The Tooth Wear Coefficient of a Harmonic Drive

Reduction of the tooth wear rate is one of the main problem to address when designing harmonic drives. The authors describe methods for evaluating wear resistance of the tooth side surfaces in a harmonic drive with a cam wave generator and a flex spline shaped as a cup with a flexible bottom. The results of numerical studies determining the influence of various parameters on the wear of the tooth side surfaces are presented. New criteria — tooth wear coefficient and average wear coefficient — are proposed for theoretical determination of the tooth wear. These criteria take into account the influence of contact stresses and friction paths on the wear. Relations between the wear coefficients and radial deformation of the flex spline, length of the flex spline shell, position of the flexible bearing, and torque are determined. All the calculations are performed using a mathematical model allowing for spatial nature of the deformation and the interaction between the elements of the harmonic drive gears. The resolving system of equations is obtained using the Bubnov–Galerkin method. The coefficients are determined on the basis of the theory of elasticity.

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