Generation of sine on random vibrations for multi-axial fatigue tests

https://doi.org/10.1016/j.ymssp.2019.02.046Get rights and content

Highlights

Abstract

This paper deals with the generation of multi-axial sine on random mixed vibration environments with specified references. Unlike pure vibration environments such as sine or random excitation, the difficulties of the superposition of sine on random vibration control lie in the separation of mixed vibration signals and simultaneous control of sine and random components. An improved correlation integral method is proposed to separate the mixed vibration signals. Considering the non-Gaussian random vibration characteristics, the control references of random component are comprised of multi-output response skewnesses, kurtoses, auto-power spectral densities, phase and coherence coefficients. The Hermite polynomial model transformation method is introduced to transform stationary Gaussian random signals to stationary non-Gaussian random signals with specified skewnesses and kurtoses. The control references of sine component consist of multi-output response amplitudes and phase differences. Closed loop control algorithms are presented to update the drive signals according to the deviations between responses and references. And finally, the results from a tri-axial sine on random mixed vibration control test show the feasibility and efficiency of the proposed methods.

Introduction

Vibration fatigue analysis for structures and mechanical components subjected to complex dynamic environments is a problem of general concern for the engineering community. It is obvious that the vibration environments are crucial to fatigue life and failure results. Currently, many vibration fatigue tests, as an effective means of investigating durability and reliability of products, are performed by a single exciter to provide a uni-axial base excitation environment [1], [2], [3], [4]. However, by virtue of the facts that many measured vibrations are multi-axial and that coupling relationships exist between different axes manifested as phase and coherence coefficients [5], [6], [7], [8]. Some attempts have been made to conduct multi-axial vibration fatigue tests, which shows the different fatigue damage results compared to uni-axial or sequential axial vibrations [9], [10], [11]. It is therefore necessary to simulate complex multi-axial vibrations for dynamic fatigue test purposes.

To achieve a prescribed multi-axial vibration environment, advanced multi-exciter multi-axis vibration control tests can be conducted. Compared to uni-axial tests, multi-axial loading inputs can provide a proper energy distribution throughout the test structure and excite more vibration modes, which may result in different multi-axial stress/strain distributions and states. It should be noted that the multi-axial concept involved in multi-exciter multi-axis dynamic fatigue tests have two meanings. One is that the vibration directions of test structures are multi-axial, and the other is that the stress states of test structures are multi-axial. There are both differences and connections between the multi-axial vibrations and multi-axial stress states. On the one hand, the stress states caused by multi-axial vibration are generally multi-axial, whereas single degree of freedom excitation may also lead to multi-axial stress states. However, problems which are specifically introduced by multi-axial vibrations are the coherence and phase relationships between the different axial vibrations that may lead to a more complex combination of stress states. This is the key to the multi-exciter multi-axis vibration fatigue tests which is different from the traditional single exciter vibration fatigue problems.

Multi-exciter multi-axis sine on random vibration control is more difficult than a simple form of multi-axial vibrations, such as onefold random, sine or shock. In nature, many vibrations are characterized by sinusoidal signals superimposed on a background random signal with a wideband frequency range, typical applications with simultaneous sine and random environments are helicopters and rocket engines. An example of sine on random vibrations is illustrated in Fig. 1. A sine signal can be determined by the amplitude, frequency and phase in the time domain. But for random signals, the traditional power spectral density in the frequency domain cannot completely describe its time-domain characteristics, such as skewness and kurtosis which may have a non-negligible impact on fatigue life results of structures. In previous works by the authors, the sequential phase modification method is used to obtain the desired multi-channel non-Gaussian random signals with specified skewnesses and kurtoses [12], [13]. This paper presents a nonlinear transformation method based on a Hermite polynomial model to control non-Gaussian characteristics. Different from the sequential phase modification method, the advantage of the nonlinear transformation method is that it can realize multi-channel non-Gaussian random signals transformation simultaneously.

The key issue in sine on random mixed vibration control is to separate the sine and random components from mixed signals. Underwood proposed a tracking filter method to extract the amplitudes and phase angles of the sweeping response sine signals [14]. A Vold-Kalman filter with order tracking is used to accurately separate the sine and random environments from each other and from noise [15]. A correlation integral method was put forward by Zhang with the advantage of high precision and computation speed, but without control of phase differences of sine signals [16]. For the multi-exciter sine on random vibration control, not only the amplitudes of the sine component need to be controlled, but also the phase differences should be taken into consideration. The control of phase differences is far more significant in practice than that of their actual phase angles. This is because that the phase relationships are sometimes very important to the structural dynamic response performances such as stress distributions.

The objective of this paper is to present a closed loop multi-axial sine on random mixed vibration control method for dynamic fatigue tests. An improved correlation integral method is proposed to extract the amplitudes and phase differences of the response sine component. The nonlinear transformation method based on the Hermite polynomial model is employed to generate multi-output non-Gaussian random signals. The drive signals are updated by the control algorithms to produce the specified reference vibration environments within prescribed tolerances. The remainder of the paper is organized as follows. Section 2 elaborates the control method for multi-axial sine on random mixed vibration control test. Discussion about non-Gaussian random component is presented in Section 3. The results from tri-axial sine on random mixed vibration control test are provided in Section 4. Conclusions are finally given in Section 5.

Section snippets

Control method

This section explains the closed loop control method for multi-exciter multi-axis sine on random vibration testing, as shown in Fig. 2. The control objectives are the time-frequency characteristics of response signals that are comprised of response power spectral densities, skewnesses and kurtoses of random component and response amplitudes and phase differences of sine component. The separation of sine on random signals is implemented by an improved correlation integral method, and then a

Discussion

The advantage of the Hermite polynomial model transformation method is that the analytic solutions of skewness and kurtosis of a transformed random signal are provided and it is therefore direct and efficient to control desired skewness and kurtosis. However, the range of application has a limitation which is manifested that when the reference skewness and kurtosis are large, the accuracy of transformed results is low. Fig. 4 shows the kurtosis of before and after transformation by using the Eqs.

Experimental results

A tri-axial sine on random mixed vibration control test is carried out and the results are presented in this section. The test system is shown in Fig. 6 where a computer is used to control the data acquisition and transmission VXI system. The vibrations of the three directions x, y and z of shake table are regarded as the control targets.

The reference spectral densities for the random component are set as described in Tables 1 and 2. Only values of the power spectral densities at the break

Conclusions

The paper presents a control method for multi-axial sine on random mixed vibration test. An improved correlation integral method is used to separate sine on random mixed signals with high precision and computational efficiency. The non-Gaussian characteristics are considered in random vibration component.

First, the Gaussian random signals are generated by reference spectra including auto-power spectral densities, phase and coherence coefficients, and then the Hermite polynomial model

Funding

This work was supported by the China Scholarship Council. (No. 201806830049).

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