Single-sensor-based reconstruction of force and displacement fields for thin-walled cylindrical shells milling

The cutting process of thin-walled cylindrical shells involves complex working conditions, and it is difficult to measure the cutting force and vibration displacement at the cutting point in real time. To address this issue, a method is proposed to reconstruct the force and displacement fields of the cylindrical shell in real time using only a single displacement sensor. Based on the first-order shear deformation theory and the artificial spring technique, the wave method can be employed to simultaneously obtain the natural frequencies and analytical mode shape functions of the cylindrical shell with elastic boundary. The dynamic behavior of the cylindrical shell is characterized by the superposition of mode shapes, thereby determining the force-displacement mapping relationship for the entire cylindrical shell. Utilizing in-situ measurement, the time-varying force and displacement fields are reconstructed in real time. Unlike existing methods for reconstructing the displacement field of thin-walled workpieces, one unique feature of this study is the simultaneous real-time reconstruction of the force and the displacement fields using single-point measurement information, providing higher reconstruction accuracy with fewer sensors, thus ensuring practicality and reliability of the results. Through simulation and experimental application to the force and displacement fields reconstruction of cylindrical shell under concentrated and moving force (e.g., cutting process), its practicality as a real-time tool for continuously monitoring cutting force and displacement of cylindrical shell during the cutting process has been demonstrated.