In the aspect of tooth surface error correction of spiral bevel gear, in the past, the tooth surface error correction only depends on the inspection and correction of rolling inspection machine, most of which depends on the experience of machine tool operators. It often needs more than ten times of trial cutting to obtain the appropriate contact area. This situation lasted for a long time until Gleason developed the tooth surface error correction technology based on the tooth surface coordinate measurement of spiral bevel gear in the 1990s. The tooth surface error correction technology reduces the error of each step of the tooth surface to the minimum value through the coordinate measurement of the tooth surface of spiral bevel gear. The evaluation of the tooth surface error is completed by using the square sum of the error and the root mean square of the error. The tooth surface modification calculation is carried out by using Gleason’s cagetm4win software module. The machine tool adjustment parameters can be obtained by automatic program. The correction of the contact area can be completed only by one or two trial cuts, replacing the traditional rolling inspection machine One of the core technologies of Gleason is that it does not disclose the complex process of external computing. In addition, Gleason also provides a method to measure the contact spots on the tooth surface by video digital imaging technology. By manually setting the rotation and magnification of the image, the theoretical tooth segment is matched with the real video imaging tooth segment, and the coordinate system of the real tooth segment is established. This method has high accuracy and belongs to the patent of Gleason company.
Due to the influence of the motion accuracy of the gear milling machine, the manufacturing and installation accuracy of the cutter head and other factors, the actual tooth surface processed according to the designed processing parameters often deviates from the theoretical tooth surface, and its transmission performance can not meet the design requirements. Therefore, the theory and method of spiral bevel gear tooth surface detection, tooth surface error correction and detection equipment have been concerned by many scholars and enterprises. Aiming at the approximation of Gleason’s calculation formula, Xiong Ya studied the tooth surface correction direction of the accurate calculation method of spiral bevel gear, so as to avoid the diagonal contact caused by curvature correction. Liu Yixing studied the relationship between the contact mark of hypoid gear pair and the curvature correction of tooth surface. Different from the curvature correction of tooth surface in the direction of tooth length and tooth height in Gleason calculation card, he investigated from the direction of contact trace and put forward the appropriate value of curvature correction. Pu Zhixiang studied the correction of the bridge contact area of spiral bevel gears. Zhang, Litvin and Lin represent the real tooth surface as the sum of two vector functions, one of which represents the function of the theoretical tooth surface determined by the adjustment parameters of the machine tool, and the other represents the function of the difference between the real tooth surface and the theoretical tooth surface. The deviation of the mesh points of the tooth surface is measured by the CNC coordinate measuring machine, and the bicubic spline function is used to represent the deviation function. Therefore, the TCA (tooth contact analysis) analysis of the tooth surface of the real spiral bevel gear can be carried out.
Gosselin proposed that the machining parameters be inversely calculated from the actual tooth surface, and the corresponding theoretical tooth surface is obtained. The tooth contact analysis is carried out to predict the transmission performance of the actual tooth surface. Suh obtains the tooth surface coordinates through three coordinate measurement, and then uses nubs surface fitting to obtain the virtual tooth surface model. By comparing with the theoretical tooth surface model, Suh obtains the tooth surface error. Tamura measures the actual tooth surface points through the CMM and uses the least square method to fit to obtain the fitting tooth surface determined by the machining parameters. Through this method, the error between the machining parameters and the theoretically designed machining parameters is obtained as the error compensation and correction basis of the machining parameters. Sun Dianzhu and others determined the meshing area and transmission error of the real tooth surface based on the measured tooth surface grid node coordinates of the CMM, and combined the surface modeling and CAGD (Computer Aided Geometric Design) theory with the classical gear meshing theory, converted the tooth surface error of the large wheel to the tooth surface of the small wheel, and only compensated the small wheel during tooth cutting. Wang Jun and Wang Xiaochun established the theoretical tooth surface model of Gleason spiral bevel gear and gave the planning method of measurement grid. The positioning and measurement method of spiral bevel gear on CMM is discussed. According to the measurement results of real tooth surface, the deviation between theoretical tooth surface and actual tooth surface is described by difference surface. Using the characteristic parameters of difference surface, the corrected values of parameters of gear cutting machine tool can be solved quickly and stably. Wang Zhi and others measure the error of the gear by meshing a special measuring gear with the measured gear, and use the error separation method to measure the single error and comprehensive error of the measured gear. Pan Weimin et al. Established the CAD model of spiral bevel gear through machining simulation, reconstructed the tooth surface based on the three-dimensional measurement results of the actual tooth surface, and adjusted the machining parameters according to the error between the actual tooth surface and the theoretical tooth surface. Zhang Hua and others studied the tooth length curvature correction of four-axis linkage spiral bevel gear milling machine. Li Tianxing and others identified and analyzed the tooth surface error and its influencing factors based on the tooth surface detection information, deduced the mapping relationship between the machine tool motion parameters and the tooth surface error, developed the automatic tooth surface error identification system to automatically determine the error type and the correction items of the machine tool motion parameters, established the motion correction model of the four-axis linkage NC gear milling machine, and realized the automatic correction of the machine tool motion parameters through numerical optimization calculation, The automatic feedback of the corrected parameters to the NC machine tool is completed through the measurement and processing network.
At present, the research on tooth surface error correction in China is in the experimental stage, and there is no mature technology with independent intellectual property rights applied to practical production. The most common method used by domestic spiral bevel gear manufacturers to adjust the gear contact area is still the roll inspection visual measurement method, that is, the spiral bevel gear is installed on the rolling inspection machine according to the designed theoretical position, the tooth surface is coated with colorant (such as red lead powder), the spiral bevel gear is allowed to observe the tooth surface contact area after operation, and the adjustment parameters of the machine tool are adjusted according to the conditions of the contact area. It is complicated for many times, and finally the appropriate adjustment parameters of the machine tool are determined. Only a few domestic spiral bevel gear processing enterprises have adopted the tooth surface error correction module (cage m4win) introduced from Gleason company, which is very expensive.