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Multi-Disciplinary Senior Design Conference
Kate Gleason College of Engineering
Rochester Institute of Technology
Rochester, New York 14623
Project Number: P10531
DETERMINING DEVELOPER TRIBO-ELECTRIC
CHARGE AND CONCENTRATION USING PIEZO
VIBRATIONS AND ELECTROSTATICS
Dean Culver (Project Manager)
Vijay Francis
(Computer Engineer)
Elizabeth Cormier
(Industrial Engineer)
Gerald Garavuso (Faculty Guide)
Thomas Siegwarth (Lead Engineer)
Thomas Bundy
(Electrical Engineer)
William Wayman (Sponsor: Xerox)
ABSTRACT
In this paper, a method of calculating the charge to mass ratio and toner concentration of developer using a
piezoelectric beam is described. This process will be run through LabVIEW computer program. The results are
analyzed to fit 20% accuracy in a 95% confidence interval. RESULTS!!!!!!!11111
Copyright © 2010 Rochester Institute of Technology
Proceedings of the Multi-Disciplinary Senior Design Conference
NOMENCLATURE
Piezo-electric: (see “Piezo-electrics” in the
Introduction section)
Tribo: quantified static charge accumulated by a
sample.
Toner Concentration (TC): the ratio of mass of toner
to mass of carrier in a given sample.
Charge to Mass Ratio: the ratio of tribo to toner mass
in a given sample.
Developer: (see “Developer Characteristics” in the
Introduction section)
95% CI: a statistical term stating that there is 95%
surety that data will fall within a confidence band.
Amplitude: the magnitude of change in the dependent
variable of an oscillator
Natural Frequency: the frequency at which a subject
resonates.
Phase (or Phase Difference): translation of the
argument in an oscillator resulting in delay or
anticipation in the behavior of the oscillator.
Transfer Function: a function describing the
relationship from inputs to outputs.
Feedback: influences on a signal from the environment
responding to said signal
Loading Profile: a term used for how forces and
moments are distributed across a beam in beam theory
or analysis.
Sum of Squares Method: a parameter optimization
method taking known data and data from an inferred
empirical equation, finding the variance between said
data sets, summing these variances, and minimizing
this sum with respect to the coefficients of the
empirical equation.
Variance: square of the difference between two sets of
data.
INTRODUCTION (OR BACKGROUND)
The purpose of P10531 is to prove the validity and
accuracy of the functionality of the piezo-electric tribo
sensing device. The customer, William Wayman of
Xerox Corporation, developed a process for
determining toner concentration and the charge to
mass ratio in a given sample of developer [1]. The
primary customer objectives are to determine these
parameters using the outlined method within 20%
accuracy at a 95% confidence interval.
Other
customer needs include a detailed SOP for the
resulting prototype, the ability to run sixty tests in an
hour, and reliability. These needs, translated into
engineering metrics, are scoped to be achieved in a
twenty-two week timetable. The below subsections
outline the findings of this twenty-two week project.
Developer Characteristics
Page 2
Developer is made up of two main components, a
toner and a carrier. The toner is used to form the
printed image or text on paper. The toner is made up
of tiny plastic particles that become statically charged
due to the carrier. The carrier is made of metal in this
case [2]. Toner will retain its charge for a period of
time, while the carrier will remain charge neutral, thus
allowing the toner to stick to the charged paper and the
carrier will just fall off. The carrier is about 10 times
as large as the toner particles, which are in the 10s of
microns range [3].
Piezo-electrics
Piezo-electric material, at the very basic level, is a
material that shrinks or attenuates when a voltage is
applied across a sample’s geometry.
This
phenomenon is also reversible; piezo-electrics can be
bent, stretched, or compressed resulting in a potential
across the geometry. Normally crystalline, these
materials can be man-made or, in some rare cases,
found in nature [4]. Piezo-electrics are used in a wide
range of applications, from printing to sensing.
Creative geometries and creative applications have
brought piezo-electrics into the spotlight in microscale systems.
In the context of this project, the piezo-electric is a
sensor. Three piezo beams are layered such that when
one voltage is applied to the surface, one layer
attenuates and one shrinks, forcing the overall beam to
bend rather than extend or shrink. The third and final
piece of the sensor is a follower, sending a signal back
out that is representative of the flexion of the sensor.
Electrostatics & Magnetics
Electrostatics describes the distribution and influence
of electric charges. A particle having a certain charge
will create an electric field surrounding it [5]. The
polarity of the charge determines which way the field
will point. An electric field can also be created by
applying a differential voltage to conductive materials
that are separated by a dielectric element such as
air [5]. If a charged particle is close enough to the
electric field created by the conductive materials it will
tend to be attracted to one of the materials, depending
on the polarity of the charge.
Magnetostatics describe the distribution and influence
of magnetic poles. Magnetic fields operate very
similarly to electric fields with the exception that
magnetic fields are created by magnetic poles. If a
ferromagnetic substance such as iron is moved into the
magnetic field created by a permanent magnet then
magnetic poles will develop within the substance. The
poles in the ferromagnetic substance will be created
such that they oppose the field that created them [6].
This will cause the substance to be attracted to the
permanent magnet.
Project P10531
Vibration
Piezo-Electric Vibration Model
Vibration describes the behavior of systems of
molecules that bounce off of each other due to a
stimulus. Vibration typically can occur as a result of
impact or, after some developments in electrical
systems, a result of alternating signals. All motion, in
reality, causes vibration. Vibrating materials can be
described mathematically through periodic motion and
damping. Frequency, period, amplitude, damping
ratio, natural frequency, and resonance are all terms
that one associates with vibration.
The property of a vibrating beam that this device takes
advantage of is the dependence of the natural
frequency of a beam on the beam’s moment of inertia
and applied load. The device sweeps through an array
of forced frequencies and determines when resonance
occurs. This is relatively easy to detect as the
amplitude and phase of a signal change drastically
very close to the natural frequency [7].
Analytical analysis of the piezo-electric sensor beam
results in a correlation between the natural frequency
of its vibration and the mass of the applied sample.
The analysis begins with an understanding of the
loading profile. Distributing the weight of the beam
itself evenly over the beam and applying two
semi-circular loads between L/2 and 5L/6 can model a
typical performing scenario. The resulting equation,
including a parameter k describing the conversion
from length to load is
q
mB g
4
5
L   5L


 2k
Lx  L2  x 2 u  x   u   x 
L
3
12
2  6


(1)
This loading profile can be illustrated as in Fig. 1.
Current Testing Schemes
Testing for the Piezo-Electric Toner Concentration and
Tribo Charge Sensor was completed utilizing a series
of software and hardware based experiments [1]. Each
subcomponent of the assembly was initially tested
separately utilizing hardware connections to ensure
their functionality. Once successfully tested, the
subcomponents were interfaced with the DAQ card to
test their functionality when driven by the LabVIEW
software program [1]. This determined whether or not
the software was capable of driving each component
within the assembly, and whether or not the
component functioned correctly under these
circumstances. The entire assembly was then
combined to undergo integration testing.
Integration testing consisted of connecting the entire
assembly together and interfacing the assembly with
the DAQ card. Experiments were then run to ensure
that the LabVIEW program would accurately drive
each component in the correct operation order for the
desired period of time. The LabVIEW program was
then optimized to meet this goal and to provide results
within the given specifications.
PROCESS (OR METHODOLOGY)
Assumptions
Consistent density within sample containers
Uniform and circular sample distribution
No transfer function from the frequency of the beam to
the frequency of the output signal
No mechanical vibration feedback from the device or
environment
Figure 1: Piezo Beam Loading
Recalling that the beam loading can be related to the
deflection through a fourth-order differential equation
EI
d4y
 q  x
dx 4
(2)
the deflection at the center of the load can be
described.
Modeling the beam as a spring, a
representative spring constant can be assigned to the
beam itself [8]. Using spring theory, this spring
constant as well as the deflection equation can be
coupled to determine a natural frequency. Therefore,
the natural frequency can be described in terms of the
sample mass by the following expression:
n 
g

mB g
4
5 2
L   5L

 

2
k
Lx

L

x2 u  x   u 
 x  dx 
   
L
3
12
2  6

  x2 L

3
(3)
At first glance, this expression is unmanageable.
However, recognizing that the expression will be
evaluated at a constant x after the integration, and
understanding that the sample mass does not vary in x,
an empirical formula can be derived using
n 
g
A  Bms
(4)
where B has units of distance per unit mass and A has
units of distance. This, in turn, translates to a fit for
mass as a function of natural frequency.
ms  A '
1
n2
 B'
Electric Field Considerations
(5)
Proceedings of the Multi-Disciplinary Senior Design Conference
The electric field produced by the grid is what is used
to keep the toner attached to the piezo while it is
vibrating. The electric field is produced by applying a
different voltage to each of the sides of the grid. The
electric field strength can be calculated as the negative
of the gradient of the applied voltage. This means that
as the fingers of the grid are moved closer together the
electric field intensity will increase. For this reason we
had four different flavors of grids constructed. The
differences between the grids are the width of the
fingers and the spacing between them. The grid with
the smallest spacing was thought to keep the most
toner on the piezo. Qualitatively this was tested by
gluing one of each of the grids to a piece of aluminum,
applying a voltage of 1000 volts, and then simulating
the effects of the prototype to see which grid held the
most toner when developer saturated the grid. The grid
with the wider spacing and thicker fingers seemed to
hold the most because the toner was attracted to the
entire finger as opposed to just the edges as was
previously thought. The grids are planned to be
quantitatively tested by inserting them, one at a time,
into the system and observing which one yields the
highest charge from the electrometer. This will be the
grid that attracts the most toner. This will be done as
soon as repeatable results can be obtained from the
prototype.
Circuitry
The multiplier chip circuit inputs two signals, X1 and
Y1 in Equation 6, and produces an output W [9].
Page 4
The toner is captured on the grid using a high voltage,
while the grid itself appears as a capacitance. The
electrometer reads the charge left on the grid after the
toner is blown off.
The air solenoid simply allows the compressed air to
blow the toner off after a signal is sent to the solenoid
to turn it on.
Fields
Electromagnetics are used in holding the developer
and later the toner to the piezoelectric device (piezo).
They are also used in separating the carrier from the
toner. The presence of a magnetic field below the
piezo holds the carrier to the piezo while an electric
field does the same for the toner. In the separation
phase the magnetic field is decreased by lowering a
magnet while the piezo is made to vibrate, this causes
the carrier beads to bounce off as they are feeling less
of the magnetic field. The toner is kept on the piezo
because the electric field is not changed at all during
this time.
Concept Selection
The team reviewed many concepts for possible
redesign on the final product. Specifically these
included: the sample placement device and the carrier
removal device. For the sample placement device
several designs were mocked up for even dispersal of
developer, including one model which has a spiral
groove design:
(6)
In the equation, X2, Y2, and Z were connected to 0 V.
The inputs are a square wave coming from a counter
on the DAQ card meant to have a well controlled
frequency, and a sine wave coming from one of the
analog outputs of the DAQ card which has accurate
amplitude.
The motor was connected to have one relay turn on the
motor to go down and another relay to turn the motor
on to go up. There is a switch in series with the motor
going up that turns it off after it reaches specified point
to prevent the magnet and screw from going through
the piezoelectric device. The relays turn on by the use
of a Power FET used as a switch.
(7)
Equation 7 is used to find the magnetic field, where
F is the Lorentz force, q is electric charge, v is
velocity, and B is the magnetic field. The magnet
needs to have a velocity in order to produce a
magnetic force. By rotating the magnet, it changes the
direction and creates a velocity. The motor was chosen
to create the velocity so that it could be automated as
well as constant over trials.
The Allflex grid attached to the piezoelectric device
measures charge by using Equation 8.
(8)
Figure 2: Spiral Groove Placement Device
After the System level design review and speaking
with the customer the team chose to go with a more
standard spoon placement technique which had been
the method utilized in the patent testing. This was
chosen in collaboration with both the client and the
team due to its proved reliability and its simplicity of
construction.
For the carrier removal device the team was involved
in several brain-storming sessions for ideas. In the end
basic concepts were combined to create five final
prototype options. Initially, a Pugh concept selection
matrix was utilized [10]. However, after final scoring
it was determined by the team that it was much harder
to differentiate the best prototypes. Therefore, the
team added weights to each of the criteria. Two final
Project P10531
prototypes were selected for presentation during the
design review (the magnet and the solenoid).
Figure 3: PUGH Concept Selection Matrix
During the final design review it was determined that
the amount of effort and development necessary to
accurately achieve the solenoid concept was well
beyond the scope of the project. Therefore, the magnet
concept was pursued as the team’s solution for carrier
removal during the development phase.
Experimentation
The team collected the results of both TC and Tribo
off of thirty samples of each sample type (high,
medium, low). Thirty samples were collected in order
to assure a full range of values and significant enough
results. The team used a student t-test to compare the
sample mean and deviation to the perceived value of
the sample since a comparison of means was tested
and the standard deviation of the actual population was
unknown.
Empirical Fitting
The empirical methods used for the vibration model
are relatively straightforward. The sum of squares
method for curve-fitting is implemented. Taking test
data relating sample mass to the resulting natural
frequency recorded by the device, parameters A and B
can be optimized, from Equation 4.
LabVIEW
The team looked at the code which had been
previously developed for this model. While some of
the pre-existing code was function in its current state
some of the processes required them to be rewritten.
The software that was designed to run the piezoelectric sensor device was written with LabVIEW.
LabVIEW was chosen because it provides the ability
to connect to a data acquisition card that can output
user controlled signals and accept input signals from
any device. LabVIEW can then interpret these given
signals and perform the desired analysis, accepting
user input along the process [11].
The customer, William Wayman, originally created
the program itself during the initial construction and
experimentation of the prototype. This pre-existing
program was utilized as a basis for the new device,
and was optimized to meet the new given
specifications. Incorporating new mathematical
models, which were theoretically derived and then
reinforced by physical experimentation, allowed for
optimization of the program.
The optimization of the program began with altering
the initial resonance frequency detection algorithm.
The original program contained an algorithm that did
not provide accurate results within a reasonable time
interval as determined by the given specifications.
Thus, this algorithm required a complete overhaul.
This was accomplished by utilizing mathematical
equations and piezoelectric beam vibration models to
formulate a new algorithm. The new algorithm still
relies on the same basis of using signal phase to detect
resonance, but performs the task in a more efficient
manner.
The next step in optimization of the program occurred
during the mass calculation and calibration. The
program was altered to utilize a new mathematical
equation for mass calculation based on resonance
frequency. This mathematical equation, Equation 5,
was derived from beam analysis and vibration
modeling. These equations provided a more precise
measurement of mass of each sample.
The last step in the program optimization involved
restructuring the graphical user interface. The user
interface was altered based on human factors analysis
to improve the user experience of the program. This
involved grouping together input parameters and
output parameters, as well as providing status
indicators and a hidden advanced section.
This process of optimization resulted in a LabVIEW
program that provided an easy to operate testing
procedure. The LabVIEW program was altered to
provide more accurate results within a timely fashion.
The team also looked at developing the user
interface (UI) to help increase ease of use. Rather than
taking multiple design objectives into account the
team focused mainly on clarity and human factors.
The team increased the size of manual buttons (Start
and Stop) to create a larger clickable surface as well as
making them easier to locate. The overall interface
was categorized into areas and advanced features a
normal operator would need to interface with were
hidden behind an advanced panel. Multiple visual cues
were added to the interface including progress lights
(for
easy
troubleshooting)
and
graphical
representations of the data.
Proceedings of the Multi-Disciplinary Senior Design Conference
Page 6
RESULTS AND DISCUSSION
This section should describe your final product or
process, whether it met specs (results of testing), and
how you evaluated its success. Most conference
papers include enough information for your work to be
reproducible.
Figure 4: LabVIEW User Interface
Device Performance
Description of the Final Device
The final version of the prototype uses a 24 V motor
donated by the customer. Attached to the motor is a
power screw, threaded through the baseplate directly
below the sensor (as shown below), which moves the
motor up and down. This, in turn, moves the magnet
that is attached to the top of the power screw towards
or away from the sample.
The following flowchart and functional diagram
describes the high-level performance of the device.
Figure 6: Device Architecture and Functional
Flowchart
Figure 5: Baseplate, Motor, and Sensor Assembly
The geometry of the magnet is a cube that is placed
such that the fields are oriented in the horizontal
direction. The piezoelectric device (above the
baseplate) is supplied from Xerox and is a standard
part used in some of their products. It is modified
slightly to suit the purposes of this project, the
modification mostly being the removal of a circuit
inside the housing. Attached to the piezoelectric
material by Krazy Glue is an Allflex, Inc grid with
spacing 400 micron fingers with 200 micron spacing.
A multiplier chip, as well as the two relays that turn
the motor on to go up or down, are built on a
protoboard that is separate from the rest of the device.
The chip and relays are connected to the device with
the use of wires. Two power FETS are used as
switches to turn on the relays and have the motor go
either up or down. The kill switch is mounted to the
bottom of the prototype and set up in a fashion so that
as the motor moves up it eventually hits the switch and
creates an open circuit, thus stopping the motor.
In order to perform accurately, the piezoelectric sensor
requires significant calibration. Factors that affect the
natural frequency include the amount of adhesive used
to mount the circuit board and the pressure on the
mounting structure of the piezo unit itself. Once these
parameters are fixed, a thirty test calibration for the
mass calculation (magnetic forces present and
magnetic forces absent) must be performed. These
tests must be run for both the magnet present and
magnet absent because initially, the sample mass is
measured with gravity and a magnetic force
influencing it. Later, the sample mass is measured
without the presence of an applied external force.
Results of these calibrations are shown below.
Project P10531
Mass Testing Without Magnetic Influence
m = A / w^2 + B : A = 9.61e5 B = -0.16785
Statistical Analysis of the Results
Liz
0.018
0.016
0.014
Discussion
Dean – Team
Mass (g)
0.012
0.01
0.008
CONCLUSIONS AND RECOMMENDATIONS
0.006
0.004
Precision Balance Mass (g)
0.002
Calculated Mass (g)
0
2305
2310
2315
2320
2325
2330
2335
2340
Natural Frequency (Hz)
Figure 7: Mass Calculation No Magnet
Mass Testing With Magnetic Influence
m = A' / w^2 + B' : A' = 5.735e5 B' = -9.770e-2
Review of Risk Assessment (Comment on what
actually occurred)
Liz, Dean
Overview of Continuation Package
Team
Comment on Final Results
Team
0.018
0.016
0.014
0.012
Mass (g)
This section should include a critical evaluation of
project successes and failures, and what you would do
differently if you could repeat the project. It’s also
important to provide recommendations for future
work.
0.01
0.008
0.006
0.004
Precision Balance Mass (g)
0.002
ACKNOWLEDGMENTS
Calculated Mass (g)
0
2265
2270
2275
2280
2285
2290
2295
Natural Frequency (Hz)
Figure 8: Mass Calculation Magnet
After calibrating the individual mass calculations, a
correction for lost toner and remaining carrier must be
included. Understanding that if the sample mass goes
to zero, no sample can then be lost. Therefore, the fit
equation must go to zero as the argument goes to zero.
Although a direct proportion could do, the following
equation returned more accurate results


k  A e Bmt  1
(9)
As such, the correction factor itself can be applied to
the mass readings and fit to data correlating to samples
with known TC values. The following equation then
experimentally calculates the sample TC
TC 
mt  k
md   mt  k 
(10)
REFERENCES
The following plot shows the performed fit.
EmpiricalFit for TC Correction
k = A (exp(B*m_t) - 1): A = .9727 B=.9726
k (g) [Correction Factor Such
That TC = (m_t - k)/(m_c+k) ]
1.20E-02
1.05E-02
9.00E-03
Observed Correction Factor
Empirical Correction Factor
7.50E-03
8.00E-03
9.00E-03
1.00E-02
The team would like to acknowledge and thank a few
key supporters in the research efforts. The team would
like to thank RIT for their facilitative, monetary and
logistics support. Within RIT the team would like to
acknowledge the following faculty and staff members
for their contributions to the project’s success as well.
These individuals include, Dr. Crassidis, Dave
Hathaway, Ken Snyder, Rick Tolleson, Dr.
Venkataraman, and John Wellin. The team would also
like to acknowledge Xerox Corporation for their
monetary support. The team would like to recognize
Bill Wayman, the project’s client, for all his support,
expertise, and the use of his prototype. The team
would like to thank Bill Nowak for his insight and
support. Lastly, Gerry Garavuso, the team’s guide,
should be recognized for his support and facilitation of
the team throughout the duration of this project.
1.10E-02
Toner Mass (g)
Figure 9:Losses and Inefficiencies Factor
1.20E-02
[1] W. Wayman, “Systems and Methods for
Determining a Charge-to-Mass Ratio, and a
Concentration, of One Component of a Mixture,”
United States of America, US20080152367, June 6,
2008.
[2] “Facts About the Safety of Xerox Products,”
Xerox, http://www.xerox.com/downloads/usa/en/e/ehs
_safetyfacts.pdf.
[3] D. Hays. “Electrical Properties of Conductive
Two-Component Xerographic Developer,” IEEE
Trans on Industry Applications, Vol. 1A-23, No. 6
pp. 970-974, November 1987.
Proceedings of the Multi-Disciplinary Senior Design Conference
[4] V. Lemanov, V., Bauer, S. Bauer-Gorgonea, S.
Lindner, M. & Schrattbauer, K., “Piezo, Pyro, and
Ferroelectricity in Biological Materials,” “Piezo, Pyro,
and Ferroelectric Materials,” Piezo Electric Material:
Advances in Science, Technology, and Applications,
Kluwer Academic Publishers, Dordrechet, the
Netherlands, pp. 1-20, 2000.
[5] D. Halliday, R. Resnick, J. Walker, Fundamentals
of Physics, Part 3, John Wiley & Sons.
[6] D. Cheng, Field and Wave Electromagnetics,
Second Edition, Prentice Hall, 2007.
[7] W. J. Palm, System Dynamics, McGraw Hill, New
York, NY, pp.563-577, ch.9, 2005.
Page 8
[8] R. G. Budynas, J.K. Nisbett, Shigley’s Mechanical
EngineeringDesign, 8th ed. McGraw Hill, New York,
Ny, pp. 142-145, ch. 4, 2008.
[9] “Low Cost Analog Multiplier Chip,” Analog
Devices, AD633ANZ, 2010.
[10] K. Otto, K. Wood, “A Basic Method: Pugh
Concept Selection.” Product Design: Techniques in
Reverse Engineering and New Product Development.
Prentice Hall, Upper Saddle River, NJ, pp. 493-497,
2001.
[11] National Instruments, 2009, National Instruments
LabVIEW
Campus
Workshop,
National
Instruments, pp.
28-30.
Project P10531