Book contents
- Frontmatter
- Contents
- Foreword by Graziano Curti
- Preface
- Acknowledgments
- 1 Coordinate Transformation
- 2 Relative Velocity
- 3 Centrodes, Axodes, and Operating Pitch Surfaces
- 4 Planar Curves
- 5 Surfaces
- 6 Conjugated Surfaces and Curves
- 7 Curvatures of Surfaces and Curves
- 8 Mating Surfaces: Curvature Relations, Contact Ellipse
- 9 Computerized Simulation of Meshing and Contact
- 10 Spur Involute Gears
- 11 Internal Involute Gears
- 12 Noncircular Gears
- 13 Cycloidal Gearing
- 14 Involute Helical Gears with Parallel Axes
- 15 Modified Involute Gears
- 16 Involute Helical Gears with Crossed Axes
- 17 New Version of Novikov–Wildhaber Helical Gears
- 18 Face-Gear Drives
- 19 Worm-Gear Drives with Cylindrical Worms
- 20 Double-Enveloping Worm-Gear Drives
- 21 Spiral Bevel Gears
- 22 Hypoid Gear Drives
- 23 Planetary Gear Trains
- 24 Generation of Helicoids
- 25 Design of Flyblades
- 26 Generation of Surfaces by CNC Machines
- 27 Overwire (Ball) Measurement
- 28 Minimization of Deviations of Gear Real Tooth Surfaces
- References
- Index
20 - Double-Enveloping Worm-Gear Drives
Published online by Cambridge University Press: 04 September 2009
- Frontmatter
- Contents
- Foreword by Graziano Curti
- Preface
- Acknowledgments
- 1 Coordinate Transformation
- 2 Relative Velocity
- 3 Centrodes, Axodes, and Operating Pitch Surfaces
- 4 Planar Curves
- 5 Surfaces
- 6 Conjugated Surfaces and Curves
- 7 Curvatures of Surfaces and Curves
- 8 Mating Surfaces: Curvature Relations, Contact Ellipse
- 9 Computerized Simulation of Meshing and Contact
- 10 Spur Involute Gears
- 11 Internal Involute Gears
- 12 Noncircular Gears
- 13 Cycloidal Gearing
- 14 Involute Helical Gears with Parallel Axes
- 15 Modified Involute Gears
- 16 Involute Helical Gears with Crossed Axes
- 17 New Version of Novikov–Wildhaber Helical Gears
- 18 Face-Gear Drives
- 19 Worm-Gear Drives with Cylindrical Worms
- 20 Double-Enveloping Worm-Gear Drives
- 21 Spiral Bevel Gears
- 22 Hypoid Gear Drives
- 23 Planetary Gear Trains
- 24 Generation of Helicoids
- 25 Design of Flyblades
- 26 Generation of Surfaces by CNC Machines
- 27 Overwire (Ball) Measurement
- 28 Minimization of Deviations of Gear Real Tooth Surfaces
- References
- Index
Summary
INTRODUCTION
The invention of the double-enveloping worm-gear drive is a breathtaking story with two dramatic characters, Friedrich Wilhelm Lorenz and Samuel I. Cone, each acting in distant parts of the world – one in Germany and the other in the United States [Litvin, 1998]. The double-enveloping worm-gear drive was invented by both Cone and Lorenz independently, and we have to credit them both for it [Litvin, 1998]. The invention of Samuel I. Cone in the United States has been applied by a company that bears the name of the inventor, known by the name Cone Drive.
The invented gear drive is a significant achievement. The special shape of the worm increases the number of teeth that are simultaneously in mesh and improves the conditions of force transmission. The conditions of lubrication and the efficiency of the invented drive (in comparison with a worm-gear drive with a cylindrical worm) are substantially better due to the special shape of lines of contact between the worm and gear surfaces (see below).
The theory of double-enveloping worm-gear drives has been the subject of intensive research by many scientists. This chapter is based on the work by Litvin [1994]. We consider in this chapter the Cone double-enveloping worm-gear drive.
GENERATION OF WORM AND WORM-GEAR SURFACES
Worm Generation
The worm surface is generated by a straight-lined blade (Fig. 20.2.1).
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- Gear Geometry and Applied Theory , pp. 614 - 626Publisher: Cambridge University PressPrint publication year: 2004