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The LEGO Masy Joule Balance

Authors:
  • Metrology ERP/ ETS Technology Services - Allergan Global Pharmaceutical Technologies

Abstract and Figures

The Masy Joule Balance:
A new look at NIST’s LEGO Watt Balance
Cesar (Jun) Bautista Ph.D., Jared Zhao, William Faulkner
September 17, 2016
Abstract
Many units of measure have previously been defined in terms of physical artifacts. These
physical artifacts are the only references defined with zero uncertainty. In mass metrology, the
International Prototype Kilogram (IPK) has been used to define the kilogram since 1879. However, with
the passing of time and the effects of the environment in which it is stored, it has been discovered that the
IPK has been losing and gaining mass. Since this discovery, a global effort has been made to redefine the
International System of Units (SI) kilogram. In the redefined system, the kilogram will be defined as a
fixed value of the Planck constant h.
I. INTRODUCTION
Many units of measure have previously been
defined using physical artifacts, which are the only
references defined to have zero uncertainty.
However, due to the passing of time and the effects
of the environment in which the artifact is stored, it
is impossible to guarantee that the artifact remains
in its original condition. In mass metrology, the
International Prototype Kilogram (IPK) has been
used to define the kilogram since 1879. However, it
has been discovered that the IPK’s mass has been
changing. Since this discovery, a global effort has
been made to redefine the International System of
Units (SI) kilogram. In the redefined system, the
kilogram will be defined as a fixed value of the
Planck constant h.
To accomplish this relationship between mass
and the Planck constant h, the gravitational force of
an object will be balanced with the electromagnetic
force generated by a current-carrying solenoid using
the Watt Balance, thus providing the relationship
between mass and electrical constants.
Our Masy Joule Balance, on the other hand,
equates the energy dissipated by the current-
carrying solenoid and the change in the gravitational
potential energy of the mass, and was developed at
Masy BioServices’ Mass Calibration Laboratory,
hence the name, “Masy Joule Balance”. Like the
NIST Watt Balance, the Masy Joule Balance finds
the relationship between mass and electrical values
by balancing the different forces acting on each side
of the balance arm, but differs in its calculations and
implementations. On the surface, both arms seem
very similar, but when we examine the calculations
used to explain our implementation, we will quickly
see the differences.
FIG. 1. Picture of completed Masy Joule Balance. The electronics are
hidden on the underside of the base.
Like NIST, we were able to build our balance
using LEGO for under $650. The parts required for
our balance are very similar to those of NISTs
LEGO Watt Balance and the differences are noted
throughout this journal. We encourage others to
improve upon our design and increase its sensitivity
and functionality, or even design a balance entirely
different, like what we have done with NISTs
LEGO Watt Balance.
II. BALANCE THEORY
As the name implies, the LEGO Masy Joule
Balance balances the different energies. The change
in gravitational potential energy of the mass being
measured is balanced against the energy consumed
by the current-carrying solenoid.
!"#$% & '()*++
(1)
Energy is the integral of two different forces
acting on the opposite ends of the balance arm from
0, the “down” position of the Masy Joule balance,
to D, the “balanced” position of the Masy Joule
balance, with respect to distance. The energy
dissipated by the current-carrying solenoid is the
integral of the Lorentz force it produces and the
change in gravitational energy experienced by the
mass is the integral of the gravitational force it
experiences.
,-./01/
2
3
& ,
4
2
3
./01/
(2)
The magnetic force of the current-carrying
solenoid and the gravitational force experienced by
the mass are substituted in, and the constants are
brought out of the integral.
5$6789: ;./01/
2
3
&<= 1/
2
3
(3)
The issue with Eqs. (3) is that it is very difficult
to accurately determine the integral of the magnetic
field as a function of distance with respect to
distance. To solve this, we will introduce the
equation that describes the voltage induced in a wire
of length L when it is moved through a magnetic
field B at a constant velocity in a separate mode of
operation that we will call “charge mode”.
>
$6?8"@?.A0 & ;./0: 1/
1A
(4)
By rearranging Eqs. (4) and taking the integral
of both sides, we get Eqs. (5).
>
$6?8"@? A1A
B
3
& : ; / 1/
2
3
(5)
By substituting Eqs. (4) into Eqs. (3), we can
eliminate the magnetic field from our equation.
5$6789 >
$6?8"@? A1A &<= 1/
2
3
B
3
(6)
Now, although our equation no longer contains
the integral of the magnetic field, we now must find
the integral of the induced voltage. We can do this
by substituting current in using Ohm’s Law.
Voltage as a function of time is related to current as
a function of time with constant resistance through
Ohm’s Law.
>.A0 & 5.A0C
(7)
Then by substituting Eqs. (7) into Eqs. (6), we
get Eqs. (8).
5$6789C 5$6?8"@? A & <= 1/
2
3
B
3
(8)
Then, by completing the integrals on both sides
of Eqs. (8), we get Eqs. (9).
5$6789CD$6?8"@? &<=E
(9)
Where D$6?8"@? is the total charge that
accumulates from the current passing through the
current-carrying solenoid during “charge mode”.
Finally, by using Ohm’s law from Eqs. (7)
again, we can substitute for the input current and
reduce the equation even further
>
$6789D$6?8"@? &<=E
(10)
Now we have completed the Masy Joule
Balance equation. However, there are still issues in
measuring these variables found in the equation
accurately.
>
$6789, E, and = can all be measured direcly,
and < is what we are looking for. What remains is
an accurate method to measure the total charge Q
that passes through the current-carrying solenoid
during “charge mode”. We can do this with
Riemann Sum approximations. By taking the ratio
of the difference between the D"*%"8%*9@? and the
D*77F#G and the D"*%"8%*9@? , we can determine the
number of samples we need to take for a given time
to obtain the total accumulated charge D$6?8"@?
with acceptable accuracy.
H I
5 A 1A JK
L5.A$0
6
$M3
B
3
5 A 1A
B
3
NOPPQ
(11)
Where L is the number of samples required for
this desired % accuracy H, A$ is the time at which the
current is being measured, and K is the total time of
the experiment. For our purposes, we will be setting
our desired % accuracy H to 1%.
The issue with Eqs. (11) is that we are not able
to take the integral or Riemann Sum of the unknown
function 5.A0. We must find a way of representing it
as a function of time A, so we can numerically
determine L.
Again, Ohm’s Law from Eqs. (7) is used to to
replace the current 5.A0 in the equation to voltage
>.A0 to enable further substitution and eventual
calculations.
H I
O
C> A 1A JO
C
K
L>.A$0
6
$M3
B
3
O
C> A 1A
B
3
NOPPQ
(12)
Now we must observe the relationship between
the voltage induced >.A0 and time A in order to
complete our integration and Riemann Sums.
By observing the relationship between the
induced voltage and the magnetic field from Eqs.
(4), we can conclude that voltage >.A0 is
proportional to the magnetic field ;./0.
> A RSR;./0
(13)
And the magnetic field B decays according to
the Inverse Cube Law, since the magnet is a dipole
source.
; / RSR O
/T
(14)
And because the current-carrying solenoid is
moved at a constant velocity during “charge mode”,
we can use the relationship between velocity, time,
and distance.
/ & UA
(15)
We finally get our relationship between desired
% accuracy H, the total time of the experiment K,
and the number of samples required L in Eqs. (16).
H I O
C
O
AT1A
B
3JK
L
O
/$T
6
$M3
O
AT1A
B
3
NOPPQ
(16)
Thus, we are able to take the integral and
Riemann Sums and determine the number of
samples L that we need over an experiment time K
for our desired % accuracy H. From Eqs. (16) and
the Masy Joule Balance equation from Eqs. (10), we
can effectively find the relationship between our
measured mass and a voltage supplied to the
current-carrying solenoid.
III. BALANCE MECHANICS
Because the Masy Joule Balance is made of
LEGO bricks, it is much more easily influenced by
imperfections. Thus, we decided to adjust our Masy
Joule Balance equation and absorb all constants into
a single constant V. By doing this we can find the
linear relationship between the mass < and the
voltage U, and the slope of the trendline of our
dataset would be that constant V.
The Masy Joule Balance was initially modeled
after NIST’s LEGO Watt Balance. Thus, the Masy
Joule Balance shares many features of NIST LEGO
Watt Balance. However, several changes have been
made to improve the accuracy and stability of the
device.
Firstly, we decreased the mass of the arm itself
to decrease the rotational inertia of the balance. This
allows us to measure much smaller masses with
increased resolution. Also, rather than using a
symmetrical design, the Masy Joule Balance utilizes
a single coil immersed in a radial magnetic field
while the opposite arm of the balance utilizes two
weighing pans, one on top of the other. This
decreases the possibility of magnetizing our test
weights since the distance from the neodymium
magnets to the weight pans has increased. The top
weighing pan is used to hold tare weights to balance
out the arm when measuring lower masses, while
the bottom pan holds the actual item or mass being
weighed. The use of tare weights improves the
range of masses that the balance can accurately
measure from 0-13g to 0-105g.
The coil was made using a standard 1-inch PVC
coupling with a 1.25-inch PVC cap secured on one
end. The wire was wound onto the PVC pipe using
a low-speed electric hand drill and secured with
epoxy. A counter was created using an Arduino Uno
to count the number of winding around the coil. The
coil had approximately 3000 windings of AWG-36
magnet wire, and the total resistance of the coil was
approximately 450. A pair of neodymium (N48)
ring magnets was secured to the base with a brass.
The magnets are oriented on the bolt so that they are
touching each other and are attracted to each other.
The specific orientation (North up or south up) does
not matter. Nuts were placed on either side of the
bolt securing the magnets to ensure they remain
stationary throughout our experiments.
A hole was drilled into the PVC cap and a
LEGO cross axle with two LEGO Wedge Belt
Wheels were passed through the hole. The assembly
was then bonded with hot glue. This was then
connected to another LEGO cross axle, which was
then connected to the beam using the LEGO
universal joint system.
The central pivot was a 4 by 1 technic brick
secured to the beam with a connector peg. The
technic brick was secured so that it balanced on its
edge as it sits on a smooth surface. This knife edge-
like balance point has much lateral movement due
to rotation and thus much higher precision than the
T brick used on the NIST LEGO Watt Balance. A
series of LEGO bricks were stacked on either side
of the tower to prevent the balance from moving out
of alignment.
FIG. 2. The balance rests on a knife edge created by turning a 4 by 1
technic brick on its side.
IV. BALANCE ELECTRONICS AND
DATA ACQUISITION
Similar to the NIST LEGO Watt Balance, the
Masy Joule Balance utilized a photodiode and a line
laser to determine the balance position and a
Phidgets 1002 Voltage Output to produce the
voltage supplied to the current-carrying solenoid.
However, we chose to use an Arduino Uno as our
voltage reference when reading from the photodiode
and line laser system.
The photodiode and the line laser were mounted
on opposite sides of the tower so that the arm could
swing freely between them.
FIG. 3. The line laser is projected onto the arm and the photodiode
behind.
During operation, the line laser is projected onto the
arm and a portion of the laser would shine through
to the photodiode. When the laser is half covered by
the arm and half projected onto the photodiode, the
arm is considered balanced. During operation, to
ensure the beam is in the balanced position
consistently during each run, the voltage across the
photodiode must remain constant at the balanced
voltage for a total of 20 consecutive samples
gathered at a sampling rate of 80ms.
The program provided by NIST for the LEGO
Watt Balance was not well suited for the Masy Joule
Balance due to the differences in wiring and setup.
Instead, a custom operating program was written in
Java. The program now lives on Github as an open-
source project.
FIG. 4. The program was developed in Java and is run without a GUI.
This program utilizes the feedback loop from the
laser-photodiode system to determine whether the
arm is too far left or too far right, and thus determine
whether the voltage supplied to the current-carrying
solenoid from the Phidgets 1002 Voltage Output
needs to increase or decrease.
V. MEASUREMENT
To ensure the Masy Joule Balance remains
consistent for each experiment, alignment lines are
drawn on the fulcrum and the top of the tower.
Before each experiment, the mass is placed onto the
weighing pan. When the test begins, the coil will
produce a magnetic field that pulls the coil toward
the magnets. The beam is then realigned using the
alignment dots. The entire beam is then pulled
toward the front face of the balance. This ensured
that the beam is aligned and is in the same position
for each measurement.
VI. ACKNOWLEDGMENTS
NISTs experience in building the LEGO Watt
Balance was extremely useful in the initial design
and planning of our Masy Joule Balance. Many of
the parts used in our design were chosen due to their
inclusion in NISTs LEGO Watt Balance physics
journal. Our balance was heavily influenced by
design choices made by the NIST in designing their
LEGO Watt Balance.
Assistance from Masy BioServices is gratefully
acknowledged. This project was completed as a
summer internship at Masy BioServices Mass
Calibration Laboratory, and the hospitality and help
received from Masy BioServices was a major
encouragement to this project.
VII. REFERENCES
1. B.Eng.(Hons.), Xavier Borg. "The Inverse Cube Law for Dipoles."
(2009): n. pag. Blaze Labs. Web. 18 Sept. 2016.
<http://www.blazelabs.com/inversecubelaw.pdf>.
2. Chao, L. S., S. Schlamminger, D. B. Newell, J. R. Pratt, F. Seifert,
X. Zhang, G. Sineriz, M. Liu, and D. Haddad. "A LEGO Watt
Balance: An Apparatus to Determine a Mass Based on the New SI."
Am. J. Phys. American Journal of Physics 83.11 (2015): 913-22. AIP
Publishing. Web. 13 July 2016.
3. Measure, By Default They. "Arduino - ArduinoBoardUno." Arduino
- ArduinoBoardUno. N.p., n.d. Web. 14 July 2016.
<https://www.arduino.cc/en/Main/ArduinoBoardUno>.
4. "Phidgets Inc. - 1002_0 - PhidgetAnalog 4-Output." Phidgets Inc. -
1002_0 - PhidgetAnalog 4-Output. N.p., n.d. Web. 18 Sept. 2016.
<http://www.phidgets.com/products.php?product_id=1002>.
5. Stock, M. "Watt Balance Experiments for the Determination of the
Planck Constant and the Redefinition of the Kilogram." Metrologia
50.1 (2012): n. pag. Web.
6. Scream3r. "Scream3r/java-simple-serial-connector." GitHub. N.p.,
24 Jan. 2014. Web. 18 Sept. 2016. <https://github.com/scream3r/java-
simple-serial-connector>.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
A global effort to redefine our International System of Units (SI) is underway, and the change to the new system is expected to occur in 2018. Within the newly redefined SI, the present base units will still exist but be derived from fixed numerical values of seven reference constants. In particular, the unit of mass (the kilogram) will be realized through a fixed value of the Planck constant h. A so-called watt balance, for example, can then be used to realize the kilogram unit of mass within a few parts in 108. Such a balance has been designed and constructed at the National Institute of Standards and Technology. For educational outreach and to demonstrate the principle, we have constructed a LEGO tabletop watt balance capable of measuring a gram-level masses to 1% relative uncertainty. This article presents the design, construction, and performance of the LEGO watt balance and its ability to determine h.
Article
Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision. It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10(8). The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant. In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.
Arduino -ArduinoBoardUno Arduino -ArduinoBoardUno. N.p., n.d. Web
  • By Default Measure
  • They
Measure, By Default They. "Arduino -ArduinoBoardUno." Arduino -ArduinoBoardUno. N.p., n.d. Web. 14 July 2016. <https://www.arduino.cc/en/Main/ArduinoBoardUno>.
The Inverse Cube Law for Dipoles
  • B Enghons
  • Xavier Borg
B.Eng.(Hons.), Xavier Borg. "The Inverse Cube Law for Dipoles." (2009): n. pag. Blaze Labs. Web. 18 Sept. 2016. <http://www.blazelabs.com/inversecubelaw.pdf>.
A LEGO Watt Balance: An Apparatus to Determine a Mass Based on the New SI
  • L S Chao
  • S Schlamminger
  • D B Newell
  • J R Pratt
  • F Seifert
  • X Zhang
  • G Sineriz
  • M Liu
  • D Haddad
Chao, L. S., S. Schlamminger, D. B. Newell, J. R. Pratt, F. Seifert, X. Zhang, G. Sineriz, M. Liu, and D. Haddad. "A LEGO Watt Balance: An Apparatus to Determine a Mass Based on the New SI." Am. J. Phys. American Journal of Physics 83.11 (2015): 913-22. AIP Publishing. Web. 13 July 2016.
Arduino -ArduinoBoardUno
  • Measure
Measure, By Default They. "Arduino -ArduinoBoardUno." Arduino -ArduinoBoardUno. N.p., n.d. Web. 14 July 2016. <https://www.arduino.cc/en/Main/ArduinoBoardUno>.