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A. Roy et al.
to a single integration point and thereby helps in eliminating the problem of parasitic
shear. In total, 60,000 brick elements were used to mesh the workpiece after a meshsensitivity study. To ensure the accuracy of FE simulations, a finer local mesh was
used in regions near the cutting zone (corresponding to a height of 10 μm). In this
study, a normal to the top surface of the workpiece coincided with the [110] crystal
orientation and the cutting direction with the [1-10] crystal orientation. A process
of removal of the workpiece material was simulated using an element-deletion technique in ABAQUS. Contact conditions between the cutting tool and the workpiece
were assumed to be frictionless.
A constant velocity was specified for the cutting tool to simulate the CM process,
whilst a harmonic motion was superimposed on the cutting tool motion to simulate the
ultrasonically assisted machining process. The relationship between the displacement
of the cutting tool with time (t) in UAM is expressed as
x(t) = V 0 t + a sin(2π f t),
(13)
where V 0 is the constant nominal velocity in the CM process, a and f are the vibration
amplitude and frequency, respectively. In the simulation of UAM, the motion of
the cutting tool was controlled by a velocity boundary condition in ABAQUS. The
velocity of the cutting tool was obtained by differentiation of Eq. (13) as
V (t) = V 0 + V c cos(2π f t), V c = 2π f a,
(14)
where V c is the critical oscillatory speed of the cutting tool. In the current study, the
values of amplitude and frequency of vibration were 15 μm and 20 kHz, respectively.
The critical oscillatory speed was calculated to be 1.885 mm/ms. Three values of V 0
were considered in our simulations: 2.0, 1.5 and 1.0 mm/ms.
4 Results and Analysis
First, data obtained from experimental studies performed on single-crystal copper
[22] were used to calibrate the material parameters of workpiece. As shown in Fig. 2,
numerical results based on the described SCP theory show an excellent match with
the experimental data for both [100] and [111] crystal orientations. The calibrated
model parameters are listed in Table 1, which were used to simulate the CM and
UAM process at the subsequent stage of the present investigation.
For the nominal velocity of 2.0 mm/ms, a relationship between the velocity and
displacement of the cutting tool and the cutting time is shown in Fig. 3 for CM
and UAM. In this case, the normal velocity, V 0 , was slightly higher than the critical
oscillatory speed, V c and the ratio of V 0 to V c was about 1.06. This implies that the
cutting tool did not separate from the workpiece during the UAM process. However,
the superimposed motion due to UAM does affect the overall kinematics of the
machining process, showing a minor difference in the average cutting forces (and
A. Roy et al.
to a single integration point and thereby helps in eliminating the problem of parasitic
shear. In total, 60,000 brick elements were used to mesh the workpiece after a meshsensitivity study. To ensure the accuracy of FE simulations, a finer local mesh was
used in regions near the cutting zone (corresponding to a height of 10 μm). In this
study, a normal to the top surface of the workpiece coincided with the [110] crystal
orientation and the cutting direction with the [1-10] crystal orientation. A process
of removal of the workpiece material was simulated using an element-deletion technique in ABAQUS. Contact conditions between the cutting tool and the workpiece
were assumed to be frictionless.
A constant velocity was specified for the cutting tool to simulate the CM process,
whilst a harmonic motion was superimposed on the cutting tool motion to simulate the
ultrasonically assisted machining process. The relationship between the displacement
of the cutting tool with time (t) in UAM is expressed as
x(t) = V 0 t + a sin(2π f t),
(13)
where V 0 is the constant nominal velocity in the CM process, a and f are the vibration
amplitude and frequency, respectively. In the simulation of UAM, the motion of
the cutting tool was controlled by a velocity boundary condition in ABAQUS. The
velocity of the cutting tool was obtained by differentiation of Eq. (13) as
V (t) = V 0 + V c cos(2π f t), V c = 2π f a,
(14)
where V c is the critical oscillatory speed of the cutting tool. In the current study, the
values of amplitude and frequency of vibration were 15 μm and 20 kHz, respectively.
The critical oscillatory speed was calculated to be 1.885 mm/ms. Three values of V 0
were considered in our simulations: 2.0, 1.5 and 1.0 mm/ms.
4 Results and Analysis
First, data obtained from experimental studies performed on single-crystal copper
[22] were used to calibrate the material parameters of workpiece. As shown in Fig. 2,
numerical results based on the described SCP theory show an excellent match with
the experimental data for both [100] and [111] crystal orientations. The calibrated
model parameters are listed in Table 1, which were used to simulate the CM and
UAM process at the subsequent stage of the present investigation.
For the nominal velocity of 2.0 mm/ms, a relationship between the velocity and
displacement of the cutting tool and the cutting time is shown in Fig. 3 for CM
and UAM. In this case, the normal velocity, V 0 , was slightly higher than the critical
oscillatory speed, V c and the ratio of V 0 to V c was about 1.06. This implies that the
cutting tool did not separate from the workpiece during the UAM process. However,
the superimposed motion due to UAM does affect the overall kinematics of the
machining process, showing a minor difference in the average cutting forces (and