A fast processing method to perform transient analysis for vibration control

Highlights

• Fast Fourier transform is proposed for vibration control of a flexible manipulator.

• The calculation time is 36 h in ANSYS and 1 second only for the FFT method.

• Proposed method is verified with ANSYS and experimental results.

• FFT method can be used to study the vibration control of complex mechanical systems.

Abstract

Transient vibration analyses of structures with complex shapes are performed by finite element (FE) methods. Transient vibration analyses take long processing times for the systems having large number of degrees of freedom. A method performing the transient analyses very fast using the Fast Fourier Transform (FFT) is introduced in this work, and it is applied to a curved manipulator. Various analyses are required to determine the input parameters for vibration control, and each analysis takes long FE solution times.

In this work, an FFT method is developed where the samples of the impulse response of the system under study is obtained by the FE software ANSYS first. The samples of the transfer function are then obtained by FFT, and transient responses are found for various vibration control parameters by using FFT. Transient response results for the complex system considered in this study are obtained approximately in 1 s with FFT method, while it takes 36 h with ANSYS.

A one degree of freedom system is considered to verify the results of FFT method. Newmark's numerical, ANSYS, and FFT method results are compared, and it is observed that the results are in good agreement. A curved non-uniform steel manipulator with a complex shape is considered after the verification. The samples of the impulse response of the manipulator is found by ANSYS. Then, FFT method is used to obtain transient responses. A trapezoidal velocity profile is considered to analyze the residual vibration. The effect of the deceleration time on the root-mean-square (rms) values of the residual vibration is studied experimentally and using FFT method. It is observed that the results are in good agreement, and it is concluded that FFT method introduced in this study is very effective to study transient vibration problems in complex systems.

Introduction

Flexible manipulators provide lightweight, low torque requirements, low energy consumption and high speed, whereas flexibility causes high residual vibration amplitudes after the motion is done. Vibration control of flexible manipulators has been researched in literature extensively [1], [2], [3], [4], [5], [6]. Wu and Deng [1, 2] studied the vibration control of a l-shaped manipulator. They aimed to move the motor fast while performing motion control and piezoelectric actuator control simultaneously to reduce the vibrations [1]. They also used an operator-based non-linear control using an on-line discrete wavelet transform to control the motor and to reduce the vibrations of the l-shaped arm [2]. Zheng et al. [3] investigated the resonance vibration control of active magnetic bearing supported flexible rotors. He et al. [4] designed a neural network controller to suppress the vibration of a flexible robotic manipulator system with input dead-zone. Forbes and Damaren studied [5] the hybrid passivity/finite gain stability theorem in terms of single input-single output control of a single-link flexible manipulator and validated the results experimentally.

The mathematical model of flexible systems can be derived by finite element (FE) methods or analytical methods [7]. Exact analytical solutions for simple systems can be found, but they are almost impossible for real systems where numerical methods are used [[8], [9], [10]–11]. Realistic systems are usually studied by using commercial engineering programs [12]. Karagülle et al. [13] presented the analysis of active vibration control in smart structures by ANSYS. Xu and Koko [14] studied active vibration control of cantilever beam by using ANSYS. Khot and Yelve [15] presented modeling and transient analysis to unit impulse of a cantilever beam by ANSYS and they compared the results by obtaining state-space model of cantilever beam in MATLAB.

Fast Fourier Transform (FFT) has been used for various applications such as vibration analysis, marine structures, composite materials and dynamic properties of structures [[16], [17]–18]. Al-Badour et al. [19] studied the application of wavelets, in particular the WPT transform, to fault detection in rotating machinery and used the traditional FFT approach in fault detection under stationary operations. Haosheng [20] used FFT analysis and Wavelet reconstruction to reveal the effect of machine vibrations on the surface topography. Kabel et al. [21] studied the effect of introducing composite voxels for Moulinec–Suquet's FFT based homogenization method.

Performing transient analysis with FE models of the structures with large number of degrees of freedom (d.o.f.) take long calculation times. In this study, an FFT method is introduced to obtain the transient responses of complex structures which have FE models with large number of d.o.f. in very short calculation times. The method is applied for the residual vibration control of a curved manipulator and the results are compared with experiments.