A Modal Expansion Method for Displacement and Strain Field Reconstruction of a Thin-Wall Component During Machining

Machining complex thin-wall components (such as compressor disks and casings in aircraft engines) has been a challenging task, because workpiece deformations and vibrations not only compromise the surface integrity, but also induce residual stresses in the final products. This paper offers a physics-based method that accounts for the damping effects and external loads for reconstructing the dynamic displacement and strain fields of a thin-wall workpiece in real time with noncontact displacement measurements during machining. Given that part dynamic behaviors can be characterized by superposition of mode shapes, the time-varying displacement and strain fields are reconstructed with modal coefficients that are updated in real time using in situ measurements. The reconstruction method has been numerically verified with finite-element analyses with the sensor locations optimized using a genetic algorithm; both static and dynamic field reconstructions are analyzed. Tradeoffs between the number of sensors and the reconstruction efficiency in terms of computation time and error are discussed. The method has been evaluated experimentally on a lathe machine testbed, where the dynamics of the distributed physical fields have been successfully captured and analyzed, demonstrating its practicality as a real-time tool for continuously monitoring the displacement and strain distributions across a disk workpiece during machining.