Helical Gears With Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis, and Stress Analysis

Abstract

The paper covers the solutions to the following problems: (1) Setting up a mathematical model for the involute helical gears; (2) Computer simulation of the conditions of meshing and bearing contact; (3) Investigation of the sensitivity of gears to the errors of manufacturing and assembly; and (4) Stress analysis of the gears. In this paper, the theory of gearing and the concept of differential geometry have been applied to deal with the relations of two mating helical gears and their bearing contact. Computer program for tooth contact analysis (T.C.A.) has been developed for the gears. The T.C.A. computer program makes it possible to simulate gear meshing and bearing contact, and to investigate the influence of gear misalignment on kinematic errors. A method of compensation for the dislocation of bearing contact and for kinematic errors induced by errors of manufacturing and assembly has been proposed. Four numerical examples have also been presented to illustrate the influence of the above-mentioned errors and the method of compensation for the dislocation of bearing contact. Based on the derived mathematical model, an automatic mesh generating computer program—AMG has been developed to define the geometry of the gears and to divide the gear tooth into elements as well as to generate nodal points automatically. The results of T.C.A. provide the locations and directions of the applied loadings for the finite element method (F.E.M.) stress analysis.

Simulations of Gear Shaving and the Tooth Contact Analysis

“…Litvin [2] proposed the basic meshing conditions of a 3D crossed-axis helical gear pair. Tsay [3] studied tooth contact and stress analysis of helical gears. Miao and others [4,5] calculated the value of the crossed-axis angle at operating pitch circle and completed constructing a mathematical model of plunge shaving cutter.…”

Pi̇nyon-Ti̇pi̇ Takimla Di̇şli̇ İmalat Si̇mülasyonunda Evolvent Parametresi̇ni̇n Efekti̇f Sinirinin Tayi̇ni̇

“…Takım yüzeyinin vektörel ifadesinden hareketle koordinat dönüşüm, diferansiyel geometri ve dişli ana kanunu uygulanarak imal edilen dişlinin matematik modeli elde edilmektedir. Çok sayıda yazar bu metodu kullanarak hemen her tipten dişlinin modellenmesi ile ilgili çalışmalar yapmıştır [2][3][4][5][6][7][8][9][10][11][12]. Ayrıca vektör metodu çeşitli fonksiyonel ve imalat modifikasyonlarının (tepe boşaltması, bombe, taşlama payı vd.)…”

Computer Simulation of Helical Gears Generated by Rack-Type Cutters

“…This approach has the flexibility for applying profile modifications to spur and helical gearing. Based on Litvin's vector approach, mathematical models for conventional and modified gear teeth have been presented [4][5][6][7][8][9][10][11]. Yang proposed a mathematical model of the helical gear with asymmetric involute teeth [10,11].…”