Ultrasonic technology is widely applied in the engineering ceramic polishing processes without the limitation of material properties and ideally integrated into computer numerical control system. Ultrasonic-induced cavitation and mechanical vibration effect could accelerate the motion of solid abrasives. The individual behaviors of microjet/shockwave of ultrasonic cavitation in gases and liquids, and micro-abrasives with simple harmonic vibrations in solids and liquids has been extensively studied. To conduct a systematic and integrated study of abrasives behavior in the polishing contact region involving abrasive, surround-workpiece wall, ultrasonic physical vibration, and ultrasonic cavitation impact, a novel model integrating the free abrasive motion velocity and fixed abrasive indentation depth under multi-scale contact was proposed according to Hertzian contact theory, Greenwood-Williamson model, indentation deformation theory, the basic equations of cavitation bubble dynamics, cavitation impact control equations, and Newton's law of motion equation. The effects of ultrasonic amplitude, ultrasonic frequency, preloading force and particle size on the proposed model were investigated by theoretical analysis and numerical simulations. Ultrasonic physical vibration mainly influences the dynamic gap and further influence the number of different abrasives. Furthermore, the indentation depth of fixed abrasive depends mainly on the abrasive geometry. As the contact gap and abrasive size decrease, the indentation depth gradually decreases. Under the synergistic effect of cavitation-induced shock wave and microjet, the velocity of free abrasive in this paper is generally 0-150 m/s, and the kinetic energy of free abrasive increases roughly linearly with increasing frequency and approximately as a quadratic function with increasing particle size. Increasing the preloading force leads to a reduction in the abrasive kinetic energy. Besides, the kinetic energy induced by the shock wave has a cliff-like increment at an amplitude of 0.7-0.8 μm. It is revealed that the abrasive kinetic energy is suppressed by the cavitation bubble expansion and collapse at smaller ultrasonic pressure amplitude and surround-wall distance. This research provides a theoretical reference for the modeling of potential defects and material removal on the workpiece surface caused by abrasive motion during polishing, and reduces the trial cost for parameter optimization in actual polishing processing.

With the rise of global industrialization, the requirements for the operating speed and carrying capacity of high-speed trains are increasingly higher. Because the wear and tear of rails gradually increases during the running of high-speed trains, strengthening or repairing rail surfaces is of paramount significance. Laser-directed energy deposition (DED) exhibits significant advantages in improving surface hardness, corrosion resistance, and abrasion resistance. Because of the multiple interacting optimization objectives, the development of a multi-objective optimization method for process parameters is significant for improving DED deposition quality. Response surface design employs multivariate quadratic regression equations to fit the functional relationship between the factors and the responses, which can be employed to find the optimal process parameters and solve multivariate problems. This study develops a multi-objective optimization model with response surface design and 2D process mappings to visually analyze the effects of scanning speed, laser power, and powder feed rate on aspect ratio, dilution rate, and microhardness. The optimal combination of process parameters for Ni-based alloys on U71Mn rail is a laser power of 431 W, a scanning speed of 5.34 mm/s, and a powder feed rate of 1.03 r/min. In addition, a multi-physics field finite element model is developed to analyze the evolution mechanism of the microstructure from the bottom to the top of the single track. This study can provide theoretical and technical support for the surface strengthening or repair of U71Mn rail.