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Research Papers

A New Method of Designing the Tooth Surfaces of Spiral Bevel Gears With Ruled Surface for Their Accurate Five-Axis Flank Milling

[+] Author and Article Information
Yuansheng Zhou

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, Hunan, China
e-mail: zyszby@hotmail.com

Zezhong C. Chen

Department of Mechanical and
Industrial Engineering,
Concordia University,
Montreal, QC H3G1M8, Canada
e-mail: zcchen@encs.concordia.ca

Jinyuan Tang

State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha 410083, Hunan, China
e-mail: jytangcsu@163.com

1Corresponding authors.

Manuscript received November 9, 2015; final manuscript received October 18, 2016; published online January 24, 2017. Assoc. Editor: Guillaume Fromentin.

J. Manuf. Sci. Eng 139(6), 061004 (Jan 24, 2017) (12 pages) Paper No: MANU-15-1562; doi: 10.1115/1.4035079 History: Received November 09, 2015; Revised October 18, 2016

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.

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References

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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Tönshoff, H. , Gey, C. , and Rackow, N. , 2001, “ Flank Milling Optimization-The Flamingo Project,” Air Space Eur., 3(3), pp. 60–63. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Litvin, F. L. , and Fuentes, A. , 2004, Gear Geometry and Applied Theory, Cambridge University Press, Cambridge, UK.
Litvin, F. L. , 1989, “ Theory of Gearing,” National Aeronautics and Space Administration, Scientific and Technical Information Division, AVSCOM Technical Report No. 88-C-035.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Achtmann, J. , and Bar, G. , 2003, “ Optimized Bearing Ellipses of Hypoid Gears,” ASME J. Mech. Des., 125(4), pp. 739–745. [CrossRef]
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. [CrossRef]
Zhang, Y. , and Wu, Z. , 2007, “ Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears,” ASME Paper No. DETC2007-34123.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Fan, Q. , 2010, “ Tooth Surface Error Correction for Face-Hobbed Hypoid Gears,” ASME J. Mech. Des., 132(1), p. 011004. [CrossRef]
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. [CrossRef]
Simon, V. V. , 2009, “ Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors,” ASME J. Mech. Des., 131(4), p. 041007. [CrossRef]
Simon, V. , 2009, “ Hed-Cutter for Optimal Tooth Modifications in Spiral Bevel Gears,” Mech. Mach. Theory, 44(7), pp. 1420–1435. [CrossRef]
Simon, V. V. , 2010, “ Advanced Manufacture of Spiral Bevel Gears on CNC Hypoid Generating Machine,” ASME J. Mech. Des., 132(3), p. 031001. [CrossRef]
Simon, V. V. , 2011, “ Generation of Hypoid Gears on CNC Hypoid Generator,” ASME J. Mech. Des., 133(12), p. 121003. [CrossRef]
Simon, V. V. , 2014, “ Optimization of Face-Hobbed Hypoid Gears,” Mech. Mach. Theory, 77, pp. 164–181. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
Di Puccio, F. , Gabiccini, M. , and Guiggiani, M. , 2005, “ Alternative Formulation of the Theory of Gearing,” Mech. Mach. Theory, 40(5), pp. 613–637. [CrossRef]
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. [CrossRef]
Wang, P. , and Zhang, Y. , 2013, “ An Invariant Approach for Curvature Analysis of Conjugate Surfaces,” Mech. Mach. Theory, 64, pp. 175–199. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Huston, R. , and Coy, J. J. , 1982, “ Surface Geometry of Circular Cut Spiral Bevel Gears,” ASME J. Mech. Des., 104(4), pp. 743–748. [CrossRef]
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. [CrossRef]
Peternell, M. , Pottmann, H. , and Ravani, B. , 1999, “ On the Computational Geometry of Ruled Surfaces,” Comput. Aided Des., 31(1), pp. 17–32. [CrossRef]
ANSI, 2005, “ Design Manual for Bevel Gears,” American Gear Manufacturers Associate, Alexandria, VA, Standard No. ANSI/AGMA 2005–D03.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]

Figures

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Fig. 1

The lengthwise curve and profile of a tooth surface

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Fig. 2

The circular lengthwise curve of the crown gear

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Fig. 3

The circular lengthwise curve of the spiral bevel gear: (a) front view and (b) top view

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Fig. 4

The profile definition of the ruled tooth surface

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Fig. 5

Three-dimensional gear model with ruled tooth surfaces design

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Fig. 6

Definition of the conical cutter surface

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Fig. 7

Tool position and orientation corresponding to a point on the contact path

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Fig. 8

Tool paths planned for one tooth slot: (a) tool path for convex tooth surface and (b) Tool path for concave tooth surface

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Fig. 9

The envelope surface of the cutter upper surface: (a) for convex tooth surface and (b) for concave tooth surface

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Fig. 10

The comparison between designed and simulate machined models

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Fig. 11

Geometric deviation analysis of the proposed designed model

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Fig. 12

Geometric deviation analysis of the generated face-milled model

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Fig. 13

The assembly of gear and pinion models

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Fig. 14

TCA results:(a) gear contact path, (b) pinion contact path, and (c) transmission errors

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