Abstract
Due to the manufacturing and assembly errors of the spiral bevel gear, the deviations between the measured tooth surface and its theoretical tooth surface will affect the measurement results of the tooth surface. After analyzing the tooth surface deviation of spiral bevel gear, this paper provided a compensation method to compensate the eccentricity and inclination errors by the registration of the theoretical and measured tooth surface. An improved iterative closest point (ICP) algorithm for the registration of the tooth surface was provided. The distance between the point in measured tooth surface and the nearest point in theoretical tooth surface is used to replace the minimum Euclidean distance, and the damping Gauss-Newton method is used to solve the geometric transformation matrix. Simulation experiments were carried out to verify the proposed compensation method. The compensation effect is over 93% for the concave tooth surface and over 89% for the convex tooth surface of the spiral bevel gear. The results also show that the improved ICP algorithm could compensate the eccentricity and inclination errors of the spiral bevel gear more precisely than the basic ICP algorithm.
Highlights
Spiral bevel gear is one of the key basic components in mechanical equipment
Simulation experiments were done to verify the compensation method, and the results show that the algorithm is useful for the precision compensation of the eccentricity and inclination errors
The results show that the improved iterative closest point (ICP) algorithm is more useful for the precisely compensation for the eccentricity and inclination errors of the tooth surface
Summary
Spiral bevel gear is one of the key basic components in mechanical equipment. It has the advantages of large coincidence, high bearing capacity, stable transmission, high transmission efficiency, long service life, and low noise, which makes it an indispensable part of many mechanical equipment. The ICP algorithm is an iterative optimization algorithm based on the least square method It repeats the process of calculating the geometric transformation matrix to updating the relationship between two groups of surface data, until it meets the best registration criteria. Combining with the definition of the tooth surface deviation of spiral bevel gear, the distance between the point Pi in the measured tooth surface (target surface) and the nearest point Q0i in the theoretical tooth surface (reference surface) is used to replace the minimum Euclidean distance in basic ICP algorithm. As the deviations between the measured tooth surface and its theoretical tooth surface is too small, and the selected initial point is considered near the optimal solution, so the damping Gauss-Newton method is suitable to solve the geometric transformation matrix.
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