Deformation Reconstruction for a Heavy-Duty Machine Column through the Inverse Finite Element Method

The processing errors for columns of heavy-duty machine tools are affected by deformation induced by a variety of force loads and thermal loads. In general, error reduction usually uses method of error compensation. However, the precondition of error compensation is to accurately obtain the machine full-field displacement. The inverse finite element method (iFEM) is an efficient tool for the real-time reconstruction of deformation. It obtains nodal degree of freedoms (DOFs) by solving the minimum value of the error least-squares function, which constitutes the relationship between the DOFs and analytical strain. Although double-sided strain rosettes are widely used in the iFEM to obtain strain information, the strain rosettes have some shortcomings, including the internal installation being difficult and measurement size being large. Fiber Bragg grating (FBG) sensors have the advantages of being lightweight, small geometric profile and being easy to installation. Therefore, this study utilizes distributed single-sided and unidirectional strain data obtained from FBG sensors. To further improve the possibility of this practical application, cubic spline interpolation is used to reduce the number of sensors and further extend the practical usefulness. Considering coordinate transformation and boundary conditions, the total deformation of the column is determined. The superior accuracy and practical applicability of the improved formulation is demonstrated after comparing the results of analytic solutions and that of the FEM. Therefore, new direction method for supporting the machining precision of heavy-duty machine tools is proposed.