Effect of nonlinear impact damping with non-integer compliance exponent on gear dynamic characteristics

Abstract

A nonlinear impact damping model of single-degree-of-freedom spur cylindrical gear with backlash and time-varying stiffness was established. Systematic analyses of the dynamic responses were performed. First, the nonlinear damping coefficient was considered as a constant parameter with two types of compliance exponent, meanwhile, dynamic factors were adopted to depict the dynamic characteristics. Second, the bifurcation graphs were plotted, where the damping coefficient was obtained along with the impact velocity and coefficient of restitution. The results show that light and heavy load conditions have an effect on the responses when the compliance exponent is integer. On the contrary, when the compliance exponent is non-integer, the dynamic responses are slightly affected, namely the system is more stable than the former situation.

Keywords

spur cylindrical gear / nonlinear impact damping / backlash / non-integer compliance exponent

References

[1] DubowskyS, FreudensteinF. Dynamics analysis of mechanical systems with clearances-Part 1: Formation of dynamical model [J]. ASME Journal of Engineering for Industry, 1971, 93(2): 305-309

[2] DubowskyS, FreudensteinF. Dynamics analysis of mechanical systems with clearances-Part 2: Dynamic responses [J]. ASME Journal of Engineering for Industry, 1971, 93(2): 310-316

[3] HuntK H, CrossleyF R E. Coefficient of restitution interpreted as damping in vibroimpact [J]. Journal of Applied Mechanics, 1975, 42(5): 440-445

[4] VeluswamiM A, CrossleyF R E. Multiple impacts of a ball between two plates. Part 1: Some experimental observation [J]. Journal of Engineering for Industry, 1975, 97(3): 820-827

[5] VeluswamiM A, CrossleyF R E. Multiple impacts of a ball between two plates. Part 2: Some mathmetical modeling [J]. Journal of Engineering for Industry, 1975, 97(3): 828-835

[6] AzarR C, CrossleyF R E. Digital simulation of impact phenomenon in spur gear systems [J]. Journal of Engineering for Industry, 1977, 99(8): 792-798

[7] HerbertR G, Mc WhannellD C. Shape and frequency composition of pulses from an impact pair [J]. Journal of Engineering for Industry, 1977, 99(3): 513-518

[8] YangD C H, SunZ S. A rotary model of spur gear dynamics [J]. Journal of Mechanism, Transmissions and Automation in Design, 1985, 107(11): 529-535

[9] YangD C H, LinJ Y. Hertzian damping, tooth friction and bending elasticity in gear impact dynamics [J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1987, 109(2): 189-196

[10] ÖzgüvenN H, HouserD R. Mathematical models used in gear dynamics-A review [J]. Journal of Sound and Vibration, 1988, 121(3): 383-341

[11] KahramanA, SinghR. Non-linear dynamics of a spur gear pair [J]. Journal of Sound and Vibration, 1990, 142(1): 49-75

[12] BlankenshipG W, SinghR. Analytical solution for modulation sidebands associated with a class of mechanical oscillators [J]. Journal of Sound and Vibration, 1995, 179(1): 13-36

[13] ChenS-y, TangJ-yuan. Study on a new nonlinear parametric excitation equation: Stability and bifurcation [J]. Journal of Sound and Vibration, 2008, 318(4): 1109-1118

[14] ChenS-y, TangJ-y, LuoC-w, WangQ-bo. Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction [J]. Mechanism and Machine Theory, 2011, 46(4): 466-478

[15] TangJ-y, HuZ-h, WuL-j, ChenS-yu. Effect of static transmission error on dynamic responses of spiral bevel gears [J]. Journal of Central South University, 2013, 20(3): 640-647

[16] TangJ-y, WangQ-b, WuL-j, ChenS-yu. Bifurcation analysis of impact model in gear transmission system [J]. Applied Mechanics and Materials, 2011, 86(4): 479-482

[17] DuanC, SinghR. Super-harmonics in a torsional system with dry friction path subject to harmonic excitation under a mean torque [J]. Journal of Sound and Vibration, 2005, 285(4): 803-834

[18] HeSEffect of sliding friction on spur and helical gear dynamics and vibro-acoustics [D], 2008, Columbus, The Ohio State University

[19] KaragiannisK, PfeifferF. Theoretical and experimental investigations of gear-rattling [J]. Nonlinear Dynamics, 1991, 2(5): 367-387

[20] PfeifferF, KunertA. Rattling models from deterministic to stochastic processes [J]. Nonlinear Dynamics, 1990, 1(1): 63-74

[21] Perret-LiaudetJ, RigaudE. Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 2: Random excitation [J]. Journal of Sound and Vibration, 2003, 265(2): 309-327

[22] RigaudE, Perret-LiaudetJ. Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation [J]. Journal of Sound and Vibration, 2003, 265(2): 289-307

[23] ZhangY, SharfI. Validation of nonlinear viscoelastic contact force models for low speed impact [J]. Journal of Applied Mechanics, 2009, 76(5): 1-12

[24] MarheflaD W, OrinD E. Simulation of contact using a nonlinear damping model [C]. Robotics and Automation, 1996, Minneapolis, IEEE: 1662-1668

[25] KimT, RookT, SinghR. Effect of nonlinear impact damping on the frequency response of a torsional system with clearance [J]. Journal of Sound and Vibration, 2005, 281(3): 995-1021

[26] LeeT W, WangA C. On the dynamics of intermittent-motion mechanisms, Part 1: Dynami model and response [J]. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1983, 105(3): 534-540

[27] LankaraniH, NikraveshP. A contact force model with hysteresis damping for impact analysis of multibody systems [J]. Journal of Mechanical Design, 1990, 112(3): 369-376

[28] KuangJ, YangY. An estimate of mesh stiffness and load sharing ratio of a spur gear pair [C]. Design Engineering Division, 1992, New York, American Society of Mechanical Engineers: 13-16

[29] KahramanA, BlankenshipG. Effect of involute contact ratio on spur gear dynamics [J]. Journal of Mechanical Design, 1999, 121(1): 112-118