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Mathematical Modeling and Characteristics Analysis of the Toroidal Drive With Elastic Deformation in the Conjugating Process

Time-variation of meshing stiffness is the main internal excitation for the vibration and noise of the gear transmission system. Elastic deformation in the rolling contact process is an important factor for the meshing stiffness variation of the toroidal drive. However, most of the previous meshing modeling of the toroidal drive is based on the rigidity hypothesis. In order to investigate the actual contact situation and improve the stability of the toroidal drive, this paper focuses on the mathematical modelling and characteristics analysis for the toroidal drive with elastic deformation in the conjugating process between the planet-worm gear and sun-worm as well as between the planet-worm gear and internal toroidal gear. The elastic deformation integrated coordinate system of the toroidal drive is introduced. The elastic deformation velocity induced by contact force is adopted for the first time in the relative velocity of the Wills law for the toroidal drive. Then, based on Hertz contact theory, the relationship between elastic deformation velocity and normal force is studied. In addition, the influences of the elastic deformation on the meshing contact curve, helix-lead angle and induced normal curvature are further discussed.