Can non-standard involute gears of different modules mesh?

Abstract

Under the current standardized involute gear systems, meshing of gears of different modules is a practical impossibility. However, by performing a fresh reinterpretation of the well-established fundamental meshing principles, a more insightful form for the compatibility equations that govern involute gear tooth generation and meshing can be obtained. This article reports some first non-standard designs based on this analysis that allows gears of different modules to mesh. By the same token, standard gears can be manufactured with non-standard hobs and vice versa. Initial investigation suggests that practical benefits such as increasing the root bending strength without affecting the pitting resistance and the sliding velocity can be achieved that may justify such deviation from standard designs.

Modelling Dependencies and Couplings in the Design Space of Meshing Gear Sets

“…The compatibility of a rack-involute gear pair, as used typically in the study of gear generation, is broken down into compatibility of pitch and of various clearances (radial and backlash), as per Spitas [1]:…”

“…Clearly, the design parameters in this case are so strongly coupled, that the real optimum must be a compromise. On the other hand, strength optimisations exist for the tooth root that do not affect the working tooth form [1][2][3][11][12], allowing for alternative routes to at least some local optima.…”

“…It has been shown recently [1][2][3] that the module-based calculus for gear geometry, stemming from practical manufacturing considerations, can only address a subset of the valid design space. It has also been shown that designs of significantly improved bending strength are to be found in the design space outside this subset, and it is therefore highly probable that other local optima besides bending strength exist and even, assuming that an agreement can be found on weighting factors of the defining criteria, a global optimum.…”

Calculation of Spur Gear Dynamic Transmission Error in Consideration of the Progressive Engagement of Compliant Profile-modified Teeth

“…After ascertaining the kinematical characteristics of the modified gears, dynamic simulation of these gears has been conducted over a wide range of speeds using a combined geometric-kinematic-dynamic model based on known analytical and numerical models for calculating gear geometry, contact and kinematics [13][14][15][16][17][18] and mechanical response of the elastic tooth mesh, also in consideration of modified tooth geometries and elastohydrodynamic lubrication-induced tooth surface deformations [19][20][21][22][23][24][25][26][27][28][29][30]. This translates into the following relationship: O (also corresponding to the position vectors marked in boldface), the incorporation of the slip angle yields from Eqs.…”

A Lightweight Model for Gear Mesh Dynamics Incorporating Variable Mesh Stiffness

“…However these models are typically either too simplistic in terms of how stiffness is modelled, or employ complex FEA analysis that is resource intensive. In this paper a novel accurate and yet computationally lightweight SDOF model for gear dynamics is developed on the basis of recently developed analytical and numerical models for calculating gear geometry, contact and kinematics [6][7][8][9][10][11][12][13] and mechanical response of the elastic tooth mesh, in consideration of various tooth geometries [14][15][16][17][18][19][20][21][22][23][24].The implications of the varying tooth stiffness during a mesh cycle on the overall dynamic response are studied and a correlation is made between the gear properties and the tooth stiffness distribution based on the results of numerous simulations.…”