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Micro-tribological interface model for friction-induced cold start-up running dynamics

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Abstract

The robustness and noise warranty costs of many automotive friction materials like transmission belts or brake pad are directly affected by the frictional properties in cold start-up running. This paper presents a friction model for start-up running under cold conditions. The absorbed water, phase changes and variable lubrication regimes in cold start-up running are taken into account. The model includes the breakage of ice adhesion, ice–ice friction between the ice films on friction pairs, melting water-mediated mixed lubrication and boundary lubrication, friction elevation due to capillary adhesive effect, as well as dry contact in the end of cold start-up running. Thermal analysis is applied in conjunction with the friction model to estimate the parameters in phase transitions. A meniscus model is also integrated into the friction model to address the friction elevation due to the variation of water film thickness. It is illustrated that if the thickness of surface ice film is larger than a critical value, the static friction coefficient could be close to 1; if the thickness of melting water film is higher than the average roughness of the surface, static friction could increase due to capillary effect, and kinetic friction could decrease due to mixed lubrication resulting in wide modulation of friction during intermittent start-up transitions. This paper also presents the application of the model to elucidate the friction mechanisms in cold brake noise where the cold wet coefficient of friction (cof) could be substantially higher than the dry cof. The effects of temperature, roughness and load on cof are also characterized.

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Abbreviations

B:

Width of brake pad

\( c_{p} \) :

Specific heat

E:

Young’s modulus of brake pad

\( F_{d} \) :

Friction contributed by asperity contact

\( F_{f} \) :

Total friction in mixed lubrication

\( F_{l} \) :

Friction contributed by water hydrodynamic regions

\( F_{m} \) :

Meniscus force

\( h \) :

Adsorption thickness on surface

\( k \) :

Thermal diffusivity

k 1, k 2 :

Thermal conductivity of component 1 and component 2, respectively

L :

Length of brake pad

\( L_{0} \) :

Sintering factor for ice friction

N :

Density of asperity peaks

\( Q \) :

Heat flux due to frictional heating

\( p_{i} \) :

Applied pressure on brake pad

p m :

Maximum Hertzian pressure

RH :

Relative humidity

R i , R o :

Inner and outer radii of the disk engaging pad

T :

Temperature rise

T 0 :

Initial temperature

t :

Thickness of pad

v :

Velocity

\( V_{l} \) :

Molar volume of the water

\( \alpha \) :

Water-pad contact angle

\( \beta \) :

Radius of asperity peaks

\( \sigma_{r} \) :

RMS of brake pad roughness

\( \gamma \) :

Surface tension of water at 20 °C

\( \eta_{50} \) :

Dynamic viscosity at 50 °C

\( \eta_{30} \) :

Dynamic viscosity at 30 °C

\( \eta_{10} \) :

Dynamic viscosity at 10 °C

\( \eta_{2} \) :

Dynamic viscosity at 2 °C

\( \rho_{Pad} \) :

Pad density

\( \mu \) :

Coefficient of friction

\( \mu_{s} \) :

Static friction coefficient

\( \sigma \) :

Compressive yield strength of ice

\( \tau \) :

Critical shear stresses or strengths of interfacial layer

\( \alpha_{1} \) :

Thermal diffusivity of component 1

\( \rho \) :

Mass density

\( \sigma_{r} \) :

RMS of roughness

\( \beta \) :

Radius of asperity peaks

\( \phi (z) \) :

Gaussian distribution of peak heights

\( \gamma \) :

Surface tension of water

r k :

Kelvin radius

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alaska Fairbanks, Fairbanks, AK, 99775-5905, USA

    Jonah H. Lee & Gang Sheng

  2. Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan

    Jen-Yuan Chang

Authors
  1. Jonah H. Lee
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  2. Gang Sheng
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  3. Jen-Yuan Chang
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Correspondence to Jen-Yuan Chang.

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Lee, J.H., Sheng, G. & Chang, JY. Micro-tribological interface model for friction-induced cold start-up running dynamics. Microsyst Technol 18, 1469–1479 (2012). https://doi.org/10.1007/s00542-012-1573-2

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  • DOI: https://doi.org/10.1007/s00542-012-1573-2

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