Research On Three-dimensional Measurement Method For Gears Based On Line Structured Light

Gear is a key transmission part widely used.Gear measurement is the main measure to ensure the accuracy and performance of gear.With the gear industry becoming the largest industry in China’s mechanical basic parts,the rapid and comprehensive measurement of large quantities of finished gears has become an urgent problem for the gear industry.Gear detection can be divided into contact measurement and non-contact measurement.At present,the gear contact measurement technology has reached the bottleneck stage,especially the measurement efficiency has been difficult to improve significantly.However,there are still some common problems in its three-dimensional measurement that are not well solved,which affects the application and popularization of line structured light（abbreviated as LSL）measurement of gears.Therefore,with the support of the national natural science foundation and national key R ＆ D program,through theoretical innovation,this paper carries out theoretical and practical research on the determination of the center of small arc mandrel standard parts under LSL,the calibration of linear structured light probe posture and turntable center of gear measuring system,the capture of complete three-dimensional profile by gear LSL offset,and the evaluation of full tooth surface error.Finally,a method of measuring gear with LSL is formed.The experimental results verify the validity and accuracy of the gear LSL measurement method.The main research work of this paper includes:（1）A method of measuring gear offset by LSL is proposed.Aiming at the problems of shadow effect,low sample density and low reliability in LSL measurement of gear "steep" tooth surface,the optimal position and orientation of offset,quantitative index and its calculation method are proposed,and the theoretical derivation is carried out from tooth surface model to offset measurement tooth surface.In order to distinguish the essential differences between the offset and non-offset alignment and the contact measurement,the gear LSL measurement experiments were carried out respectively.The verification results show that the accuracy and reliability of the offset measurement of LSL is higher than that of the center alignment measurement of LSL.The point cloud of tooth surface obtained by this method is more in line with the requirements of the latest international gear accuracy standards,and the evaluation index results are basically consistent with the reference values measured by klingelnberg P26 gear measurement center.（2）A new determination method for determining the reference point of gear measurement is proposed.Aiming at the basic problem of reference point determination in gear measurement,it is a difficult and common problem in the research field to accurately determine the reference point of small arc profile.The mathematical model of geometric cylindrical mandrel contour is established,and the parametric ellipse contour is introduced to represent the mandrel arc captured by the LSL.The mapping relationship between the parameter angle and the orthogonal distance error of the contour point is constructed.Finally,the Levenberg-Marquardt iterative search achieves the global minimum of the objective function,that is,the optimal ellipse corresponding to the profile satisfies the minimum sum of squares of the error set.The robustness,anti noise and accuracy of the proposed method are verified by simulation and experimental results.The experimental analysis shows that the new method can adaptively achieve the accurate acquisition of the reference point.Even if the LSL sensor has installation error,the method can still accurately calculate the real center feature of the mandrel and the ellipse parameters intercepted by the structured light plane.The new method is suitable for obtaining the datum point of gear measurement and meets the technical needs of gear measurement with LSL.（3）A new calibration method of coordinate relationship for gear measurement under LSL is proposed.Aiming at the problem of poor repeatability caused by the difference of light field in different curvatures of LSL in traditional spherical calibration.In the new method,the cylindrical mandrel is used as the calibration part,and the curvature of the captured contour parameters is relatively stable and the calculation accuracy is high,which ensures the repeatability and accuracy of calibration.Secondly,based on the uniqueness of the mandrel calibration center,a method of simultaneously calibrating the extrinsic parameters of the LSL system and the tilt of the turntable tip is proposed.Multiple groups of non-collinear calibration points are obtained by two scanning strategy.These generated non-collinear calibration points are satisfied with the calculation of extrinsic parameters of relative motion model.Experimental results verify the accuracy and effectiveness of the proposed method in the integrated system.In particular,the calibration process of the proposed method is easy to implement and has high accuracy,which is suitable for fast calibration and field calibration of CNC measurement system integrated with LSL.（4）The error evaluation system of gear full tooth surface based on threedimensional information is proposed.A new system of circumferential,normal and tooth pattern based on 3D representation of tooth surface error is proposed,including the mathematical model expression of OCPH,the construction of new statistical indicators,and the accuracy evaluation and analysis.The method avoids the simplification of error representation,effectively reduces the interference of random error measurement,and can directly and concretely obtain the information of the error size,dispersion degree and distribution position of the complete gear.The simulation and the experimental results verify the effectiveness and practicability of the proposed evaluation system,effectively solve the shortcomings of the traditional small sample measurement and evaluation methods,which is obviously superior to the traditional representation and evaluation methods.The gear error multi line set or surface set representation analysis is in line with the demand of tooth surface analysis with large sample size,and more suitable for the gear line structural light measurement.（5）The data processing software of gear line structured light is developed.On the basis of solving the key problems of datum point calculation,system coordinate relationship calibration,tooth surface data acquisition and error three-dimensional characterization,the gear LSL data processing software is developed by using G language software labview and matlab.The software provides a non-contact gear measurement data processing method,realizes the basic parameter calculation,error characterization and accuracy evaluation of 2D and 3D tooth surface,and provides a practical verification calculation platform for gear non-contact multi-dimensional rapid measurement theory.The various methods and theories of this paper are integrated by the software,and successfully applied in the gear LSL measuring machine.