Mathematical Model of Universal Hypoid Generator With Supplemental Kinematic Flank Correction Motions

A mathematical model of universal hypoid generator is proposed to simulate virtually all primary spiral bevel and hypoid cutting methods. The proposed mathematical model simulates the face-milling, face-hobbing, plunge cutting, and bevel-worm-shaped hobbing processes with either generating or nongenerating cutting for the spiral bevel and hypoid gears. The supplemental kinematic flank correction motions, such as modified generating roll ratio, helical motion, and cutter tilt are included in the proposed mathematical model. The proposed mathematical model has more flexibility in writing computer program and appropriate for developing the object oriented computer programming. The developed computer object can be repeatedly used by various hypoid gear researchers to reduce the effort of computer coding.

[1]  Aizoh Kubo,et al.  Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces , 1998 .

[2]  Faydor L. Litvin,et al.  Methods of Synthesis and Analysis for Hypoid Gear-Drives of “Formate” and “Helixform”—Part 1. Calculations For Machine Settings For Member Gear Manufacture of the Formate and Helixform Hypoid Gears , 1981 .

[3]  J. J. Coy,et al.  Surface Geometry of Circular Cut Spiral Bevel Gears , 1982 .

[4]  F. Litvin,et al.  Gear geometry and applied theory , 1994 .

[5]  Y. Davidov.  General idea of generating mechanism and its application to bevel gears , 1998 .

[6]  Chung-Biau Tsay,et al.  MATHEMATICAL MODEL OF SPIRAL BEVEL AND HYPOID GEARS MANUFACTURED BY THE MODIFIED ROLL METHOD , 1997 .

[7]  Yi Zhang,et al.  Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gears , 1991 .

[8]  M. S. Shunmugam,et al.  Establishing gear tooth surface geometry and normal deviationPart II—bevel gears , 1998 .

[9]  Hermann J. Stadtfeld.  Handbook of bevel and hypoid gears : calculation-manufacturing-optimization , 1993 .

[10]  Chung-Biau Tsay,et al.  Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface-deviation , 1998 .

[11]  Faydor L. Litvin,et al.  Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements , 1993 .

[12]  Chung-Biau Tsay,et al.  A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears , 1991 .

[13]  Zhang-Hua Fong,et al.  A study on the tooth geometry and cutting machine mechanisms of spiral bevel gears , 1991 .

[14]  Louis Cloutier,et al.  The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method , 1993 .

[15]  Faydor L. Litvin,et al.  Determination of Settings of a Tilted Head-Cutter for Generation of Hypoid and Spiral Bevel Gears. , 1988 .