Surface roughness prediction in ball screw whirlwind milling considering elastic-plastic deformation caused by cutting force: Modelling and verification

[Display omitted] •A novel theoretical model is proposed to predict the surface roughness of workpiece.•Surface roughness model is based on tool-workpiece contact motion.•The model considers the effect of elastic–plastic deformation caused by cutting force.•The relationship between cutting force and surface roughness is revealed.•An optimal machining strategy to reduce cutting force and achieve good surface roughness is proposed. Functioning as one key assessment index of surface quality, surface roughness exerts an essential impact upon the fatigue strength, wear resistance, and contact stiffness of the workpiece. The roughness degree is greatly affected by cutting force during the cutting. In this paper, a surface roughness theoretical model of the ball screw whirlwind milling is established. The theoretical modeling for surface roughness is developed by combining influences of elastic–plastic deformation and residual height. According to the dissection on the motion of tool-workpiece contact, the residual height modeling for the surface of the workpiece is constructed. On this basis, the elastic recovery height model resulting from the cutting force is presented according to the Hertz elastic contact theory. Based on the friction and wear calculation principle, the plastic deformation height model caused by cutting force is put forward. That surface roughness model was validated with the whirlwind milling experiment, and the value of the theoretical model corresponds well to the value of the experiment. The maximum error, minimum error and average error are 9.19%, 1.18% and 6.33%, respectively. The relationship between surface roughness and cutting force was revealed. These consequences showed that the surface roughness is lessened as cutting force grows under the identical set of cutting parameters. Furthermore, the best processing tactics to reduce cutting force and procure a good surface roughness are presented.