Abstract
Gear eccentricity, one of the most common defects of gear systems, affects not only dynamic behavior but also mesh stiffness. Accurate mesh stiffness under defect conditions is vital for the dynamic simulation and fault diagnosis of gear systems. Hence, the timevarying mesh stiffness affected by gear eccentricity, which is commonly neglected in most studies, is incorporated in the proposed twostage spur gear dynamic model and calculated by a novel gear mesh model with an improved potential energy method. The effects of mesh stiffness with and without gear eccentricity on the gear system are compared on the basis of the constructed dynamic model. The influences of gear eccentricity on dynamic transverse and torsional responses, as well as dynamic transmission errors, are also quantitatively studied. Some helpful analytical results are then presented.
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References
X. Liang, M. J. Zuo and Z. Feng, Dynamic modeling of gearbox faults: A review, Mech. Syst. Signal Process., 98 (2018) 852–876
H. Nevzat Özgüven and D. R. Houser, Mathematical models used in gear dynamics — A Review, J. Sound Vib., 121 (3) (1988) 383–411.
A. Parey and N. Tandon, Spur gear dynamic models including defects: A review, Shock Vib. Dig., 35 (6) (2003) 465–478.
X. Gu and P. Velex, On the dynamic simulation of eccentricity errors in planetary gears, Mech. Mach. Theory, 61 (2013) 14–29
H. Iida et al., Coupled torsinal-flexural vibration of a shaft in a geared system of rotors, Bull. JSME, 23 (186) (1980) 2111–2117.
A. Kahraman et al., Dynamic analysis of geared rotors by finite elements, J. Mech. Des., 114 (3) (1992) 507–514.
P. Velex and M. Maatar, A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour, J. Sound Vib., 191 (5) (1996) 629–660.
S. T. Choi and S. Y. Mau, Dynamic analysis of geared rotorbearing systems by the transfer matrix method, J. Mech. Des., 123 (4) (2001) 562–568.
A. S. Lee and J. W. Ha, Prediction of maximum unbalance responses of a gear-coupled two-shaft rotor-bearing system, J. Sound Vib., 283 (3–5) (2005) 507–523.
W. Yu, C. K. Mechefske and M. Timusk, The dynamic coupling behaviour of a cylindrical geared rotor system subjected to gear eccentricities, Mech. Mach. Theory, 107 (2017) 105–122
G. Wang et al., Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method, Mech. Mach. Theory, 109 (2017) 1–13
E. Wehrle et al., Design optimization of planetary gear trains under dynamic constraints and parameter uncertainty, Proc. ECCOMAS Themat. Conf. Multibody Dyn., Prague, Czech Republic (2017).
F. Concli et al., A mixed FEM and lumped-parameter dynamic model for evaluating the modal properties of planetary gearboxes, J. Mech. Sci. Technol., 32 (7) (2018) 3047–3056.
J. P. Raclot and P. Velex, Simulation of the dynamic behaviour of single and multi-stage geared systems with shape deviations and mounting errors by using a spectral method, J. Sound Vib., 220 (5) (1999) 861–903.
Y. Zhang et al., Dynamic analysis of three-dimensional helical geared rotor system with geometric eccentricity, J. Mech. Sci. Technol., 27 (11) (2013) 3231–3242.
T. Fakhfakh et al., Effect of manufacturing and assembly defects on two-stage gear systems vibration, Int. J. Adv. Manuf. Technol., 29 (9–10) (2006) 1008–1018.
A. Saxena, A. Parey and M. Chouksey, Effect of shaft misalignment and friction force on time varying mesh stiffness of spur gear pair, Eng. Fail. Anal., 49 (2015) 79–91
Z. Wan et al., An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack, Eng. Fail. Anal., 42 (2014) 157–177
X. Tian, Dynamic simulation for system response of gearbox including localized gear faults, Diss. M.S. Thesis, University of Alberta, Edmonton (2004).
D. C. H. Yang and J. Y. Lin, Hertzian damping, tooth friction and bending elasticity in gear impact dynamics, J. Mech. Transm. Autom. Des., 109 (2) (1987) 189–196.
P. Sainsot, P. Velex and O. Duverger, Contribution of gear body to tooth deflections—A new bidimensional analytical formula, J. Mech. Des., 126 (4) (2004) 748–752.
H. Ding and A. Kahraman, Interactions between nonlinear spur gear dynamics and surface wear, J. Sound Vib., 307 (3–5) (2007) 662–679.
M. Kubur et al., Dynamic analysis of a multi-shaft helical gear transmission by finite elements: Model and experiment, J. Vib. Acoust., 126 (3) (2004) 398–406.
H. H. Lin, R. L. Huston and J. J. Coy, On dynamic loads in parallel shaft transmissions: Part I—Modelling and analysis, J. Mech. Transm. Autom. Des., 110 (2) (1988) 221–225.
V. K. Tamminana, A. Kahraman and S. Vijayakar, A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs, J. Mech. Des., 129 (1) (2007) 75–84.
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Recommended by Associate Editor Jin Woo Lee
Xiaoqin Zhou is currently a Professor in the School of Mechanical and Aerospace Engineering, Jilin University, China. His research interests are ultraprecision machining, manufacturing of key automobile components, and vibration diagnosis of mechanical machining.
Xiuzhi He is currently a Ph.D. candidate in the School of Mechanical and Aerospace Engineering, Jilin University, China. His research interests are gear system dynamics and fault diagnosis of gear systems.
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He, X., Zhou, X., Xue, Z. et al. Effects of gear eccentricity on time-varying mesh stiffness and dynamic behavior of a two-stage gear system. J Mech Sci Technol 33, 1019–1032 (2019). https://doi.org/10.1007/s12206-019-0203-7
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DOI: https://doi.org/10.1007/s12206-019-0203-7