Geometric Modeling Of Spiral Bevel Gear Based On Virtual Gear Measuring Center

Spiral bevel gear is one of the main components for driving with intersecting axes, and the tooth surface accuracy and meshing behavior are the keys to ensure the overall performance including the product efficiency, motion noise, driving accuracy and service life. As the tooth surface geometry and machining process of spiral bevel gear are extremely complex, the tooth surface accuracy and meshing behavior are difficult to control, and the accurate detection of the tooth surface is the basis of improving the machining accuracy.The tooth surface is generally detected by using special measuring software in gear measuring machine or three-coordinate measuring machine, and the measurement results commonly rely on the comparison between different instruments. The tooth profile is commonly measured by comparing the theoretical measurement points and the actual, however, different programmers probably adopt different schemes, resulting in the measurement results cannot be compared.It is put forward that to measure the tooth surface model for error known in the virtual gear measuring center to verify the rationality and validity of the measurement procedure. The tooth surface model was built based on the milling machining process and meshing theory, which solved STL file conversion loss by artificial structure to establish the high accuracy model. In addition, the error control strategies for the tooth surface were proposed, and the tooth surface model with known error was constructed to be tested in the virtual gear measuring center to verify the accuracy of the measurement scheme. The main achievements and innovations are as follows:Firstly, on the basis of studying the meshing theory and the actual process of spiral bevel gear, the basic processing model of machine tools was abstracted, and the tooth surface equations of a gear pair were derived from the cutter blade surface equations through a series of transformation for machining coordinate systems, and finally their tooth surface mathematical models were established.Secondly, according to the requirements of virtual gear measuring center on the virtual workpiece, the entity model for visualization and gear tooth surface model for collision detection were established. The model for visualization, established by a third-party software, has relatively low accuracy. It was mainly used to display the virtual workpiece in the virtual gear measuring center. The establishing approach of the tooth surface model for collision detection solves low accuracy when the STL file converts, STL files were put forward to be man-madly structured, which greatly improved accuracy of the data in the STL file and possessed high theoretical value and practical significance on the virtual workpiece modeling for high precision. In addition, this design method helps to accurately complete the accurate detection of the virtual tooth surfaces, providing high reference value for the modeling of other else complex workpieces in future.Thirdly, the error sources of virtual workpiece established in two ways were analyzed in detail, and the error of the gear tooth model for collision detection were quantitatively calculated, and finally according to the virtual measurement requirements, the error control strategies were put forward. In addition, the tooth surface model for error known was established, providing the effective theoretical data source for the verification of measuring scheme and solving no comparison problem of the measurement results between different instruments, and the error brought by measurement software was successfully isolated, lay a solid foundation for error separation in actual measuring process.