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Purpose – This paper aims to investigate the mechanism of spur gears running-in and to solve the lubrication problems of teeth running-in. Design/methodology/approach – The elastohydrodynamic lubrication (EHL) model considering solid particles was established by applying multi-grid and multiple-grid integration methods to the numerical solution. Findings – In the region where debris settle, transient pressure increases sharply, and a noticeable increase in the running-in load causes a remarkable increase in both the centre and maximum pressures and a slight increase in the minimum film thickness. Roughness wavelength makes a considerable difference to the minimum film thickness at double-to-single tooth transient. A considerable increase in rotation velocity can cause a remarkable reduction in both the centre and maximum pressures but an amazing increase in the minimum film thickness. The effects of roughness amplitude on the maximum pressure are considerably distinct. Research limitations/implications – Research on EHL of spur gears in the running-in process considering solid particles, surface roughness and time-variant effect is meaningful to practical gears running-in. Thermal effect can be included in the next study. Practical implications – The analysis results can be applied to predict and improve lubrication performance of the meshing teeth. Social implications – The aim is to reduce gears’ manufacture and running-in costs and improve economic performance. Originality/value – The EHL model that considers solid particles was established. The Reynolds equation was deduced taking the effects of solid particles into account. The EHL of spur gears running-in was investigated considering the time-variant effect, surface roughness, running-in load and rotation speed.

Numerous friction and wear experiments have demonstrated that nanoparticles (NNPs) perform excellently in friction coefficient reduction and anti-wear. However, theoretical explanation of the facilitated lubrication mechanism of NNPs is of complexity. This paper proposed a revised Reynolds equation taking moving particles into consideration. Through mutually coupling the governing equations the causes of wear reduction contributed by NNPs are well understood. Considering thermal effect, time-varying effect and particles motion, effects of particles motion on the tribology performance of elliptical contact was investigated. Furthermore, the influences of two deterministic particles’ distributions compared with base oil were discussed. Results show that the motion of moving particles from inlet to outlet induces remarkable increases in film thickness and considerable decreases in coefficient of friction, while also leads to evident rise of temperature and significant backflows in inlet zone. Additionally, particles with appropriate concentration are beneficial to the enhancement of lubricating film performance.

In this paper, the mathematical model of gear elastohydrodynamic lubrication is presented. The transient impact operating condition and underdamped load condition are considered. Taking thermal effect and squeeze effect into account, the full numerical solution of gear pairs is obtained. In this numerical calculation, multigrid method is applied to compute the film pressure; multigrid integration technique is used to calculate the solid surface deformation; column by column scanning technique is employed to calculate temperature. The simulation results show that an entrapped film dimple forms under transient impact condition; transient impact causes remarkable increases in film pressure and film temperature. Compared with the normal case the minimum thickness of the impact case is smaller, which is not beneficial to teeth lubrication. Thermal effect induces some decreases in film thickness because of the viscosity–temperature relationship. Vibrational load with high damped frequency causes greater increases in film thickness and greater decreases in the coefficient of friction than that of low damped frequency. However, the film temperature of high damped frequency is higher than that of low damped frequency.