The advantages of the five-axis flank milling of (developable) ruled surfaces include that (1) the machined surfaces could be very accurate and smooth and (2) the machining efficiency is high. Currently, spiral bevel gears are machined on the machine tools specially used for gear manufacturing. The disadvantages are that the cost is high for small batch, prototype, or repair. If a small group of spiral bevel gears are needed, the current methods are not valid. Thus, it is expected to machine the gears on five-axis computer numerical control (CNC) milling centers. Unfortunately, when tooth surfaces are designed based on the conventional gear manufacturing methods, they cannot be accurately machined in five-axis flank milling. This work is to develop the new technique for the five-axis flank milling of spiral bevel gears. First, a new method of designing the tooth surface of spiral bevel gears with ruled surface is proposed. Second, the cutter locations and orientations are calculated for five-axis flank milling the tooth surfaces. Third, the actual tooth surfaces are accurately represented with the cutter envelope surface in five-axis flank milling. It is confirmed that the difference of the actual tooth surface and the designed tooth surface is within the tolerance. Then, a pinion is generated to mesh with the gear, and the tooth contact analysis (TCA) is conducted. The good result demonstrates that the proposed method is valid, thus it can be used in industry.

References

1.
Suh
,
S.
,
Jih
,
W.
,
Hong
,
H.
, and
Chung
,
D.
,
2001
, “
Sculptured Surface Machining of Spiral Bevel Gears With CNC Milling
,”
Int. J. Mach. Tools Manuf.
,
41
(
6
), pp.
833
850
.
2.
Suh
,
S.-H.
,
Jung
,
D.-H.
,
S.-Lee
,
W.
, and
Lee
,
E.-S.
,
2003
, “
Modelling, Implementation, and Manufacturing of Spiral Bevel Gears With Crown
,”
Int. J. Adv. Manuf. Technol.
,
21
(
10–11
), pp.
775
786
.
3.
Alves
,
J. T.
,
Guingand
,
M.
, and
de Vaujany
,
J.-P.
,
2013
, “
Designing and Manufacturing Spiral Bevel Gears Using 5-Axis Computer Numerical Control (CNC) Milling Machines
,”
ASME J. Mech. Des.
,
135
(
2
), p.
024502
.
4.
Yao
,
L.
,
Gu
,
B.
,
Haung
,
S.
,
Wei
,
G.
, and
Dai
,
J. S.
,
2010
, “
Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive
,”
ASME J. Mech. Des.
,
132
(
2
), p.
021008
.
5.
Álvarez
,
A.
,
de Lacalle
,
L. L.
,
Olaiz
,
A.
, and
Rivero
,
A.
,
2015
, “
Large Spiral Bevel Gears on Universal 5-Axis Milling Machines: A Complete Process
,”
Procedia Eng.
,
132
, pp.
397
404
.
6.
Kawasaki
,
K.
,
Tsuji
,
I.
,
Gunbara
,
H.
, and
Houjoh
,
H.
,
2015
, “
Method for Remanufacturing Large-Sized Skew Bevel Gears Using CNC Machining Center
,”
Mech. Mach. Theory
,
92
, pp.
213
229
.
7.
Tönshoff
,
H.
,
Gey
,
C.
, and
Rackow
,
N.
,
2001
, “
Flank Milling Optimization-The Flamingo Project
,”
Air Space Eur.
,
3
(
3
), pp.
60
63
.
8.
Young
,
H.-T.
,
Chuang
,
L.-C.
,
Gerschwiler
,
K.
, and
Kamps
,
S.
,
2004
, “
A Five-Axis Rough Machining Approach for a Centrifugal Impeller
,”
Int. J. Adv. Manuf. Technol.
,
23
(
3–4
), pp.
233
239
.
9.
Harik
,
R. F.
,
Gong
,
H.
, and
Bernard
,
A.
,
2013
, “
5-Axis Flank Milling: A State-of-the-Art Review
,”
Comput. Aided Des.
,
45
(
3
), pp.
796
808
.
10.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
, Cambridge, UK.
11.
Litvin
,
F. L.
,
1989
, “
Theory of Gearing
,” National Aeronautics and Space Administration, Scientific and Technical Information Division,
AVSCOM Technical Report No. 88-C-035
.
12.
Litvin
,
F. L.
, and
Zhang
,
Y.
,
1991
, “
Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gears
,” DTIC Document,
Technical Report No. 90-C-028
.
13.
Fong
,
Z. H.
, and
Tsay
,
C. B.
,
1991
, “
A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears
,”
ASME J. Mech. Des.
,
113
(
2
), pp.
174
181
.
14.
Tsay
,
C. B.
, and
Lin
,
J. Y.
,
1993
, “
A Mathematical Model for the Tooth Geometry of Hypoid Gears
,”
Math. Comput. Model.
,
18
(
2
), pp.
23
34
.
15.
Lelkes
,
M.
,
Play
,
D.
, and
Marialigeti
,
J.
,
2002
, “
Numerical Determination of Cutting Parameters for the Control of Klingelnberg Spiral Bevel Gear Geometry
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
761
771
.
16.
Achtmann
,
J.
, and
Bar
,
G.
,
2003
, “
Optimized Bearing Ellipses of Hypoid Gears
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
739
745
.
17.
Tsai
,
Y.-C.
, and
Hsu
,
W.-Y.
,
2008
, “
The Study on the Design of Spiral Bevel Gear Sets With Circular-Arc Contact Paths and Tooth Profiles
,”
Mech. Mach. Theory
,
43
(
9
), pp.
1158
1174
.
18.
Zhang
,
Y.
, and
Wu
,
Z.
,
2007
, “
Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears
,”
ASME
Paper No. DETC2007-34123.
19.
Fan
,
Q.
,
2006
, “
Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1315
1327
.
20.
Fan
,
Q.
,
2007
, “
Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
31
37
.
21.
Fan
,
Q.
,
DaFoe
,
R. S.
, and
Swanger
,
J. W.
,
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.
Fan
,
Q.
,
2010
, “
Tooth Surface Error Correction for Face-Hobbed Hypoid Gears
,”
ASME J. Mech. Des.
,
132
(
1
), p.
011004
.
23.
Vimercati
,
M.
,
2007
, “
Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears and Its Application to Contact Analysis and Stress Calculation
,”
Mech. Mach. Theory
,
42
(
6
), pp.
668
690
.
24.
Simon
,
V. V.
,
2009
, “
Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors
,”
ASME J. Mech. Des.
,
131
(
4
), p.
041007
.
25.
Simon
,
V.
,
2009
, “
Hed-Cutter for Optimal Tooth Modifications in Spiral Bevel Gears
,”
Mech. Mach. Theory
,
44
(
7
), pp.
1420
1435
.
26.
Simon
,
V. V.
,
2010
, “
Advanced Manufacture of Spiral Bevel Gears on CNC Hypoid Generating Machine
,”
ASME J. Mech. Des.
,
132
(
3
), p.
031001
.
27.
Simon
,
V. V.
,
2011
, “
Generation of Hypoid Gears on CNC Hypoid Generator
,”
ASME J. Mech. Des.
,
133
(
12
), p.
121003
.
28.
Simon
,
V. V.
,
2014
, “
Optimization of Face-Hobbed Hypoid Gears
,”
Mech. Mach. Theory
,
77
, pp.
164
181
.
29.
Shih
,
Y. P.
,
Lin
,
G. C.
, and
Fong
,
Z. H.
,
2007
, “
Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
38
47
.
30.
Shih
,
Y.-P.
, and
Fong
,
Z.-H.
,
2008
, “
Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator
,”
ASME J. Mech. Des.
,
130
(
6
), p.
062604
.
31.
Shih
,
Y.-P.
,
2010
, “
A Novel Ease-Off Flank Modification Methodology for Spiral Bevel and Hypoid Gears
,”
Mech. Mach. Theory
,
45
(
8
), pp.
1108
1124
.
32.
Brecher
,
C.
,
Klocke
,
F.
,
Brumm
,
M.
, and
Hardjosuwito
,
A.
,
2013
, “
Analysis and Optimization of Bevel Gear Cutting Processes by Means of Manufacturing Simulation
,”
Simulation and Modeling Methodologies, Technologies and Applications
,
Springer
, Berlin, pp.
271
284
.
33.
Chen
,
C. K.
,
Chiou
,
S. T.
,
Fong
,
Z. H.
,
Lee
,
C. K.
, and
Chen
,
C. H.
,
2001
, “
Mathematical Model of Curvature Analysis for Conjugate Surfaces With Generalized Motion in Three Dimensions
,”
Proc. Inst. Mech. Eng. Part C
,
215
(
4
), pp.
487
502
.
34.
Di Puccio
,
F.
,
Gabiccini
,
M.
, and
Guiggiani
,
M.
,
2005
, “
Alternative Formulation of the Theory of Gearing
,”
Mech. Mach. Theory
,
40
(
5
), pp.
613
637
.
35.
Di Puccio
,
F.
,
Gabiccini
,
M.
, and
Guiggiani
,
M.
,
2007
, “
An Invariant Approach for Gear Generation With Supplemental Motions
,”
Mech. Mach. Theory
,
42
(
3
), pp.
275
295
.
36.
Wang
,
P.
, and
Zhang
,
Y.
,
2013
, “
An Invariant Approach for Curvature Analysis of Conjugate Surfaces
,”
Mech. Mach. Theory
,
64
, pp.
175
199
.
37.
Chen
,
B.
,
Liang
,
D.
, and
Li
,
Z.
,
2014
, “
A Study on Geometry Design of Spiral Bevel Gears Based on Conjugate Curves
,”
Int. J. Precis. Eng. Manuf.
,
15
(
3
), pp.
477
482
.
38.
Zhou
,
Y.
, and
Chen
,
Z. C.
,
2015
, “
A New Geometric Meshing Theory for a Closed-Form Vector Representation of the Face-Milled Generated Gear Tooth Surface and Its Curvature Analysis
,”
Mech. Mach. Theory
,
83
, pp.
91
108
.
39.
Du
,
J.
, and
Fang
,
Z.
,
2016
, “
An Active Tooth Surface Design Methodology for Face-Hobbed Hypoid Gears Based on Measuring Coordinates
,”
Mech. Mach. Theory
,
99
, pp.
140
154
.
40.
Wang
,
J.
,
Kong
,
L.
,
Liu
,
B.
,
Hu
,
X.
,
Yu
,
X.
, and
Kong
,
W.
,
2014
, “
The Mathematical Model of Spiral Bevel Gears—A Review
,”
Strojniški Vestn.-J. Mech. Eng.
,
60
(
2
), pp.
93
105
.
41.
Huston
,
R.
, and
Coy
,
J.
,
1981
, “
Ideal Spiral Bevel Gears—A New Approach to Surface Geometry
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
127
132
.
42.
Huston
,
R.
, and
Coy
,
J. J.
,
1982
, “
Surface Geometry of Circular Cut Spiral Bevel Gears
,”
ASME J. Mech. Des.
,
104
(
4
), pp.
743
748
.
43.
Drago
,
R.
,
1981
, “
Discussion: Ideal Spiral Bevel Gears—A New Approach to Surface Geometry (Huston, R. L., and Coy, J. J., 1981, ASME J. Mech. Des., 103(1), pp. 127–132)
,”
ASME J. Mech. Des.
,
103
(
1
), p.
132
.
44.
Peternell
,
M.
,
Pottmann
,
H.
, and
Ravani
,
B.
,
1999
, “
On the Computational Geometry of Ruled Surfaces
,”
Comput. Aided Des.
,
31
(
1
), pp.
17
32
.
45.
ANSI
,
2005
, “
Design Manual for Bevel Gears
,” American Gear Manufacturers Associate, Alexandria, VA, Standard No. ANSI/AGMA 2005–D03.
46.
Yuansheng
,
Z.
,
2015
, “
Five-Axis Flank Milling and Modeling the Spiral Bevel Gear With a Ruled Tooth Surface Design
,”
Ph.D thesis
, Concordia University, Montreal, QC.
47.
Zhou
,
Y.
,
Chen
,
Z. C.
, and
Yang
,
X.
,
2015
, “
An Accurate, Efficient Envelope Approach to Modeling the Geometric Deviation of the Machined Surface for a Specific Five-Axis CNC Machine Tool
,”
Int. J. Mach. Tools Manuf.
,
95
, pp.
67
77
.
48.
Chiou
,
J. C.
,
2004
, “
Accurate Tool Position for Five-Axis Ruled Surface Machining by Swept Envelope Approach
,”
Comput. Aided Des.
,
36
(
10
), pp.
967
974
.
49.
Hang
,
D.
,
Jinyuan
,
T.
, and
Jue
,
Z.
,
2016
, “
A Hybrid Modification Approach of Machine-Tool Setting Considering High Tooth Contact Performance in Spiral Bevel and Hypoid Gears
,”
J. Manuf. Syst.
,
41
, pp.
228
238
.
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