Abstract:According to the processing principle of cylindrical gear with variable hyperbolic circular-arc-tooth-trace (VH-CATT) and the deduced tooth surface equation of the gear,the range of parameters was determined.Based on the obtained tooth surface equation and the differential geometry,the calculation method of the principal curvature of concave and convex gear of VH-CATT was obtained.Based on the principle of spatial meshing,the relative velocity of gear teeth on meshing point at an input angular velocity was calculated.According to the calculated method of the curvature of the tooth surface and the relative velocity,the formula for calculating the sliding ratio of VH-CATT pair was derived.Setting a certain VH-CATT design parameters for example,principal curvature,induced curvature and sliding ratio were calculated and their change trends were analyzed.Sliding ratios under different design parameters were obtained,as the reference of analysis and optimization for gear design.Analysis results showed that for the VH-CATT pair,the greater the modulus,tooth number ratio and tooth trace radius,the smaller the range of sliding ratio of gears is,and the abrasion in working process would be more uniform.Gear pair with larger modulus,smaller tooth number ratio,greater tooth trace radius has better performance in wear process.The quantitative relationship between sliding ratio and wear of VH-CATT was established,which provides reference for the calculation of gear wear.