Nonlinear Dynamic Analysis of a Multi-Gear Train With Time-Varying Mesh Stiffness Including Modification Coefficient Effect

The nonlinear dynamic analysis of a multi-gear train with time-varying mesh stiffness on account of the modification coefficient effect is in vestigated in this paper. The proposed application of the modification coefficient will revise the center distance of the gear pair, avoid undercut and raise the mesh stiffness of the designed gear system. In this study, the gear profile is generated from the relationship between the rack cutter and the gear work piece by using the envelope theory. The rack cutter with the modification coefficient increases the mesh stiffness and thus enhances the strength of the gear tooth. Then the time-varying mesh stiffness at the contact position of the gear pair is calculated from the tooth deflection analysis using the generated gear profile. With the obtained time-varying mesh stiffness, the nonlinear dynamic behavior of multi-gear train is investigated by using Runge-Kutta integration method. The numerical results of the studied examples show the harmonic motion, sub-harmonic motion, chaotic motion and bifurcation phenomenon of the gear train.

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The Effects of Bearing Stiffness on Nonlinear Dynamic Behaviors of Multi-Mesh Gear Train

Volume 7: Structures and Dynamics, Parts A and B ◽

10.1115/gt2012-69490 ◽

2012 ◽

Author(s):

T. N. Shiau ◽

T. H. Young ◽

J. R. Chang ◽

K. H. Huang ◽

C. R. Wang

Keyword(s):

Chaotic Motion ◽

Nonlinear Dynamic ◽

Equations Of Motion ◽

Nonlinear Dynamic Analysis ◽

Gear Train ◽

Time Varying ◽

Kutta Method ◽

Dynamic Behaviors ◽

Runge Kutta Method ◽

Bearing Stiffness

In this study, the nonlinear dynamic analysis of the multi-mesh gear train with elastic bearing effect is investigated. The gear system includes the three rigid shafts, two gear pairs and elastic bearings. The stiffness and damper coefficient of elastic bearing are considered. The equations of motion of nonlinear time-varying system are derived using Lagrangian approach. The Runge-Kutta Method is employed to determine the system dynamic behaviors including the bifurcation and chaotic motion. The results show that the periodic motion, quasi-periodical motion and chaos can be excited with the elastic bearing effect. Especially, the results also indicate the dynamic response will go from periodic to quasi-periodical before the chaotic motion when the bearing stiffness is increased.

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Non-Linear Vibration Modeling and Simulation of a Gear Pair Based on ADAMS and Simulink

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.681.219 ◽

2013 ◽

Vol 681 ◽

pp. 219-223 ◽

Cited By ~ 1

Author(s):

Chun Jing Huo ◽

Hui Liu ◽

Zhong Chang Cai ◽

Ming Zheng Wang

Keyword(s):

Gear Train ◽

Transmission Model ◽

Time Varying ◽

Gear Pair ◽

Mesh Stiffness ◽

Feedback Model ◽

Non Linear ◽

Speed Fluctuation ◽

Set Up ◽

Multi Body

To set up the virtual prototype of a gear train system in the dynamic analysis software ADAMS, the torsional vibration model of a gear pair was transformed into an equivalent transmission model in which a multi-body model was established in ADAMS and its meshing force solution model was established in Simulink. The time-varying mesh stiffness, gear clearance, meshing errors and other non-linear factors can be included in the gear meshing feedback model, more importantly, the influence of gear speed fluctuation on the time-varying mesh stiffness was taken into consideration. The simulation results contrastively prove the feasibility of co-simulation for obtaining the dynamic characteristics of gear meshing process.

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