Akihiko Hirota

Prediction of Chip Formation and Cutting Forces in Milling with Ball End Mills. (2nd Report). Comparison of Calculated and Experimental Results, and Cutting Force Prediction Based on the Geometric Similarity.

In the 1st part of this investigation, a cutting model and energy method developed for the drilling, in which the condition of side-curl of the chip is considered, has been extended to the milling with ball end mills. In this paper, three components of the cutting force and the chip formation such as radius of side-curl and shear angle are measured, and compared with those through theoretical prediction. Therefore the predicted results are good agreement with the experimental results. Then, geometrical similarity conditions for relating ball end mills of various diameters are discussed. In the milling with similar ball end mills, shape of the cutting cross-section at any rotational angle of the cutter also becomes similar, when both ratios of feed to tool diameter and depth of cut to that are held in constant. Furthermore, it is confirmed that the relationships between cutting forces and square of tool diameter, and between side-curl of the chip and tool diameter become linear respectively, when the similarity conditions are satisfied. Using the geometric similarity and a few data with respect to the cutting forces, any other cutting forces for ball end mills of various diameters can be easily estimated.

Prediction of Chip Formation and Cutting Forces in Milling with Ball End Mills. (1st Report). Geometry of a Ball End Mill and Cutting Model.

Cutting edge of a sphere portion (end cutting edge) of the ball end mills is treated as the intersection of a spherical surface and a rake face approximated by a plane surface. The cutting edge configuration is geometrically analyzed, and variation of inclination angle and normal rake angle along the cutting edge is discussed. In addition, it is assumed that the line elements along the curved cutting edge of the sphere portion do not undergo extension or contraction, and the modified condition of sidecurl of the chip is introduced. Then a cutting model and energy method developed for the drilling process is extended to the milling process. Expressions such as area of the shear plane and projected area of the cutting cross-section on the rake face are derived for slot milling. From the analytical results obtained through energy method, it is found that the center of side-curl of the chip is fixed near the top of the sphere portion of ball end mills and the chip is produced under this restricted condition. Furthermore, predicted result shows that Stablers chip flow rule does not hold for the milling with ball end mills.

Prediction of Chip Formation and Cutting Forces in Drilling with Curved Cutting Edge Drills (2nd Report). Comparison of Calculated and Experimental Results.

In the 1st part of this investigation a cutting model and energy method considering the condition of side-curl of the chip was extended to the drilling with curved cutting edge drills. In this paper the torque and thrust force and the chip formation such as shear angle chip flow angle are measured and compared with those through theoretical prediction. In the case of the drills having concave or convex main cutting edges the predicted results are in good agreement with the experimental results. By using the measured values relating to the radius of side-curl of the chip and the chip flow angle at the midpoint of the cutting edge the cutting model including the cutting edge at the drill center enables to explain the variation of the torque chip flow angle and chip thickness along the cutting edge when the chip form changes from conical-helical chip into long-pitch helical one. As a result, it becomes clear that the whole chip formation along the cutting edge of the drill having curved cutting edges can be treated by using the values based on the chip form expanded to a plane.

Prediction of Chip Formation and Cutting Forces in Drilling with Curved Cutting Edge Drills(1st Report). Drill Geometry, Cutting Model and Energy Method.

Carbide-tipped drills having various shapes of main cutting edges, and circular or straight cutting edges or non-cutting zone at the drill center have been manufactured and widely used in recent years. In order to compare the cutting phenomena with these drills, the tool angles such as inclination angle and normal rake angle along the cutting edge, which control the cutting force and chip formation, are discussed. In addition. a cutting model and energy method. in which elemental chip at each point on the cutting edge is described by simple shear plane oblique cutting model and the condition of side-curl of the chip is considered. is extended to drilling with the drills. In the analysis, it is assumed that the chip produced with whole cutting edge consisting of the main cutting edge and the cutting edge at the drill center can be expanded to be a plane. Two cases for chip separating or no chip separating at the junction of the main cutting edge and the cutting edge at the drill center are treated and discussed. Predicted result shows that Stablers chip flow rule does not hold for the curved cutting edge drills.

Mechanics of three dimensional cutting process involving chip curl and cutting velocity difference along the cutting edge.

In previous papers an oblique cutting model taking account of up-curl of the chip and chip flow direction was proposed. In this paper, a cutting model also including side-curl of the chip and the cutting velocity difference along the cutting edge is developed. It is assumed that the deformation at any point on the cutting edge takes place as in oblique cutting model. The whole process of chip formation is treated as a combination of elemental oblique cutting models varying at each point on the cutting edge. On the basis of the cutting model the energy method is extended to predict cutting force components, radius of chip curl and others. From the numerical computation it is shown that the radius of side-curl of the chip easily changes from an infinite value in oblique cutting to a value of three or four times cutting width along the cutting edge in the case of large cutting velocity difference.

Analytical prediction of chip formation and cutting forces in drilling operation. (4th report). Comparison of predicted and experimental results for chisel edge.

In the 3rd part of this investigation a cutting model with restricted tool-chip contact length, which represents the formation of a helical chip produced by the chisel edge, was proposed. By specifying the frictional stress on the rake face of the chisel edge, the model enables to predict the chip formation, and torque and thrust force through the energy method. To evaluate the condition on the rake face, two-dimensional cutting experiment was done with fairly negative rake angle tools having differently restricted tool-chip contact length. It is clear that the value of frictional stress on the rake face of the chisel edge approximates to 0.2 times the value of shear stress on the shear plane. The torque and thrust force, direction of translational velocity and others are measured and compared with those predictions. On the torque and thrust force, the predicted results are in good agreement with the experimental results.

Analytical Prediction of Chip Formation and Cutting Forces in Drilling Operation (2nd Report):Comparison of Predicted and Experimental Results

Analytical Prediction of Chip Formation and Cutting Forces in Drilling Operation (2nd Report) Comparison of Predicted and Experimental Results Akihiko HIROTA and Kazuo KASAHARA In the 1st part of this investigation a cutting model considering the condition of side curl of the chip was proposed, and the energy method was extended to the case of drilling process for predicting the chip formation and the cutting forces. In this paper a dynamometer with piezo-electric load washer is constructed and used to measure the cutting forces. In order to freeze the actual process of chip formation for measurement of chip flow angles along the cutting edge, a quick-stop apparatus is also designed and constructed. The experimental tests are run with various pilot holes. The cutting forces and the chip formation such as chip flow angle, normal shear angle, radius of side curl of the chip are measured and compared with those from the theoretical prediction. It is clarified that the process of chip formation depends on the width of the engaged cutting edge with the workpiece. The predicted results appear to give good qualitative and quantitative explanations of the experimental results.