## Abstract

In this paper a novel modified scheme and effective computer representation for hobbing operation of precision involute gears is presented. The specific goals of the paper are as follows: (a) to provide a comprehensive understanding of the principal features of addendum modification of an involute gear hob tooth, (b) to come up with a novel approach for the computation of parameters of modification of the hob tooth addendum, (c) to determine the applicability and advantages of the application of the developed approach. The key concept in this paper is satisfaction of the necessary conditions of proper part surface generation (Radzevich, S. P., 2002, Computer Aided Design, 34, pp. 727–740) in gear hobbing operation. The research is performed with the application of the novel $DG∕K$ approach of surface machining earlier developed by the author. The $DG∕K$ approach of surface generation is based on fundamental results obtained in differential geometry of surfaces, and in kinematics of multiparametric motion of a rigid body in $E3$ space. The interested reader may wish to go to the monographs (Radzevich, S. P., 2001, Monograph Kiev, Rastan; 1991, Monograph, Kiev, Vishcha Shkola Publishing) for details. Both of the monographs are available from The Library of Congress. A novel approach for the computation of constraints on the actual values of addendum modification of an involute hob is reported in this paper. The advantages of the developed approach are threefold. It yields the computation: (a) of the minimum and the maximum allowed value of the normal pressure angle; (b) of the maximum allowed value of addendum modification of an involute hob, and (c) of the maximum allowed reduction of addendum of a gear hob. In the way of implementation is also described.

1.
,
S. P.
, 2002, “
Conditions of Proper Sculptured Surface Machining
,”
Comput. Aided Surg.
1092-9088,
34
, pp.
727
740
.
2.
3.
,
S. P.
, 1991, Sculptured Surface Machining on Multi-Axis NC Machine. Monograph. Kiev, Vishcha Shkola Publishing House. A copy of the monograph is available from The Library of Congress.
4.
,
S. P.
, 1985, Machining of Hardened Gears, Moscow, VNIITEMR.
5.
,
S. P.
, 1992, Cutting Tools for Machining of Hardened Gears, Moscow, VNIITEMR.
6.
Patent No.3.786.719, 409/12, 407/26, published on 22/01/74 (Azumi).
7.
Yu
,
M.
, and
Mertz
,
R.
, 1993, An Evaluation of Smirnov Hob Cutter, Technical Data Report, June 1, 1993, GMGC#0112, General Motors Gear Center, Romulus, MI48174-1376.
8.
Medveditskov
,
S. N.
, 1981, High-Productive Gear Hobbing, Moscow, Mashinostroyeniye.
9.
Medveditskov
,
S. N.
,
,
S. P.
, and
Smirnov
,
N. N.
, 1985, “
Involute Hobs with the Optimum Cutting Diagrams
,” Mashinostroitel’, pp.
22
25
.
10.
Smirnov
,
N. N.
, “
Multi-Thread Hob with New Cutting Diagram
”, Gear Technology, July/August 1991.
11.
,
S. P.
, Patent No. 1.009.661, USSR, Gear Hob. filed 10.21.81, Int. Cl. B23F21/16.
12.
,
S. P.
et al.
, Patent No. 1.134.318, USSR, Gear Hob. filed: 04.07.83, Int. Cl. B23F21/16.
13.
,
S. P.
et al.
, Patent No. 1.537.425, USSR, Gear Hob. Filed: 06.02.87, Int. Cl. B23F21/16.
14.
Denavit
,
J.
, and
Hartenberg
,
R. S.
, 1955, “
A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
,”
ASME J. Appl. Mech.
0021-8936,
77
, pp.
215
221
.
15.
,
S. P.
, 2002, “
About Hob Idle Distance in Gear Hobbing Operation
,”
ASME J. Mech. Des.
1050-0472,
124
, pp.
772
786
.
16.
Townsend
,
D. P.
, 1992, in
Dudley’s Gear Handbook. The Design, Manufacture, and Application of Gears
, 2nd ed.,
McGraw-Hill
, New York.
17.
ANSI/AGMA1012-F90
, 1990, American National Standard: Gear Nomenclature, Definitions of Terms with Symbols.
18.
,
S. P.
, 1982, “
Design and Investigation of Skiving Hobs for Finishing of Hardened Gears
,” Ph.D. thesis, Kiev Polytechnic Institute, Kiev.
19.
,
C.
, 2005, “
Computer Aided Analysis of Bending Strength of Involute Spur Gears with Asymmetric Profile
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
477
484
.
20.
Guingand
,
M.
,
de Vaujany
,
J. P.
, and
Icard
,
Y.
, 2005, “
Analysis and Optimization of the Loaded Meshing of Face Gears
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
135
143
.
21.
Figliolini
,
G.
, 2005, “
Synthesis of the Base Curves for N-Lobed Elliptical Gears
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
997
1005
.