Dynamic Tangential Contact Stiffness and Damping Model of the Solid–Liquid Interface

Abstract

In order to establish the tangential contact stiffness and damping model of the solid–liquid interface by tangential exciting vibration force under mixed lubrication, the finite difference method was firstly used to solve the average flow equation considering the effect of roughness on the lubrication effect, and the bearing capacity, shear force, and friction coefficient of the oil film were obtained, and thereby the dynamic tangential contact stiffness and damping of the oil film under tangential harmonic excitation were calculated. Then, according to the relationship between the normal deformation and the load of the solid contact microconvex body in the elastic/elastic–plastic/plastic deformation stage, integrating the tangential stick–slip theory, considering the effect of fluid lubrication on the solid contact friction coefficient, and tangential dynamic excitation, the tangential contact stiffness and damping of the microconvex body in three deformation stages were calculated. Furthermore, the dynamic tangential contact stiffness and damping of the solid–liquid interface were obtained by summing the solid surface contact part and the solid–liquid contact part in parallel according to the assumption of microconvex Gaussian distribution. Finally, through simulation analysis and experiments, the variation of the tangential dynamic contact stiffness and damping of the solid–liquid interface with normal load, tangential exciting frequency, and displacement amplitude was revealed and verified.

Theoretical Model of Tangential Contact Stiffness and Damping of Solid-Liquid Interface in Macroscopic Relative Motion

“…Zhou et al [24][25] proposed a tangential stiffness and damping model by considering the coupling of gear stiffness and damping and oil film stiffness and damping. Peng et al [26] established a model of tangential stiffness and damping of solid-liquid interface when normal static load and tangential harmonic vibration occur, and thus verified it by experiments. Dwyer-Joyce et al [27] measured the normal contact stiffness of lubricating steel balls from static, mixed to full-film state when sliding on the steel disk by ultrasonic reflection method, and found that with the increase of sliding velocity, the contribution of liquid stiffness to the total stiffness gradually increased, and even became the main part, even in the static state, the liquid stiffness also contributed to the total stiffness.…”

“…From theoretical analysis and experimental demonstration in References [23,26,49], it can be seen that the total tangential contact stiffness of the relative motion solidliquid interface is the sum of the solid contact stiffness and the oil film tangential stiffness, and the total tangential damping is the sum of the solid contact damping and the oil film tangential damping. The tangential contact stiffness of solid-liquid interface is obtained from Equations ( 27) and ( 47).…”

“…The parameters in the model are dimensionless with reference to reference [26], and represented by the symbol "*".…”

A time‐varying meshing stiffness model for gears with mixed elastohydrodynamic lubrication based on load‐sharing

“…Li et al 21 utilized a quadratic function to describe the profile of asperities and analyzed the influence of parameters such as lubrication medium, solid material, and asperity size on contact stiffness. Peng et al 22 developed a model for tangential contact stiffness and damping of the solid-liquid interface by considering tangential exciting vibration forces under mixed lubrication conditions. The dynamic tangential contact stiffness and damping of the solid-liquid interface were determined by summing the contributions from the solid surface contact and the solid-liquid contact in parallel under a microconvex Gaussian distribution.…”

“…utilized a quadratic function to describe the profile of asperities and analyzed the influence of parameters such as lubrication medium, solid material, and asperity size on contact stiffness. Peng et al 22 . developed a model for tangential contact stiffness and damping of the solid‐liquid interface by considering tangential exciting vibration forces under mixed lubrication conditions.…”