Abstract
Abstract. The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new type of gear. In order to research the contact characteristics of the VH-CATT cylindrical gear, tooth surface mathematical models of this kind of gear pair are derived based on the forming principle of the rotating double-edged cutting method with great cutter head in this regard. Then, according to the differential geometry theory and Hertz theory, the formula of the induced normal curvature and equation of the contact ellipse are derived based on the condition of continuous tangency of two meshing surfaces, which proves that the contact form of VH-CATT cylindrical gear is point contact. The present work establishes analytical solutions to research the effect of different parameters for the contact characteristic of the VH-CATT cylindrical gear by incorporating elastic deformation on the tooth surface, which have shown that the module, tooth number and cutter radius have a crucial effect on the induced normal curvature and contact ellipse of the VH-CATT cylindrical gear in the direction of tooth trace and tooth profile. Moreover, a theoretical analysis solution, a finite element analysis and the gear tooth contact pattern are carried out to verify the correctness of the computerized model and to investigate the contact type of the gear; it is verified that the contact form on the concave surface of the driving VH-CATT cylindrical gear rotates from dedendum at the heel to the addendum at toe and is an instantaneous oblique ellipse due to elastic deformation of the contact tooth profile, and the connecting line of the ellipse center is the contact trace path. It is indicated that the research results are beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The results also have a certain reference value for development of the VH-CATT cylindrical gear.
Highlights
The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new kind of mechanical transmission part (Wei et al, 2018b)
The contact forms of the VH-CATT cylindrical gear have been strictly proved by a mathematical method
The contact performance of the VH-CATT cylindrical gear is closely related to the tooth surface geometry characteristics and the transmission principle
Summary
The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new kind of mechanical transmission part (Wei et al, 2018b). A mathematical model of a curvilinear cylindrical gear with variable tooth trace generated by a pair of independent face-milling cutters was proposed, its contact characteristics were analyzed, and the stress analysis was accomplished (Parsons et al, 2004). 2. based on differential geometry theory and Hertz theory, the calculation formulas of the induced normal curvature and the contact ellipse were derived, and the finite element analysis model of the VHCATT cylindrical gear and the contact experiment were established. Based on differential geometry theory and Hertz theory, the calculation formulas of the induced normal curvature and the contact ellipse were derived, and the finite element analysis model of the VHCATT cylindrical gear and the contact experiment were established This was used to verify the contact form of the VH-CATT cylindrical gear. The present study has certain reference value for the dynamic design and noise reduction of the VH-CATT cylindrical gear by the doubleedged cutting method with great cutter head
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