Analytical Elastostatic Contact Mechanics of Highly-Loaded Contacts of Varying Conformity

Abstract

In applications requiring high load carrying capacity, conforming contacting pairs with a relatively large contact footprint are used. These include circular arc, Novikov, and Wildhaber gears found, for example, in helicopter rotors. Closely conforming contacts also occur in many natural endo-articular joints, such as hips, or their replacement arthroplasty. The main determining factors in contact fatigue are the sub-surface shear stresses. For highly loaded contacts, classical Hertzian contact mechanics is used for many gears, bearings, and joints. However, the theory is essentially for concentrated counterforming contacts, where the problem is reduced to a rigid ellipsoidal solid penetrating an equivalent semi-infinite elastic half-space. Applicability is limited though, and the theory is often used inappropriately for contacts of varying degrees of conformity. This paper presents a generic contact mechanics approach for the determination of sub-surface stresses, which is applicable to both highly conforming as well as concentrated counterforming contacts. It is shown that sub-surface shear stresses alter in magnitude and disposition according to contact conformity, and lead to the different modes of fatigue failure noted in practice.

Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears

“…Johns-Rahnejat et al [34] provided an analytical generic solution for sub-surface stresses generated in an elastic solid under a parabolic pressure distribution. However, EHL contact pressure distribution does not follow a simple analytical expression.…”

“…However, EHL contact pressure distribution does not follow a simple analytical expression. Johns-Rahnejat et al [34] spread the arbitrary pressure distribution over the contacting face of an elastic solid of revolution approximated by a parabola, as shown in Figure 4. Here, the solid of revolution is a long roller, representing an instantaneous geometry of a gear tooth during a meshing cycle.…”

“…To capture these effects and those due to asperity interactions of rough counter faces [32] a suitably detailed numerical analysis is required as highlighted by Johns-Rahnejat [30,33]. Recently, a generic semi-analytical model was presented by Johns-Rahnejat et al [34] which can be adopted for the evaluation of sub-surface stress fields for all gear contacts with varying degrees of conformity. This approach is used here for the case of lubricated contact of spur gear pairs.…”

Fundamentals and Advances in Elastohydrodynamics: The Role of Ramsey Gohar

“…A more up-to-date review of predictive methods and recent contributions is provided by Sadeghi [16]. A generic semi-analytical method for all contacts of varying conformity is provided in [125], based on the general approach of Muskhelishvili [126]. The predictive contact mechanics analysis of sub-surface stress fields has received much attention.…”

Tilting Pad Journal Bearing Ball and Socket Pivots: Experimental Determination of Stiffness

“…The effects of normal loads and friction coefficients on the distribution of both axial and circumferential contact stress in spherical plain bearings are studied, adopting both theoretical methods and FE simulations, in [10]. A generic contact mechanics analytical approach for the determination of sub-surface stresses, which is applicable to both highly conforming as well as concentrated counter-forming contacts, is presented in [11]. Robust, mathematically closed-form contact models, easy-to-implement for non-Hertzian soft and conformal contacts, using a set of independent Kelvin-Voigt elements spread all over the contact surfaces, are proposed in [12] and validated through FE analysis.…”