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Research Papers

# Analysis of Three-Dimensional Cutting Process With Thin Shear Plane Model

[+] Author and Article Information
Eiji Shamoto

e-mail: shamoto@mech.nagoya-u.ac.jp

Rei Hino

Department of Mechanical
Science and Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received July 5, 2010; final manuscript received March 4, 2013; published online July 17, 2013. Assoc. Editor: Burak Ozdoganlar.

J. Manuf. Sci. Eng 135(4), 041001 (Jul 17, 2013) (12 pages) Paper No: MANU-10-1191; doi: 10.1115/1.4024531 History: Received July 05, 2010; Revised March 04, 2013; Accepted March 08, 2013

## Abstract

A new and basic analytical model of three-dimensional cutting is proposed by assuming multiple thin shear planes with either the maximum shear stress or minimum energy principle. The three-dimensional cutting process with an arbitrarily shaped cutting edge in a flat rake face is formulated with simple vector equations in order to understand and quickly simulate the process. The cutting edge and workpiece profile are discretized and expressed by their position vectors. Two equations among three unknown vectors, which show the directions of shear, chip flow, and resultant cutting force, are derived from the geometric relations of velocities and forces. The last vector equation required to solve the three unknown vectors is obtained by applying either the maximum shear stress or minimum energy principle. It is confirmed that the directions and the cutting forces simulated by solving the proposed vector equations agree with experimentally measured data. Furthermore, the developed model is applied to consider the three-dimensional cutting mechanics, i.e., how the chip is formed in the three-dimensional cutting with compressive stress acting between the discrete chips, as an example.

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## Figures

Fig. 1

Three-dimensional cutting process with discretized cutting edge

Fig. 2

Discretized workpiece profile and cutting edge

Fig. 3

Parameters in three-dimensional cutting process

Fig. 4

Areas sheared by discrete cutting edges

Fig. 5

Velocity relation

Fig. 6

Force relation

Fig. 7

Direction of resultant cutting force to generate each shear plane in maximum shear stress principle: (a) 1st shear plane and (b) kth shear plane

Fig. 8

Relation among vector equations and parameters to represent three-dimensional cutting process: (a) maximum shear stress model and (b) minimum energy model

Fig. 9

Setup for planing experiments with ultraprecision machine tool

Fig. 10

Setup for turning experiments with conventional lathe

Fig. 11

Analytical and experimental results of ultraprecision planing with V-shaped diamond tool. Experimental and simulation conditions: workpiece material was brass, depth of cut d = 20 μm, feed rate f = 8–40 μm, cutting speed Vw = 3 m/min, dry cutting, V-shaped single crystal diamond tool, ψt = 90 deg, γ = 15 deg (see Appendix B), αf = 5 deg, αt = 0 deg, identified material properties τ = 500 MPa, β = 5.5–9.0 deg.

Fig. 12

Analytical and experimental results of turning with sintered carbide tool with nose radius. Experimental and simulation conditions: workpiece material was tough-pitch copper, combination of depth of cut and feed rate (d, f) = (475, 250), (344, 310), (226, 410), (173, 500), and (145, 590) μm, cutting speed Vw = 85 m/min, mineral oil was supplied as cutting fluid, sintered carbide tool with mirror-finished rake face, Rt = 0.2 mm, ψt = 80 deg, γ = 5 deg, αf = 0 deg, αt = 0 deg, identified material properties τ = 500 MPa, β = 28.4 deg (averaged).

Fig. 13

Three-dimensional cutting processes simulated by applying developed thin shear plane model and either minimum energy or maximum shear stress principle and comparisons of chip sections between simulations and experiments. The other experimental and simulation conditions are same as shown in Fig. 12. (a) Depth of cut d = 475 μm, feed rate f = 250 μm, minimum energy principle. (b) Depth of cut d = 145 μm, feed rate f = 590 μm, maximum shear stress principle.

Fig. 14

Three-dimensional cutting process predicted by maximum shear stress model. Simulation conditions are same as Fig. 13(b). Viewing directions are aligned with shear direction in left illustration and perpendicular to parallel plane in right illustration, respectively.

Fig. 15

Oblique cutting process and parameters predicted by maximum shear stress model at condition of inclination angle = 30 deg, normal rake angle = 10 deg, and friction angle β = 30 deg.

Fig. 16

Discrete points on cutting edge and workpiece profile in turning process. (a) At small feed rate and small depth of cut and (b) at large feed rate and large depth of cut.

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