A method is presented for the determination of the influence of gear hobbing on the precision and loaded tooth contact of worm gears. In order to get a worm gear set with fully conjugated teeth surfaces the gear teeth should be processed by a hob whose generator surface is identical to the worm surface. This requirement can be achieved by the use of a hob whose diameter is equal to the worm diameter and with infinite number of cutting edges. But because of the teeth in the hob are relieved, the diameter of the new hob should be slightly larger than the worm diameter to provide tool life. On the other hand, because of the finite number of hob teeth, the gear tooth surface, manufactured by such a hob, is not a smooth surface; it consists of a relatively big number of small parts of helical surfaces formed by the cutting edges of the hob. In this paper a method is presented for the determination of differences between the gear tooth surface processed by an oversized hob of finite number of teeth or by a flying tool, and the theoretically required gear tooth surface. Also the influence of hob oversize and machine tool settings on tooth contact pressure and transmission errors is determined. The full geometry and kinematics of gear tooth processing by an oversized hob or by flying tool is included. The theoretical background is implemented by a computer program. By using this program, the influence of relevant design parameters of worm gear set and hob and of machine tool settings on processed gear tooth errors and on loaded tooth contact of the worm gear pair is investigated and discussed. By another computer program the influence of cutter diameter and machine tool settings for pinion teeth processing on tooth contact pattern in spiral bevel gears is investigated and presented.

Volume Subject Area:
Manufacturing (Research Oriented)
Topics:
Gears, Worm gears, Gear teeth, Machine tools, Computer software, Cutting, Errors, Design, Generators, Geometry, Kinematics, Pressure, Spiral bevel gears
1.
Litvin
 
F. L.
,
Seol
 
I. H.
,
Kim
 
D.
,
Lu
 
J.
,
Wang
 
A. G.
,
Egelja
 
A.
, and
Zhao
 
X.
,
1996
, “
Kinematic and Geometric Models of Gear Drives
,”
ASME Journal of Mechanical Design
,
118
, pp.
544
–
550
.
2.
Seol
 
I. H.
, and
Litvin
 
F. L.
,
1996
, “
Computerized Design, Generation and Simulation of Meshing and Contact of Modified Involute, Klingelnberg and Flender Type Worm-Gear Drives
,”
ASME Journal of Mechanical Design
,
118
, pp.
551
–
555
.
3.
Simon, V., 1996, “Characteristics of a New Type of Cylindrical Worm Gear Drive,” Proceedings of 7th International Power Transmission and Gearing Conference, San Diego, pp. 703–708, ASME Journal of Mechanical Design, 1998, 120, pp. 139–146.
4.
Fang
 
H. S.
, and
Tsay
 
C. B.
,
1996
, “
Mathematical Model and Bearing Contacts of the ZK-Type Worm Gear Set Cut by Oversize Hob Cutters
,”
Mechanism and Machine Theory
,
31
, pp.
271
–
282
.
5.
Fang
 
H. S.
, and
Tsay
 
C. B.
,
2000
, “
Mathematical Model and Bearing Contacts of the ZN-Type Worm Gear Set Cut by Oversize Hob Cutters
,”
Mechanism and Machine Theory
,
35
, pp.
1689
–
1708
.
6.
Drobni, J., Siposs, I., and Pa´y, G., 2000, “Undergrinding the Flying Cutter of Worm Gears Ground by Toroidal Wheel,” Proceedings of The International Meeting of the Carpathian Region Specialists in the Field of Gears, Baia Mare, pp. 134–141.
7.
Simon, V., 1998, “Precise Worm Gears in Machine Tools,” Proceedings of XIIIth Conference on Machine Tools, Miskolc, pp. 145–150.
8.
Simon, V., 2000, “Influence of Hob Diameter on Load Distribution in Worm Gears,” Proceedings of Tenth International Conference on Tools, Miskolc, pp. 103–109.
9.
Simon
 
V.
,
1988
, “
Computer Aided Manufacturing of High Precision Hobs
,”
International Journal of Machine Tools and Manufacture
,
28
, pp.
443
–
452
.
10.
Simon
 
V.
,
1993
, “
Hob for Worm Gear Manufacturing with Circular Profile
,”
International Journal of Machine Tools and Manufacture
,
33
, pp.
615
–
625
.
11.
Winter
 
H.
, and
Wilkesmann
 
H.
,
1981
, “
Calculation of Cylindrical Worm Gear Drives of Different Tooth Profiles
,”
ASME Journal of Mechanical Design
,
103
, pp.
73
–
81
.
12.
Octrue, M., 1988, “A New Method for Designing a Wormgear,” AGMA Technical Paper 88FTM6, Alexandria, VA.
13.
Litvin
 
F. L.
, and
Kin
 
V.
,
1992
, “
Computerized Simulation of Meshing and Bearing Contact for Single-Enveloping Worm-Gear Drives
,”
ASME Journal of Mechanical Design
,
114
, pp.
313
–
316
.
14.
Seol
 
I. H.
,
2000
, “
The Design, Generation, and Simulation on Meshing of Worm-Gear Drive with Longitudinally Localized Contacts
,”
ASME Journal of Mechanical Design
,
122
, pp.
201
–
206
.
15.
Su
 
X.
, and
Houser
 
D. R.
,
2000
, “
Alternative Equation of Meshing for Worm-Gear Drives and Its Application to Determining Undercutting and Reverse Engineering
,”
ASME Journal of Mechanical Design
,
122
, pp.
207
–
212
.
16.
Su, D., Zhan, D., Gentle, R., 2004, “3D Modeling and Tooth Contact Analysis of a Globoid Involute Enveloping Worm Gear Drive,” Proceedings of 11th World Congress in Mechanisms and Machine Science, Tianjin, pp. 760–763.
17.
Su, D., Yang, F., and Gentle, C.R., 2000, “Finite Element Modeling and Analysis for Involute Worm Gears with Localised Tooth Contact,” 8th International Power Transmission and Gearing Conference, Baltimore, Proceedings in CD-ROM, Paper No. DET2000/PTG-14402.
18.
Simon
 
V.
, 2000, “
Load Distribution in Cylindrical Worm Gears
,” Proceedings of 8th International Power Transmission and Gearing Conference, Baltimore, Proceedings in CD-ROM, Paper No. DET2000/PTG-14400.
ASME Journal of Mechanical Design
,
2003
,
125
, pp.
356
–
364
.
19.
Simon, V., 2003, “Computer Aided Tooth Contact Analysis in Cylindrical Worm Gears,” ASME/AGMA 2003 International Power Transmission and Gearing Conference, Chicago, Paper No. DET2003/PTG-48109, Journal of Machine Design, 2005, 127 (in press).
20.
Greening, J. H., Barlow, R. J., and Loveless, W. G., 1980, “Load Sharing on the Teeth of Double Enveloping Worm Gear,” II International Power Transmission and Gearing Conference, San Francisco, Paper No. 80-C2/DET-43.
21.
Simon
 
V.
,
1993
, “
Load Distribution in Double Enveloping Worm Gears
,”
ASME Journal of Mechanical Design
,
115
, pp.
496
–
501
.
22.
Qin, Da., Qin, Do., Yang, Y., and Hu, J., 2000, “Tooth Contact Analysis of Double Enveloping Hourglass Worm Gearing on the Condition that Errors Mixed with Deformation,” 8th International Power Transmission and Gearing Conference, Baltimore, Proceedings in CD-ROM, Paper No. DET2000/PTG-14401.
23.
Shi
 
W.
,
Qin
 
D.
,
Xu
 
W.
,
2004
, “
Meshing Control of the Double-Enveloping Worm Gearing Under the Conditions of Existing the Errors and the Load
,”
Mechanism and Machine Theory
,
39
, pp.
61
–
74
.
24.
Simon, V., 1999, “The Influence of Misalignments on Load Distribution in Hypoid Gears,” Proceedings of 4th World Congress on Gearing and Power Transmission, Paris, pp. 637–649.
25.
Simon
 
V.
,
1996
, “
Displacements in Worm Gears with Ground Concave Worm Profile
,”
Mechanism and Machine Theory
,
31
, pp.
1130
–
1140
.
26.
Simon, V., 1995, “Tooth Contact Analysis of Mismatched Worm Gears,” Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms, Milano, pp. 530–534.
27.
Simon, V., 2005, “Computerized Simulation of Tooth Contact Analysis of Mismatched Spiral Bevel Gears,” ASME Journal of Mechanical Design, (submitted).
28.
Simon, V., 2005, “Load Distribution in Spiral Bevel Gears,” ASME Journal of Mechanical Design, (submitted).
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