Meshing characteristics of variable hyperbolic circular-arc tooth trace cylindrical gears with cutter errors

Abstract. We investigate the relationship between cutter errors and meshing characteristics of the variable hyperbolic circular-arc tooth trace (VH-CATT) cylindrical gears. Firstly, based on the tooth surface forming principle, the tooth surface mathematical model with cutter errors is derived. Next, the mathematical models of tooth contact analysis and load tooth contact analysis are developed to calculate the contact trace, load transmission error, tooth surface load, and load distribution coefficient. Then, the equation of the tooth surface contact ellipse and the formulas of the main curvature direction angle are derived. Finally, the influences of the cutter errors on the contact ellipse, tooth surface contact trace, load transmission error, tooth surface load, and load distribution coefficient are analyzed. The research shows that all of the cutter errors have a certain influence on the contact ellipses, except for the translation error Δx. The rotation angle error γ and the translation error Δy make the contact position deviate from the middle section; all the cutter errors have a certain influence on the actual meshing line, except for the translation error Δx and the tooth line radius error ΔRT. The rotation angle error γ and the tooth line radius error ΔRT have a bigger influence on the maximum load; the cutter errors mainly affect the load distribution coefficient of the single-tooth meshing area. Except for the tooth line radius error ΔRT, all cutter errors make the amplitude of the load transmission error increase. These research results are helpful for the performance improvement and service life study of the VH-CATT cylindrical gears.