Research On Error Measurement And Analysis Method Of Non-circular Gear

Non-circular gears,which are mostly used in transmission with non-constant ratio,show a great potential in engineering equipment,agricultural equipment,textile equipment and other fields.Though the design and processing theories of non-circular gears are becoming perfect in recent years,the error measurement problem has become an obstacle that limits its development.Therefore,the error measurement and error analysis have great theoretical and practical values for the development of non-circular gears.Measurement method and analysis theory of the circumferential errors,topological errors of tooth surface,and compositive kinematic errors are studied in this dissertation to solve the existing problems in error measurement of non-circular gears.The main researches are showing below:The first part is about the measurement method and analysis theory of circumferential errors.Firstly,the key technologies of tooth profile sampling by Coordinate Measuring Machine(CMM)are studied,including the establishment of measurement coordinate system,the transformation of designing coordinate and measurement coordinate,and the compensation method of probe's radius errors.Since the analytic method in solving the intersection points between pitch curve and tooth profile shows a low efficiency,a numerical solution method is proposed,and the validity and efficiency of the numerical solution method are verified via a specific example.Then the circumferential errors measurement and analysis of the third-order non-circular gear pairs are finished,and the pitch errors and tooth thickness errors of the gear pairs are calculated.A comparative experiment of circumferential errors measurement is carried out by employing the CNC image measurement instrument.The results of these two methods are highly consistent,verifying the validity of the measurement results of CMM.The two experimental results show the feasibility of using the CMM as a measurement tool for the profile of non-circular gears and the correction of the proposed calculation and analysis method of the circumferential errors.The second part is about the measurement method and analysis theory of topological errors of tooth surface.A method of mesh point sampling by CMM is firstly studied,and the mesh planning of the tooth surface and the overall measurement path planning are discussed respectively.Then a mathematical model of topological errors of tooth surface is established,and five statistical error indicators are proposed to measure the errors of the tooth surface.The method of separating the error components of each order in the differential surface is studied.Finally,the third-order non-circular gear pair's topological errors of tooth surface are measured and analyzed,and statistical error indicators of tooth surface,error surfaces from zero-order to second-order are calculated.The experimental results show that it is feasible to use CMM as a tool to measure the three-dimensional tooth surface of non-circular gears and the proposed calculation and analysis method of the topological errors of tooth surface are correct.The third part is about the measurement method and analysis theory of compositive kinematic errors.First of all,based on the measurement principle of compositive kinematic errors,an electronic meshing instrument is developed,which can be used for both single-sided meshing and double-sided meshing.Then the central distance variation and transmission angle errors of the third-order non-circular gear pair are measured via the double-sided and single-sided meshing functions of the electronic meshing instrument respectively.The mathematic model of radial compositive errors of pitch curve is established,and the double-sided meshing function of electronic meshing instrument is employed to realize the variable central distance transmission which is composed of non-circular gear and circular gear.In this case,the measurement of radial compositive errors of pitch curve of third-order non-circular gear is completed.The experimental results show that the proposed electronic meshing instrument can correctly measure the variations of central distance,transmission angle errors,and radial compositive errors of pitch curve of non-circular gears.