Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

Abstract

In this paper, a three-dimensional model for the estimation of the deflections, load sharing attributes, and contact conditions will be presented for pairs of meshing teeth in a spur gear transmission. A nonlinear iterative approach based on a semi-analytical formulation for the deformation of the teeth under load will be employed to accurately determine the point of application of the load, its intensity, and the number of contacting pairs without a priori assumptions. At the end of this iterative cycle the obtained deflected shapes are then employed to compute the pressure distributions through a contact mechanics model with non-Hertzian features and a technique capable of obtaining correct results even at the free edges of the finite length contacting bodies. This approach is then applied to a test case with excellent agreement with its finite element counterpart. Finally, several results are shown to highlight the influence on the quasi-static behavior of spur gears of different kinds and amounts of flank and face-width profile modifications.

Impact of a rigid sphere onto an elastic membrane

“…We anticipate this to occur when the kinetic energy of the membrane during the impact process is negligible when compared with its elastic energy. Such kinetic and elastic energies can be estimated to leading order by E k ∼ μΛ 2 (δ/t c ) 2 and E e ∼ τ δ 2 [21], respectively, where μ is the area density of the membrane, Λ is the membrane radius, τ is the membrane tension and δ is the maximum deflection of the membrane during an impact occurring over a time scale t c . By requiring E k E e , we find the condition…”

Effect of Web Flexibility in Gear Engagement: A Proposal of Analysis Strategy

“…where the STE is computed using the code GeDy TrAss as described in [32] and r b is the base radius. The damping model chosen is the classical proportional Rayleigh damping…”

Impact of a rigid sphere onto an elastic membrane

“…We anticipate this to occur when the kinetic energy of the membrane during the impact process is negligible as compared to its elastic energy. Such kinetic and elastic energies can be estimated to leading order by E k ∼ µΛ 2 (δ/t c ) 2 and E e ∼ τ δ 2 [21], respectively, where µ is the area density of the membrane, Λ is the membrane radius, τ is the membrane tension, and δ is the maximum deflection of the membrane during an impact occurring over a time scale t c . By requiring E k ≪ E e we find the condition…”

“…Mechanical contact problems arise naturally in countless industrial and scientific applications. Classical examples include the study of the deformation and stress in gear teeth [1,2,3], ball bearings and ball joints [4], impact absorbers [5], propagation of stress waves in colliding solids [6], and models of granular materials [7]. Contact problems also frequently arise in problems relating to material characterisation, where a localised indenter is used to infer properties of solid substrates [8].…”