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.
Highlights
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
Aim of this paper has been to establish an accurate model to determine gear deflections under load and the contact condition that are present during meshing
On the basis of well established semi analytical (SA) foundations a nonlinear iterative scheme was implemented seeking for a natural equilibrium condition between the location of the contact point, which slides due to the deflections, the load intensity, since the change in contact position alters the stiffness as well, and, the number of the engaged teeth pairs
Summary
Due to their inherent nature, load and stiffness fluctuations are the main source of excitation and cause of failure in geared transmissions [1,2,3]. Hertzian theory [36] of cylinder-to-cylinder contact is generally employed to model the contact between engaging flanks, simplifying several key aspects of the gears, such as the continuously varying curvature and the presence of sharp edges. Said model is first compared to Hertzian theory with great agreement, and side and tip mirroring corrections are introduced to relieve the stresses on the free surfaces of the finite-length bodies in contact allowing accurate representation of the varying curvature and discontinuities of the flanks. This entire approach is tested against a 3D FE model showing very similar results both in terms of STE and contact pressures. Several results are shown on a test case to highlight the influence of micro-geometrical modifications on the quantities of interest and conclusions are drawn and future work is introduced
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