动应变与加速度在机械系统动力学描述中的关联与比较

Recently, the fiber Bragg grating(FBG) strain sensor has been widely used in structural health monitoring and the fault diagnosis of the machinery. Due to the limitation of the bandwidth of strain gauges and FBG strain sensors, strain has always been considered as a semi-static variable, therefore the dynamic strain has not got enough attention. Whether and how people can use dynamic strain signals to describe dynamic characteristics has not been sufficiently discussed and explored. To the best of the authors' knowledge, the concepts of strain rate the strain acceleration have not been developed and applied. To bridge the gap, this work will propose the concepts of strain rate and strain acceleration and two basic assumptions, i.e. the dynamic strain can be used to describe the dynamics of the mechanical system like the displacement and the dynamic strain ratio and strain acceleration can be obtained by numerical differentiating the strain signals with respect to the time. When we obtain strain, strain ratio and strain acceleration simultaneously, we can use them as physical parameters to characterize the dynamic properties to verify the dynamics model. It opens new path to compare and verify the theoretical model with the data of strain. Moreover, present study develops the dynamic model with the strain, strain ratio and strain acceleration. The theoretical relationships between the original signal and the one which is differentiated and integrated from the original signal in frequency and amplitude are given. The performances of the commonly used numerical differentiation and numerical integration methods are compared with the tests data in gear box and hydraulic pipe system. The results indicate that the high fidelity in frequency components and amplitudes is kept when the dynamic strain measured by the FBG is differentiated to obtain the strain rate and strain acceleration. However, the numerical integration in obtaining the velocity and displacement from the acceleration lose its accuracy in frequency components and amplitudes.