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

Technical Paper
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Abstract

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.

Keywords

Gear system Computational algorithm Nonlinear vibration Gear backlash 

Abbreviations

\(x\)

Dynamic transmission errors

\(\dot{x}\)

Relative speed

\(C\)

Viscous damping

\(L\)

Total backlash

\(t\)

Time in seconds

\(t_{f}\)

Time of one excited period cycle

\(\Delta t\)

Time interval

\(F_{n} \left( t \right)\)

Nonlinear elastic contact force

\(I_{p,g}\)

Rotational inertia of the pinion and gear

\(I_{eq}\)

Equivalent mass

\(\dot{\theta }_{p,g}\)

Rotational velocity of the pinion and gear

\(\ddot{\theta }_{p,g}\)

Rotational acceleration of the pinion and gear

\(R_{p,g}\)

Pitch radius of the pinion and gear

\(T_{p,g}\)

Driving and driven torque

\(T_{pm}\)

Mean part of the drag torque

\(T_{pp}^{k}\)

Amplitude of vibratory part of the \(k{\text{th}}\) harmonic

\(\varphi_{p}^{i}\)

Initial phase of \(i{\text{th}}\) harmonic

\(\zeta_{1,2}\)

Critical viscous damping ratio of lubricant and solid

\(K_{1,2}\)

Stiffness of lubricant and solid

\(N\)

Initial resolution of the numerical solution

\(M\)

Number of the period

\(\omega\)

Fundamental frequency

Profile contact ratio of the gears

\(\varepsilon\)

Small value defining transition area

\(\nabla t_{ - , + }^{max}\)

Maximum time step for lubricant and solid contact

\(\theta_{p,g}\)

Rotational displacements of the pinion and gear

Notes

Acknowledgement

The authors acknowledge the financial support from National Natural Science Foundation of China (Grant No. 51305378), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 17KJB460016), China Postdoctoral Science Foundation funded project (2016M590643), Jiangsu Provincial Science and Technology Department (BY2015057-25) and the Research Laboratory of Mechanical Vibration (MVRLAB).

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.College of Automobile EngineeringYancheng Institute of TechnologyJiangsuChina
  2. 2.Department of Engineering MechanicsShanghai Jiao Tong UniversityShanghaiChina

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