Design of a Nano-vibration System for Nanomanufacturing
Lauren Blake
Micro and Nano Manufacturing Lab
Dr. Murali Sundaram
Mechanical Engineering
WISE Program
August 17, 2012
Design of a Nano-vibration System for Nanomanufacturing
Lauren Blake
School of Dynamic Systems, University of Cincinnati, Cincinnati, Ohio 45221, USA
Table of Contents
Abstract ........................................................................................................................................... 1
Acknowledgements ......................................................................................................................... 1
Introduction/Background ................................................................................................................ 2
Research Methods ........................................................................................................................... 5
Results and Discussion ................................................................................................................... 6
Conclusion ...................................................................................................................................... 7
References ....................................................................................................................................... 8
Abstract
Nano machining is the modification of material features ranging from 1-1000 nanometers. One
of the ways in which to make these modifications is to vibrate a small cutting tool or the
workpiece under an Atomic Force Microscope (AFM). However, a probe on an AFM is fragile
and expensive so lessening tool wear is necessary in order to be cost-efficient. Our hypothesis is
that non-contact vibration processes can accomplish this goal and we are therefore designing a
nano vibration system that will more accurately set a constant machining gap required for the
vibration assisted nanomachining. This is done by studying the amplitude of the piezo transducer
vibrations, using a laser vibrometer, and then establishing a calibration curve that can be used to
expand the piezo until it reaches a cutting tool, and then contract the piezo back to a zero point,
so that with a known voltage the machining gap can be calculated. It was found from the
experimental calibration curve values that a transducer expands at a linear rate and that as the
workpiece mass increases on a transducer, the amplitude of the vibration exponentially decays.
Acknowledgements
This research project is supported by the National Science Foundation under Grant Nos. CMMI
1137968 and CMMI 1120382. Other contributions were Dr. Murali Sundaram, Sagil James, and
Abishek Balsamy Kamaraj. Help from the WISE Program administrator, Dr. Urmila Ghia, is also
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much appreciated. The research facilities provided by the University of Cincinnati are
acknowledged as well.
The WISE Program has positively changed my future. Through the program I have gained
experience with a male-dominated lab environment, Masters and PhD students, and a lab
research experience as a whole. I have learned how to answer my own questions because
research is not like course work in that a professor can explain every problem because all the
problems have been done before. Because of the WISE program, I have affirmed my decision to
pursue a Masters Degree in Mechanical Engineering after I get my Bachelors Degree in
Biomedical Engineering and I can therefore focus my energy for the next four years into this
goal. The lasting relationship that I will now have with my mentor Dr. Sundaram will make my
pursuit of obtaining my Masters degree entirely possible. I will also have the opportunity to
present my work at a conference and be a co-author on a published journal or conference paper.
Not only will these opportunities simply build my resume but they open doors to the professional
world in which innovation is based on sharing and presenting your findings to other scientists
and engineers. The experience that I have received with different mechanical engineering
software and machines has improved my ability to problem solve and increase the slope of my
learning curve, as learning new technologies forces one’s brain to work in more creative,
independent ways.
Introduction/Background
Nanomanufacturing is a prerequisite to unveil the full potential of nanotechnology. Efficient
nanomachining practices must be developed to save manufacturing facilities time and money.
The ability to set a nano-sized gap between a cutting tool and a workpiece, as intended in this
research, is important for lessening tool wear and preventing tool breakage while machining a
nano sized hole. It is found that vibration assisted non-contact machining in which the probe
vibrates against nanoparticles and occur at a distance from the workpiece can help to lessen tool
wear and increase tool life. Included is some background research regarding vibrating a cutting
tool, vibrating a workpiece, and nanopositioning using piezoactuators that can help set a
machining gap in order to create a distance between the tool probe and the workpiece.
Vibration of a cutting tool is a common procedure to machining nano features such as holes,
grooves, and scratches. [1]. It is done using the AFM and vibrating the cutting tool itself. This
usually occurs while the AFM is in tapping mode. However, this can take a long time, and may
often result in high tool wear because the cantilever is pushing, pulling, cutting, or indenting into
the workpiece at a less controllable rate. Some findings were that combined first and second
order sliding mode achieved robust chattering-free vibration control of AFM tip.
The force between the tip and the surface is an important factor that determines the success of
the machining process. The tip is modeled as a driving oscillator with damping and is effected by
the tip radius (which needs to be small or else it will lead to machining error and failure of the
nanomachining process). These experiments showed that a sharper tip and harder cantilever
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optimized the machining process. The larger the Young’s modulus, the smaller the machining
depth and the larger the tapping force necessary [2].
Workpiece vibration, although not very popular at this current time, is being considered by a few
lab groups, to see if it optimizes the machining process. Masazuwa and Egashira were one of the
first to research the possibilities of vibrating the workpiece instead of the tool to make a cut [3].
Their method is called microultrasonic machining (MUSM). They found improvements in
machinable hole size and the ability to machine smaller holes. The machining rates of the
materials increase when the vibration amplitude or machining load increases. This method is
similar to micro-EDM machines which allow high-precision tool rotation by a spindle
mechanism. Masazuwa succeeded in machining microholes of 20 micrometers on silicon,
however, the rotation of the tool was very eccentric and therefore the machined holes lacked
roundness, thus disallowing for the technique to be used to make smaller microholes (or
nanoholes).
Micro-EDM involving workpiece vibration has typically had better results including
improvement in machining accuracy on the micro scale. The workpiece vibration in EDM allows
for the machining of smaller-than-usual microshapes with greater material removal rate (MRR),
lessened tool wear, and less surface roughness [3, 4].
Dr. Murali Sundaram et al. (2007) performed experiments on ultrasonic assisted micro electro
discharge machining, using ultrasonic vibration to the workpiece [5]. Since this was a microEDM process, material removal was based on the thermoelectric energy that existed between the
workpiece and some kind of electrode within a dielectric fluid. Some important performance
measures in micro EDM are the material removal rate and tool wear, which help to determine the
rate of production. The work piece was ultrasonically vibrated using a piezo-electric transducer
of 40 kHz frequency and 10 micrometers maximum amplitude of vibration in the z-axis. They
used a variable transformer to vary the power input to the generator to control the amplitude.
The process parameters that are used to select the best conditions for stability were capacitance,
percent of peak power used for ultrasonic vibration, feed rate, and machining time.
In another study by Li Zhang et al., the workpiece was vibrated in the x, y, and z direction [6].
The resulting ultrasonic force from the sample is utilized to regulate the machining depth. They
have found that the cantilever begins to indent into the sample only when the frequency of the
cantilever is significantly lesser than the frequency of the probe. At low frequencies on the
sample, the cantilever follows the sample vibration. However, when the vibration frequency is
much greater than the resonant frequency of the cantilever, the cantilever cannot follow the
sample vibration due to its inertia, so the tip can enter the sample surface.
The set up for enacting vibrations on the x, y, and z axes included a high frequency circular
motion of the tip in the x-y plane added to achieve better control and to overcome the limitations
of mechanical scratching (which results in high tool wear and slow machining speed) [6]. Two
piezoelectric actuators provide the circular motion, in the horizontal and vertical directions.
There were xyz nanopositioners which served as nano-vibrators. The z-piezo and sample are on
top of a pillar, which converts x-y piezo motions into circular motion. The z-vibration amplitude
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and hole depth had a linear trend. The amplitude that was used was 110 nanometers and the
frequency used was 16,400 Hz.
Nanopositioning is very important in nanomachining because one needs to be able to machine in
the desired spot of the manufacturer using a method that is repeatable and accurate. Because
piezoelectric transducers expand at known levels with known voltages, piezo actuators can be
used to position a workpiece sample on the x, y, and z axis, using piezoelectric transducers. A
piezoelectric translator can be simplified into a basic spring/mass system, which is controlled by
a piezoelectric force. One of the control mechanisms is known as piezo-electric-mechanical
actuation, and one study utilizes a piezoelectric actuator to provide adaptive clamping forces [7].
The main findings of this specific study were that position feedback can be used to minimize
unwanted displacement of the workpiece. Force feedback control is stable but has a lower
bandwidth than position feedback control. This experiment also determined that piezoelectric
materials should be placed directly on the part, since piezoelectric materials are very stiff and the
clamper material between the part and the piezo actuator would hinder movement.
Positioning on the vertical axis is an important aspect of positioning. In an experiment at the
Hong Kong University of Science and Technology [8], high frequency signals were used in order
to achieve active control of the process. A separate piezoelectric actuator will be required to
support the workpiece in order to have small, quick control actions. To attain accurate resolution,
static and dynamic stiffness, and dynamic response, workpiece micro-positioning tables using
PZT are used as a “feed mechanism.” To improve the high speed positioning accuracy on the
vertical axis, a workpiece micro-positioning table was developed, with a piezoelectric translator
at the center, producing a displacement of up to 48 micrometers, using a pushing force of up to
1000N. Due to the effect of spring stiffness, the range of the workpiece table is brought down to
45 micrometers. The PZT (piezoelectric material) pushes the moving part into the workpiece on
the table. In their specific set up, four ball bearing guides support the moving part to provide a
rigid horizontal plane. A rigid horizontal plane is necessary to reduce deformation from the
grinding force and to reduce errors.
The previous method is for micropositioning, researchers in 2002 developed an ultra-precision
positioning system based on a dual servo loop and nonlinearity compensation [9]. Linearity
compensation was used to improve the position accuracy of the system. Experiments suggested
that the longer the motion range of the positioning system, the worse the repeatability of the
process. Hysteresis, the dependence of a system on its present and past environment, is taken into
account also in regards to PZT, as well as the creep, or the tendency for the PZT to deform
permanently under the influence of high stress such as being heated for long periods. In order to
correct the PZT’s hysteresis and nonlinearity, these researchers have utilized an Exact Model
Matching (EMM) control model as seen in figure 1 [9]. This EMM control mechanism has
improved the repeatability up to five times.
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Fig. 1. EMM Control Model
Research Methods
After much research on the theory behind piezo and the aspects, we determined the need for a
piezo transducer that was flat enough that a workpiece could lay on it. Because this would later
be applied to making nanoholes on an Atomic Force Microscope (AFM), the piezo had to be
smaller than 1.5 cm in diameter, which is the size of a hole on the AFM stage in which the
workpiece lies. A piezo disk that was 11.88 mm in diameter and .2 mm in thickness was used to
find a calibration curve. A function generator was used to apply the desired frequency, voltage,
and wave shape. The frequency we used was the resonance frequency, or 3.2 kHz, which is the
frequency in which our particular piezo transducer expands the most. The wave shape we chose
for our experiments was a sine wave because that is what fits the equations from a theoretical
model and would give us the best results.
The expansion of the piezo transducer is measured by setting the transducer on top of a board
with a small hole in it. The transducer, which is attached to lead wires connected to the function
generator, is above a machine called a laser vibrometer. The laser vibrometer can measure the
velocity of the expansion of the piezo, and send the velocity information at a point over ten
seconds to a computer which will allow us to obtain the amplitude from deriving equations.
After calculating the amplitude values from the velocity values, the amplitude values must be
graphed to obtain a line of best fit as it relates to the increasing voltage. This line of best fit can
later be used to set or find out a machining gap.
Workpiece mass was another parameter tested in this case. The same set up with the laser
vibrometer was used before, except that different known masses were added on top of the piezo
disk to study the damping effect on the piezo transducer’s vibrations. These velocity values were
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also obtained to calculate the amplitude, then plotted to view the trend of the amplitude as more
and more mass is added.
Results and Discussion
As seen in figure 2, the piezo transducer was found to expand in a linear fashion with added
voltage. A line of best fit was put through the data points to create an equation for the linear fit
which can then be used to know how much piezo expands with a change in voltage. This
calibration curve can be used to set a gap as well. For some research, a machining gap of about
100-200 nanometers is preferred to ensure less tool wear. To achieve this gap, the desired gap
size must be input into the best fit equation in order to figure out the voltage that should be input
into the piezo to maintain a desired machining gap.
Voltage vs. Piezo Expansion (Experimental)
500
450
y = 45*x + 32
Amplitude (Nanometers)
400
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
Voltage (Volts)
7
8
Fig. 2. Voltage vs. Piezo Expansion
9
10
data 1
linear
Since we will be adding a workpiece on top of the piezo transducer, it became necessary to see
how adding masses affected the amplitude of the transducer with a constant voltage and constant
frequency. On top of a mini piezo disk, we added different workpiece masses up to 20 grams.
From our experimental values which are shown in figure 3, it is evident that as workpiece mass
increases, the expansion of the piezo decreases in an exponentially decaying manner.
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Workpiece Mass vs. Piezo Expansion (Experimental)
500
450
Amplitude (Nanometers)
400
350
300
250
200
150
100
50
0
0
5
10
15
Mass (Grams)
20
25
Fig. 3. Workpiece Mass vs. Piezo Expansion
data 6
Conclusion
Using the function generator to apply voltage to the piezo, we were able to vibrate the piezo and
measure the vibrations using a laser vibrometer. Based on the linear piezo transducer expansion
trend, we were able to determine for our specific piezo how much our piezo expanded based on
the voltage applied. We were also able to determine that the amplitude exponentially decayed as
the workpiece mass on the piezo increased. This information will be used in future experiments
and a calibration curve for the piezo will need to be developed every time a change in piezo is
made. Future researchers who are using the system of controlling the gap will need to take into
consideration how a workpiece mass affects the calibration curve, but hopefully using a
theoretical model of equations that takes into consideration the mass of the workpiece will allow
for researchers to not use a different calibration curve each time they are machining on a new
workpiece.
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