Prediction Of The Cutting Force And Tool Deflection Error In Ball End Milling Of Sculptured Surfaces

Sculptured surface machining has an important status in some industry such as aerospace, automobile and die & molds. It is also the major object of NC machining and CAD/CAM technology for both research and application. Increasing the productivity and precision of machined surfaces are the endlessly target in manufacture industry. However, due to the lack of effective tools for describing the variation of physical factors such as cutting force during machining, the conservative cutting parameters are usually adopted. Consequently, the productivity is depressed and the cost is increased. Study on the physical factors such as cutting force, can provide an appropriate academic guidance in technologic planning, furthermore, increasing the productivity and controling the cost in sculptured surface machining. This paper investigates the cutting force and surface diemensional error in sculptured surface machining. The main contents are presented as follows:1) The axial position angle of cutting element is adopted as the parameter in the cutting force model and chip thickness model. With this modification, the cutting force model can agree well with the varying cutting parameters in sculptured surface machining. Based on the average cutting force of slotting, an apparent model for polynomial cutting coefficients calibration is presented. The criterion of slotting parameters chosing and the method of determination minimum number of slotting are also proposed by analysing the least square parameter evaluation.2) The whole process of sculptured surface machining is segmented at a path interval of feed per tooth along tool path, such that it can be considered as the consitution of a series of small slope surface machining. Based on these segmented cutting, the feed direction is determined according to the start/end points and the cutter engagement area is determined by the Z-Map method. In this case, the cutting force of the whole sculptured surface machining can be obtained by simulating the cutting force of each segmented cuts.3) With a calculation example, the cantilever beam methods in literature are analyzed. It is concluded that the limit of cantilever with distribution load has no precise lose according to the example results. Then based on this limit form, an integral step cantilever beam model is suggested for describing the tool deflection of ball end mill. The stiffness coefficients are calibrated with a hanging experiment. 4) For the ball end milling of slope surface with contouring tool path, at the position of tool deflection error occuring, a feedback model of tool deflection on cutting edge contact is presented, and the limitation of minimum distance between tool paths is discussed. Then, based on the ideal of differential, an approach of tool deflection error prediction is proposed for sculptured surface machining with contouring tool path by utilized this feedback model.5) By analyzing the methods of tool deflection error compensation, it is concluded that the cutting equilibrium in compensation machining can be directly refined from the ideal cutter position. Considering the difference between the tool deflection and tool deflection error in sculptured surface milling, and the cutting characteristics in compensation machining, a new tool deflection error compensation method, in which the tool deflection is directly adopted as the compensation variable, is presented.