Problems and Solutions in Identification of the Parameters of Mechanical Joints

In this work, the problems in the identification of the parameters of mechanical joint directly from the measured frequency response functions (FRFs) of the structure were discussed. The problems include the problem of measurement noise, the problem of using the least squares method and the problem due to the characteristics of the structure itself. The causes of the problems and the associated solutions were discussed by theoretical and experimental examples. The results show that the measurement noise in the FRFs is the basic problem in identification; however, the severity of the noise problems is magnified by the other problems. INTRODUCTION The most troublesome problem encountered in the dynamic simulation of a real mechanical system is the difficulty of knowing the accurate system parameters. A real mechanical system usually consists of many components which are connected together through different joints. The dynamic properties of the joints generally are very difficult to know by theoretical methods. Therefore, the experimental identification method becomes an important approach to find the joint properties. In the past, great efforts have been made in the field of parameter identification. Some of the identification methods were developed to identify the dynamic parameter of the whole structure (Fritzen, 1986; Mottershead and Stanway, 1986; Wang, 1988), some other methods were especially developed for the identification of joint parameters (Yoshimura, 1977, 1979; Yuan and Wu, 1985; Tsai and Chou, 1988). Yoshimura (1977, 1979) proposed an iterative method to identify the joint properties, but the method required considerable computer time due to the iterative procedure. Yuan and Wu (1985) used the finite element method combined with the dynamic data system to identify the joint properties of machine tool. However, the method required the mass, damping and stiffness matrices to form the mathematical model of the whole structure. The method proposed by Tsai and Chou (1988) used the measured frequency response functions (FRFs) of the substructures and whole structure to extract the joint properties. The method is very simple; however, it is too sensitive to measurement error or noise. There are many advantages to use the measured FRFs to extract the joint parameters. However, if the measured FRFs are used to extract the joint parameters, the unavoidable measurement noise in the FRFs could be the biggest trouble, (Juang and Pappa, 1986; Ren and Beard, 1993; Wang and Liou, 1990, 1991, 1993). Although in the past some methods have been proposed to minimize the noise effect, it is found that, with the same noise level, the accuracy of the identified result is very structure dependent. In other words, in order to improve the accuracy of identification, one could not consider the noise effect only. In this work, the problems and solutions in the identification of the joint parameters were discussed. The accuracy and feasibility of the proposed solutions were verified theoretically and experimentally. THEORETICAL FORMULATION A mechanical structure usually consists of many components which are connected together by different joints. Therefore, the whole structure can be divided into two substructures from the joint to be identified. It is assumed that the dynamic behavior of the joint can be modeled as linear spring and damper elements, as shown in Fig.1. The objective of the parameter identification is to extract the joint parameters experimentally from the frequency response functions (FRFs) of the whole structure and the substructures.