Nonlinear Forced Oscillations and Stability Analysis of the Automotive Gearbox System

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Hasan Salarieh
Keyword(s):  
Mathematical Modeling ◽  
Stability Analysis ◽  
Multiple Scale ◽  
Dynamic Parameter ◽  
Gear System ◽  
Forced Oscillations ◽  
Jump Phenomenon ◽  
Scale Method ◽  
Vibration Responses ◽  
Manufacturing Parameters

In this paper, nonlinear oscillation of the automobile gear system is studied. The backlash dynamic parameter is included in the nonlinear mathematical modeling of the problem. Using multiple scale method, forced vibration responses of the gear system including Primary, Sub-harmonic and Super-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system on the time responses are analyzed. Simulation and nonlinear analysis of the problem are developed in MAPLE and MATLAB environments.

Shaft Instabilities in Two-Stage Gear Systems

2013 ◽  
Vol 275-277 ◽  
pp. 930-935
Author(s):  
Zhe Rao ◽  
Chun Yan Zhou
Keyword(s):  
Multiple Scale ◽  
Gear System ◽  
Dynamic Equations ◽  
Time Varying ◽  
Kutta Method ◽  
Two Stage ◽  
Scale Method ◽  
System A ◽  
Runge Kutta Method ◽  
Intermediate Shaft

The present paper is focused on the torsional instabilities of the intermediate shaft in a two stage gear system. A theoretical model is established taking account in the torsional flexibility of the intermediate shaft and the meshing time-varying stiffness of the gears. Multiple scale method is applied to analysis the instability areas of the gear system for which the generalized modal coordinate is adopted. The result is certificated by numerical integrals of the dynamic equations by Runge-Kutta Method.

scholarly journals Identification of the Essential Features of the Transient Amplification of Mistuned Systems

2020 ◽  
Author(s):  
Luigi Carassale ◽  
Vincent Denoël ◽  
Carlos Martel ◽  
Lars Panning-von Scheidt
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Asymptotic Expansions ◽  
Damping Ratio ◽  
Multiple Scale ◽  
Analytic Solutions ◽  
Sweep Rate ◽  
Scale Method ◽  
Complex Manner

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transienttype response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω˙. The analytic solutions are calculated through the multiple-scale method.

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

Five DOF Pneumatic Vehicle Vibration Model and Stability Analysis

2013 ◽  
Vol 739 ◽  
pp. 476-480
Author(s):  
Chun Li Wei
Keyword(s):  
Mathematical Modeling ◽  
Stability Analysis ◽  
Solar Energy ◽  
Reliability Analysis ◽  
Degrees Of Freedom ◽  
Environmentally Friendly ◽  
Motor Drive ◽  
Air Motor ◽  
Vibration Model ◽  
Vehicle Vibration Model

This paper analyzes the object vane motor and composite solar energy environmentally friendly cars , focusing on its air motor drive way , abstracted into five degrees of freedom vibration model vehicle , mathematical modeling , its stability and reliability analysis of research , and to optimize its speed and acceleration , and proved its stability and reliability of data through a lot of practice .

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