Gear Transmission Performances Oriented Precision Design Methodology Of Spiral Bevel Gear Milling Machine

Spiral bevel gear milling machine is a key equipment of spiral bevel gear manufacturing. The precision of the machine directly influences the machining precision of the gears, and further influences the transmission performances as the accuracy, the stability and the load uniformity of the gear transmission. Due to the complexity of the structure and the working principle of the machine, and thus the difficulty to set up the mapping relationship between the precision of the machine and the machining precision of the gear, the up-to-date conventional precision design of the spiral bevel gear milling machine is still experience based. Such precision design may lead to a poor design with insufficient precision, or over precision unnecessarily increasing manufacturing cost and difficulty. Aimed to improve such a shortage of the precision design and to give an appropriate estimation of the cost-effective precision of the machine, the gear transmission performance oriented design methodology for the precision of the spiral bevel gear milling machine is proposed and studied in this thesis. The methodology is expected to help engineers to design cost-effective machine tool. The contens and contributions of the thesis are as follows:(1) Mathematical models for the tooth meshing surface and the transition surface are established of the gear by hobbing with uniform rolling ratio and the pinion by hobbing with modified rolling ratio. The models are validated to be correct via the comparative analysis between the theoretical and model-calculated discrete points of the tooth surface.(2) Two types of topology are clarified for normal and undercutting tooth profiles of the spiral bevel gears. A numerical algorithm for judging undercutting is set up via introducing a variable of tooth height ratio. A 3-D modeling method is proposed for the spiral bevel gear by planning and calculating the discrete points on the axial cross section of the gear. This method is applicable to both normal and undercutting tooth profiles.(3) Algorithms for solving the boundary of contact trajectory with adaptive iterative step and for setting initial coordinates of the contact points on the tooth surfaces are proposed, which resolved the unstability in solving the contact points and the difficulty in determining the boundary of contact trajectory. An algorithm is developed based on the real tooth surface for solving the contact region in spiral bevel gear pair, which can eliminate the error in the conventional tooth contact analysis (TCA) of parabolic tooth surface approximation.(4) Adjacent body transformation matrixes for the spiral bevel gear milling machine are established, which comprehensively contain geometrical errors of the machine with multi-body kinematics. Then the tooth surface models with geometrical errors are obtained. Choosing tooth profile error and circular pitch error as items of tooth surface error evaluation, approximate models of tooth profile error and circular pitch error are established by regression analysis.(5) According to the requirements of tooth surface precision, precision analysis of the machine is carried out by Monte Carlo method. The initial values and bounds of accuracy specifications are determined from the precision analysis. A comprehensive optimal model is established,by taking the minimization of the manufacturing cost of the machine as the objective and the requirements of tooth surface precision as the constraints. The optimal precision specifications of the machine are obtained by solving the optimal model with Directed Heuristic Search algorithm. The optimal precision specifications are in better accordance with the mockup test results, which shows that the proposed design methodology for the precision of the machine in this thesis is reasonable.(6) A technical flowchart for the precision design of the spiral bevel gear milling machine is summarized based on the achievements of this thesis. And a software system for the precision design is developed with using re-development of CAD and database technique.Although the object of this thesis is the spiral bevel gear milling machine, the idea and the principle of the methodology are also applicable to other manufacturing equipments of complicated structure and working principle.