Research On Measurement Error Compensation Method Of Spiral Bevel Gear Tooth Surface Based On Tooth Surface Registration Technology

As an important transmission component,spiral bevel gears have an irreplaceable position in many fields,with the advantages of smooth transmission,high transmission efficiency and strong load-bearing capacity.With the development of manufacturing industry,the manufacturing quality and measuring accuracy of spiral bevel gear are required more strictly.CNC gear measuring machine,as the main gear measuring equipment at present,can realize efficient and accurate measurement of spiral bevel gears.However,the gear measuring machine has a complex mechanical structure,high sensitivity to the measurement environment,and the measurement process is not coincident with the measured gear design reference and the measurement reference.The existence of all these factors will lead to the generation of measurement errors.Therefore,this paper analyzes the coordinate measurement method of spiral bevel gears,plans the tooth surface measurement path,explores the sources of measurement errors,and investigates the compensation method for the measurement errors that exist between the actual measured tooth surface and the theoretical tooth surface.In this paper,the error compensation problem was transformed into the rigid alignment problem of the surface,and the alignment models of the measured tooth surface based on the improved Horn method,point-to-point ICP algorithm and point-to-plane ICP algorithm were established respectively by combining the point cloud characteristics of the tooth surface,and the limitations of each model were analyzed.Secondly,this paper took Genetic Algorithm(GA)as the main body,proposes to combine the evolutionary algorithm with the alignment algorithm,used the correspondence between the Euler angle and the rigid transformation matrix,transformed the rigid transformation motion parameters into a six-dimensional genetic chromosome,and searched for the optimal transformation matrix to align the measured point cloud to the ideal point cloud by the powerful optimization-seeking ability of the genetic algorithm.Aiming at the problems of unstable operation results,high demand on initial population and easy to fall into local optimal,the initialization method and search process of genetic algorithm were proposed to improve.Horn method was combined to limit the population generation space.Then the initial population was screened by the reverse learning strategy within the limited range.Finally,adaptive strategy and simulated annealing algorithm were combined to disturb the genetic search process to avoid falling into local optimal.Finally,the error compensation model of tooth surface measurement based on improved genetic algorithm was established.The experimental results show that by improving the Genetic Algorithm error compensation model,the average error between the measured tooth surface and the theoretical tooth surface can be reduced from 9.45μm to 2.36μm,and the error compensation rate can reach about 74%.Compared with the Horn method compensation model,it has faster convergence speed and better error compensation effect,and compared with the ICP algorithm model,it has stronger searching ability.This algorithm provides an effective means for the error compensation of ordered point cloud obtained by contact measurement.