Creation of Curved Surface by Lathe Turning

Creation of Curved Surface by Lathe Turning
Available online at
Procedia CIRP 1 (2012) 114 – 119
5th CIRP Conference on High Performance Cutting 2012
Creation of Curved Surface by Lathe Turning
-Development of CAM system using original tool layoutYoshitaka Morimoto a*, Souichiro Emoto a, Takayuki Moriyama a, Hideharu Kato a,
Katsuhiro Nakagaki b, Naohiko Suzuki b, Yoshiyuki Kaneko b and Minoru Isobe b
a : Advanced Materials Processing Research Laboratory, Kanazawa Institute of Technology, Japan
b Takamatsu Machinery Co., ltd. , Japan
* Corresponding author. Tel.: +81-76-274-9274 ; Fax: +81-76-274-9251 E-mail address: [email protected]
The machining of 3D curved surfaces with an un-axisymmetric axis by lathe turning is proposed considering the best machinable
tool layout. The best offset tool layout from the central axis of a spindle enables us to machine curved surfaces and to obtain a long
tool life for hard material workpieces using a rotary tool. A dedicated NC program for the 3D surface using the original CAM
system has been developed and applied to what. The machining results and the validity of our system are evaluated in this paper.
2012 The
Elsevier BV.
under responsibility
of Prof. Konrad
© 2012
by Elsevier
and/or peer-review
under responsibility
of Professor
Konrad Wegener
Open access under CC BY-NC-ND license.
Keywords: Lathe cutting, Grinding, Multiaxis control, Non-circle cutting, 3D surface, CAD/CAM
1. Introduction
A new CNC lathe driven by a linear motor has been
developed to improve its productivity through highspeed motion. Recently, a linear motor-driven lathe as a
typical high-speed machining tool has been offered
commercially. The merit of this system is the reduction
in air cut time and consequently the shortening of the
limited machining time. There are a few applications
that take advantage of the high-speed feed rate of this
NC lathe.
On the other hand, the machining of curved surfaces
with complex non-axisymmetric shapes such as
eccentric axes, and conical cams is realized by milling
and grinding [1]. In this case, there is a serious problem.
It takes a long time to machine by milling or grinding.
Furthermore, the machining point between a curved
surface and a milling tool or a grinding wheel is a single
point contact, the just as in same as lathe turning.
Two methods of machining have been introduced by
machine tool companies [2]-[5]. One is plunge grinding,
which is used for machining 3D curved surface profiles
by calculating the NC code for each cross sectional
profile along the Z-axis direction [6]. This method is the
most practical in the manufacturing industry. The only
key change is in the profile of the grinding wheel,
according to the 3D curved surface profile. Although no
modification of the grinding machine is needed in this
method, there exists a serious problem, that is, the
profile is strictly limited by the radius of the grinding
Fig. 1 Example of un-axisymmetric curved surface
2212-8271 © 2012 The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of Professor Konrad Wegener
Open access under CC BY-NC-ND license.
Yoshitaka Morimoto et al. / Procedia CIRP 1 (2012) 114 – 119
axisymmetric surfaces. A new rotary tool is used to
obtain a long tool life for the hard material workpiece.
Fig.2 Appearance of linear-motor-driven NC lathe
Table 1 Specifications of lathe developed
Fig.4 Occurrence of interference between tool flank surface and
Fig.3 Conventional tool layout of curved surface by lathe cutting
The other method is traverse grinding [7]. This method
is rather complex to apply for practical use. This
conventional machining method cannot achieve
significant advancement in productivity.
Therefore, a new cutting process instead of milling or
grinding is strongly required by the manufacturing
Then, we apply lathe turning to the machining of a
curved surface. Our new prototype CNC lathe has been
developed for machining curved profiles by turning
instead of by conventional machining. The key factor for
a breakthrough is to speed up tool posting on a moving
In this paper, the best machinable tool layout by lathe
turning has been proposed for machining curved non-
A dedicated NC program for curved surfaces is
needed for machining curved surfaces. An original CAM
system has also been developed. This system enables us
to automatically derive such an NC program by the
proposed method. The creation of a dedicated NC
program including some conversion processes is needed
for building curved paths for lathe turning. To create an
efficient and exact tool path from shape data, such
conversion processes should be calculated carefully. The
original CAM system devised extracts the data of all the
points on a curved surface from 3D CAD to obtain a
precise tool path. Our original CAM system turns
complex processes into simple processes and can
sufficiently derive an accurate NC program.
In this report, the proposed system is also evaluated
from the machining results of representative examples.
The measurement results of the machined examples are
2. Machining method for curved surfaces
Figure 1 shows an example of a workpiece with a
curved surface profile. To machine this workpiece by
lathe turning, a linear motor-driven NC lathe has been
developed, which is shown in Fig. 2. The developed
lathe has orthogonal 2 axes, and is of the Swiss type with
two linear motors. Its main specifications are shown in
Table 1.
Figure 3 shows the conventional tool layout. The Zaxis corresponds to the spindle rotational axis. In this
figure, the horizontal center line of the spindle axis of
Yoshitaka Morimoto et al. / Procedia CIRP 1 (2012) 114 – 119
the curved surface corresponds to the height of the tool
rake surface set on the X-axis. A spindle axis, which
holds a workpiece and rotates, and the C-axis, which can
position rotational angle, are equipped on the Z-axis
table. A linear encoder is set in both the X- and Z-axes.
The least resolution is 10 nm. Encoders are set to
minimize the effect of yawing motion and to detect
accurate table positions. In the case of machining a
curved surface, high-speed acceleration is not always
needed for the Z and C-axes.
On the other hand, a high acceleration and a high
response are needed for the X-axis. The C-axis is needed
to rotate with a constant revolution and to follow the Xand Z-axes. Therefore, a linear motor is used to obtain a
high acceleration for the X-axis table.
Fig.5 Interference part by conventional tool layout
Fig.6 Proposed machinable tool layout
3. Proposed lathe cutting for curved surfaces
3.1. Proposed new tool
Figure 4 shows the conventional tool layout. In the
case of lathe cutting, the height of the tool rake surface is
set to that of the horizontal center line of the spindle
rotational axis, as shown in Fig. 3. A non-axisymmetric
curved surface always changes its radius depending on
spindle rotational angle. Therefore, the interference
between the tool flank face and the workpiece surface
must be considered, as shown in Fig. 4. This result leads
us to a failure in applying the turning process to the
curved surface machining. Turning cannot avoid
interferences at the curved
conventional tool layout [8].
Fig.7 Detection of interference area by tool offset
Fig.8 Top view of tool layout and calculated spline curve
Fig.9 Isometric view of tool offset and calculated spline curve
To avoid interferences, the unique and processible
tool layout for the curved surface has been proposed.
The tool cutting edge always moves along the curved
surface by the proposed method.
3.2. Detection of interference and avoidance method
The occurrence of the interference between the
workpiece and the cutting tool can be avoided using a
new tool layout. Interference is evaluated by the
following method. The representative cross section is
chosen and its tangential angle at the cutting point is
calculated. Figure 5 shows the conventional tool layout.
Yoshitaka Morimoto et al. / Procedia CIRP 1 (2012) 114 – 119
φi 0 is the tangential angle at the cutting point on the
curved surface, and ș is the angle between the tool rake
face and the tool flank face. In this case, interference
occurs when φi 0 becomes larger than ș. To avoid this
interference problem, it is necessary for the tool to offset
to the Y-direction, where the inclination angle φi is
smaller than θ as shown in Fig. 6. φ is the angle
determined tool offset at the cutting point. Figure 7
shows the change in the inclination angle φi at the
representative cross-sectional contour of the workpiece.
Offset angle φ is generally set to be 90 degrees or
less, the rotary tool is also in this range. From Fig. 7, a
portion whose i 0 exceeds 90 degrees can be seen at the
spindle position from 180 to 270 degrees. In this range,
interference occurred. The red line shows the result of
change in inclination angle i , where the tool offset " is
applied in the Y-direction. In this tool layout, when the
change of φi does not exceed 90 degrees, no interference
When the tool offset is completed, as shown in
Fig. 10, cutting points become uneven in the Zdirection because the feed rate by the tool path
calculated from the tool center is not considered.
Therefore, the distance of the tool path data in the
Z-axis direction is not constant. Spline curve
approximation is performed again to equalize
feed rate. By this operation, a constant interval of
the Z-axis can be obtained.
(5) Concatenation of spline data points
Figure 11 shows the calculation method of
concatenating data points from spline curves
depending on rotational angle. These are
consolidated sequentially for lathe turning as
spiral trajectory data in our system.
(6) Completion of NC program
The NC program for a curved surface machining
is completed by these operations. This data is fed
to the high-speed servo controller.
4. Method of calculating tool path
In conventional lathe turning, the NC program is
made from the X- and Z-axes. In the case of machining a
curved surface, as shown in Fig. 1, the X-axis has to be
changed depending on the rotational position of the
spindle. Therefore, the synchronization control of the X-,
Z- and C-axes must be considered to calculate the tool
path of the curved surface by lathe turning. As the
conventional CAM system does not accept our tool
layout, an original CAM system has been developed.
4.1. Creation of NC program using original CAM system
The original CAM system requires 6 steps to obtain
the NC program. The steps are as follows:
(1) Reading of curved surface data
The IGES data are read using conventional 3DCAD.
(2) Creation of line at intersection between tool rake
face and curved surface
The spline of the intersection for the curved surface
and tool rake face at the representative spindle position
is obtained, as shown in Figs. 8 and 9. This spline is part
of the tool path at the tool cutting edge at a
representative rotational angle. From this figure, the tool
offset " is determined, where no interference occurs.
(3) Extraction of data points on each spline curve
The point data created from the spline curve are
extracted according to the feed rate of the Z-axis.
(4) Calculation of tool radius offset data
The previous operation for a curved surface only
derives cutting positions on the surface. In this
process, tool radius is considered. Therefore, the
tool radius offset for the rotary tool at the cutting
point data is considered, as shown in Fig. 10.
Fig.10 Method of calculating tool path
Fig.11 Concatenation of cutting points
Yoshitaka Morimoto et al. / Procedia CIRP 1 (2012) 114 – 119
In Fig. 13, the solid line shows the calculation result
obtained using Eq. (1). The red dots show the
experimental results. This model shows good agreement
with the experiment.
The frequency response shows good performance up
to 20 Hz. No distinct resonant frequency appears in this
frequency range. This system can be used for machining
a curved surface from the experimental result.
6. Table behaviour during lathe cutting
6.1. Experimental setup
Fig.12 Block diagram of linear-motor-driven lathe
Fig.13 Frequency response of X-axis table
5. Frequency response of tool post
The frequency response of a linear motor-driven NC
lathe is the most important characteristic of curvedsurface cutting, because the position of the X-axis table
(tool post) is controlled depending on the spindle
position. Figure 12 shows the block diagram of the
linear-motor-driven table. The table response is
measured using both sinusoidal inputs and table
positions from the linear scale. Figure 13 shows the
measurement result. The response can be assumed using
the second lag system, which is a typical feature of a
linear-motor-driven NC table. There is a time lag for the
motion of this table. Therefore, by adding the element of
the primary delay system, the equivalent transfer
function of the second lag system can be expressed as
G( s) =
K1 − Ls
K䞉2 F
e 䞉
Ts + 1
ms + cs + K䞉2 F ,
where, K1 and K2 are coefficients, m, c, and F denote
the mass, damping coefficient, and thrust force,
The linear-motor-driven NC lathe for machining the
curved surface is operated using the created NC
program. In this case, the NC table behavior recorded in
the memory of the CNC system is used to compensate
for the linear motor motion. This experiment is executed
using the installed rotary tool and originally calculated
NC program. The NC program is verified by comparing
the NC program with the measured positions of the table
motion. Figure 14 shows the experimental result for the
maximum stroke of the tool post motion. In Fig. 14, the
black solid line shows the designed curve. The red solid
line shows the NC table motion measured from the
linear encoder. On the other hand, the blue solid line
shows the acceleration of the designed curve. The green
solid line shows the acceleration calculated from the
measured position.
As shown in this figure, high-speed processing is
actually performed. Our main purpose is to verify the
table motion and to evaluate our CAM system. The
cutting experiment has been executed by air cutting as
previously described. After the confirmation of the tool
post motion, machinable wax is machined by the
proposed method. A workpiece is machined previously
using an end mill. Lathe turning is performed to finish
cutting. In this process, according to the calculated NC
program, the X-, Z-, and C-axes are controlled by a
simultaneously synchronized operation.
6.2. Experimental result
The supposed cutting conditions to achieve the
desired curved surface are shown in Table 2. The NC
table motion that shows rapid acceleration and
deceleration follows with the designed profile. The
acceleration calculated using a linear encoder exceeds
6G at its peak. On the other hand, the measured
maximum stroke of the X-axis motion is 10 mm. The
present setup shows that the measured value cannot
reach the target value. The NC table motion has to be
improved for the finish machining of the curved surface.
Figure 15 shows an enlarged image of Fig. 14. This
figures shows the controlled results compensated for in
Yoshitaka Morimoto et al. / Procedia CIRP 1 (2012) 114 – 119
the cases of feed-forward control and repetitive control.
The X-axis table position is designed to move by an 10.5
mm stroke, and responses of 10.3 mm (feed forward
control), and 10.5 mm (repetitive control) are obtained
using the compensated NC program by these two
methods. In particular, the responses are actually
improved to the desired points of the surface. Both
compensation methods are available for the control of
cutting tools. The setting of repetitive control is easier
than that of feed-forward control. We apply this control
method to curved surface machining. Figure 16 shows a
machined-curved surface obtained by our lathe turning.
This experimental procedure demonstrated that our
system is sufficiently practical for machining curved
surfaces by lathe turning.
Table 2 Cutting conditions
Fig.16 Curved surface machined using our developed system
7. Conclusions
A new method of machining curved surfaces by lathe
turning has been proposed and its feasibility is evaluated
by experiments. The following findings are obtained.
(1) A new tool layout for machining of curved surfaces
has been developed.
(2) The interference between a tool and a workpiece
can be avoided by our proposed tool layout.
(3) A curved surface can be machined using the
original CAM system.
(4) Our system is feasible for machining curved
surfaces by lathe turning.
Fig.14 NC table behavior of maximum stroke and its acceleration
Fig.15 NC table behavior of maximum position
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