Bibliography. [1] Buckingham, Earle: "Analytical Mechanics of Gears", McGraw-Hill, New York, 1949, and republished by Dover, New York, 1963.

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1 Bibliography The first five references listed are books on gearing. Some of them deal not only with the geometry, but also with many other aspects of gearing. However, the books are included in this bibliography because they all contain excellent material on the geometry of gears. The sixth reference is a Standard published by the American Gear Manufacturers Association. It is the only AGMA publication referred to directly in the text of this book, but there are many other useful publications on gearing available from the AGMA, at 1500 King Street, Suite 201, Alexandria, Virginia 22314, U.S.A. The remaining five references are papers reporting the results of specific research projects. There are a few results in this book which, because of space limitations, have been quoted without proof. The full derivations of these results are given in the papers listed in references [7-11]. [1] Buckingham, Earle: "Analytical Mechanics of Gears", McGraw-Hill, New York, 1949, and republished by Dover, New York, [ 2 ] Dudley, Dar le W., (Edi tor) : "Gear Handbook", McGraw-Hill, New York, [3] Tuplin, W.A.: "Involute Gear Geometry", Chatto and Windus, London, 1962, and also published by Ungar, New York. [4] Merritt, H.E.: "Gear Engineering", Pitman, London, [ 5 ] Dudley, Darle W.: "HandtJook of Pract ical Gear Design", McGraw-Hill, New York, 1984.

2 526 Bibliography [6] "AGMA Standard For Rating the Pitting Resistance and Bending Strength of Spur and Helical Involute Gear Teeth", AGMA , Dec [7] Dolan, T.J. and Broghamer, E.L.: "A Photoelastic Study of Stresses in Gear tooth Fillets", Univ. Illinois Eng. Expt. Sta. Bull. 335, March [8] Wellauer, E.J. and Seireg, A.: "Bending Strength of Gear Teeth by Cantilever-Plate Theory", Journal of Engineering for Industry, Trans. ASME, Vol 82, Series B, No.3, pp , Aug [9] Polder, J.W.: "Overcut Interference in Internal Gears", Proc. International Symposium on Gearing and Power Transmissions", Tokyo, [10] Colbourne, J.R.: "Optimum Number of Teeth for Span Measurement", AGMA Paper No. 85 FTM 9, Oct [11] Colbourne, J.R.: "Effect of Oblique Loading on the Fillet Stress in Helical Gears", AGMA Paper No. 86 FTM 6, Oct

3 Index Addendum c i rc Ie Addendum, measured from the standard pitch circle measured f rom the pi tch c i rc Ie Addendum modification Angle of contact Angles of approach and recess Angular pi tch Axial assembly of internal gear pairs Axial contact ratio Backlash, in a spur gear pair in a helical gear pair Balanced strength design Base cylinder, of a spur gear of an internal gear of a hel ical gear Base helix Base helix angle Base pitch, of a spur gear Basic rack, for gears in general for involute gears for helical gears Bearing reactions, crossed helical gears Center distance, in a spur gear pair Chordal addendum Chordal tooth thickness, of spur gears Clearance Close-mesh operation Conjugate profiles , ,

4 528 Index Contact force, in spur gear pairs in helical gear pairs in crossed helical gear pairs Contact length, in helical gear pairs Contact line inclination angle Contact ratio, in a spur gear pair when one gear is undercut in a rack and pinion in an internal gear pair in a helical gear pair Contact stress, in spur gears Correction in hel ical gears Cutting center distance, spur gear and pinion cutter internal gear and pinion cutter helical gear and pinion cutter Cutting circular pi tch Cutting point Cutting pressure angle Cutting, spur gears internal gears helical gears Cycloidal gears Dedendum circle Dedendum, measured from the standard pitch circle measured from the pi tch circle Developed cylinder Diametral pi tch Differential End points of the path of contact during cutting Equivalent spur gear Euler-Savary equation External gears Face contact ratio Face-width minimum value, for crossed helical gears , ,

5 Index 529 Fillet Fillet circle Fillet shape, cut by a rack cutter of an undercut gear cut by a pinion cutter of internal gears Fillet stress, in spur gears in helical gears Form cutting Form diameter Gear-tooth vernier caliper Generating cutting Generator Generator inclination angle Geometric design, of spur gear pairs of internal gear pairs of helical gear pairs Geometry factor kc Geometry factor k t Geometry factors I and J Helical factor Helical gears Helix Hel ix angle, of a gear of a rack of a crossed helical rack Highest point of single-tooth contact Hobbing machine gear train layout Hobbing, of spur gears Imaginary rack Interference, in a spur gear pair in an internal gear pair in a helical gear pair Interference points Internal gears Inverse involute function Involute Involute function 48 91, , , , , , ,

6 530 Index Involute helicoid Law of Gearing Lead Lead angle of a hob Left-handed helical gear Limit circle Line of action Long and short addendum system Low face contact ratio gear pairs Lowest point of single-tooth contact Measurement between pins Measurement over pins Module Normal direction to involute helicoid surface Normal section Normal section tooth profile Operating helix angle Operating pressure angle, of a spur gear pair of a rack and pinion of a pinion meshed wi th a rack of a spur gear transverse, of a helical gear pair, of a helical gear Path of contact, of a spur gear pair of a crossed helical gear pair Pinion Pinion cutter, spur helical Pitch, circular operating circular, axial of a rack pitch cylinders, of a spur gear pair of a pinion meshed wi th a rack of a helical gear pair of a crossed helical gear pair Pitch line of a rack pi tch point Plane of action , ,57,67, , ,28, , ,67 17,55 312, ,

7 Index 531 Pressure angle, of a rack of a spur gear Profile angle, of a rack of a spur gear Transverse, normal Profile contact ratio Profile modification Profile shift, of spur gears of internal gears Rack Radial assembly of internal gear pairs Radius of curvature, of the involute tooth profile of spur gear tooth fillets of internal gear tooth fillets Recess action gears Reference line of a rack Reference plane of a helical rack Region of contact Right-hand rule of vectors Right-handed helical gear Roll angle Root circle Root relief Rubbing, during cutting of internal gears Shaft angle Shaping, spur gears with a pinion cutter spur gears wi th a rack cutter internal gears helical gears wi th a pinion cutter helical gears with a rack cutter Sliding velocity, in a rack and pinion in a spur gear pair Space width Span measurement, of spur gears Specification, of a spur gear of a hel ical gear , , ,

8 53-2 Index Spur gears Standard center distance, of a spur gear pair of a helical gear pair of a crossed helical gear pair Standard cutting center distance Standard pi tch cyl inder, of a spur gear of a helical gear Standard shaft angle Stress concentration factor Swivel angle Threads on a hob Tip circle Tip interference Tip relief Tooth thickness Tooth thickness measurement, of spur gears of internal gears Total contact ratio Transverse section, through a gear through a rack through crossed helical gears Undercut circle Undercutting, in a spur gear in an internal gear in a helical gear Vectors, use of Very low face contact ratio gear pairs Whole depth of teeth Working depth , , , ,

The Geometry of Involute Gears

The Geometry of Involute Gears J.R. Colbourne The Geometry of Involute Gears With 217 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo J.R. Colbourne Department of Mechanical