Inverse Finite Element Method for Reconstruction of Deformation in the Gantry Structure of Heavy-Duty Machine Tool Using FBG Sensors

Abstract

The deformation of the gantry structure in heavy-duty machine tools is an important factor that affects machining accuracy. In order to realize real-time monitoring of the deformation of the gantry structure, which is statically indeterminate and complex in shape, the reconstruction algorithm based on inverse Finite Element Method (iFEM) is proposed and fiber Bragg grating (FBG) sensors are used to measure strain data. The elements of the gantry structure are divided and the displacement functions of each element are determined. The shape function is obtained by substituting degree of freedoms (DOF) of element nodes into displacement functions. Through a differential method, the relation between strain and DOF of element nodes is established by the strain matrices. Subsequently, the DOF of element nodes are obtained by minimizing an error functional defined as the least-squares error between the analytic strain data and the corresponding experimental strains. Considering coordinate transformation and problem-specific displacement boundary conditions, the total deformation of the gantry structure is obtained. Following this, the experiment was carried out. The deformation simulated by ANSYS was used to replace the experimentally measured deformation and then compared with the deformation reconstructed by iFEM under the same loading condition. The accuracy of iFEM for reconstructing deformation of the gantry structure in heavy-duty machine tools is verified. It provides a new view for improving the machining precision of heavy-duty machine tools.

Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

“…Once the nodal dofs (i.e., the displacement field) have been computed, strains are defined as in any direct finite element analysis [ 23 , 24 ]. Different iFEM’s formulations are available in the literature for beam [ 18 , 19 , 25 , 26 , 27 ] and shell-like structures, covering most of the engineering applications. In particular, focusing on shells, three main types of elements have been developed: (i) An inverse three nodes element based on bilinear anisoparametric shape functions, namely iMIN3 [ 17 , 28 ]; (ii) the iQS4, a four nodes flat element with bilinear anisoparametric shape functions [ 29 , 30 , 31 ]; and (iii) the curved eight nodes iCS8 element with quadratic isoparametric shape functions [ 32 ].…”

An approach to identify the weak parts of stiffness for the machine tool cantilever structure

“…Firstly, the static stiffness testing is utilized to mainly measure the deformation of each structure by applying load to the key parts. Then the conversion center is selected as the weak part of the structure, 3 and the maximum deformation position of the machine tool is calculated. On the other hand, the second method calculates the maximum deformation location through the finite element (FE) static analysis.…”

Simulation, Modeling and Experimental Research on the Thermal Effect of the Motion Error of Hydrostatic Guideways

“…Therefore, the study on motion accuracy considering the thermal effect is urgently required for the practical application of the hydrostatic guideway. Liu [20] studied the thermal deformation of machine tool components. Zhang [21] established a model of the relationship between spatial error and thermal factors.…”