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.
Highlights
IntroductionReal-time monitoring of structural deformations using strain measurements is a vital technology for actuation and control of smart structures, as well as for Structural Health Monitoring (SHM) [1,2,3]
Real-time monitoring of structural deformations using strain measurements is a vital technology for actuation and control of smart structures, as well as for Structural Health Monitoring (SHM) [1,2,3].This technology is known as “shape sensing”
Some researchers have presented deformed shape monitoring by using strain data measured by strain gauge (SG) or fiber Bragg grating (FBG) [4,5,6]
Summary
Real-time monitoring of structural deformations using strain measurements is a vital technology for actuation and control of smart structures, as well as for Structural Health Monitoring (SHM) [1,2,3]. The reconstruction algorithm based on iFEM in this paper has the following advantages: (1) it can reconstruct the gantry structure deformation of heavy-duty machine tools without considering the magnitude and form of the force acting on it; (2) it can reconstruct the deformation of a gantry structure which is statically indeterminate and complex in shape; (3) in order to realize real-time monitoring, experimental strain data are measured by FBG which possess many merits such as high sensitivity, anti-electromagnetic interference, strong stability, wavelength division multiplexing and easy installation. The reconstruction method based on iFEM presents aSensors new2018, way real-time monitoring and compensation of gantry structure deformation which.
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