Hisataka Tanaka

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.

Prediction of cutting forces and machining error in ball end milling of curved surfaces. II. Experimental verification

Abstract This paper presents the results of a series of experiments performed to examine the validity of a theoretical model for evaluation of cutting forces and machining error in ball end milling of curved surfaces. The experiments are carried out at various cutting conditions, for both contouring and ramping of convex and concave surfaces. A high precision machining center is used in the cutting tests. In contouring, the machining error is measured with an electric micrometer, while in ramping it is measured on a 3-coordinate measuring machine. The results show that in contouring, the cutting force component that influences the machining error decreases with an increase in milling position angle, while in ramping, the two force components that influence the machining error are hardly affected by the milling position angle. Moreover, in contouring, high machining accuracy is achieved in “Up cross-feed, Up cut” and “Down cross-feed, Down cut” modes, while in ramping, high machining accuracy is achieved in “Left cross-feed, Downward cut” and “Right cross-feed, Upward cut” modes. The theoretical and experimental results show reasonably good agreement.

Temperature Variation in the Cutting Tool in End Milling

This paper describes the cyclic temperature variation beneath the rake face of a cutting tool in end milling. A newly developed infrared radiation pyrometer equipped with two optical fibers is used to measure the temperature. A small hole is drilled in the tool insert from the underside to near the rake face, and an optical fiber is inserted in the hole. One of the optical fibers runs through the inside of the machine tool spindle and connects to the other optical fiber at the end of the spindle. Infrared rays radiating from the bottom of the hole in the tool insert during machining are accepted and transmitted to the pyrometer by the two optical fibers. For a theoretical analysis of the temperature in end milling, a cutting tool is modeled as a semi-infinite rectangular corner, and a Greens function approach is used. Variation in tool-chip contact length in end milling is considered in the analysis. Experimentally, titanium alloy Ti-6Al-4V is machined in up and down milling with a tungsten carbide tool insert at a cutting speed of 214 m/min. In up milling, the temperature beneath the rake face increases gradually during the cutting period and reaches a maximum just after the cutting. In contrast, in down milling, the temperature increases immediately after cutting starts; it reaches a maximum and then begins to decrease during cutting. This suggests that the thermal impact to the cutting tool during heating is larger in down milling than in up milling, whereas that during cooling is larger in up milling than in down milling. Temperature variation is measured at different depths from the rake face. With increasing depth from the rake face, the temperature decreases and a time lag occurs in the temperature history. At 0.6 mm from the major cutting edge, the temperature gradient toward the inner direction of the tool insert is about 300°C/0.5 mm. The calculated and experimental results agree well.

Study on Machining Error in Ball End Milling of Spherical Surface

This paper presents the results of a series of experiments performed to examine the validity of a theoretical analysis for evaluation of machining error in ball end milling of spherical surface. In the analysis, the trochoidal paths of cutting edges are considered in the evaluation of chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from cutting force induced tool deflections are calculated at various parts of the machined surface. The experiments are carried out at various cutting conditions for convex spherical surface, and the influences of cutting mode and milling position angle on machining error are examined.

Regenerative Chatter Vibration in Ball End Milling of Curved Surfaces

This paper presents an analysis of chatter vibration in ball end milling of curved surfaces using time domain approach. A model for dynamic cutting process, which takes into consideration the variation of helix angle of the ball end mill along the cutting edge, is developed. The vibration of the tool is calculated by using a lumped-parameter model with two degrees of freedom. The chatter stability limit is indicated by the critical nominal depth of cut. The results show that chatter stability is very low for low spindle speeds. Also, the stability is lower for low and high milling position angles, and higher for intermediate milling position angles.