CLC number: TH132.41
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2019-05-20
Cited: 0
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Xiao-le Wang, Jian-wei Lu, Shi-qin Yang. Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments[J]. Journal of Zhejiang University Science A, 2019, 20(6): 411-430.
@article{title="Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments",
author="Xiao-le Wang, Jian-wei Lu, Shi-qin Yang",
journal="Journal of Zhejiang University Science A",
volume="20",
number="6",
pages="411-430",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1900021"
}
%0 Journal Article
%T Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments
%A Xiao-le Wang
%A Jian-wei Lu
%A Shi-qin Yang
%J Journal of Zhejiang University SCIENCE A
%V 20
%N 6
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%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1900021
TY - JOUR
T1 - Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments
A1 - Xiao-le Wang
A1 - Jian-wei Lu
A1 - Shi-qin Yang
J0 - Journal of Zhejiang University Science A
VL - 20
IS - 6
SP - 411
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%@ 1673-565X
Y1 - 2019
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1900021
Abstract: Accurate evaluation of the misalignment sensitivity of hypoid gears is a significant foundation for analysis of its dynamics and for the calculation of machining parameters. A tooth contact analysis (TCA) methodology considering four kinds of misalignments is presented to calculate the contact pattern and transmission error. A sensitivity model of contact pattern to misalignments is established to investigate the effects of different alignment errors on meshing performance. By parameterizing the contact pattern, the influences of offset error, angular error, and the axial error of pinion and gear on the direction, shape, and position features of contact pattern are studied. Coefficients of four evaluation indexes to different misalignments are defined respectively, and the minimum sum of the weighted coefficients is utilized to establish a multi-objective comprehensive sensitivity model. Three curvatures of the pitch cone of the pinion are taken as the control variables, and a global selection space is then built within the reasonable range of those curvatures. An improved multi-population genetic algorithm (MPGA) is used to find the optimal set of curvatures to achieve the minimum synthetic sensitivity. TCA results indicate that the offset error and angular error have the greatest influence on the contact pattern. By adopting this methodology appropriately, the sensitivity of the contact pattern to misalignments can be reduced. The contributions of this paper can be summarized as: (1) an accurate parameterized measurement model of the contact pattern; (2) a comprehensive sensitivity model of the contact pattern to misalignments; (3) an optimization framework consisting of a calculation model of the machining parameters, a TCA model considering misalignments, and a misalignment sensitivity evaluation model.
This paper presents an optimization methodology for determining profile modification based on contact pattern and transmission error. This process is for unloaded contact conditions.
[1]Achtmann J, Bär H, 2003. Optimized bearing ellipses of hypoid gears. Journal of Mechanical Design, 125(4):739-745.
[2]ANSI-AGMA, 2005. Design Manual for Bevel Gears, ANSI/ AGMA 2005-D03. National Standards of America, USA.
[3]ANSI-AGMA, 2008. Assembling Bevel Gears, ANSI/AGMA 2008-C01. National Standards of America, USA.
[4]Artoni A, Bracci A, Gabiccini M, et al., 2008. Optimization of the loaded contact pattern in hypoid gears by automatic topography modification. Journal of Mechanical Design, 131(1):011008.
[5]Baxter ML, Spear GM, 1961. Effect of misalignment on tooth action of bevel and hypoid gears. ASME Design Conference, ASME 61-MD-20.
[6]Bracci A, Gabiccini M, Artoni A, et al., 2009. Geometric contact pattern estimation for gear drives. Computer Methods in Applied Mechanics and Engineering, 198(17-20):1563-1571.
[7]Deng XZ, Wei BY, 2012. The New Methodology of the Bevel Gear’s Design. Science Press, Beijing, China (in Chinese).
[8]Ding H, Zhou YS, Tang JY, et al., 2016. A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears. Mechanism and Machine Theory, 109:155-170.
[9]Elisaus V, Mohammadpour M, Theodossiades S, et al., 2017. Effect of teeth micro-geometrical form modification on contact kinematics and efficiency of high performance transmissions. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 231(3):538-555.
[10]Fan Q, 2011. Optimization of face cone element for spiral bevel and hypoid gears. Journal of Mechanical Design, 133(9):091002.
[11]Fan Q, Wilcox L, 2007. New developments in tooth contact analysis (TCA) and loaded TCA for spiral bevel and hypoid gear drives. Gear Technology, 24(3):26-35.
[12]Gabiccini M, Bracci A, Guiggiani M, 2010. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments. Journal of Mechanical Design, 132(4):041010.
[13]Guo WC, Mao SM, Yang Y, et al., 2016. Optimization of cutter blade profile for face-hobbed spiral bevel gears. The International Journal of Advanced Manufacturing Technology, 85(1-4):209-216.
[14]Hotait MA, Kahraman A, Nishino T, 2011. An investigation of root stresses of hypoid gears with misalignments. Journal of Mechanical Design, 133(7):071006.
[15]Kolivand M, Kahraman A, 2009. A load distribution model for hypoid gears using ease-off topography and shell theory. Mechanism and Machine Theory, 44(10):1848-1865.
[16]Litvin FL, Fuentes A, 2004. Gear Geometry and Applied Theory (2nd Edition). Cambridge University Press, New York, USA.
[17]Litvin FL, Tsung WJ, Lee HT, 1987. Generation of Spiral Bevel Gears with Conjugate Tooth Surfaces and Tooth Contact Analysis. NASA Contractor Report No. 4088, National Aeronautics and Space Administration, USA.
[18]Litvin FL, Zhang Y, Handschuh RF, 1991. Local Synthesis and Tooth Contact Analysis of Face-milled Spiral Bevel Gears. NASA Contractor Report No. 4342, National Aeronautics and Space Administration, USA.
[19]Litvin FL, Chen JS, Sep TM, et al., 1995. Computerized simulation of transmission errors and shift of bearing contact for face-milled hypoid gear drive. Journal of Mechanical Design, 117(2A):262-268.
[20]Mermoz E, Astoul J, Sartor M, et al., 2013. A new methodology to optimize spiral bevel gear topography. CIRP Annals, 62(1):119-122.
[21]Mohammadpour M, Theodossiades S, Rahnejat H, et al., 2014. Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 228(1):19-33.
[22]Pourvaziri H, Naderi B, 2014. A hybrid multi-population genetic algorithm for the dynamic facility layout problem. Applied Soft Computing, 24:457-469.
[23]Simon V, 1996. Tooth contact analysis of mismatched hypoid gears. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, 88:789-797.
[24]Simon V, 1998. The influence of misalignments on mesh performances of hypoid gears. Mechanism and Machine Theory, 33(8):1277-1291.
[25]Simon V, 2008. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors and misalignments. Journal of Mechanical Design, 130(8):082603.
[26]Simon VV, 2014. Optimal tooth modifications in face-hobbed spiral bevel gears to reduce the influence of misalignments on elastohydrodynamic lubrication. Journal of Mechanical Design, 136(7):071007.
[27]Stadtfeld HJ, 1993. Handbook of Bevel and Hypoid Gears. Gleason Works, Rochester Institute of Technology, New York, USA.
[28]The Gleason Works, 1971. Method for Designing Hypoid Gear Blanks. The Gleason Works, Rochester, USA.
[29]Vivet M, Mundo D, Tamarozzi T, et al., 2018. An analytical model for accurate and numerically efficient tooth contact analysis under load, applied to face-milled spiral bevel gears. Mechanism and Machine Theory, 130:137-156.
[30]Vogel O, Griewank A, Bär G, 2002. Direct gear tooth contact analysis for hypoid bevel gears. Computer Methods in Applied Mechanics and Engineering, 191(36):3965-3982.
[31]Wang P, Zhang YD, Wan M, 2016. Global synthesis for face milled spiral bevel gears with zero transmission errors. Journal of Mechanical Design, 138(3):033302.
[32]Wang Q, Zhou C, Gui LJ, et al., 2018. Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a Kriging model. Mechanism and Machine Theory, 122:432-449.
[33]Wang XC, Ghosh SK, 1994. Advanced Theories of Hypoid Gears. Elsevier, Amsterdam, The Netherlands.
[34]Wu XT, 2009. Gear Engagement Principle (2nd Edition). Xi’an Jiaotong University Press, Xi’an, China (in Chinese).
[35]Xu H, Kahraman A, 2007. Prediction of friction-related power losses of hypoid gear pairs. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 221(3):387-400.
[36]Zeng T, 1989. Design and Manufacture of Spiral Bevel Gear. Harbin Institute of Technology Press, Harbin, China (in Chinese).
[37]Zhuo YB, Xiang XY, Zhou XJ, et al., 2017. A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 18(5):377-392.
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