Simulation of vibro-impact gear model considering the lubricant influence with a new computational algorithm

In this paper, a vibro-impact gear model incorporating the influences of the lubricant and backlash is formulated. Then, a new computational algorithm validated in comparison with the “stiff” solvers, by defining a transition area and adopting the double-changed time step, is proposed to identify the influences of the lubricant on the dynamic system. The results obtained in this paper indicate that the proposed numerical algorithm not only guarantees the precision of solutions, but also reduces the calculation speed of the whole system. The lubricant can potentially reduce the vibrations in the gear system, and the boundaries for double-sided impacts, single-sided impact and no impact are mainly dependent on the fluctuating driving torque and the stiffness of the lubricant. These results could provide a good source of information on the utilization of vibro-impact modeling and simulation for the study of spur gears dynamic performance, and quantification of the factors such as gear backlash, input power or torque fluctuations, lubrication, rattle, etc. In addition, the proposed numerical method could be used as a basic program of vibro-impact in Matlab environment.

[1]  Ernesto Rocca,et al.  An analysis of the automotive driveline dynamic behaviour focusing on the influence of the oil squeeze effect on the idle rattle phenomenon , 2007 .

[2]  W. A. Tuplin.  Gear-Tooth Stresses at High Speed , 1950 .

[3]  Jinguo Liu,et al.  Zooming image based false matches elimination algorithms for robot navigation , 2017 .

[4]  Riccardo Russo,et al.  A gear rattle model accounting for oil squeeze between the meshing gear teeth , 2005 .

[5]  Richard C Aiken,et al.  Stiff computation , 1985 .

[6]  Ahmet Kahraman,et al.  Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions , 2005 .

[7]  H. Lankarani,et al.  A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids , 2015 .

[8]  Fuhao Liu,et al.  Dynamic analysis of drag torque for spur gear pairs considering the double-sided films , 2017 .

[9]  Stephanos Theodossiades,et al.  Periodic and chaotic dynamics of motor-driven gear-pair systems with backlash , 2001 .

[10]  S. Theodossiades,et al.  Lightly loaded lubricated impacts: Idle gear rattle , 2007 .

[11]  S. Narayanan,et al.  Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method , 1999 .

[12]  Rajendra Singh,et al.  Analysis of automotive neutral grear rattle , 1989 .

[13]  Li Na Zhang,et al.  Study on the Nonlinear Dynamics of a Single-Stage Gear Vibro-Impact System , 2014 .

[14]  Ian Howard,et al.  THE DYNAMIC MODELLING OF A SPUR GEAR IN MESH INCLUDING FRICTION AND A CRACK , 2001 .

[15]  Hassan Salarieh,et al.  Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity , 2012 .

[16]  Rajendra Singh,et al.  Non-linear dynamics of a geared rotor-bearing system with multiple clearances , 1991 .

[17]  Riccardo Russo,et al.  Theoretical and experimental investigation into the influence of the periodic backlash fluctuations on the gear rattle , 2011 .

[18]  D. M. McFarland,et al.  Analytical characterization of damping in gear teeth dynamics under hydrodynamic conditions , 2015 .

[19]  Qinkai Han,et al.  Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives , 2012 .

[20]  Todd E. Rook,et al.  Computational Issues Associated with Gear Rattle Analysis , 1995 .

[21]  Giorgio Bonori,et al.  Non-smooth dynamics of spur gears with manufacturing errors , 2007 .

[22]  F. R. E. Crossley,et al.  Digital Simulation of Impact Phenomenon in Spur Gear Systems , 1977 .

[23]  Robert G. Parker,et al.  NON-LINEAR DYNAMIC RESPONSE OF A SPUR GEAR PAIR: MODELLING AND EXPERIMENTAL COMPARISONS , 2000 .

[24]  Hanjun Jiang,et al.  Dynamic features of three-dimensional helical gears under sliding friction with tooth breakage , 2016 .

[25]  Liang Zhang,et al.  Stability investigation of velocity-modulated gear system using a new computational algorithm , 2017 .

[26]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[27]  Homer Rahnejat,et al.  Gear teeth impacts in hydrodynamic conjunctions promoting idle gear rattle , 2007 .

[28]  R Manoj,et al.  Gear rattle modelling and analysis for automotive manual transmissions , 2001 .

[29]  Raynald Guilbault,et al.  Nonlinear damping calculation in cylindrical gear dynamic modeling , 2012 .

[30]  T. Lim,et al.  An enhanced multi-term harmonic balance solution for nonlinear period-one dynamic motions in right-angle gear pairs , 2012 .

[31]  W. Thomson.  Theory of vibration with applications , 1965 .

[32]  Robert G. Parker,et al.  Nonlinear Dynamics of Planetary Gears Using Analytical and Finite Element Models , 2007 .

[33]  Ming J. Zuo,et al.  Simulation of spur gear dynamics and estimation of fault growth , 2008 .

[34]  Bernd Bertsche,et al.  Experimental study on transmission rattle noise behaviour with particular regard to lubricating oil , 2015 .

[35]  Rajendra Singh,et al.  Non-linear dynamics of a spur gear pair , 1990 .

[36]  Homer Rahnejat,et al.  Mode identification in impact-induced high-frequency vehicular driveline vibrations using an elasto-multi-body dynamics approach , 2004 .

[37]  Ahmet Kahraman,et al.  Period-one motions of a mechanical oscillator with periodically time-varying, piecewise-nonlinear stiffness , 2005 .

[38]  Hanjun Jiang,et al.  Dynamic modeling and analysis of spur gears considering friction–vibration interactions , 2017 .

[39]  J. Dupal,et al.  Analytical solution of spur gear mesh using linear model , 2017 .

[40]  Hengan Ou,et al.  A finite element method for 3D static and dynamic contact/impact analysis of gear drives , 2007 .

[41]  Shaopu Yang,et al.  Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method , 2006 .

[42]  P. Velex,et al.  Instability analysis in oscillators with velocity-modulated time-varying stiffness—Applications to gears submitted to engine speed fluctuations , 2008 .

[43]  Rajendra Singh,et al.  Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system , 1991 .

[44]  Hanjun Jiang,et al.  Dynamic behavior analysis of spur gears with constant & variable excitations considering sliding friction influence , 2016 .

[45]  Donald R. Houser,et al.  Mathematical models used in gear dynamics—A review , 1988 .