Global tool path optimization of high-resolution image reproduction in ultrasonic modulation cutting for structural coloration

Diffraction gratings are capable of splitting and diffracting parallel white light into a wide diffractive spectrum containing light with different wavelengths travelling in different directions. The apparent angle-dependent color effect is a form of structural coloration. In this paper, a rendering strategy for grating-induced high-resolution image reproduction has been demonstrated based on tool path optimization. The grating structures are generated by ultrasonic modulation cutting due to the cutting depth modulation. The high-resolution image rendering is accomplished by tailoring the interaction between visible light and grating structures through the design and optimization of the distribution of machined grating arrays. Fabricating the desired grating arrays requires a complex objective tool path with ever-changing discontinuous step velocity profiles, which is not achievable for any existing machine tools considering the limited acceleration capability. Unlike conventional toolpath optimization methods, the proposed research aims to relate the cutting process to high-resolution image rendering performance and optimize the quality of machined images through optimally approximating the objective tool velocity-location curve with a series of parametric splines in terms of minimum overall velocity error. A recursive optimization method has been developed to ensure the global optimum of the tool velocity profile considering the physical limitation of motion axes. The fitting performance of proposed method is quantitatively analyzed and evaluated through the simulation and experiment by comparing the real-time velocity-location profiles to the objective curves. In addition, the reproduction quality of machined images is evaluated by measuring the similarity between the reproduced and original images with both simulation and experimental results.