Experimental Investigation of Vibration Response of a Flexible Coupler In a Four Bar Mechanism Due to Varying Crank Length and Crank Speed

Effort to increase productivity calls for increasingly higher operating speed. Consequently, many part of a machinery are made as light as possible to avoid the detrimental inertial effects. This condition means several of the elements are no longer rigid and tend to experience elastic deformation in operation. The existence of the deformation yields element possessing position dependent dynamic parameters. Mechanisms with time-varying parameter have a phenomenon known as parametric instability where the mechanism could becomes dynamically unstable at several frequency bands, even at relatively low excitation frequency. This research investigates the dynamic behaviour of a flexible coupler on an experimental four-bar mechanism setup. The study examines the coupler vibration response due to varying crank length and crank speed.

Download Full-text

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0241 ◽

1995 ◽

Author(s):

Régis Dufour ◽

Alain Berlioz ◽

Thomas Streule

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Ritz Method ◽

Parametric Instability ◽

Experimental Tests ◽

Time Varying ◽

Periodic Force ◽

Modal Reduction ◽

Time Varying Parameter ◽

The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Download Full-text

Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions

Journal of Vibration and Acoustics ◽

10.1115/1.2893852 ◽

1998 ◽

Vol 120 (2) ◽

pp. 461-467 ◽

Cited By ~ 22

Author(s):

R. Dufour ◽

A. Berlioz

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Ritz Method ◽

Parametric Instability ◽

Experimental Tests ◽

Time Varying ◽

Periodic Force ◽

Modal Reduction ◽

Time Varying Parameter ◽

The Stability

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Download Full-text

Vibration Response of the Planetary Gears with a Float Sun Gear and Influences of the Dynamic Parameters

Shock and Vibration ◽

10.1155/2020/8886066 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Yinghui Liu ◽

Dong Zhen ◽

Huibo Zhang ◽

Hao Zhang ◽

Zhanqun Shi ◽

...

Keyword(s):

Phase Modulation ◽

Vibration Response ◽

Operating Conditions ◽

Mechanical Transmission ◽

Time Varying ◽

The Sun ◽

Dynamic Parameters ◽

Planetary Gearbox ◽

Pressure Angle ◽

Overlap Ratio

Planetary gearboxes are widely used in mechanical transmission systems due to their large transmission ratio and high transmission efficiency. In a planetary gearbox, the sun gear is usually set to float to balance the sharing of loads among planet gears. However, this floating set will result in the variation of pressure angle, overlap ratio, and meshing phase in the meshing progress and when gear faults occur, the variation will be enlarged. In the previous studies, these parameters were reduced to constant. To study the influence of the dynamic parameters on the vibration response of planetary gearboxes under different operating conditions, a new lumped-parameter model containing the time-varying pressure angle (TVPA), time-varying overlap ratio (TVOR), and time-varying meshing phase (TVMP) is established. Based on this model, the vibration response mechanism of the sun gear is analyzed. Moreover, the comparison with the previous model is made and the rule of phase modulation caused by these dynamic parameters is revealed. By comparing the dynamic responses under different loads and rotation speeds, the phase modulation is studied in detail. Finally, the sun gear fault is introduced, and the phase modulation is analyzed in different fault degrees. This study can provide theoretical reference for the condition monitoring and fault diagnosis of planetary gearbox based on vibration analysis.

Download Full-text

Determination of Parametric Resonances in Distributed Parameter Systems Using Frequency Analysis

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2007-34171 ◽

2007 ◽

Author(s):

Yong-Kwan Lee ◽

Leonid S. Chechurin

Keyword(s):

Theoretical Analysis ◽

Parametric Instability ◽

Synchronous Generator ◽

Constant Current ◽

Time Varying ◽

Digital Controllers ◽

Stator Windings ◽

Distributed Parameters ◽

Time Varying Parameter ◽

Parametric Resonances

Theoretical analysis of parametric instability for the control systems with distributed parameters shall be given. The approach to the solution of such systems can be composed of two parts, i.e. modeling and estimation of the distributed parameters and instability estimation of the periodical time-variant elements using parametric circumference. A control system with mechanical distributed parameters such as robot manipulators is introduced as an example. Theoretical analysis shows that the parametric instabilities occur by digital controllers or time-varying elements which excite the resonance regions of distributed parameters. An electro-mechanical transformer which consists of constant current motor and synchronous generator is applied as another example. Inductance between stator windings and rotor of the synchronous generator serves as a periodical time-varying parameter and long electrical line plays a role of an element with distributed parameters. Instability condition of the transformer rotation owing to the parametric resonance excitement was obtained.

Download Full-text