Spiral bevel gears are widely used in mechanical transmission systems with intersecting or staggered shafts, and their tooth surface accuracy directly affects the performance of spiral bevel gears. For the single tooth surface detection technology, the digital precision measurement and reverse adjustment correction technology can be used to truly and quantitatively express the tooth surface deviation information; Compared with the traditional rolling inspection technology to determine the accuracy of the tooth surface, its detection efficiency and accuracy are significantly improved. Many scholars have studied the digital measurement and feedback correction of spiral bevel gears. Wang Zhonghou et al. gridded the tooth surface of spiral bevel gear, constructed a digital real tooth surface containing tooth profile error and installation error, and proposed a high-precision digital real tooth surface contact analysis method of spiral bevel gear. On the basis of integrating digital tooth surface measurement and anti modulation correction of spiral bevel gear measuring center, Li Jubo et al. proposed a network closed-loop manufacturing model of spiral bevel gear to improve the machining efficiency and quality of tooth surface. Li et al. put forward a method for accurately measuring three-dimensional surface based on one-dimensional probe by digitizing the tooth surface. The above related research results have been widely used in the production and tooth surface inspection of spiral bevel gears in enterprises.
In the actual tooth surface heat treatment process, it is difficult to detect the error of each tooth surface as a whole, and the tooth surface quality of the whole batch of spiral bevel gears only depends on sampling inspection to determine; And the probability distribution of these data is unknown, which can only estimate and predict the trend and law of tooth surface changes after heat treatment of spiral bevel gears. How to detect and evaluate the machining quality of the whole batch of spiral bevel gears efficiently and accurately with the help of data statistics theory is a key problem that must be solved in the production of spiral bevel gears.
Self help method is a method that can resample small sample data, generate large samples and simulate the overall characteristics. Its feature is that it can make an approximate estimation of the whole sample based on existing small sample data. It has been more than 40 years since Efron first proposed this method, and has basically formed a complete theoretical system. Xia Xintao et al. applied the self-service method to bearings and accurately evaluated the machining error of machine tools. Qin Luosheng et al. constructed the prior distribution of bearing life distribution parameters through self-service method, and obtained the reliability analysis results under bearing competitive failure to improve the reliability of bearings. More and more scholars have applied the self-help method to other fields and achieved good research results, but there are few reports on the literature of error statistics of spiral bevel gears.
(1) Under the condition of small samples, the self-service method can effectively estimate the confidence interval and true value of the mean and variance of the gear surface measurement sequence points with 95% confidence.
(2) The tooth surface is reconstructed by NURBS method, and the position relationship between the actual mean difference surface and the self-help mean difference surface is compared. The position relationship between the actual mean difference surface and the theoretical surface remains unchanged; With the increase of sample elements, the variation of tooth surface deviation can be more accurately reflected.
(3) Through the application of self-help method, the variation range of tooth surface error of spiral bevel gear after heat treatment is determined, and the variation law of tooth surface deviation of spiral bevel gear after heat treatment is effectively predicted, which provides a theoretical basis for guiding the modification of tooth surface processing parameters and efficient and stable production.
The self-service statistical model is used to analyze the data of tooth surface measurement points of the same batch of spiral bevel gears with the same spiral bevel gear material, CNC milling method and heat treatment specification, which provides a theoretical basis for guiding tooth surface processing parameter correction and efficient and stable production.