Abstract
There are a number of widely used machine components, such as rolling element bearings, gears and cams, which operate in the lubrication regime known as Elastohydrodynamics (EHD), where lubricant film thickness is governed by hydrodynamic action of convergent geometry, elastic deformation between non-conformal contacting surfaces, and the increase of lubricant viscosity with pressure. Variable loading conditions occur not only in all the machine components mentioned above, but also in natural joints such as hip or knee joints of humans or many vertebrates. Experimental studies of the behaviour of EHD films under variable loading are scarce and to authors’ knowledge systematic studies of the evolution of lubricant film thickness in EHD contacts subjected to forced harmonic variation of load are even less common. The aim of the present study is to explore the effect of load amplitude on the EHD film behaviour. This is done in alternating cycles with the load varying about a fixed, preset value at various amplitudes. Experimental results are compared with a simple theoretical analysis based on the speed of change of contact’s dimensions, a semi-analytical solution which includes both speed variation and squeeze effect, and finally with a full numerical solution.
Highlights
Abbreviations hc Central film thickness (m) hst Steady state film thickness under static load (m) h(t) Transient film thickness E Young’s modulus E∗ Reduced modulus of elasticity U Entrainment velocity in x direction (m/s) u0 Absolute velocity of the surfaces of the ball and disc (m/s) Absolute viscosity 0 Absolute viscosity at p = 0 and constant temperature Density R Reduced radius of curvature (m) Rx Reduced radii of curvature in x direction (m)
K1 Dimensionless number, Ertel-Grubin, K1 = aph ue0 Entrainment speed in the contact under stationary conditions (m/s) a Hertzian contact radius (m), a = (8WR∕ E∗)1∕2 t Time (s) T Dimensionless time, T = tue0∕a a EHD contact subjected to forced harmonic vibration; the effect of load amplitude on EHD films is subsequently extracted from the experimental results and compared to theoretical analyses
This paper fills the gap in further understanding the effect of load amplitude on the behaviour of EHD film
Summary
Circular frequency of the load cycle (rad/s) (t) Normal approach fluctuation of the two surfaces (m) v(x, t) Elastic displacement associated with the resulting pressure (m) x Coordinate (m) X Dimensionless coordinate, X = x∕a R Contact radius (m) h Film thickness (m) H Dimensionless in the semi-analytical solution,. K1 Dimensionless number, Ertel-Grubin, K1 = aph ue0 Entrainment speed in the contact under stationary conditions (m/s) a Hertzian contact radius (m), a = (8WR∕ E∗)1∕2 t Time (s) T Dimensionless time, T = tue0∕a a EHD contact subjected to forced harmonic vibration; the effect of load amplitude on EHD films is subsequently extracted from the experimental results and compared to theoretical analyses
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