Limitation of estimation method of surface texture parameters by inverse analysis of hammering test data with disturbance

Abstract

The surface texture formed by the micro asperities on the surface of the solid members induces the stiffness reduction of the structure constructed by screws and bolts. In recent years, the fixing by screws and bolts is one of the primary fixing methods to construct multi-material structures, and the fixing state such as the interfacial stiffness at the clamped part is required to be evaluated for the proper fixing. The interfacial stiffness affects the total stiffness of the structure and is dominated by the surface texture and the clamping force. Especially, the standard deviation of the asperity peak heights and the homogenized elastic modulus collectively named as the surface texture parameters mainly determine the interfacial stiffness. This study has developed an estimation method of the surface texture parameters by the inverse analysis of the hammering test data, and numerically investigated the basic behavior and the estimation error of the inverse analysis for the establishment of the methodology to find the limitation of the proposed method against the disturbance in the hammering test data. In the investigation, a theoretical limitation of the inverse analysis has been derived by the linear approximation, and a numerical simulation which is the same approach as the Monte Carlo simulation has been performed by using a bolted joint model consisting of two plates joined by the eight sets of the bolt and nut. From the results of the numerical simulation, the followings were summarized: 1) The recalculation error of the natural frequency subjected to the clamping force is as large as the disturbance in the hammering test data. 2) The sensitivity of the homogenized elastic modulus is much smaller than that of the standard deviation of the asperity peak heights in the inverse analysis. 3) The theoretical limitation of the linear approximation can qualitatively predict the estimation errors of the surface texture parameters.

Keywords

• inverse problem
• finite element method
• homogenization method
• surface texture
• natural frequency
• fixing
• tribology
• surface roughness
• interfacial stiffness
• multi-material structures