Noncircular bevel gears are applied in variable-speed transmissions with intersecting axes. Since dedicated machines for manufacturing noncircular bevel gears are not available, noncircular bevel gears are normally manufactured using universal computer numerically controlled (CNC) machining centers, resulting in poor productivity. This paper describes a face-milling method for generation of noncircular spiral bevel gears, which is analogous to the generation of spiral bevel and hypoid gears using CNC hypoid gear generators, such as Gleason free-form hypoid generators. As a result, the productivity is significantly improved. Based on the theory of gearing, this paper first describes the basic concept of generation of conjugate noncircular spiral bevel gears. Generation of the tooth surfaces using crown-gear generation concept is analytically discussed with association to the face-milling process of generation of the proposed noncircular spiral bevel gears. The tooth surface geometries are represented by the position vectors and normals. The kinematical model of free-form machines is developed. The machine motion parameters are determined based on the theoretically defined tooth surfaces using the crown-gear generation concept. The developed method is verified by manufacturing a real pair of noncircular spiral bevel gears with satisfactory contact patterns which agree well with those modeled using a commercial cae software program.

References

References
1.
Litvin
,
F. L.
,
Gonzalez-Perez
,
I.
,
Fuentes
,
A.
, and
Hayasaka
,
K.
,
2008
, “
Design and Investigation of Gear Drives With Non-Circular Gear Applied for Speed Variation and Generation of Functions
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
45–48
), pp.
3783
3802
.
2.
Ottaviano
,
E.
,
Mundo
,
D.
,
Danieli
,
G. A.
, and
Ceccarelli
,
M.
,
2008
, “
Numerical and Experimental Analysis of Non-Circular Gear and Cam-Follower Systems as Function Generators
,”
Mech. Mach. Theory
,
43
(
8
), pp.
996
1008
.
3.
Chibing
,
H.
,
Yazhou
,
W.
,
Yang
,
H.
, and
Yongping
,
L.
,
2012
, “
Calculation and Analysis of Pitch Curve of Third-Order Non-Circular Planetary Gear Mechanism
,”
J. Lanzhou Univ. Technol.
,
10
, pp.
21
24
.
4.
Terada
,
H.
,
Zhu
,
Y.
,
Suzuki
,
M.
,
Cheng
,
C.
, and
Takahashi
,
R.
,
2012
, “
Developments of a Knee Motion Assist Mechanism for Wearable Robot With a Non-Circular Gear and Grooved Cams
,”
Mech. Mach. Sci.
,
3
, pp.
69
76
.
5.
Modler
,
K.-H.
,
Lovasz
,
E.-C.
,
Bär
,
G. F.
,
Neumann
,
R.
,
Perju
,
D.
,
Perner
,
M.
, and
Mărgineanu
,
D.
,
2009
, “
General Method for the Synthesis of Geared Linkages With Non-Circular Gear
,”
Mech. Mach. Theory
,
44
(
4
), pp.
726
738
.
6.
Emura
,
T.
, and
Arakawa
,
A.
,
1992
, “
A New Steering Mechanism Using Noncircular Gear
,”
JSME Int. J. Ser. III
,
35
, pp.
604
610
.
7.
Mundo
,
D.
,
2006
, “
Geometric Design of a Planetary Gear Train With Non-Circular Gear
,”
Mech. Mach. Theory
,
41
(
4
), pp.
456
472
.
8.
Lin
,
C.
,
Hou
,
Y.
,
Gong
,
H.
,
Zeng
,
Q.
, and
Nie
,
L.
,
2011
, “
Flow Characteristics of High-Order Ellipse Bevel Gear Pump
,”
J. Drain. Irrig. Mach. Eng.
,
29
, pp.
379
385
(in Chinese).
9.
Zhao
,
Y.
,
Ma
,
Y.
,
Hua
,
L.
, and
Liu
,
J.
,
2008
, “
Planar Unfolding Algorithm of Noncircular Bevel Gear
,”
China Mech. Eng.
,
19
, pp.
2046
2049
.
10.
Ollson
,
U.
,
1959
, “
Non Circular Bevel Gear
,” The Royal Swedish Academy of Engineering Sciences, Stockholm, Sweden.
11.
Figliolini
,
G.
, and
Angeles
,
J.
,
2011
, “
Synthesis of the Pitch Cones of N-Lobed Elliptical Bevel Gears
,”
ASME J. Mech. Des.
,
33
, p.
031002
.
12.
Xia
,
J.
,
Liu
,
Y.
,
Geng
,
C.
, and
Jiang
,
H.
,
2008
, “
Noncircular Bevel Gear transmission With Intersecting Axes
,”
ASME J. Mech. Des.
,
130
(5), p.
054502
.
13.
Jing
,
L.
,
2012
, “
Tooth Surface Generation and Geometric Properties of Straight Noncircular Bevel Gear
,”
ASME J. Mech. Des.
,
134
, p.
084503
.
14.
Jia
,
J.
, and
Gao
,
B.
,
2012
, “
Study on a New Type of Differential With Variable Ratio for Off-Road Vehicles
,”
China Mech. Eng.
,
23
(23), pp.
2844
2847
.
15.
Lin
,
C.
,
Zhang
,
L.
, and
Zhang
,
Z.
,
2014
, “
Transmission Theory and Tooth Surface Solution of a New Type of Non-Circular Bevel Gear
,”
J. Mech. Eng.
,
13
, pp.
66
76
(in Chinese).
16.
Litvin
,
F. L.
, and
Zhang
,
Y.
,
1991
, “
Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gear
,” NASA Technical Report, Report Nos. NASA CR-4342 and AVSCOM TR-90-C-028.
17.
Achtmann
,
J.
, and
Bär
,
G.
,
2003
, “
Optimized Bearing Ellipses of Hypoid Gear
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
739
745
.
18.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
,
Cambridge, UK
.
19.
Litvin
,
F. L.
,
Fuentes
,
A.
,
Fan
,
Q.
, and
Handschuh
,
R. F.
,
2002
, “
Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-Milled Formate Generated Spiral Bevel Gear
,”
Mech. Mach. Theory
,
37
(
5
), pp.
441
459
.
20.
Fan
,
Q.
,
2006
, “
Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gear Manufactured by Gleason Face Hobbing Process
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1315
1327
.
21.
Fan
,
Q.
,
DaFoe
,
R.
, and
Swanger
,
J.
,
2008
, “
Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears
,”
ASME J. Mech. Des.
,
130
(
7
), p.
072601
.
22.
Xu
,
H.
,
Kahraman
,
A.
, and
Houser
,
D. R.
,
2005
, “
A Model to Predict Friction Losses of Hypoid Gears
,” AGMA Fall Technical Meeting, Detroit, MI, Paper No. 05FTM06.
23.
Fuentes
,
A.
,
Gonzalez-Perez
,
I.
,
Litvin
,
F. L.
,
Hayasaka
,
K.
, and
Yukishima
,
K.
,
2005
, “
Design, Manufacture, and Evaluation of Prototypes of Low-Noise High-Endurance Spiral Bevel Gear Drives
,”
ASME
Paper No. DETC2005-84013.
24.
Simon
,
V.
,
2007
, “
Computer Simulation of Tooth Contact Analysis of Mismatched Spiral Bevel Gear
,”
Mech. Mach. Theory
,
42
(
3
), pp.
365
381
.
25.
Shih
,
Y. P.
, and
Fong
,
Z. H.
,
2008
, “
Flank Correction for Spiral Bevel and Hypoid Gear on a Six-Axis CNC Hypoid Generator
,”
ASME J. Mech. Des.
,
130
(
6
), p.
062604
.
26.
Kolivand
,
M.
, and
Kahraman
,
A.
,
2009
, “
An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gear Having Local and Global Surface Deviations
,”
ASME
Paper No. DETC2009/PTG-86786.
27.
Artoni
,
A.
,
Kolivand
,
M.
, and
Kahraman
,
A.
,
2009
, “
An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears
,”
ASME J. Mech. Des.
,
132
(
1
), p.
011010
.
28.
Simon
,
V.
,
2014
, “
Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator
,”
ASME J. Manuf. Sci. Eng.
,
136
(
3
), p.
031008
.
29.
Shih
,
Y. P.
,
2010
, “
A Novel Ease-Off Flank Modification Methodology for Spiral Bevel and Hypoid Gear
,”
Mech. Mach. Theory
,
45
(
8
), pp.
1108
1112
.
30.
Simon
,
V.
,
2010
, “
Advanced Manufacture of Spiral Bevel Gear on CNC Hypoid Generating Machine
,”
ASME J. Mech. Des.
,
132
(
3
), p.
031001
.
31.
Fan
,
Q.
,
2015
, “
Ease-Off and Application in Tooth Contact Analysis for Face-Milled and Face-Hobbed Spiral Bevel and Hypoid Gears
,”
Theory and Practice of Gearing and Transmissions
(Mechanisms and Machine Science), Vol.
34
,
Springer
,
Berlin
, pp.
321
339
.
32.
Litvin
,
F. L.
,
Gonzalez-Perez
,
I.
,
Yukishima
,
K.
,
Fuentes
,
A.
, and
Hayasaka
,
K.
,
2007
, “
Generation of Planar and Helical Elliptical Gear by Application of Rack-Cutter, Hob, and Shaper
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
4321
4336
.
33.
Lin
,
C.-Y.
,
Tsay
,
C.-B.
, and
Fong
,
Z.-H.
,
1997
, “
Mathematical Model of Spiral Bevel and Hypoid Gear Manufactured by the Modified Roll Method
,”
Mech. Mach. Theory
,
32
(
2
), pp.
121
136
.
34.
Simon
,
V.
,
2008
, “
Machine-Tool Settings to Reduce the Sensitivity of Spiral Bevel Gear to Tooth Errors and Misalignments
,”
ASME J. Mech. Des.
,
130
(
8
), p.
082603
.
35.
Wang
,
H.
,
Zhang
,
C.
,
Lin
,
Z.
, and
Chen
,
G.
,
2005
, “
Meshing Analysis of the Planetary Indexing Cam Mechanisms
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
340
346
.
36.
Fuentes
,
A.
,
Ruiz-Orzaez
,
R.
, and
Gonzalez-Perez.
,
I.
,
2015
, “
Compensation of Errors of Alignment Caused by Shaft Deflections in Spiral Bevel Gear Drives
,”
Theory and Practice of Gearing and Transmissions
(Mechanisms and Machine Science), Vol.
34
,
Springer
,
Berlin
, pp.
301
320
.
37.
Ding
,
Y.
,
Zhang
,
X.
, and
Ding
,
H.
,
2015
, “
Harmonic Differential Quadrature Method for Surface Location Error Prediction and Machining Parameter Optimization in Milling
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
024501
.
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