Abstract

Face milling is not only a primary machining technique for the mass production of bevel gears, but it has also become a standardized process integrated into computer numerical control (CNC) bevel gear-cutting machines in the last two decades. Controlling suitable feed rates for face milling is one of the most direct and pivotal factors influencing processing efficiency for CNC machines. Despite being programmed through numerical codes, the feed rates provided by the gear machines most rely on experiential insights rather than optimization. Therefore, leveraging material removal rate (MRR) directly correlates with machining power and will hold immense potential for optimizing feed rates and enhancing efficiency. Because commercial software solutions cannot accurately predict the MRR for face milling operations, this paper uses a novel ring-dexel-based model for cutting simulation to address this issue. The main aim of this model is to provide a more precise prediction of the MRR across all face milling cuttings. By controlling the cutting depth and generating angle, the ring gear's plunging process and the pinion's single-roll generating process were successfully simulated. Thus, the MRRs through all cutting processes were calculated. Experimental results showed that tool torques are positively correlated with the MRRs. Finally, by appropriately increasing the cutting feed rate based on the MRR, the pinion and ring gear machining times were reduced by 44% and 18%, respectively.

References

1.
Klingelnberg
,
J.
,
2016
,
Bevel Gear, Fundamentals and Applications
, 1st ed.,
Springer Verlag
,
Berlin
, Chap. 6.
2.
Shih
,
Y. P.
,
Sun
,
Z. H.
, and
Lai
,
K. L.
,
2017
, “
A Flank Correction Face-Milling Method for Bevel Gears Using a Five-Axis CNC Machine
,”
Int. J. Adv. Manuf. Technol.
,
91
(
9–12
), pp.
3635
3652
.
3.
Lv
,
J.
,
Jia
,
S.
,
Wang
,
H.
,
Ding
,
K.
, and
Chan
,
F. T. S.
,
2021
, “
Comparison of Different Approaches for Predicting Material Removal Power in Milling Process
,”
Int. J. Adv. Manuf. Technol.
,
116
(
1–2
), pp.
213
227
.
4.
Gleason Works
,
1971
, “
Calculation Instructions: Generated Spiral Bevel Gears, Fixed Setting Method for Finishing Pinions (For Machines With Modified Roll) Including Grinding
,” Rochester, NY.
5.
Gleason Works
,
1971
, “
Calculation Instructions: Generated Hypoid Gears, Duplex-Helical Method, Including Grinding
,” Rochester, NY.
6.
Litvin
,
F. L.
, and
Gutman
,
Y.
,
1981
, “
Methods of Synthesis and Analysis for Hypoid Gear-Drives of Formate and Helixform-Part 1. Calculations For Machine Settings For Member Gear Manufacture of the Formate and Helixform Hypoid Gears
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
83
88
.
7.
Litvin
,
F. L.
, and
Gutman
,
Y.
,
1981
, “
Methods of Synthesis and Analysis for Hypoid Gear-Drives of Formate and Helixform-Part 2. Machine Setting Calculations for the Pinions of Formate and Helixform Gears
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
89
101
.
8.
Litvin
,
F. L.
, and
Gutman
,
Y.
,
1981
, “
Methods of Synthesis and Analysis for Hypoid Gear-Drives of Formate and Helixform-Part 3. Analysis and Optimal Synthesis Methods for Mismatch Gearing and Its Application For Hypoid Gears of Formate and Helixform
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
102
110
.
9.
Litvin
,
F. L.
,
Zhang
,
Y.
,
Lundy
,
M.
, and
Heine
,
C.
,
1988
, “
Determination of Settings of a Tilted Head Cutter for Generation of Hypoid and Spiral Bevel Gears
,”
ASME J. Mech. Des.
,
110
(
4
), pp.
495
500
.
10.
Krenzer
,
T. J.
, and
Hunkeler
,
E. J.
,
1991
, “
Multi-axis Bevel and Hypoid Gear Generating Machine
,” US Patent No. 4981402.
11.
Fong
,
Z. H.
,
2000
, “
Mathematical Model of Universal Hypoid Generator With Supplemental Kinematic Flank Correction Motions
,”
ASME J. Mech. Des.
,
122
(
1
), pp.
136
142
.
12.
Wang
,
P. Y.
, and
Fong
,
Z. H.
,
2006
, “
Fourth-Order Kinematic Synthesis for Face-Milling Spiral Bevel Gears With Modified Radial Motion (MRM) Correction
,”
ASME J. Mech. Des.
,
128
(
2
), pp.
457
467
.
13.
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
.
14.
Shih
,
Y. P.
,
Fong
,
Z. H.
, and
Lin
,
G. C. Y.
,
2007
, “
Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
38
47
.
15.
Hsu
,
R. H.
,
Shih
,
Y. P.
,
Fong
,
Z. H.
,
Huang
,
C. L.
,
Chen
,
S. H.
,
Chen
,
S. S.
,
Lee
,
Y. H.
,
Chen
,
K. H.
,
Hsu
,
T.-P.
, and
Chen
,
W. J.
,
2020
, “
Mathematical Model of a Vertical Six-Axis Cartesian Computer Numerical Control Machine for Producing Face-Milled and-Face Hobbed Bevel Gears
,”
ASME J. Mech. Des.
,
142
(
4
), p.
043301
.
16.
Ratchev
,
S.
,
Liu
,
S.
,
Huang
,
W.
, and
Becker
,
A. A.
,
2004
, “
Milling Error Prediction and Compensation in Machining of Low-Rigidity Parts
,”
Int. J. Mach. Tool Manuf.
,
44
(
15
), pp.
1629
1641
.
17.
Lorensen
,
W. E.
, and
Cline
,
H. E.
,
1987
, “
Marching Cubes: A High Resolution 3D Surface Construction Algorithm
,”
ACM SIGGRAPH Comput. Graph.
,
21
(
4
), pp.
163
169
.
18.
Van Hook
,
T.
,
1986
, “
Real-Time Shaded NC Milling Display
,”
ACM SIGGRAPH Comput. Graph.
,
20
(
4
), pp.
15
20
.
19.
Peng
,
X.
, and
Zhang
,
W.
,
2009
, “
A Virtual Sculpting System Based on Triple Dexel Models With Haptics
,”
Comput.-Aided Des. Appl.
,
6
(
5
), pp.
645
659
.
20.
Inui
,
M.
,
Huang
,
Y.
,
Onozuka
,
H.
, and
Umezu
,
N.
,
2020
, “
Geometric Simulation of Power Skiving of Internal Gear Using Solid Model With Triple-Dexel Representation
,”
Proc. Manuf.
,
48
, pp.
520
527
.
21.
Habibi
,
M.
, and
Chen
,
Z. C.
,
2016
, “
An Accurate and Efficient Approach to Undeformed Chip Geometry in Face-Hobbing and Its Application in Cutting Force Prediction
,”
ASME J. Mech. Des.
,
138
(
2
), p.
023302
.
22.
Efstathiou
,
C.
, and
Tapoglou
,
N.
,
2021
, “
A Novel CAD-Based Simulation Model for Manufacturing of Spiral Bevel Gears by Face Milling
,”
CIRP J. Manuf. Sci. Technol.
,
33
, pp.
277
292
.
23.
Efstathiou
,
C.
, and
Tapoglou
,
N.
,
2022
, “
Simulation of Spiral Bevel Gear Manufacturing by Face Hobbing and Prediction of the Cutting Forces Using a Novel CAD-Based Model
,”
Int. J. Adv. Manuf. Technol.
,
122
(
9–10
), pp.
3789
3813
.
24.
Brecher
,
C.
,
Klocke
,
F.
,
Schröder
,
T.
, and
Rütjes
,
U.
,
2008
, “
Analysis and Simulation of Different Manufacturing Processes for Bevel Gear Cutting
,”
J. Adv. Mech. Des. Syst. Manuf.
,
2
(
1
), pp.
165
172
.
25.
Janßen
,
C.
,
Brimmers
,
J.
, and
Bergs
,
T.
,
2021
, “
Validation of the Plane-Based Penetration Calculation for Gear Skiving
,”
Proc. CIRP
,
99
, pp.
220
225
.
26.
Kamratowski
,
M.
,
Brimmers
,
J.
, and
Bergs
,
T.
,
2023
, “
Validation of a Planar Penetration Calculation for Face Hobbing Generating of Bevel Gears
,”
Proc. CIRP
,
118
, pp.
477
482
.
27.
Shih
,
Y. P.
,
Sheen
,
B. T.
,
Ting
,
C. F.
,
Chang
,
W. C.
, and
Hong
,
J. L.
,
2024
, “
Face-Milling Cutting Simulation of Bevel Gears Using Ring-Dexel Method
,”
Adv. Mech. Mach. Sci.
,
149
, pp.
13
26
.
28.
Zhang
,
C.
, and
Chen
,
T.
,
2001
, “
Efficient Feature Extraction for 2D/3D Objects in Mesh Representation
,”
Proceedings of 2001 International Conference on Image Processing
,
Thessaloniki, Greece
,
Oct. 7–10
, Vol.
3
, pp.
935
938
.
29.
Fanuc Series 0+ Mate-Model D Operator's Manual
, B-64304EN/02.
You do not currently have access to this content.