Ultraprecision sculpturing of hardened steel by applying elliptical vibration cutting
Norikazu Suzuki1
1

Nagoya University, Nagoya, Japan

Abstract – Elliptical vibration cutting technology is well-known for its excellent performance in ultraprecision machining of steel
materials with single crystal diamond tools. This paper presents two approaches to attain high-performance micro- and macro-scale
sculpturing for steel materials by utilizing elliptical vibration cutting. In order to attain free-form sculpturing in macro-scale, a 4-axis
controlled machining method has been proposed. An ultrasonic elliptical vibration system for the proposed method was developed andexperimental verifications were conducted. A novel micro/nano-scale sculpturing method was also introduced. In this method, a depthof cut is actively controlled in elliptical vibration cutting by controlling vibration amplitude in the vertical direction. By utilizing thisas a fast tool servo function, high performance micro/nano sculpturing of steel materials can be attained directly by single crystal
diamond tool without using conventional fast tool servo technology. A practical sculpturing system was developed and applied tovarious applications, such as textured grooving, picture image machining and dimple pattern sculpturing.
Key Words: cutting, ultraprecision cutting, elliptical vibration cutting, sculpturing, difficult-to-cut material

1. Introduction

intermittent cutting process at an ultrasonic frequency is also effective

Hardened steel is often used as mold materials in manufacturing

in preventing the tool wear and the adhesion, and thus, diamondindustry. Some of them are required to have mirror surface quality andcutting of hardened steel can be realized as reported in the pastsophisticated free-form shape simultaneously. Ultraprecision cutting

literatures7).

technology is generally useful to attain such mirror surface

While elliptical vibration cutting is beneficial in various aspects,

sculpturing. By utilizing a sharp single crystal diamond tool and an

there is also a disadvantage, i.e., a cutting speed is restricted to be

ultraprecision machine tool, arbitrary micro and macro structures canrelatively lower than the vibration speed. Because of this restriction,

be machined with mirror surface quality. However, conventional

the vibration speed is generally limited to be less than about 5 m/min

diamond cutting is not applicable directly to steel materials due toin practice. Its machining time, consequently, becomes longer in someextremely rapid tool wear and surface deterioration. Therefore,cases as compared with the conventional methods. However,

Nickel-phosphorous (NiP) electroless plating is generally applied onmachining efficiency can be increased contrarily when it is applied tothe steel mold surfaces, and only thin NiP plating layer is machined

sculpturing. The present paper summarizes novel high-performanceby the single crystal diamond tool with less tool wear1). Otherwise,

sculpturing methods in micro- and macro-scale by applying ellipticalpolishing needs to be applied as a finishing process following thevibration cutting and their applications.

sculpturing of the steel molds by conventional machining methods,

2. Macro-scale sculpturing by applying elliptical vibration cutting

such as end milling, grinding and electric discharge machining. BothFigure 1 shows the proposed mirror surface finishing method. The

conventional methods result in a decrease in efficiency and an

tool is supposed to be vibrated elliptically in the desirable plane, andincrease in cost. The polishing can also cause surface shape

it is fed along the sculptured surface while the relative rotational

deterioration, especially at sharp edges. So, reduction of these

position between the tool and the workpiece is precisely controlled inprocesses in mold manufacturing has been a major focus ofaccordance with the sculptured surface orientation as shown in the

production engineering in industry. And thus, a number of researchers

figure. The conventional and proposed methods are compared in Fig.

have dedicated to attain diamond machining of steel materials2), 3).

2. In the proposed method, the tool is not rotated at the constant speed,

Moriwaki and Shamoto have applied ultrasonic vibration into theunlike conventional rotating end mills, but the rotational position ofultraprecision cutting of the steel materials, and it was verified thatthe tool is precisely controlled. Thus, the proposed method needs aultrasonic vibration cutting can be effective to decrease the tool wear

precision machine tool with at least 4 axes, i.e., X, Y, Z and C, toand to attain mirror surface machining of the steel material directly bymachine the sculptured surfaces, while the conventional end milling

single crystal diamond tool4). Shamoto has extended conventionalcan be operated with 3-axis controlled machine tool. Both the5)linear vibration cutting to elliptical vibration cutting , andelliptical vibration cutting and the end milling processes areinvestigated its superior cutting performances6). In elliptical vibrationintermittent, but the vibration frequency is much higher and the radius

cutting, the tool is vibrated elliptically and fed in the nominal cutting

is smaller in the ultrasonic elliptical vibration cutting. These

direction relatively to the workpiece simultaneously, so that the chipdifferences enable the mirror surface machining with diamond tools.

is formed intermittently and pulled out in each vibration cycle. Since

Unlike the end milling process, the feed speed is identical with thethe friction between the chip and the tool rake face is drasticallycutting speed in the proposed method. Although the cutting speed in

reduced or reversed, the shear angle is increased. Consequently, thethe elliptical vibration cutting is not high as mentioned above, it is not

cutting force and the cutting energy are reduced significantly. The

low or rather high as the feed speed in sculpturing processes.

U axisTool supports

Z axisPZT actuatorsfor bending vibration

V axisUltrasonic
elliptical vibrator
Diamond tool tip

Fig.1

PZT sensorsPZT actuatorsfor longitudinal vibration

Elliptical vibration cutting for three-dimensional free surface
Fig.3

Developed 3 DOF ultrasonic elliptical vibration tool(a) Vibrations in U, V and Z directions(a) Ball end milling process(b) Proposed method
Fig.2 Comparison between end milling and proposed machining for
sculptured surfaces(b) Lissajous figure in U-V plane(c) Lissajous figure in U-Z plane
Fig.4 Measured elliptical vibration
Consequently, machining efficiency can be relatively higher withhigher cutting feed speed and with smaller theoretical roughness ascompared with the end milling technology8).
In the proposed machining, a slender tool like an end mill needs tobe vibrated elliptically at an ultrasonic frequency in an inclined plane
as shown in the figure. Additionally the ultrasonic elliptical vibration
locus has to be kept to a constant ultra-precisely in the inclined plane
while cutting in order to guarantee machining accuracy. Note that
amplitude variation in the depth of cut direction can cause variation of
the depth of cut, which results in machining accuracy deterioration.
In order to attain the desirable vibration, a three-degree-of-freedom(3-DOF) ultrasonic vibrator shown in Fig. 3 was developed. The
vibrator can be actuated by some attached PZT actuators. Since thevibrator is designed to have same resonant frequencies in thelongitudinal and bending modes, it can generate large longitudinal andbending vibrations simultaneously at the same ultrasonic frequency of

Fig.5

Experimental setup for sculpturing applications

about 34.4 kHz by exciting the actuators. The vibration can also be
detected in real time by attached PZT sensors. The vibration in each9)

vibration mode is controlled with a feedback control system . Thus,

simpler as compared with the 3-DOF system, and thus it is easy tocontrol in practice.

an arbitrary 3-DOF elliptical vibration can be obtained at the diamond

Feasibility of mirror surface sculpturing for practical applications

tool tip mounted on the insert tool shank by combining both resonant

was experimentally verified. A precision machine tool, which was

vibration modes with some phase shift. Figure 4 shows examples ofdeveloped based on a commercial machining center (MU-400VA-DD:

measured vibrations. A similar 2-DOF vibration system, which can

OKUMA Corporation), was utilized10). Figure 5 shows a setup for

generate similar ultrasonic elliptical vibration in appropriate direction,

sculpturing experiments. The developed vibration tool is attached to a

was also developed. The configurations of the 2-DOF system are

C-axis air spindle, and it is connected to the control system by aFig.8

Photgraph of sculptured workpiece

Fig.6 Photgraph of spherical surface machined by developed system[Cutting conditions] Feed rate: 15 µm/rev, Depth of cut: about 3 µm,
Cutting speed: 0-1.27 m/min, Cutting fluid: oil mist, [Tool] Material:
single crystal diamond, Rake angle: 0 deg, Clearance angle: 15 deg,
Nose radius: 1 mm, [Workpiece] Material: die steel (JIS: NAK80),
Hardness: HRC40, [Vibration conditions] Vibration amplitude: 6-6-3µmp-p, Frequency: 34.4 kHz, Phase: 90-90 deg

50 µm

0.2 µm(a) Measured in cutting direction

50 µm

Fig.7

0.2 µm

Fig.9 Machined molds (left: cores, right: cavity)[Cutting conditions] Feed rate: 20 µm/rev, Depth of cut: 5 µm, Cutting
speed: less than 0.64 m/min, Cutting fluid: oil mist, [Tool] Material:
single crystal diamond, Rake angle: 0 deg, Clearance angle: 10 deg,
Nose radius: 1 mm, [Workpiece] Material: die steel (JIS: SUS420J2),
Hardness: HRC54, [Vibration conditions] Vibration amplitude: 4 µmp-p(circular), Frequency: 38 kHz(b) Measured in feed direction
Surface profiles of spherical workpiece
seems to be as fine as that of the spherical center part, though it isbunch of electric wires, thus the C axis cannot be rotated infinitely.

difficult to measure the surface roughness.

The tool is fed along the sculptured surface at each Z level and rotated

The mold cores were machined with same 2-DOF vibration control

in accordance with the cut surface orientation in the proposedsystem. Total machining time for the mold cores and cavity were 110

sculpturing method, as shown in Fig. 1. Therefore, the C axis needs tomin and 120 min. Mirror quality surfaces were obtained successfully

be counter-rotated to rewind the wires after each rotation. Workpieces

by applying the developed vibration system, as shown in Fig. 9.

were machined precisely by the ball end milling before the cutting

Almost all surfaces were consequently machined without any surface

tests in advance.

quality deteriorations. Maximum surface roughness was 124 nm Rz.

Figure 6 shows a photograph of the spherical steel mirror finishedThe quality seems to be remarkably fine considering the motion

with the 3-DOF elliptical vibration system. The result indicates that

accuracy of the machine tool used in the experiment. However thesimple curved mirror surfaces of hardened die steel can be obtained

self-excited chatter vibration occurred while machining steep surfaces,by the proposed elliptical vibration cutting with the 4 axis control.

which are almost parallel to the axial direction, even at a small depth

Figure 7 shows surface profiles measured by the surface profilerof cut of 5 µm. Since the chatter vibration can cause surface(ET4000: Kosaka Laboratory Ltd.) at the position where the normal

deterioration and critical damage on the cutting edge, it needs to bevector makes 30 deg with that at the top of the sphere. The maximum

suppressed in practice. Now, this chatter generation mechanism isroughness of about 280 nm Rz is achieved for the spherical surface, as

under investigation as well as chatter stability analysis andshown in the figure.

suppression methods.

Subsequently, sculpturing test of more complicated geometry of

3. Nano-scale sculpturing by applying elliptical vibration cutting

hardened steel workpiece was conducted by using the 2-DOF

In order to apply elliptical vibration cutting technology toelliptical vibration system. The photograph of machined workpiece isultraprecision cutting applications similarly to the conventional

shown in Fig. 8. As shown in the figure, mirror quality surface can bediamond cutting, it is important to keep the elliptical vibration locus

obtained successfully. Measured surface roughness of the sphericalultra-precisely constant. Otherwise, the depth of cut varies andcenter part was less than 100 nm Rz. Surface quality of other parts

ultra-precision cutting cannot be achieved in practice. On the otherhand, this fact means at the same time that the depth of cut can be
actively controlled by controlling the vibration amplitude in the depthof cut direction while machining. By utilizing this function to serve asa sort of fast tool servo (FTS), the ultra-precision sculpturing ofdifficult-to-cut materials in micro/nano scale is achieved efficiently.
Figure 10 shows the proposed machining with depth of cut control
in elliptical vibration cutting. The vibration amplitude in the depth ofcut direction is controlled simultaneously in the proposed machining
process. The trajectory of the cutting edge, then, changes dynamically,
and its envelope is transferred to the finished surface. By controllingthe amplitude ultra-precisely at high speed, the ultra-precisionsculpturing of the difficult-to-cut materials can be achieved efficiently

Fig.10 Machining by controlling amplitude in elliptical vibration cutting

without using conventional FTS technology11). In other words, theelliptical vibration cutting technology is equipped with a FTS function
by itself. And thus, it is redundant and even disadvantageous tocombine the elliptical vibration tool with the conventional FTS, sinceboth devices have actuators and the vibration tool is too heavy to be
actuated at high frequency by the FTS.
Although amplitude control command is not completely identicalwith the envelope of the cutting edge trajectory, as shown in Fig. 10,
this difference is insignificant in practice when the slope is not steep.
The depth of cut can be controlled within half of the maximum
amplitude in the depth of cut direction, and available frequency rangeof the amplitude control is limited to that which is relatively lower
than the elliptical vibration frequency. Therefore, performance in therole as FTS strongly depends on the specifications of the vibrator.
Figure 11 shows the developed system of the high-speed amplitudecontrol of elliptical vibration at a frequency of about 36 kHz. A
2-DOF elliptical vibration tool12), which was designed to generate
arbitrary elliptical vibration, is utilized. The vibrator is actuated by

Fig.11 2-DOF vibration control system for elliptical vibration cutting

using some PZT actuators, which are sandwiched with metal
cylindrical parts, namely a bolt clamped Langevin type transducer(BLT). As the vibrator is designed to have same resonant frequencies
in second resonant mode of longitudinal vibration and fifth resonantmode of bending vibration, it can generate large longitudinal andbending vibrations simultaneously at the same ultrasonic frequency byapplying exciting voltages to the actuators. Thus, an arbitrary 2-DOF
elliptical vibration can be obtained at the diamond tool tip attached to
the vibrator by combining both resonant vibration modes with somephase shift. Longitudinal vibration direction corresponds to depth ofcut direction in the present study.
Gain of the amplifier can be controlled by external input in theFig. 12Frequency response of amplitude control

developed system, and thus the exciting voltage supplied to theactuator is changed. The amplitude is, consequently, controlled by the

The developed control system was applied to grooving experiments.

external input. As the maximum amplitude in the depth of cut

Figure 13 shows an experimental setup. The ultrasonic ellipticaldirection is 4 µmp-p, the vibration amplitude can be controlled tovibration tool is mounted on an ultra-precision planing machine,change the depth of cut within 2 µm by this system. Measured

NIC-300 (Nagase Integrex Co., Ltd.), which consists of three feedfrequency response of amplitude control is shown in Fig. 12. It istables with double hydrostatic oil guideways in XYZ axes, two rotary

possible to control the vibration amplitude with a frequency

index tables in BC axes and a five-axis control system. The vibration

bandwidth of more than 300 Hz. This frequency bandwidth istool was fed in the X-axis direction. The vibration amplitude wasrelatively narrow as compared with that of conventional FTS. It might

controlled with various wave commands such as sinusoidal, ramp andnot, however, be a crucial problem because the elliptical vibration

zigzag waves, at the same time, and then, micro textured grooves

cutting technology is available only at relatively low cutting speed.

were formed on the surface of a hardened steel workpiece. The

And this low cutting speed is also not disadvantage in sculpturing asvibration amplitude was controlled to change from 2 µmp-p to 4 µmp-p

mentioned in chapter 2.

in the commands. This corresponds to the depth of cut variation of 1

Fig.13

Experimental setup for micro/nano sculpturing tests
Fig.15 Micro/nano sculpturing system using elliptical vibration cutting

Fig.14 Microphotographs of textured grooves[Cutting conditions] Maximum depth of cut: 2.5 µm, Cutting speed: lessthan 0.2 m/min, [Tool] Material: single crystal diamond, Rake angle: 0deg, Clearance angle: 10 deg, Nose radius: 1 mm, [Workpiece] Material:
die steel (JIS: SUS420J2), Hardness: HRC53, [Vibration conditions]Vibration amplitude: 4 µmp-p (circular), Frequency: 38 kHz, Command
wave: zigzag, Command frequency: 100 Hzµm. On the other hand, the amplitude in the cutting direction is set tobe constant, 4 µmp-p.
Figures 14 shows microphotographs of a groove machined at the
cutting speed of 0.2 m/min by the single crystal diamond tool with anose radius of 1 mm. It is obviously confirmed that the groove withultra-precision micro texture can be machined successfully on thehardened steel, and mirror surface quality can be obtained. Surface
profiles of the grooves were measured, and it was also confirmed thatmeasured surface profiles roughly agreed with the command waves.
However, steep corners of zigzag grooves are rounded, and thus, thestep heights are relatively smaller than the variation range ofcommand waves of 1 µm due to less frequency response.



Fig.16 Photographs of sculptured letters (overview and close up)[Cutting conditions] Pick feed: 20 µm, Depth of cut: 20 µm, Cutting
speed: 1 m/min, Cutting fluid: oil mist, [Tool] Material: single crystal
diamond, Rake angle: 0 deg, Clearance angle: 10 deg, Nose radius: 1
mm, [Workpiece] Material: die steel (JIS: SUS420J2), Hardness:
HRC53, [Vibration conditions] Vibration amplitude: 2-4 µmp-p,
Frequency: 36 kHz

In order to attain arbitrary sculpturing, an ultra-precision

or by using an external optical sensor. In every cutting feed, an X-axis

micro/nano sculpturing system was developed by using the developed

coordinate is detected after the feed speed becomes constant but

vibration control system and the ultra-precision planing machine.

before the cutting starts. The dynamic command signal for vibration

Figure 15 shows the developed sculpturing system, where the planing

amplitude control is subsequently input to the elliptical vibration

machine is simply controlled to machine a plane surface at constantcontrol system based on the detected X-axis coordinate, the cutting

cutting speed. The ultrasonic elliptical vibration tool is attached on the

speed, and the amplitude command table, which is calculated from

Z-axis table of the machine tool. The vibration amplitude in the depth

CAD data of objects. Thus, the amplitude is controlled to change theof cut direction along the Z-axis is controlled in synchronization withdepth of cut in accordance with the CAD data in real time.

cutting feed motion in the X-axis, and then, arbitrary micro/nanoConsequently, sophisticated structures can be machined on the steel

sculpturing can be attained on a flat top surface of a steel workpiece.

materials efficiently by merely combining simple planing operations

The X-axis coordinate value is constantly monitored in theat constant cutting speed with high-speed depth of cut control. An

developed system by directly communicating with NC control system

industrial computer is utilized to detect the X-axis coordinate and togenerate the voltage signal for controlling vibration amplitude.
The developed machining system was applied to sculpturingexperiments of picture images. CAD data for sculpturing were
produced from letter image. As the vibration amplitude was changed
within a range from 2 µmp-p to 4 µmp-p, the depth of cut was changed
within 1 µm. Hardened steel workpieces (64x48 mm) were machinedwith a diamond tool, whose nose radius is 1 mm. The size of original
images is set to 3200x2400 pixels, and thus, 1 pixel corresponds to20x20 µm. Figure 16 shows photographs of letters sculptured on thehardened steel. The whole surface is machined in about 260 minuteswith the developed sculpturing system. All letters were machined tobe concave with a depth of 1 µm. As shown in the figure, the letters
are sculptured successfully. It was confirmed that the measured stepheight of sculptured letters agreed with the desired depth of 1 µm.
Any unusual tool damages were not observed after the experiment.
Nano sculpturing experiments involving various dimple patterns
were also carried out with the developed sculpturing system.
Sinusoidal commands to control the vibration amplitude were input tothe elliptical vibration control system during machining, and the phaseof the sinusoidal commands was changed by 180 deg in every cutting
feed, so that precisely aligned patterns were sculptured. Figure 17
shows a microphotograph and a profile of sculptured dimples. The
hexagonal dimple patterns, whose borders are sharp, can be observed.
It was also confirmed that the measured dimple depth of 0.78 µm
corresponds well with an expected dimple depth of 0.75 µm, which is
calculated theoretically from the vibration conditions, the cutting
conditions and the tool geometry. The experimental results show thata variety of dimple patterns are obtained directly on the steel materials
by using the developed sculpturing system.
4. Conclusion

Fig.17 Microphotograph and measured profile of dimples[Cutting conditions] Pick feed: 34 µm, Maximum depth of cut: 10 µm,
Cutting speed: 0.8 m/min, Cutting fluid: oil mist, [Tool] Material: single
crystal diamond, Rake angle: 0 deg, Clearance angle: 10 deg, Noseradius: 1 mm, [Workpiece] Material: die steel (JIS: SUS420J2),
Hardness: HRC53, [Vibration conditions] Vibration amplitude: about 2-4µmp-p, Frequency: 36.7 kHz, Command wave: sinusoidal, Command
frequency: 100 Hz

Novel micro- and macro-scale sculpturing methods by applying
elliptical vibration cutting were presented. They are not only

6)

applicable to mirror surface sculpturing of steel materials but also
high-performance in cutting efficiency. Practical machining systems

cutting, Annals of the CIRP, 44/1: 31-34.
7)including sophisticated ultrasonic vibration system were developed.
surfacesculpturing

of

molds

and

micro/nano-scale

E. Shamoto, T. Moriwaki, 1999, Ultaprecision diamond cuttingof hardened steel by applying elliptical vibration cutting, Annals

Experimental investigations indicated that practical macro-scalemirror

T. Moriwaki, E. Shamoto, 1995, Ultrasonic elliptical vibrationof the CIRP, 48/1: 441-444.
8)

E. Shamoto, N. Suzuki, E. Tsuchiya, Y. Hori, H. Inagaki, K.

ultraprecision sculpturing on plane surfaces can be attained. And thus,

Yoshino, 2005, Development of 3 DOF ultrasonic vibration tool

feasibility of proposed sculpturing was verified. Now, morefor elliptical vibration cutting of sculptured surfaces, Annals ofchallenging machining method combining both scale sculpturing isunder investigation.

the CIRP, 54/1: 321-324.
9)

N. Suzuki, R. Hino, E. Shamoto, 2007, Development of 3 DOF

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