The derivation of transformation matrix before and after thermal distortion for modification

Abstract

The transformation matrix before and after thermal distortion is deduced for modification. Firstly, the thermal distortion equation of tooth profile is deduced based on noninvolute characteristic caused by the change of temperature. Secondly, the equation of temperature distribution along the direction of tooth surface width is deduced according to the measured temperature of instantaneous contact points. By combining it with the equation of temperature change along the radial direction, the temperature distribution of whole gear can be given. Finally, the thermal distortion equation of tooth surface and the transformation matrix before and after thermal distortion are deduced. Illustrated by an example of a high-speed helical gear, the surface equation of thermal distortion is obtained by the above methods. Compared with tooth surface before thermal distortion, the tooth surface after thermal distortion has significant change. In addition, compared with the theoretical values, the calculated values have little difference. The derivation of transformation matrix before and after thermal distortion provides the basis of theory for modification using the method of tooth contact analysis and loaded tooth contact analysis.

Keywords

Coordinate transformation matrix thermal distortion noninvolute characteristic high-speed transmission modification

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