The digital modeling of Cycloid Bevel Gear and hypoid gear is to establish the three-dimensional solid model of Cycloid Bevel Gear and hypoid gear by using the computer analysis and drawing function according to the coupling principle or processing method. Combined with domestic and foreign research literature, according to the different methods of establishing gear solid model, the digital modeling methods of Cycloid Bevel Gear and hypoid gear can be divided into analytical tooth surface modeling and simulation forming modeling; According to the different principles of establishing mathematical models, analytical tooth surface modeling methods can be divided into tooth surface discrete point modeling and tooth profile curve fitting modeling.
(1) Discrete point modeling of tooth surface
When modeling with discrete points on the tooth surface, first obtain the discrete point information evenly distributed on the tooth surface, including the coordinates of the tooth surface points and their normal vectors, and then import the discrete point data file by using three-dimensional modeling software, such as pro/e, UG, etc, The solid model is established by fitting the surface directly from points or constructing the surface after fitting the curve from points. Among them, there are three kinds of sources of discrete points: a) generated by generating tooth surface equation; b) Given by the simulation program; c) Measured by coordinate measuring machine.
(2) Tooth profile curve fitting modeling
When using the tooth profile curve fitting to build the model, first derive the mathematical equation expression of the tooth profile curve, generally including the tooth line and tooth profile curve, then import the three-dimensional modeling software, use the parametric modeling module to build the surface and establish the gear solid model. Among them, according to the different forming principles of the tooth profile curve, the sources of the tooth profile curve are divided into two categories: (a) based on the gear processing characteristics and the tooth profile forming principle, the long epicycloid and spherical involute equations of bevel gears are derived; (b) The equation of tooth profile curve is solved by using spherical involute theory.
(3) Simulation forming modeling
Simulation forming modeling includes two types:
(a) Simulation of gear machining process with cutting tools: first, select and establish the simulation machining environment, generally including traditional mechanical machine tools and numerical control machining machines, analyze and complete the three-dimensional solid modeling of wheel blank and cutter head, and then install the wheel blank and adjust the machining parameters according to the actual machining state, Then let them move according to the actual machining situation, do Boolean operations at each instant to get the gear solid model, and finally reconstruct the tooth surface according to the accuracy requirements of the tooth surface, and output the solid model.
(b) For the simulation of the meshing between two gears, first establish the solid model of the big wheel (or small wheel) and the solid model of the small wheel (or large wheel) blank, install and adjust the gear position according to the actual meshing state, and then let them move according to the actual meshing situation, and do Boolean operations at each instant to get the gear solid model, Finally, the tooth surface is reconstructed according to the accuracy requirements of the tooth surface, and the solid model is output.