Elastic deflection of cutting tools relative to the workpiece is one of the major factors contributing to dimensional part inaccuracies in machining. This paper examines the effect of tool deflection in gear shaping and its effect on the gear's profile form error, which can cause transmission error and noise during gear operation. To simulate elastic tool deflection in gear shaping, the tool's static stiffness is estimated from impact hammer testing. Then, based on simulated cutter-workpiece engagement and predicted cutting forces, the elastic deflection of the tool is calculated at each time-step. To examine the effect of tool deflection on the profile error of the gear, a virtual gear measurement module is developed and used to predict the involute profile deviations in the virtually machined part. Simulated and measured profile deviations were compared for a one-pass external spur gear process and a two-pass external spur gear process. The simulated profile errors correlate very well with the measured profiles on the left flanks of the workpiece teeth, which are cut by the leading edges of the cutter teeth. However, additional research is needed to improve the prediction of the right flanks, which are cut by the trailing edges of the cutter teeth.

References

References
1.
Chaari
,
F.
,
Fakhfakh
,
T.
,
Louati
,
J.
, and
Haddar
,
M.
,
2006
, “
Influence of Manufacturing Errors on the Dynamic Behavior of Planetary Gears
,”
Int. J. Adv. Manuf. Technol.
,
27
(
7
), pp.
738
746
.
2.
Katz
,
A.
,
Erkorkmaz
,
K.
, and
Ismail
,
F.
,
2018
, “
Virtual Model of Gear Shaping—Part I: Kinematics, Cutter-Workpiece Engagement, and Cutting Forces
,”
ASME J. Manuf. Sci. Eng.
, in press.
3.
Budak
,
E.
, and
Altintas
,
Y.
,
1994
, “
Peripheral Milling Conditions for Improved Dimensional Accuracy
,”
Int. J. Mach. Tools Manuf.
,
34
(
7
), pp.
907
918
.
4.
Soori
,
M.
,
Arezoo
,
B.
, and
Habibi
,
M.
,
2016
, “
Tool Deflection Error of Three-Axis Computer Numerical Control Milling Machines, Monitoring and Minimizing by a Virtual Machining System
,”
ASME J. Manuf. Sci. Eng.
,
138
(
8
), p.
081005
.
5.
Budak
,
E.
, and
Altintas
,
Y.
,
1995
, “
Modeling and Avoidance of Static Form Errors in Peripheral Milling of Plates
,”
Int. J. Mach. Tools Manuf.
,
35
(
3
), pp.
459
476
.
6.
Tuysuz
,
O.
, and
Altintas
,
Y.
,
2017
, “
Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining
,”
ASME J. Manuf. Sci. Eng.
,
139
(
7
), p.
071013
.
7.
Duan
,
X.
,
Peng
,
F.
,
Yan
,
R.
,
Zhu
,
Z.
,
Huang
,
K.
, and
Li
,
B.
,
2015
, “
Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility
,”
ASME J. Manuf. Sci. Eng.
,
138
(
4
), p.
041001
.
8.
Phan
,
A.-V.
,
Baron
,
L.
,
Mayer
,
J.
, and
Cloutier
,
G.
,
2003
, “
Finite Element and Experimental Studies of Diametral Errors in Cantilever Bar Turning
,”
Appl. Math. Modell.
,
27
(
3
), pp.
221
232
.
9.
Tobias
,
S.
,
1965
,
Machine Tool Vibrations
,
Wiley
,
New York
.
10.
Tlusty
,
J.
, and
Polacek
,
M.
,
1963
, “
The Stability of Machine Tools Against Self-Excited Vibrations in Machining
,”
ASME Int. Res. Prod. Eng.
,
1
, pp.
465
475
.
11.
Merritt
,
H.
,
1965
, “
Theory of Self-Excited Machine-Tool Chatter
,”
ASME J. Eng. Ind.
,
87
(
4
), pp.
447
454
.
12.
Tlusty
,
J.
,
Zaton
,
W.
, and
Ismail
,
F.
,
1983
, “
Stability Lobes in Milling
,”
CIRP Ann.
,
32
(
1
), pp.
309
313
.
13.
Altintas
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP Ann.
,
44
(
1
), pp.
357
362
.
14.
Comak
,
A.
,
Ozsahin
,
O.
, and
Altintas
,
Y.
,
2016
, “
Stability of Milling Operations With Asymmetric Cutter Dynamics in Rotating Coordinates
,”
ASME J. Manuf. Sci. Eng.
,
138
(
8
), p.
081004
.
15.
Abrari
,
F.
,
Elbestawi
,
M.
, and
Spence
,
A.
,
1998
, “
On the Dynamics of Ball End Milling: Modeling of Cutting Forces and Stability Analysis
,”
Int. J. Mach. Tools Manuf.
,
38
(
3
), pp.
215
237
.
16.
Altintas
,
Y.
, and
Ko
,
J.
,
2006
, “
Chatter Stability of Plunge Milling
,”
CIRP Ann.
,
55
(
1
), pp.
361
364
.
17.
Ahmadi
,
K.
, and
Ismail
,
F.
,
2010
, “
Machining Chatter in Flank Milling
,”
Int. J. Mach. Tools Manuf.
,
50
(
1
), pp.
75
85
.
18.
Lu
,
Y.
,
Ding
,
Y.
, and
Zhu
,
L.
,
2017
, “
Dynamics and Stability Prediction of Five-Axis Flat-End Milling
,”
ASME J. Manuf. Sci. Eng.
,
139
(
6
), p.
061015
.
19.
Singh
,
K. K.
,
Kartik
,
V.
, and
Singh
,
R.
,
2016
, “
Modeling of Dynamic Instability Via Segmented Cutting Coefficients and Chatter Onset Detection in High-Speed Micromilling of Ti6Al4V
,”
ASME J. Manuf. Sci. Eng.
,
139
(
5
), p.
051005
.
20.
Budak
,
E.
, and
Ozlu
,
E.
,
2007
, “
Analytical Modeling of Chatter Stability in Turning and Boring Operations: A Multi-Dimensional Approach
,”
CIRP Ann.
,
56
(
1
), pp.
401
404
.
21.
Axinte
,
D.
,
2007
, “
An Experimental Analysis of Damped Coupled Vibrations in Broaching
,”
Int. J. Mach. Tools Manuf.
,
47
(
14
), pp.
2182
2188
.
22.
Datta
,
P. P.
,
Chattopadhyay
,
T. K.
, and
Banerjee
,
R. N.
,
2004
, “
Computer Aided Stress Analysis of Fellow's Gear-Shaping Cutter at Different Stages of a Cutting Stroke
,”
Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
,
218
(
12
), pp.
1297
1306
.
23.
Datta
,
P.
,
Banerjee
,
R.
, and
Chattopadhyay
,
T.
,
2004
, “
Computer Aided Stress and Deflection Analysis of Fellow's Gear-Shaping Cutter, for Different Cutting Process Parameters
,”
Proc. Inst. Mech. Eng., Part B J. Eng. Manuf.
,
218
(
12
), pp.
1755
1765
.
24.
Inman
,
D. J.
,
2014
,
Engineering Vibration
,
Pearson Education
,
Upper Saddle River, NJ
.
25.
Manufacturing Automation Laboratories
, 2017, “CUTPRO Simulation Software,” Manufacturing Automation Laboratories, Inc., Vancouver, BC, Canada, accessed Mar. 28, 2018, https://www.malinc.com/products/cutpro/
26.
Goch
,
G.
,
2003
, “
Gear Metrology
,”
CIRP Ann.
,
52
(
2
), pp.
659
695
.
27.
Goch
,
G.
,
Ni
,
K.
,
Peng
,
Y.
, and
Guenther
,
A.
,
2017
, “
Future Gear Metrology Based on Areal Measurements and Improved Holistic Evaluations
,”
CIRP Ann.
,
66
(
1
), pp.
469
474
.
28.
AGMA,
2014
, “Cylindrical Gears—ISO System of Flank Tolerance Classification—Part 1: Definitions and Allowable Values of Deviations Relevant to Flanks of Gear Teeth,” American Gear Manufacturers Association, Alexandria, VA, Standard No.
ANSI/AGMA ISO 1328-1-B14
.
You do not currently have access to this content.