Transcript Modeling Static Friction of Rubber

Modeling Static Friction of
Rubber-Metal Contact
MANE 6960
Friction & Wear of Materials
Katie Sherrick
1
Introduction
• 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
2
Single-Asperity Contact
3
Contact Pressure: Elastic-Rigid
Hertzian Contact
P
δ
G = shear modulus (sphere)
a = contact radius
4
Viscoelasticity
• Rubber and elastomeric materials are
viscoelastic in behavior  exhibit both
viscous and elastic properties when
undergoing deformation
• Time-dependent strain
5
SLS Model
• Standard Linear Solid (Zener)
  d

 

  E 2 dt
d

dt
E1 E 2
E
2

E 1  

More accurate than the Kelvin or Maxwell models for elastomeric materials
Accounts for both creep and stress relaxation
6
Normal Viscoelastic-Rigid Single Asperity Contact
• Correspondence principle  elastic
solution is used to obtain viscoelastic
7
Tangential Loading
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
P
Q
Limiting displacement for an
asperity couple: Q = μP
δ
8
Static Friction Force
9
Model Validation
Static Friction Force as a function of Normal Approach (δn)
4.00E-07
3.00E-07
2.50E-07
2.00E-07
1.50E-07
1.00E-07
5.00E-08
3.50E-08
3.00E-08
2.50E-08
2.00E-08
1.50E-08
1.00E-08
5.00E-09
0.00E+00
0.00E+00
Static friction force (N)
3.50E-07
Normal Approach (m)
10
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
11
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
12
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
13
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
14
Multi-Asperity Results
Material Properties
Effect of Surface Roughness
Model results are comparable to experimental values at low pressures
15
Questions?
16