Prediction of oil-film thickness and shape in elliptical point contacts under combined rolling and sliding motion

Abstract

The paper presents a numerical solution for elliptical point contact conjunctions under combined rolling and sliding motion. This condition is prevalent in many practical applications, such as rolling element bearings and conformal gears. An effective influence Newton-Raphson method is employed in local point distributed or global line distributed low-relaxation iterations. This method enables determination of the pressure distribution and film shape at high loads such as are encountered in many practical applications. Some of the numerical predictions have been validated against experimental results.

Non-Newtonian mixed elastohydrodynamics of differential hypoid gears at high loads

“…Also, simulation studies were carried out at low input torque, not representative of vehicle differentials. There is experimental evidence of angled entrainment flow, for example by Gohar [25], as well as numerical predictions by Jalali-Vahid et al [26]. These indicate the importance of including the correct contact footprint shape, as well the the directions of entraining motion and side-leakage of the lubricant.…”

Boundary Conditions for Elastohydrodynamics of Circular Point Contacts

“…Validity of the numerical predictions was confirmed by optical interferometric studies, pioneered by Gohar and Cameron [7] However, many conjunctions such as those of balls in their raceway grooves are subject to combined rolling and sliding motion and have an elliptical footprint owing to the slight conformance of the mating solids. Solutions include those by Chittenden et al [8] and Jalali-Vahid et al [9,10]. The latter showed agreement between their numerical predictions and the optical interferometric studies of Thorp and Gohar [11] for elliptical point contacts of ball-raceway grooves and angled entraining flow of lubricant into the contact conjunction.…”

“…The process is fully described in [10,38]. This method is widely used in elastohydrodynamic studies.…”

Elastohydrodynamics of Hypoid Gears in Axle Whine Conditions

“…The Reynolds equation is discretised using finite differences in the same manner as described by Jalali-Vahid et al [16]. The solution for pressure at any nodal position (i, j) with a sufficient computation grid covering the entire solution domain is based on the low line relaxation effective influence Newton-Raphson method with Gauss-Seidel iterations.…”

“…Therefore, a suitable method of solution is the distributed line low relaxation effective influence Newton-Raphson method. This method was used for ball bearings by Jalali-Vahid et al [16] and for elliptical contacts with angled flow, but in both cases for moderate loads. The same model has been used in a hypoid gear application by Mohammadpour et al [15] for film thickness investigations only.…”