Gear Geometry and Applied Theory, Second Edtion
An invaluable reference for designers, theoreticians, students, and manufacturers, this text covers the theory, design, geometry, and manufacture of all types of gears and gear drives.
TABLE OF CONTENTS Gear Geometry and Applied Theory, Second Edtion
Chapter 8: Mating Surfaces Curvature Relations, Contact Ellipse
8.1 INTRODUCTION
Consider that two solids (1 and 2) are provided with interacting surfaces ? 1 and ? 2, and perform the prescribed transformation of motion. Surfaces ? 1 and ? 2 are in continuous tangency. These conditions are typical for the case of generation of surfaces by a tool, and for transformation of motion by gear tooth surfaces.
Henceforth, we differentiate two cases of tangency: (i) the interacting surfaces ? 1 and ? 2 are in line contact at every instant, and ? 2 is the envelope to the family of surfaces that is generated by ? 1 in coordinate system S 2; and (ii) surfaces ? 1 and ? 2 are in point contact at every instant (the contact of ? 1 and ? 2 is localized).
We consider as given surface ? 1 and the location of point P of surface tangency ( P is the point of the characteristic on ? 1 in the case in which ? 2 is the envelope, or the single point of tangency of ? 1 and ? 2); given as well are the value of transmission function 
( 
) at point P and the derivative ?/ ? ( ( )) at P. (The characteristic is the instantaneous line of contact of enveloping surfaces). Our goals are to determine (i) direct relations between...
Copyright Faydor L. Litvin and Alfonso Fuentes 2004 under license agreement with Books24x7
