Theoretical and Experimental Identification of Cantilever Beam With Clearances Using Statistical and Subspace-Based Methods

Clearance turns up in a large number of engineering structures because of the errors during assembling, manufacturing, and wearing. The presence of clearance in engineering structures changes the normal dynamic response and will result in low precision and short lifetime. The clearance parameter identification of such nonlinear system is the prerequisite to control and eliminate the effect of clearance nonlinearity. In this paper, a derivative plot of probability density function (DPPDF) for displacement response is proposed to precisely identify the clearance value of continuous system, and the nonlinear subspace identification (NSI) method is modified to recognize the related contact stiffness based on the frequency response function (FRF) equations of continuous system. The DPPDF method is carried out by analyzing the distribution characteristic of displacement response, and the clearance value is derived through inspecting the probability density function (PDF) plot and the second derivative plot of the PDF. Based on the identified clearance, the clearance nonlinearity is regarded as external force, and the relationship between the dynamic responses and the external forces in frequency domain can be expressed as the form of FRF equations. Based on the FRF equations, the contact stiffness in continuous system is obtained with modified NSI method. This combined identification process is verified by a single-degree-of-freedom (SDOF) system and a cantilever beam system with clearances, and some influence factors of this identification process, including noise, transfer error, and force level, are discussed in detail. In the end, an experiment device with changeable clearance and contact stiffness was designed to conduct identification experiments, and the results show that the proposed methods perform effectively in identifying the clearance parameters.