Research On Visual Measurement Technology For Tooth Profile And Radial Circle Runout Of The Involute Cylindrical Gear

Tooth profile and radial runout are two important tested parameters of the involute cylindrical gear.Radial runout can be divided into radial circle runout and total radial runout.It is usually just required to measure the radial circle runout of the gear in production due to its narrow width.Based on existing gear non-contact measurement technology and according to the national standard GB/T 13924-2008,this paper studies the vision measurement method for the involute profile and radial circle runout of the involute cylindrical gear and gear shaft.Using CCD camera and standard industrial lens,three-dimensional coordinates of the detected points of tooth profile are obtained by pinhole imaging principle of the camera.On the basis of reducing the influence of the projection distortion of the gear center,the measurement model of tooth profile and radial circle runout of the involute cylindrical gear is established and verified by experiments.Firstly,the method to obtain 3D coordinates of the detected points on the gear is studied by pinhole imaging principle of the camera.The gear is measured by machine vision and the gear shaft is measured by line structured light vision due to their different structures.Gear end-face is the measurement plane of the gear.To calibrate the gear end-face,a calibration method only by a ring with known diameter is proposed.The method can solve the problem that,the calibration accuracy may be influenced by diameter and chamfer of the gear center hole,and flatness of the gear end-face.A measurement system is established when measuring the gear shaft by line structured light vision,and the measurement system is calibrated by the multi-objective optimization algorithm.Secondly,it is necessary to determine centers of circles and ellipses on the gear measurement plane for the vision measurement of the involute tooth profile and radial circle runout.Therefore,the method to reduce the influence of projection distortion on the acquisition of circle and ellipse centers on the gear measurement plane is studied.To obtain the general circle center on the gear end face,a method to reduce the influence of projection distortion is proposed by establishing the oblique cone equation of the addendum circle imaging.To obtain the center of gear center hole on the end face,three identical rings are placed in the hole to reduce the influence of projection distortion and avoid the influence of the chamfer of the center hole on the edge detection.To obtain the light ellipse center of gear shaft addendum,a method to reduce the influence of projection distortion is proposed by establishing the oblique elliptical cone equation of the light ellipse imaging.Thirdly,aiming at the involute tooth profile and radial circle runout,the machine vision measurement model of gear and the line structured light vision measurement model of gear shaft are established respectively.The gear involute profile is usually short,so it is difficult to ensure the fitting accuracy of involute profile by algebraic fitting method.Therefore,the least square geometric fitting method of involute profile is proposed to improve the measurement accuracy and the effectiveness of the method is tested by measuring the pitch deviation.The measurement model of gear radial circle runout value and direction is established by geometriccally fitting the involute profile and addendum circle.Finally,vision measurement methods for tooth profile and radial circle runout of the involute cylindrical gear are analyzed and verified by experiments.The simulation and experimental results show that the measurement methods can effectively realize non-contact measurement of the gear involute profile and radial circle runout,and the measurement accuracy is mainly affected by the calibration accuracy and the accuracy of detected points on the image.This research plays an important role in the development of machine vision measurement technology and advanced manufacturing technology.