Advanced Theories of Hypoid Gears

Preface. Analysis of Combined Mismatched Tooth Surfaces Up To and Including Third Order Contact. Introduction. Establishment of moving frames. Differential forms of moving frames. Restricting conditions for contact. Second order contact analysis. Third order contact analysis. Example calculation. Conclusion. A Direct Method for Calculating Geometric Parameters of Tooth Surfaces Up To and Including Third Order. Introduction. The curvature tensor of a surface. Geometric parameters of the generating flank. Second order geometric parameters. Third order geometric parameters. Example calculation. Conclusion. Analysis of Rates of Change of Contact Situations of a Gear Pair under Vertical (V) and Horizontal (H) Check. Introduction. The longitudinal direction and geodetic curvature of longitudinal line. The rates of movement in V and H directions. The rates of change of the second order contact situations. Example calculation and experimental results. Conclusion. A Direct Method for Determining the Parameters of Mating Tooth Surfaces according to Predetermined Contact Situations. Introduction. The basic formulae of point-contact tooth surfaces. Situation of predetermining contact parameters on known surface. Situation of predetermining contact parameters on unknown surface. Example calculation. Conclusion. A Simple Method of Obtaining Machine-Setting Parameters for Spiral Bevel and Hypoid Gears. Introduction. The machine root angle and forming position of reference point. The difference surface and generating flank. Machine setting parameters for generators with neither modified-roll nor workhead-vertical-feed mechanism. Machine setting parameters for generators with modified-roll mechanism. Machine setting parameters for allcone method. Example calculation. Conclusion. An Optical Synthesis of Spiral Bevel and Hypoid Gears. Introduction. The reference point on generating and gear tooth flank. The objective function for optimal synthesis. Optimal synthesis process. Reasonable presetting of contact parameters. Conclusion. Analysis of Error Sensitivity of the Contact Situations with Respect to Mounting Errors. Introduction. Mounting error vector of a gear pair. Error sensitivity matrix of the position of tooth bearing centre. Error sensitivity matrix of second-order contact parameters. The background of application. The relationship between error sensitivity matrices and vertical (V) and horizontal (H) check results. Numerical example. Conclusions. References. Appendices. Subroutines. Main program for machines with cutter-tilt mechanism. Main program for machines with modified-roll mechanism. Numerical example. User's guide for appendices 2 and 3.