Research On Tooth Surface Modeling And Measurement Method Of Cylindrical Worm Gear

Worm drives with smooth transmission,strong bearing capacity.low noise.small vibration,etc,arc widely used in automotive,machine tool.enoineering machinery and other fields.As the main components of mechauical products,the processing accuracy and manufacturing level of worm gear directly affect the performance and the quality of mechanical products.However,because of the adjustment of the machining parameters and tool in the wonn gear machining,it must have some errors in the tooth surface which affccts the precision of transmission system and dynamic characteristics(especially vibration and noise)directly.Therefore,the processing principle and method of worm and worm gear are studied,and the real tooth surface of worm oear is analyzed and constructed.It lays the foundation for further analysis of worm gear tootb error measurement and motion simulation,also providcs the basis for the correction theory and technical adjustment of machine tool.In this paper:the modeling of the cylindrical worm gear tooth surface which is most widely used is researched,and calculate the theoretical tooth surface of the Archimedes worm oear(ZA-Type wonn gear)and Involute worm gear(ZI-Type worm gear).Firstly,based on the processing principle of the worm and worm gear,the coordinate system of the worm machuiing and the meshing coordinate system of the worm and worm gear is established According to the gear meshino principle,the meshing equation of the worm and worm gear is deduced.Finally.the tooth surface equation and the unit normal vector of the worm gear are solved.It lays a theoretical foundation for the calculation and measurement for tooth surface of worm gear.Secondly,based on the rotation projection method,the worm gear tooth surface is projected onto the shaft section,and the grid planning is carried out,then the grid node coordinates are solved according to the geometric relations of the grid points.According to the basic parameters of worm and worm gear and grid planning,the nonlinear equations based on coordinate formula and meshing equation of grid nodes are calculated by MATLAB,and the theoretical tooth surface coordinates and the unit normal vector of the ZA-Type worm gear and ZI-Type worm gear are solved.Then,the parameters input interface is designed using the MFC tool of VC++,using MATLAB as a calculation tool to generate MATLAB dynamic link library,then VC++ call MATLAB dynamic link library and complete the design of worm gear calculation software.Finally,the principle and composition of the three coordinate measuring machine is introduced.According to the measuring procedure of the three coordinate measuring machine,the workpiece coordinate system and the measuring coordinate system of the worm gear are converted.In the three coordinate measuring machine,the actual tooth surface of ZA worm gear is detected,and the normal deviation of tooth surface is obtained.The detection result proves that the mathematical model of the worm and worm gear and the method for solving grid coordinate points is feasible.