
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Hertzian Contact
P
δ
G = shear modulus (sphere) a = contact radius
4

• Rubber and elastomeric materials are viscoelastic in behavior  exhibit both viscous and elastic properties when undergoing deformation
• Time-dependent strain
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• Standard Linear Solid (Zener) d


E

2 dt
 d

E
2 dt
E
1

 
E
2

E
1

More accurate than the Kelvin or Maxwell models for elastomeric materials
Accounts for both creep and stress relaxation
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Normal Viscoelastic-Rigid Single Asperity Contact
• Correspondence principle  elastic solution is used to obtain viscoelastic
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If tangential load Q is applied to the normally-loaded asperity couple, the distribution of shear stresses is per Mindlin: c is radius of the stick zone
Q
Limiting displacement for an asperity couple: Q = μP
P
δ
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4,00E-07
3,50E-07
3,00E-07
2,50E-07
2,00E-07
1,50E-07
1,00E-07
5,00E-08
0,00E+00
Static Friction Force as a function of Normal Approach ( δ n
)
Normal Approach (m)
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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 η s
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• 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
δ t
= tangential displacement
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• All contacts with a height larger than s cr 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
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• When F partially-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
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Material Properties Effect of Surface Roughness
Model results are comparable to experimental values at low pressures
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