Research On Fundamental Theory & Its Practice Of Gear Integrated Error Measurement

Gears, embedded in the national emblem as the symbol of industry, are most widely used fundamental key parts of many kinds of machines. The quality of gears influences the performance of whole machines. Measurement and evaluation are the main approaches to make sure the quality of gears. Automotive gear industry is the most important economic component in gear industry of China. Fast and in-line gear measurement is a key problem to be solved urgently in automotive gear industry. The gear integrated error(GIE) measuring technique, which is invented by Chinese experts, has the characteristics of high efficiency and comprehensive information, and is especially suitable for the in-line rapid inspection of batch produced automobile gear. However, due to some key problems of the fundamental theory of GIE measurement are not solved, the development and application of the GIE measurement have encountered a bottleneck.Through theoretical innovation, this paper solves the four key problems of calculating the theoretical unit curve of GIE, determining the profile evaluation area, compensating the different point contact error during GIE measurement and taking full advantage of the GIE measurement results, and provides a strong support for successfully applying GIE measuring technique to the area of fast inspecton of automotive gears. The correctness, validity and practicability of the proposed method and theory have been verified by targeted experiments. The GIE data processing software that integrates the four innovations has been successfully applied to the workshop.The main contents of this dissertation are as follows:(1) A new method for calculating the theoretical unit curve of GIE is proposed in this paper. This method puts forward the specialized mathematical models of flanks of the gear and the worm, introduces optimization algorithms to replace the solution of a system of implicit differential equations based on meshing theory, and acquires the GIE curves of the involute stage, the approach stage and the recess stage by one set of equations. The misalignment of the worm and gear, as well as the modifications or errors of the tooth flanks of the gear, has been considered in the procedure of calculation. The proposed method solves the problem of the acquisition of the GIE theoretical unit curve and fulfills the needs of the GIE measuring technique.(2) A new method to determine the profile evaluation areas in measured GIE curves is proposed in this paper. Compared with the traditional methods, the new method has three important improvements. The most important one is to put forward the judgment that the reliabilities of data in different stages of the GIE unit curve are different. Based on this point, a new method to determine the locations of profile evaluation areas of a GIE curve mainly according to the data of recess stages is proposed. In order to verify the correctness and effect of the proposed method, experiments of measuring the master gear and the part gear under different rotational speeds are conducted and the results of three different methods are compared to each other. The experimental data shows that the new method has better consistency of the calculated start positions of GIE units and can meet the requirements of rapid inspection of automobile gears. Especially when it comes to measure part gears, the accuracy of new method is much better than that of the conventional method.(3) The different point contact error and its correction method in GIE measurement are proposed. By analyzing the phenomena of different point contact in GIE measurement, the definition and calculation method of different point contact error and the error correction method based on quasi-morphological filtering are proposed. The inherent difference between the errors resulted from the different point contact and the curvature interference are identified. Simulations of the different point contact error correction and experiments of the different point contact error correction for actual measured data are conducted. Theoretical analysis and experimental data show that the measurements after correction are closer to the true shape of the actual measured tooth profile, and the application of this method has significant effect and can improve the measurement accuracy of the gear instruments based on GIE measuring technique.(4) A new system for evaluating gear accuracy based on full information is proposed in this work. First, a three-dimensional model to express the tooth surface errors is proposed. Then, the definitions and extraction methods of the characteristic data sets are proposed based on the three-dimensional expression of errors. The calculation formulas of new parameters of accuracy are presented. Then, the evaluation system of gear accuracy based on full information is established by composed of selected parameters. Simulation and actual experiments show that the new evaluation system can take full advantage of the gear integrated error measurements, the proposed parameters are less sensitive to the random measuring errors and can correctly and fully reflect the actual performance of the gear. The new evaluation system is helpful to analyze the error source of manufacture and to evaluate the stability of process, and is especially suitable for the high efficiency in-line measurement of automotive gears.(5) The data processing software of GIE is designed and applied. Combined with the evaluation system of gear accuracy based on full information, the data processing software of GIE is designed based on the solving of the key problems of calculating the theoretical unit curve of GIE, determining the profile evaluation area and compensating the different point contact error during GIE measurement. The software provides a universal method for processing the GIE data and improves the consistency and reliability of the evaluating results of gear accuracy. The theories and methods proposed in this paper are integrated in this software, and the software has been successfully applied on an in-line rapid inspection machine of automotive gears.