Gear shaping, commonly regarded as the most widely used machining method for cylindrical gear, is in fact an ideal manufacturing method for noncircular gear due to its merit of not being restricted by gear type or pitch curve in contrast to gear hobbing. However, concerning researches are mainly focused on the generation of noncircular straight external gear, paying rare attention to noncircular internal gear and noncircular helix gear. Considering that this paper, through using a three-linkage computer numerical control (CNC) shaping machine, aims to synthesize shaped noncircular gear, covering external, internal, straight, and helix gear. The mathematical model, a three-linkage model, is first established. The corresponding manufacturing process in practice is subsequently discussed. Finally, with practical shaping experiments, the correctness of the proposed model and the appropriateness of the manufacturing process are verified.
Issue Section:
Research Papers
Keywords:
Design for manufacturing
References
1.
Freudenstein
, F.
, and Chen
, C. K.
, 1991
, “Variable-Ratio Chain Drives With Noncircular Sprockets and Minimum Slack-Theory and Application
,” ASME J. Mech. Des.
, 113
(3
), pp. 253
–262
.2.
Emura
, T.
, and Arakawa
, A.
, 1992
, “A New Steering Mechanism Using Noncircular Gears
,” JSME Int. J., Ser. III
, 35
(4), pp. 604
–610
.3.
Litvin
, F. L.
, Gonzalez-Perez
, I.
, Fuentes
, A.
, and Hayasaka
, K.
, 2008
, “Design and Investigation of Gear Drives With Non-Circular Gears Applied for Speed Variation and Generation of Functions
,” Comput. Methods Appl. Mech. Eng.
, 197
(45–48), pp. 3783
–3802
.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.
Liu
, J. Y.
, Chang
, S. L.
, and Mundo
, D.
, 2006
, “Study on the Use of a Non-Circular Gear Train for the Generation of Figure-8 Patterns
,” J. Mech. Eng. Sci.
, 220
(8
), pp. 1229
–1236
.6.
Mundo
, D.
, 2006
, “Geometric Design of a Planetary Gear Train With Non-Circular Gears
,” Mech. Mach. Theory
, 41
(4
), pp. 456
–472
.7.
Zheng
, F.
, Hua
, L.
, and Han
, X.
, 2016
, “The Mathematical Model and Mechanical Properties of Variable Center Distance Gears Based on Screw Theory
,” Mech. Mach. Theory
, 101
, pp. 116
–139
.8.
Zheng
, F.
, Hua
, L.
, Han
, X.
, Li
, B.
, and Chen
, D.
, 2016
, “Synthesis of Indexing Mechanisms With Non-Circular Gears
,” Mech. Mach. Theory
, 105
, pp. 192
–212
.9.
Han
, J. Y.
, 1997
, “Complete Balancing of the Shaking Moment in Spatial Linkages by Adding Planar Noncircular Gears
,” Arch. Appl. Mech.
, 67
(1–2), pp. 44
–49
.10.
Dooner
, D. B.
, 1997
, “Use of Noncircular Gears to Reduce Torque and Speed Fluctuations in Rotating Shafts
,” ASME J. Mech. Des.
, 119
(2
), pp. 299
–306
.11.
Ottaviano
, E.
, Mundo
, D.
, Danieli
, G. A.
, and Ceccarelli
, M.
, 2008
, “Numerical and Experimental Analysis of Non-Circular Gears and CAM-Follower Systems as Function Generators
,” Mech. Mach. Theory
, 43
(8
), pp. 996
–1008
.12.
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 Gears
,” Mech. Mach. Theory
, 44
(4
), pp. 726
–738
.13.
Mundo
, D.
, Gatti
, G.
, and Dooner
, D. B.
, 2009
, “Optimized Five-Bar Linkages With Non-Circular Gears for Exact Path Generation
,” Mech. Mach. Theory
, 44
(4
), pp. 751
–760
.14.
Chen
, C. F.
, and Tsay
, C. B.
, 2004
, “Computerized Tooth Profile Generation and Analysis of Characteristics of Elliptical Gears With Circular-Arc Teeth
,” J. Mater. Process. Technol.
, 148
(2
), pp. 226
–234
.15.
Tan
, W. M.
, Hu
, C. B.
, Xian
, W. J.
, and Qu
, Y.
, 2001
, “Concise Mathematical Model for Hobbing Non-Circular Gear and Its Graphic Simulation
,” Chin. J. Mech. Eng.
, 37
(5
), pp. 26
–29
(in Chinese).16.
Litvin
, F. L.
, Gonzalez-Perez
, I.
, Yukishima
, K.
, Fuentes
, A.
, and Hayasaka
, K.
, 2007
, “Generation of Planar and Helical Elliptical Gears by Application of Rack-Cutter, Hob, and Shaper
,” Comput. Methods Appl. Mech. Eng.
, 196
(41–44), pp. 4321
–4336
.17.
Liu
, Y. Y.
, Han
, J.
, Xia
, L.
, and Tian
, X. Q.
, 2012
, “Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage
,” J. Mech. Eng.
, 58
(12), pp. 701
–708
.18.
Xia
, L.
, Liu
, Y. Y.
, Li
, D. Z.
, and Han
, J.
, 2013
, “A Linkage Model and Applications of Hobbing Non-Circular Helical Gears With Axial Shift of Hob
,” Mech. Mach. Theory
, 70
, pp. 32
–44
19.
Figliolini
, G.
, and Angeles
, J.
, 2003
, “The Synthesis of Elliptical Gears Generated by Shaper-Cutters
,” ASME J. Mech. Des.
, 125
(4
), pp. 793
–801
.20.
Cheng
, S. L.
, and Tsay
, C. B.
, 1998
, “Computerized Tooth Profile Generation and Undercutting Analysis of Noncircular Gears Manufactured With Shaper Cutter
,” ASME J. Mech. Des.
, 120
(1
), pp. 92
–99
.21.
Bair
, B.-W.
, 2002
, “Computerized Tooth Profile Generation of Elliptical Gears Manufactured by Shaper Cutters
,” J. Mater. Process. Technol.
, 122
(2–3), pp. 139
–147
.22.
Jiangang
, L.
, Xutang
, W.
, and Shimin
, M.
, 2007
, “Numerical Computing Method of Noncircular Gear Tooth Profiles Generated by Shaper Cutters
,” Adv. Manuf. Technol.
, 33
(11–12), pp. 1098
–1105
.23.
Zheng
, F.
, Hua
, L.
, Han
, X.
, Li
, B.
, and Chen
, D.
, 2016
, “Linkage Model and Manufacturing Process of Shaping Non-Circular Gear
,” Mech. Mach. Theory
, 96
(Part 1), pp. 192
–212
.24.
Huang
, C. L.
, Fong
, Z. H.
, Chen
, S. D.
, and Chang
, K. R.
, 2009
, “Profile Correction of a Helical Gear Shaping Cutter Using the Lengthwise-Reciprocating Grinding Method
,” Mech. Mach. Theory
, 44
(2
), pp. 401
–411
.25.
Bair
, B.-W.
, 2002
, “Computer Aided Design of Elliptical Gears
,” ASME J. Mech. Des.
, 124
(4
), pp. 787
–793
.26.
Dooner
, D. B.
, 2012
, Kinematic Geometry of Gearing
, Wiley
, Chichester, UK
.27.
Litvin
, F. L.
, 2004
, Gear Geometry and Applied Theory
, Cambridge University Press
, New York, pp. 20
–25
.28.
Jiqiang
, X.
, Yuanyuan
, L.
, Chunming
, G.
, and Han
, J.
, 2008
, “Noncircular Bevel Gear Transmission With Intersecting Axes
,” ASME J. Mech. Des.
, 130
(5), pp. 1
–6
.29.
Bair
, B. W.
, Sung
, M. H.
, Wang
, J. S.
, and Chen
, C. F.
, 2009
, “Tooth Profile Generation and Analysis of Oval Gears With Circular-Arc Teeth
,” Mech. Mach. Theory
, 44
(6
), pp. 1306
–1317
.30.
Dai
, J. S.
, 2014
, “Screw Algebra and Kinematic Approaches for Mechanisms and Robotics
,” Springer
, London
, pp. 60
–61
.31.
Tsay
, C.-B.
, Liu
, W.-Y.
, and Chen
, Y.-C.
, 2000
, “Spur Gear Generation by Shaper Cutters
,” J. Mater. Process. Technol.
, 104
(3
), pp. 271
–279
.32.
Shih
,Y.-P.
, Huang
,Y.-C.
, Lee
,Y.-H.
, and Wu
, J.-M.
, 2013
, “Manufacture of Face-Hobbed Straight Bevel Gears Using a Six-Axis CNC Bevel Gear Cutting Machine
,” Adv. Manuf. Technol.
, 68
(9), pp. 2499
–2515
.33.
Bouzakis
, K.-D.
, Lili
, E.
, Michailidis
, N.
, and Friderikos
, O.
, 2008
, “Manufacturing of Cylindrical Gears by Generating Cutting Processes: A Critical Synthesis of Analysis Methods
,” CIRP Ann. Manuf. Technol.
, 57
(2
), pp. 676
–696
.34.
Litvin
, F. L.
, Chen
, N. X.
, and Chen
, J.-S.
, 1995
, “Computerized Determination of Curvature Relations and Contact Ellipse for Conjugate Surfaces
,” Comput. Methods Appl. Mech. Eng.
, 125
(1–4), pp. 151
–170
35.
Zheng
, F.
, Hua
, L.
, Han
, X.
, and Chen
, D.-F.
, 2016
, “Generation of Non-Circular Bevel Gears With Free-Form Tooth Profile and Tooth Lengthwise Based on Screw Theory
,” ASME J. Mech. Des.
, 138
(6
), p. 064501
.36.
Zheng
, F.
, Hua
, L.
, Chen
, D.-F.
, and Han
, X.
, 2016
, “Generation of Non-Circular Spiral Bevel Gears by Face-Milling Method
,” ASME J. Manuf. Sci. Eng.
, 138
(8
), p. 081013
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