Abstract
This paper provides a method coupling the 2D microtopography filtered by ISO Gaussian filter of spur gears, which is typically used in power transmission devices, and Transmission error (TE) together. A gearbox with certain transmission ratio is selected as a research object for analysis. This gearbox comprises a mathematical model of TE calculation based on the Monte Carlo method and the coordinate transformation method, which couples the 2D microtopography of spur gears and TE. Two TE models are established to study their effects on the coupling results: a) The single TE model, which means only one gear owns TE, and b) the synthetic TE model, which means both gears possess TE. The new model of the 2D microtopography of tooth surfaces can be utilized further to investigate the mechanism of engagement and the approximate contact position of asperities on the tooth surface. The new model is also significant in studying the tooth root bending stress.
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References
H. Zhao et al., Status and problem research on gear study, Journal of Mechanical Engineering, 49 (19) (2013) 11–20.
Z. He et al., Parametric modeling and contact analysis of helical gears with modifications, Journal of Mechanical Science and Technology, 30 (11) (2016) 4859–4867.
X. Wang et al., Study on super-harmonic resonance for gear transmission based on teeth surface friction, Journal of Mechanical Science and Technology, 29 (11) (2015) 4631–4638.
H. Liu et al., Coefficient of friction of a starved lubricated spur gear pair, Journal of Mechanical Science and Technology, 30 (5) (2016) 2171–2177.
S. Cho et al., Numerical estimation of dynamic transmission error of gear by using quasi-flexible-body modeling method, Journal of Mechanical Science and Technology, 29 (7) (2015) 2713–2719.
C.-H. Lin and Z.-H. Fong, Numerical tooth contact analysis of a bevel gear set by using measured tooth geometry data, Mechanism and Machine Theory, 84 (2) (2015) 1–24.
C. Putignano et al., A new efficient numerical method for contact mechanics of rough surfaces, International Journal of Solids and Structures, 49 (2) (2012) 338–343.
O. Rezvanian et al., Surface roughness, asperity contact and gold RF MEMS switch behavior, Journal of Micromechanics & Microengineering, 17 (10) (2007) 2006.
Y. Wu, J. Wang and Q. Han, Static/dynamic contact FEA and experimental study for tooth profile modification of helical gears, Journal of Mechanical Science and Technology, 26 (5) (2012) 1409–1417.
G.-J. Cheon, Analysis of the nonlinear behavior of gear pairs considering hydrodynamic lubrication and sliding friction, Journal of Mechanical Science and Technology, 23 (8) (2009) 2125–2137.
S. Akarapu, T. Sharp and M. O. Robbins, Stiffness of contacts between rough surfaces, Physical Review Letters, 106 (20) (2011) 204301.
G. Carbone et al., Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties, The European Physical Journal E, 29 (3) (2009) 275–284.
R. Rego, J. O. Gomes and A. M. Barros, The influence on gear surface properties using shot peening with a bimodal media size distribution, Journal of Materials Processing Technology, 213 (12) (2013) 2152–2162.
I. Al-Tubi et al., Probabilistic analysis of gear flank micropitting risk in wind turbine gearbox using supervisory control and data acquisition data, Renewable Power Generation, IET, 9 (6) (2015) 610–617.
J. Sun et al., Thermohydrodynamic lubrication analysis of misaligned plain journal bearing with rough surface, Journal of Tribology, 132 (1) (2010) 011704.
P. Bajpai, A. Kahraman and N. E. Anderson, A surface wear prediction methodology for parallel-axis gear pairs, Journal of Tribology, 126 (3) (2004) 597–605.
R. Leach and H. Haitjema, Bandwidth characteristics and comparisons of surface texture measuring instruments, Measurement Science and Technology, 21 (3) (2010) 032001.
N. Jouini et al., Multi-scale analysis of high precision surfaces by stylus profiler, scanning white-light interferometry and atomic force microscopy, International Journal of Surface Science and Engineering, 3 (4) (2009) 310–327.
R. Leach, Optical measurement of surface topography, Springer (2011).
D. Remond and J. Mahfoudh, From transmission error measurements to angular sampling in rotating machines with discrete geometry, Shock and Vibration, 12 (2) (2005) 149–161.
H. Zhao and P. Sheng, The measurement and evaluation method of global error of spiral bevel gear, Advanced Materials Research, 204 (2011) 1299–1304.
F. Ville, Gear tooth pitting modelling and detection based on transmission error measurements. European Journal of Computational Mechanics, 22 (2–4) (2013) 106–119.
M. H. Tsai and Y. C. Tsai, A method for calculating static transmission errors of plastic spur gears using FEM evaluation, Finite Elements in Analysis and Design, 27 (4) (1997) 345–357.
M. S. Tavakoli and D. R. Houser, Optimum profile modifications for the minimization of static transmission errors of spur gears, Journal of Mechanisms, Transmissions and Automation in Design, 108 (1) (1986) 86–94.
S. Li, Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications, Mechanism and Machine Theory, 42 (1) (2007) 88–114.
S. Li, Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears, Mechanism and Machine Theory, 42 (6) (2007) 698–726.
W. H. Chen, H. F. Zhu and X. Y. Fan, Monte-Carlo simulation analysis of transmission error for gear drive systems, Chinese Journal of Scientific Instrument, 4 (2004) 004.
M. Miller et al., Surface roughness criteria for cement paste nanoindentation, Cement and Concrete Research, 38 (4) (2008) 467–476.
M. Krystek, A fast Gauss filtering algorithm for roughness measurements, Precision Engineering, 19 (2) (1996) 198–200.
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Recommended by Associate Editor Jungsoo Lee
Changjiang Zhou received his Ph.D. in Mechanical Engineering from Hunan University, China, in 2013. He is currently a Professor at Hunan University. His research interests include gear transmission, mechanical tribology, and dynamics.
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Zhou, C., Wang, Z. & Chen, S. Coupling of the 2D microtopography of tooth surface and transmission error. J Mech Sci Technol 32, 723–730 (2018). https://doi.org/10.1007/s12206-018-0121-5
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DOI: https://doi.org/10.1007/s12206-018-0121-5