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A Model of Tangential Contact Damping Considering Asperity Interaction and Lateral Contact

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Abstract

A precise tangential contact damping model is proposed, which includes the lateral contact of the upper–lower asperities and the interaction of adjacent asperities. The effects of the normal static preload, frequency, and amplitude of tangential displacement on the tangential contact damping were analyzed by simulation, respectively. Furthermore, the results of simulation are verified by experiment. The tangential contact damping of considering the interaction and lateral contact of asperity is very close to the experimental results.

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Abbreviations

\(F_i \) :

Normal static force on asperity

\(Q_i \) :

Tangential dynamic force on asperity

z :

Asperity height from the mean height for asperities to the asperity top

d :

The distance between the smooth rigid plane and the mean height of the asperities

h :

The distance between the smooth rigid flat and the mean height of the rough surface

\(y_\mathrm{s} \) :

The gap between the mean surface height and the mean asperity height

R :

Equivalent radius of asperity

\(R_1, R_2 \) :

Mean asperity radii on the upper and lower rough surfaces, respectively

\(\xi \) :

Tangential displacement

\(\sigma \) :

The mean square deviation of the equivalent rough surface

\(\sigma _z \) :

The standard height deviation of asperity

\(\beta \) :

The topographic characteristics of the rough surface

\(\eta \) :

The density of asperities per unit area

\(P_n \) :

A uniform pressure

\(A_\mathrm{l} \) :

The territory of the local deformation

2a :

A square shape with length

\(\delta \) :

Total deformation of an asperity

\(\delta _s \) :

The deformation by contacting

\(\delta _g \) :

The deformation by interaction

E :

Equivalent Young’s modulus

\(E_1, E_2 \) :

Young’s moduli of upper and lower rough surfaces, respectively

\(\nu _1, \nu _2 \) :

Poisson’s ratios of upper and lower rough surfaces, respectively

G :

Equivalent shear modulus

\(\delta _\mathrm{c} \) :

The critical deformation that marks the transition from the elastic to the elastic-perfectly plastic deformation regime

\(F_{ic}\) :

Critical force

\(S_\mathrm{y}\) :

Yield strength

L :

Hardness factor

B :

The material dependent exponent

\(e_\mathrm{y}\) :

The yield strength to elastic modulus ratio

\(H_\mathrm{G}\) :

Geometrical hardness limit

\(r_{i(j)}^*\) :

The radius of the contact area in the elastic and elastic-plastic stages

\(\xi _c^*\) :

The dimensionless critical displacement that causes initial gross sliding

\(\mu \) :

Friction coefficient

\(F_n\) :

Normal static force

\(F_\tau \) :

Tangential dynamic force

\(n\hbox {o}\tau \) :

Global coordinate system

\(n^{\prime }\hbox {o}^{\prime }{\tau }^{\prime }\) :

Local coordinate system

\(\theta \) :

The contact angle between two lateral contacting asperities

\(Q_{in}\) :

Normal component split by the tangential force

\(Q_{i\tau }\) :

Tangential component split by the tangential force

\(F_{in}\) :

Normal component split by the normal force

\(F_{i\tau }\) :

Tangential component split by the normal force

\(E_{i(j)}^*\) :

Energy dissipation of a pair of contacting asperities during one cycle

A :

Nominal contact area

\(n_z \) :

The number of contacting asperity

m :

Related to a number of cycles the contact has undergone.

n :

The number of the lateral contact asperities

\(C^{{*}}\) :

Equivalent viscous damping

\(\omega ^{*}\) :

The dimensionless angular frequency

\(\xi _m^*\) :

The dimensionless amplitude of tangential displacement

f :

The dynamic tangential force

\(m_{1}\) :

The mass of the middle test piece

\(K_{\tau }\) :

Interfacial tangential stiffness

\(C_{\tau }\) :

Interfacial tangential damping

\(x_{1}, sx_{2}\) :

Displacements of the left and right test pieces, respectively

\({\ddot{x}}_1\) :

Acceleration

\(x_\tau \) :

Relative displacement of interface

\(f_\tau \) :

Tangential dynamic force

\(F_\tau \) :

The amplitude of the dynamic tangential force

\(\omega \) :

Angular frequency

t :

Time

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Acknowledgements

This research was supported by National Natural Science Foundation of China under Grant Nos. 51275407, 51475363. The authors gratefully acknowledge financial support provided by NNSF.

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Authors and Affiliations

  1. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    W. P. Fu, Z. Q. Gao, W. Wang & J. B. Wu

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  1. W. P. Fu
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Correspondence to W. P. Fu.

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Fu, W.P., Gao, Z.Q., Wang, W. et al. A Model of Tangential Contact Damping Considering Asperity Interaction and Lateral Contact. Acta Mech. Solida Sin. 31, 758–774 (2018). https://doi.org/10.1007/s10338-018-0050-6

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