U.S. Patent Nov. 30, 2021 Sheet 18 of 31 US 11,187,571 B2

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US 11,187,571 B2

15

Sensitivity of the absolute mass balance was adjusted by
shifting the center of gravity of the balance wheel. Two
threaded brass masses attached to the CMS of the balance
beam allowed to translate in X and Z provided such adjust-
ments. Sensitivity of the absolute mass balance was mea-
sured to be about 0.05 N/m (or 5 nN/rad with respect to the
wheel angle) near the weighing position, depicted by FIG.
18. The force mode controller held the position of the coil to
within 0+0.5 m.

With regard to measuring and data analysis, once align-
ment was complete, an acrylic dome was placed over the
absolute mass balance to shield the absolute mass balance
from air currents. A hole in the dome provided communi-
cation for the interferometer laser beam. A the mass of a
copper cylinder with a value of 10.164780(5) g (k=1,
calibrated by the NIST Mass and Force Group) was subject
to determination by the absolute mass balance.

Velocity mode operates with the 10 g mass disposed on.
the mass pan and the absolute mass balance balanced. The
measurement started with 14 up and 15 down velocity
sweeps with a constant velocity of 1 mm/s while sampling
the DVM every 2 power line cycles (NPLC) or 33 ms. These
parameter values were chosen based on examining the
power spectrum of velocity noise and a separate parametric
study between differing NPLC and velocity values. The
FPGA triggered the sampling of the TIA and DVM. Each
voltage measurement was bracketed by 17 position and time
readings, wherein each set was averaged to a single position
and time. The velocity during the voltage measurement was

determined by a difference of two consecutive position 3

readings divided by the sample time. From the voltage and
velocity data pairs, a quotient was calculated as BL. Each
sweep included 60 BL measurements each with a Z position
ranging from Z=+2.2 mm. For this data set, a least squares

regression was performed. FIG. 19 shows data of 29 up and 3

down sweeps superimposed on each other, wherein solid
lines show polynomial fits of the empirical data. FIG. 20
shows the average of the BL values extracted from the
polynomial fits at Z=0 for each velocity mode set over the
span of 4.5 hours. Force mode measurements occurred
between each of these points.

Afier a set of velocity mode measurements, the system
toggled to force mode, and the balance was servoed to Z=0,
wherein the maximum of the BL curve resided. A motorized
translation stage first removed the mass, and the perturbation.
due to this process was suppressed with tight control gains.
The balance then underwent a hysteresis erasing procedure
where the balance followed a decaying sinusoidal trajectory
with an initial amplitude larger than that of the perturbation
caused by the mass removal. This occurred because the pivot
points were not ideal, frictionless surfaces and had a bias
restoring force that depended on a direction and amplitude
of the excursion from mass exchanges. After the erasing
procedure, controller feedback switched to a set of gains
optimized for current noise. After some settling time, 300
current measurements were taken, once every power line
cycle. The process was repeated for a mass on measurement.
In total, a set of 9 mass on-then-off measurements were
taken per force mode set as shown in FIG. 21. The weighings
were asymmetric, i.e.:

[Magle|Moy! 4)

due to mechanical limitations of the absolute mass balance.

After conclusion of a measurement of 15 velocity mode
and 14 force mode sets, the force mode voltage measure-
ments were converted to mass via a linearly interpolated BL
value from bracketing velocity mode sets that provided 7

0

2

60

16

mass calculations per force mode set as shown in FIG. 22.
The first mass calculation was:

Mog = Mog2 (6)

= Mont

The second mass calculation was:

Mont ~ Mona 6)

Mog

and so on to remove linear time-dependent drift of the
magnetic field due to temperature fluctuations since mass on
and mass off were measured at different times. FIG. 21
shows a force mode set. A full measurement set of mass
determinations is shown in FIG. 23.

Some systematic uncertainties had relative effects at or
below 1x10, i., local acceleration of gravity, laser wave-
length and frequency, refractive index and buoyancy
changes due to environmental fluctuations, resistor and
DVM drift, and the like. Temperature, air pressure, and
humidity were monitored, and an index of refraction cor-
rection for the laser wavelength was applied. In FIG. 23,
fourteen data points are shown with statistical uncertainties
The weighted mean of the data has a relative statistical
uncertainty of 1.2x10-°. The 7? is 28 for N-1=13 degrees of
freedom. Individual uncertainties were increased by

y7/(N-1)=1.47. This led to a relative statistical uncertainty
of the mean of 1.7x10°. The data in FIG. 23 show a
non-stationary pattern. The data indicates the precision of
the particular absolute mass balance had an uncertainty of
1.7x10-* for the 10-g mass, but the difference between the
measured value and true value was 6.2x10~*

Example 2. Performance of the KIBB-g1 Tabletop
Kibble Balance

In this example, equation numbers start again at (1).

An absolute mass balance (tabletop-sized Kibble balance)
was constructed and directly realized mass at the gram-level
range with uncertainties on the order of parts in 10°. The
masses of a nominally 5-g and 1 g weight were determined
with 1-o standard uncertainties of 9.0 g and 6.7 g, respec-
tively. The corresponding relative uncertainties were 1.8x
10°° and 6.3x10°°.

OIML class E, weights, typically used for calibrating
weighing instruments, ranging from 1 g to 10 g undergo
scheduled calibrations by accredited metrology institutes
The absolute mass balance directly measured small masses
and realized the unit of mass with the same level of
uncertainties associated with a set of calibration weights.
Advantageously, operating at this level of relative uncer-
tainty relaxed demand for direct connection to quantum
electrical standards, gravimeters, and high vacuum environ-
ments.

The absolute mass balance made absolute mass measure-
ments by comparing the weight of an object to a frequently
calibrated electromagnetic force determined by electrical
quantities that involved two modes of operation, velocity
mode and force mode. Velocity mode was based on Fara-
day’s law of induction. A coil of wire length L was moved
at a vertical velocity v through a magnetic field of flux


US 11,187,571 B2

7

ment, pivot contactor 227 includes contact mount 228,
wherein ball 225 disposed on contact mount 228.

Dual diameter wheel 202 is in mechanical communication
with main mass receiver 207. In an embodiment, with
reference to FIG. 1 and FIG. 2, main mass receiver 207
includes mass pan 229 that receives object 201; and mass
pan gimbal 230 interposed between mass pan 229 and main
magnet system 212. Mass pan 229 can include a plate that
supports a weight of object 201 and can be aluminum,
copper, and the like. Exemplary mass pan 229 includes a
structural support platform for object 201 and the like.
Moreover, mass pan 229 includes a three-winged star cutout
for allowing passage of a similar shaped column for sepa-
rating object 201 from mass pan 229. It is contemplated that
absolute mass balance 200 can include an element that
receives a hanging format of object 201 so that instead of
disposed object 201 on mass pan 229, object 201 can be
hung from absolute mass balance 200 to be in mechanical
communication with main coil 208. Further, mass pan
gimbal 230 can include a free-hanging pendulum with no
restoring force. Exemplary mass pan gimbal 230 includes
two cross bars oriented orthogonal relative to each other
where each bar pivots independently about an axis provided
by two pins disposed in corresponding grooves and the like.
Moreover, mass pan gimbal 230 behaves like a free-hanging
pendulum and allows for self-centering of object 201 with
respect to the mass pan 229. In an embodiment, mass pan
gimbal 230 provides mechanical communication between
the coil 208 and the mass pan 229

Main mass receiver 207 is in mechanical communication 3

with dual diameter wheel 202 via main coil 208 of main
magnet system 212. In an embodiment, with reference to
FIG. 3, FIG. 10, and FIG. 11, main magnet system 212
includes: housing 237 in mechanical communication with

bulkhead 223. Housing 237 can include a circular sleeve 3

enclosing main coil 208 while providing the return path of
the magnetic circuit and can be made from ferromagnetic
materials such as steel. Exemplary housings 237 two iden-
tical mild steel sleeves stacked on top of one another, and the
like. A height and diameter of housing 237 independently
can be from 2 mm to 500 mm, specifically from 10 mm to
250 mm, and more specifically from 80 mm to 120 mm.
Moreover, housing 237 has a nonuniform wall thickness to
aid in steering the magnetic circuit toward the main coil 208.
In an embodiment, housing 237 is in mechanical commu-
nication with bulkhead 223. Main magnet system 212
includes coil former 235 on which first main coil 208.1 and
second main coil 208.2 are disposed and that is disposed in
housing 237 and that moves with main mass arm 205 and
main mass receiver 207. Coil former 235 can include a rigid
ring for which the main coil 208 can be wound on and can
be fabricated from nonmagnetic materials such as plastic or
ceramic. Exemplary coil formers 235 include an inverted
cup shaped mechanism with two rectangular cross section
grooves cut along the circumference for the main coil 208
made from plastic, and the like. A height and diameter of coil
former 235 can be from 2 mm to 500 mm, specifically from
10 mm to 250 mm, and more specifically from 50 mm to 90
mm. Moreover, coil former 235 contains vent holes on the
top surface for trapped air to escape during velocity mode
and threaded holes for mounting. In an embodiment, coil
former 235 includes a direct surface for holding main coil
208 and is in mechanical communication with mass pan
receiver 207 and linear shaft 219,

Main coil 208 (¢.g., 208.1, 208.2) can include conductive
wire forming one or more loops. Exemplary coils 208
include insulated circular cross section copper wire forming

S

2

40

8

over 3000 turns for both 208.1 and 208.2, and the like. A
height of main coil 208 can be from 1 mm to 50 mm,
specifically from 3 mm to 30 mm, and more specifically
from 5 mm to 15 mm. A diameter of main coil 208 can be
from 10 mm to 500 mm, specifically from 30 mm to 300
mm, and more specifically from 50 mm to 100 mm. More-
over, main coil 208 is wound from fine gauge wire to
maximize a number of turns and packing density in the
grooves provided on coil former 235. In an embodiment,
main coil 208 is in mechanical communication with coil
former 235 and electrical communication with the electrical
system 250 and electronics system 251

First yoke 236.1 is disposed in housing 237 and in
mechanical communication with housing 237, and second
yoke 236.2 is disposed in housing 237 opposing first yoke
236.1 and in mechanical communication with housing 237
and first yoke 236.1, wherein permanent magnet 209 is
disposed on and interposed between first yoke 236.1 and
second yoke 236.2. Yoke 236 (e.g., 236.1, 236.2) can include
cylinders composed of ferromagnetic material for guiding
magnetic flux. Exemplary yokes 236 include mild steel
cylinders with and extrusion to match the diameter of the
permanent magnet 209, and the like. A height of yoke 236
can be from 5 mm to 200 mm, specifically from 10 mm to
100 mm, and more specifically from 30 mm to 60 mm. A
diameter of yoke 236 can be from 5 mm to 200 mm,
specifically from 10 mm to 100 mm, and more specifically
from 40 mm to 80 mm. Moreover, yoke 236 incorporates
circular extrusion to match the diameter of permanent mag-
net 209 and three shallow ledges cut into the extrusion for
interfacing with an external device necessary for separating
the permanent magnet 209 from yokes 236. A central tapped
hole on the opposite surface allows for mounting to a
baseplate, such as a bulkhead. In an embodiment, yoke 236
is in mechanical communication with permanent magnet
209 and housing 237 while in electromagnetic communica-
tion with main coil 208. Permanent magnet 209 can include
a solid disk generating a permanent magnetic field along its
axial direction and can be rare earth materials such as
samarium cobalt or neodymium. Exemplary permanent
magnets 209 include a samarium cobalt disk with an axial
magnetization, and the like. A magnetic flux density of
permanent magnet 209 can be from 0.01 T to 3 T, specifi-
cally from 0.05 T to 2 T, and more specifically from 0.1 T
to I T. Moreover, permanent magnet 209 generates a mag-
netic field that is more temperature stable than other rare
earth permanent magnetics of similar size. In an embodi-
ment, permanent magnet 209 is in mechanical communica-
tion with yokes 236, magnetic communication with yokes
236 and housing 237, and electromagnetic communication
with main coil 208. Permanent magnet can be shimmed to
produce a selected spatial profile of magnetic flux density.
Shimming can be performed by raising yokes 236 and
permanent magnet 209 with respect to housing 237 or vice

5 versa. In an embodiment, shim 255 includes a thin, rigid disk

of a nonmagnetic material able to withstand compressive
forces. Exemplary shims 255 include aluminum washers,
hard plastic rings, and the like. In an embodiment, shim 255
is in mechanical communication with yokes 236 and hous-
ing 237.

To counter-act pendular modes of various components of
absolute mass balance 200 and to provide force mode
operation of absolute mass balance 200, absolute mass
balance 200 includes counter mass magnet system 215.

5 Counter mass magnet system 215 includes counter mass coil

231 in mechanical communication with eddy current damper
214; and counter mass magnet 232 in which counter mass


US 11,187,571 B2

25
TABLE 2-continued

Sq measurement __1 ¢ measurement

Source Item Subtotal Item —_ Subtotal
Optics Thermal Drift 00 00
Electronics Error On On
Interferometer Readout On On
Abbe Error 0.0 0.0

Off Axis Motions 00 00

Cosine Error on O41
Alignment O. O.
Timing Jitter 00 00
Wavelength Compensation 0.2 02

Velocity 0.2 0.2
Field Gradient 00 00

Material Thermal Expansion 0.4 04

Coil Z Position 04 04
Statistical 07 2
BL Interpolation 02 02

Individual BL Profile 7 07

Profile Fitting 07 07
Resistor ol ol

DVM (Force Mode) 04 04

DVM (Velocity Mode) 04 04

Electrical 0.8 0.8
Magnetic Suse. of Mass 00 00

Balance Sensitivity 0.0 0.0

Buoyancy Ou O41

Balance Mechanics 0.2 1.0

Gravity 03 03

Magnet Nonlinearity 04 04

Air Bearing Pressure 1 54

Forces on mass 12 55
Total 18 63

Analyzing the 5 g and 1 g blind measurement data yielded
the following values with their associated uncertainties
(k=1) shown in Table 3. These data were compared to mass

measurements conducted with the conventional subdivision 3

method scaling from a 1 kg artifact and shown in Table 3
Here, Am is a difference in g between two different mea-
surement types, and absolute uncertainties are added in
quadrature. Further, Am/mx10° is the same difference but
expressed in relative terms, parts in 10°. Table 4 shows a
comparison of max permissible relative uncertainties of
class E, weights with relative uncertainties for the absolute
mass balance.

TABLE 3
5 g mass 1 g mass
Conventional 5.018042. g = 05g 1.067562g = O1g
absolute mass balance 5.018042g = 90g 10675S7g = 6.7g
Am Og = 908 Sg 2 678
‘Am/m x 10° 0 = 18 5 = 63
TABLE 4
5 g mass 1 g mass
Amza/mgy x 10° 2 5
‘Amim x 10° 18 63

Various techniques were available in the voltage measure-
ment without access to a PJVS and that created greater
uncertainty. The voltage measurement uncertainties were
calculated as 4x10-®, 14x10-°, and 4x10-° for the absolute
mass balance 5 g, 1 g, and velocity mode measurements,
respectively, shown in FIG. 33.

The 14x10°° voltage uncertainty estimated from manu-
facturer specifications for the 1 g measurement was due to

20

40

45

50

3!

26

sampling near the bottom of the 1 V range. Using a 10 kQ
instead of a 1 kQ resistor to convert the weighing current
into a voltage would reduce this estimate of the 1 g force
mode voltage uncertainty term to 3x10~°. Further optimi-
zation of the magnet and coil designs can reduce voltage
measurement uncertainties to approximately 2x10~°

For well-characterized Zener references, frequently cali-
brate the DVM for a lower uncertainty. For even higher
accuracy measurements without a quantum standard, use a
fixed resistive divider connected to the Zener and use the
absolute mass balance to provide a fixed point mass deter-
mination.

The absolute mass balance directly realized gram-level
masses in air with uncertainties on the order of a few parts
in 10°, and the overall measurement uncertainties were
competitive with E, mass standards.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The
suffix “(s)” as used herein is intended to include both the
singular and the plural of the term that it modifies, thereby
including at least one of that term (e.g., the colorant(s)
includes at least one colorants). “Optional” or “optionally”
means that the subsequently described event or circumstance
can or cannot occur, and that the description includes
instances where the event occurs and instances where it does
not. As used herein, “combination” is inclusive of blends,
mixtures, alloys, reaction products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjunc-
tion “or” is used to link objects of a list or alternatives and
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances.

What is claimed is:

1. An absolute mass balance for determining an absolute
mass of an object, the absolute mass balance comprising:

a dual diameter wheel comprising:

a balance fulcrum on which the dual diameter wheel
pivots; and


U.S. Patent Nov. 30, 2021 Sheet 12 of 31 US 11,187,571 B2

218 Parallel air bearing shafts for linear
coil motion

_ Circular cross
section shaft x2
—p— 220
any es
a a
219— ey Om 219
oe
3 a Air bearing
ee YW, LA bushing x2
220—7>
208 —

FIG. 12


US 11,187,571 B2

Sheet 22 of 31

Nov. 30, 2021

U.S. Patent

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US 11,187,571 B2

17
density B so that a voltage V was induced. The induced
voltage was related to the velocity through the flux integral
BL:

V=BLy a)

Force mode was based on the Lorentz force. The gravi-
tational force on a mass m was counteracted by an upward
electromagnetic force F generated by the same coil, now
energized with a current I in the same magnetic field:

F=BLI=mg (e3)

where g is the local gravitational acceleration.

‘An expression that equates electrical and mechanical
power leading to a solution for mass was obtained by
combining equations (1) and (2):

vi
VI= mgy > m= —
@

Since the absolute mass balance provides relative uncertain-
ties on the order of a few parts in 10°, the Planck constant
makes an appearance for absolutely calibrating the voltmeter
and resistance standard used for electrical measurements.
The absolute mass balance was 57 cm tall and fits on a 30
cm diameter circular optical breadboard and included a main
mass side (MMS) that included features for velocity and
force mode and a counter mass side (CMS) that included a
driving motor for velocity mode. With reference to FIG. 1

and FIG, 24, starting from the top of the absolute mass 3

balance, a dual-diameter truncated wheel pivots about a
precision ground, tungsten carbide knife edge resting on a
diamond-like carbon coated tungsten carbide surface. The
truncated wheel behaves as a pulley. The motion of the

hanging coils along the Z-axis is constrained by rotation of 3

the wheel about the Y-axis. The MMS beam arc has a
smooth, curved surface with a radius 1.4 times that of the
CMS arc. Both arcs are centered on the pivot axis. The
radius mismatch allows for increased space on the MMS
without increasing the form factor of the entire apparatus.

‘The hanging MMS and CMS assemblies are connected to
the wheel via annealed, titanium fibers. The MMS suspen-
sion included an air bearing shaft, mass pan gimbal for
holding the test mass, and two coils with 3253 turns each and
mean diameter of 73 mm wound from magnet wire with a
diameter of 0.06 mm. The CMS suspension included a coil
and copper tube, a dual purpose deadweight and eddy
current damper for suppressing pendulum modes of the
hanging assembly. The CMS coil were disposed inside a
closed-circuit NdFeB/mild steel magnet system.

The absolute mass balance included an air bearing. The
MMS coils were rigidly connected to a square cross section
shaft inside an air bearing housing. This linear guidance
mechanism provided almost zero-friction, single degree of
freedom (DOF) translation. A single degree of freedom
constrained coil motion can be insensitive to some misalign-
ments, such as an alignment of the coil motion trajectory to
the gravity vector. If the linear trajectory of the coil was
misaligned to gravity, this misalignment was present in both
velocity mode and force mode, cancelling out

The square air bearing was disposed on a tip/tilt stage for
aligning the trajectory to vertical to reduce risk of contact
friction between the air bearing shaft and the bearing sur-
face, e.g., at low air pressure, and to adjust the angle of the
coil inside the magnet.

Parametric studies were conducted to examine the effect
of the air bearing on the weighing mode measurement noise

20

2

40

50

60

6:

18

and bias force. The effect of the temperature of the com-
pressed air on the weighing mode measurement bias force
was studied by heating the air with a power resistor on a
small copper section of the intake tube where no correlation
between mass determinations and intake air temperature was
found. The effect of input air pressure amplitude on mea-
surement noise was examined, and the air bearing was
operated at 41 kPa above atmosphere.

With regard to optical and electrical features of the
absolute mass balance, a dual frequency 2.83 MHz Zeeman-
split laser was a light source for the Michelson heterodyne
interferometer for measuring and controlling the displace-
ment of the main coil along Z. The measurement laser beam
of the interferometer projected onto a flat mirror disposed
and centered on the top surface of the coil former adjustable
in angle about X and Y. Because the angular degrees of
freedom of the coil were constrained by the air bearing, a
simple flat mirror was chosen instead of a retroreflector. The
reference arm projected onto a mirror mounted to the top
edge of the magnet in a similar fashion. This location
minimized the optical path difference between the two arms
and for common mode rejection of mechanical vibration
between the coil and magnet. The interferometer signals was
acquired through time interval analyzers (TIA). One TIA
was a continuous position and time readout for feedback
control, and a second TIA was a measurement readout for
velocity when triggered. A horizontal displacement sensor
included a laser beam which reflected from a corner cube
disposed on a top surface of the coil former and back onto
a 2D position sensor for monitoring minute parasitic X and
Y motions of the coil during measurements.

The position and voltage measurement schematic is
shown in FIG, 25. The two TIAs derived their timebase from
a 10 MHz clock synchronized to a GPS signal. A field
programmable gate array (FPGA) deployed trigger pulses
for sampling both the position and time measurements from
the TIA and the voltage measurements from a digital volt-
meter (DVM).

The electrical circuit shown in FIG. 26 included four
low-noise latching relays. Critical connections are made
with PTFE insulated twisted pair wires. Wire segments to
both the MMS coils and CMS coil are made from 23 m
diameter wires.

With regard to magnetic features of the absolute mass
balance, the MMS magnet system included a single SmCo
disk that was 12.7 mm in height and 50.8 mm in diameter as
a source of the magnetic circuit. Two mild steel cylinders
sandwiched the magnet, shown in FIG. 3. The inner yoke
assembly included these three components. Two symmetric
tubes made from the same steel were stacked and locked to
each other via three dowel pins and were the outer yoke
assembly. The inner and outer yoke assemblies were bolted
to a bulkhead that included an aluminum base plate that
provided tip, tilt, and vertical translation.

The upper and lower 7.6 mm wide and 35.6 mm tall air
gaps contained the radial magnetic field and guided linearly
increasing or decreasing magnetic flux densities with respect
to Z as seen in FIG. 16 and FIG. 17. The combined magnetic
flux density curve was uniform in the neighborhood of Z=0.
Due to asymmetries of the magnet yoke pieces, a magnetic
field profile with a slope of 0.7x10-%/m near Z=0 was
measured as shown in FIG. 29. Weighing mode controls
were optimized to hold weighing position to within 0.06 m,
and the effect of the slope had a minor influence on overall
uncertainty. The field can be shaped such that a flat spot is
achieved around the weighing position.


U.S. Patent

Nov. 30, 2021 Sheet 3 of 31

236.1

US 11,187,571 B2

208.1

237-4

209

208.2

T

E t— 208.1

Tt 232

E t-— 208.2

236.2

FIG. 8


US 11,187,571 B2

3

FIG. 10 shows an original state of the magnet assembly
and the magnetic flux density profile with no shimming;

FIG. 11 shows a shimmed state of the magnet assembly
and the magnetic flux density profile with shimming;

FIG. 12 shows a linear motion member;

FIG. 13 shows a plan view of a linear motion member in
panel A, and panel B shows a cross-section along line A-A
of the linear motion member shown in panel A:

FIG. 14 shows an absolute mass balance;

FIG. 15 shows an absolute mass balance;

FIG. 16 shows a finite element simulation of magnetic
flux density through top and bottom air gaps of half of a
magnet, wherein the field where the coil resides in weighing
mode is approximately 0.4 T;

FIG. 17 shows a magnetic flux density profile of an upper
air gap (B_u), a lower air gap (B_l), and an average of the
two (B_ay) versus vertical position of the coil Z, wherein an
MMS coil includes two individual coils electrically con-
nected in series opposition so a theoretical profile reflects a
shape of B_av with a local minimum at Z=0;

FIG. 18 shows measured data of mechanical balance
sensitivity between Z=-0.02 mm to Z=0.02 mm; wherein a
force change as a function of Z position is about 0.05 N/m;

FIG. 19 shows 29 up/down sweeps superimposed on top
of each other in a single velocity mode data set; wherein BL.
is plotted against Z position of the coil; induced voltage was
measured at 2 NPLC, 1 mm/s from Z=-2.2 mm to +2.2 mm,
and a least squares regression was applied to each sweep;

FIG. 20 shows BL determinations of a full measuremer
a relative statistical uncertainty of each determination was,
on average, 2x10°(-6) (k=1), wherein overlying drift was a
change of magnetization due to temperature fluctuations;

FIG. 21 shows raw force mode data. Mass imbalance

experienced by an absolute mass balance converted from

voltage to grams via an interpolated value of BL from
bracketing velocity mode measurements is plotted; top: four
mass on measurements. Each cluster is 300 data points taken.
over 30 seconds. Bottom: five sets of mass off measurements
with the same amount of data points and time duration. All
clusters had relative uncertainty of about 2x10°(-5) (k=1);

FIG. 22 shows mass calculations in a force mode set,
wherein relative statistical uncertainty of each force mode
set was on average 5x10°(-6) (k=1);

FIG. 23 shows mass determinations for a copper cylinder
with a mass value of 10.164780(5) g, wherein weighting the
data provided a value of 10.16541 g (horizontal line) with a
relative statistical uncertainty of 1.2x10°(-6) (k=1), and the
uncertainty is subject to multiplication by an expansion
factor of 1.47;

FIG. 24 shows an absolute mass balance 200;

FIG. 25 shows a Michelson heterodyne interferometer
that measures motion of an air bearing shaft rigidly mounted
to a coil; a reference laser beam and measurement laser
beam were directed into receivers connected to two time
interval analyzers (TIAS), one of which continuously mea-
sured position and time, and the other measured when
triggered; a field programmable gate array (FPGA) provided
trigger pulses for the measurement TIA and the DVM,
wherein TIAs were in communication with a 10 MHz
reference clock synchronized with a GPS timer, and a
separate laser measured horizontal motions of an air bearing;

FIG. 26 shows a circuit for use in force mode operation
of an absolute mass balance, DVM measures a voltage drop
across the resistor, and a current source supplies the main
mass coil; velocity mode occurred when all four relays were

40

45

4

toggled, wherein DVM measures the induced voltage from
the main coil while the current source drives the counter
mass coil;

FIG. 27 shows a single set of velocity mode BL measure-
ments; each solid line is a second order fit of a 60-point
sweep ranging between Z=+2.2 mm at 1 mm/s. In total, 6
sweeps are conducted per velocity mode measurement,
wherein each data point is an average value of one set of fits
taken at Z=0. The slope around Z=0 is 0.118 T m/mm;

FIG. 28 shows BL determinations of a full measurement
for a 5-g mass determination. The relative statistical uncer-
tainty of each determination was on average 2x10°(-6)
(k=1), wherein drift was caused by change of magnetization
due to temperature changes:

FIG, 29 shows a complete run with 27 mass determina-
tions for a copper cylinder with a mass value of 5.018 042(5)
g. Averaging the data gives a value of 5.018 042 g (dashed
horizontal line) with a relative statistical uncertainty of
0.7x10°(-6) (k=1) (shaded band). The measured value was
determined to be 0.03x10°(-6) lower than the true value and
this difference was rounded down to 0.

FIG. 30 shows a complete run with 41 mass determina-
tions for a copper cylinder with a mass value of 1.067 562(2)
g. Averaging data gives a value of 1.067 557 g (dashed

S horizontal line) with a relative statistical uncertainty of

2.8x10°(-6) (k=1) (shaded band). The measured value was
determined to be 4.1x10°(-6) less than the true value; and

FIG. 31 shows voltage readings and associated relative
uncertainties, wherein 1 V and 100 mV ranges are plotted.
The left dotted line indicates the voltage level measured for
a 1 g determination and the right dotted line indicates the
voltage level measured for 1 mm/s velocity sweeps and a 5
g determination,

DETAILED DESCRIPTION

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion.

It has been discovered that absolute mass balance 200
determines an absolute mass of object 201 by comparing a
weight of object 201 to a calibrated electromagnetic force.
In an embodiment with reference to FIG. 1, FIG. 2, FIG. 3,
FIG, 14, FIG. 15, and FIG. 24, absolute mass balance 200
includes dual diameter wheel 202. Further with reference to
FIG. 6, dual diameter wheel 202 includes balance fulcrum
203 on which dual diameter wheel 202 pivots; and balance
beam 204 disposed on balance fulcrum 203 and that pivots
about balance fulcrum 203. Balance beam 204 includes
main mass arm 205 in mechanical communication with
balance fulcrum 203; and counter mass arm 206 laterally
disposed proximate to main mass arm 205 and in mechanical
communication with balance fulcrum 203. Main mass
receiver 207 is in mechanical communication with main

5 mass arm 205, receives object 201, and moves with main

mass arm 205. Main magnet system 212 includes first main
coil 208.1 in mechanical communication with main mass
receiver 207 and main mass arm 205, interposed between
main mass receiver 207 and dual diameter wheel 202. Main
magnet system 212 produces first magnetic field 210.1 and
moves with main mass arm 205. Main magnet system 212
also includes second main coil 208.2 in mechanical com-
munication with main mass receiver 207 and main mass arm
205, interposed between main mass receiver 207 and first

§ main coil 208.1. Second main coil 208.2 produces second

magnetic field 210.2, wherein second main coil 208.2 is in
electrical communication with first main coil 208.1 and


US 11,187,571 B2

Sheet 19 of 31

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5

moves with main mass arm 205. Main magnet system 212
also includes permanent magnet 209 disposed between first
main coil 208.1 and second main coil 208.2 and produces a
third magnetic field 210.3 that interacts with first magnetic
field 210.1 and second magnetic field 210.2. Absolute mass
balance 200 also includes displacement measuring system
211 in mechanical communication with permanent magnet
209 such that displacement measuring system 211 provides
a null position of dual diameter wheel 202 and measures a
velocity of main magnet system 212; and driving motor 213
in mechanical communication with counter mass arm 206.
Displacement measuring system 211 includes eddy current
damper 214 in mechanical communication with counter
mass arm 206 that moves with counter mass arm 206,
provides a constant velocity of main mass receiver 207, and
suppresses a pendulum mode of the driving motor 213; and
counter mass magnet system 215 in mechanical communi-
cation with eddy current damper 214.

A material of construction of elements of absolute mass
balance 200 can include a metal (e.g., aluminum, copper,
stainless steel, iron, an alloy, and the like), a polymer (e.g.,
thermoplastic and the like), a glass, a ceramic, a combination
thereof (e.g.. a composite) and the like, as appropriate the
function and material strength and design of the specific
component.

In an embodiment, absolute mass balance 200 includes
main mass tether 216 in mechanical communication with
main mass arm 205 and main mass receiver 207. Counter
mass tether 217 is in mechanical communication with coun-

ter mass arm 206 and eddy current damper 214. Counter 3

mass tether 217 and main mass tether 216 independently can
include a fiber or cable that includes a metal (e.g. titanium),
composite (e.g. carbon fiber), and the like that has a tensile
strength to withstand a maximum tensile force, e.g. 30 N,
specifically 22N, and more specifically 7 N.

0

According to an embodiment, absolute mass balance 200

includes linear motion member 218 in mechanical commu-
nication with main mass arm 205 and main magnet system
212. Linear motion member 218 provides linear motion
between main mass arm 205 and first main coil 208.1 and
second main coil 208.2. With reference to FIG, 12 and FIG.
13, linear motion member 218 includes linear bearing 219 in
mechanical communication with main mass arm 205 and
main magnet system 212; and linear bearing 220 disposed
around linear shaft 219. With reference to FIG. 12, two
circular cross section shafts 219 with smooth surface fin-
ishes are rigidly mounted to two sides of the first coil 208.1.
The two shafts reside in two circular air bearings 220. This
orientation allows for vertical motion only. With reference to
FIG. 13, a single square cross section shaft 219 with a
smooth surface finish on alll vertical faces is rigidly mounted
to the top surface of the first coil 208.1 and resides in a single
square cross section air bearing 220.

Linear motion member 218 couples and communicates
motion of balance beam 204 of dual diameter wheel 202
through main mass tether 216 to main coil 208 and main
mass receiver 207. With reference to FIG. 1, FIG. 2, FIG. 7,
and FIG. 8, dual diameter wheel 202 can include a shape to
provide such communication of motion. Exemplary shapes
include a circular shape as shown in FIG. 7 and FIG. 8 that
can have a selected outer radius that can be from 1 mm to
1000 mm, specifically from 10 mm to 300 mm, and more
specifically from 40 mm to 90 mm; an annular shape as
shown in FIG. 8 that can have a selected inner radius that can
be from 0.5 mm to 900 mm, specifically from 5 mm to 200
mm, and more specifically from 20 mm to 70, wherein the
inner radius and outer radius provide a radial thickness of

40

&

0

0

6

dual diameter wheel 202; a truncated circular shape as
shown in FIG. 1 and FIG. 2 that can have a radius (e.g., one
radius, two radii, and the like) that independently can be
from 0.5 mm to 900 mm, specifically from 5 mm to 200 mm,
and more specifically from 20 mm to 70; and the like.

In an embodiment, with reference to FIG. 5 and FIG. 6,
dual diameter wheel 202 can include balance beam 204 that
include center-of-mass adjuster 221 can include objects of
arbitrary geometries made from dense materials such as
copper or tungsten capable of rigid mechanical communi-
cation with the balance beam 204. Balance fulcrum 203 is
disposed on balance beam 204 and can include a physical
line contact provided by a knife edge 222 or a virtual line
contact provided by two point contacts 227. Exemplary
balance fulcrums 203 include a prism-shaped member,
wherein flat portion 256 of balance fulcrum 203 opposes
knife edge 222 such that knife edge 222 contacts bulkhead
223 that supports dual diameter wheel 202 and on which
knife edge 222 pivots to produce motion of dual diameter
wheel 202. With regard to bulkhead 223, bulkhead 223 can
include a rigid mounting plate made of aluminum or the like
that provides a horizontal surface for interfacing with the
knife edge 222 and a vertical surface for mounting the linear
bearing 220. Exemplary bulkheads 223 includes a structural
support, e.g., an aluminum plate, bracket, or optical bread-
board, and the like that can include mounting provisions
(e.g., threaded holes to receive a threaded fastener such as a
screw or bolt) for mounting various components of absolute
mass balance 200 thereto. In this manner, bulkhead 223
provides structural support and a reference position of
components that are statically mounted to bulkhead 223
(e.g. displacement measuring system 211, linear bearing
220, housing 237, permanent magnet 209, and the like)
relative to free-moving components of absolute mass bal-
ance 200 such as dual diameter wheel 202, main mass
receiver 207 (when not immobilized for force mode opera-
tion of absolute mass balance 200), main coil 208, eddy
current damper 214, yoke 236, and the like.

In some embodiments, with reference to FIG. 7 and FIG.
8, dual diameter wheel 202 can include pivot contactor 227
that can be disposed on bulkhead 223, wherein dual diameter
wheel 202 pivots about pivot contactor 227 relative to
bulkhead 223. It is contemplated that balance beam 204 can
be interposed between pivot contactor 227 and dual diameter
wheel 202 to provide mechanical communication therebe-
tween. Pivot contactor 227 can include contact mount 228 in
which is disposed pin 226 having pin point 224, ball 225,
and the like, wherein pivot contactor 227 pivots dual diam-
eter wheel 202 about pin point 224 or ball 225. In certain
embodiment, air bearing disk 253 can be disposed proximate
to and spaced apart from dual diameter wheel 202 to provide
an additional physical constraint for a single point contact
knife edge 222.

According to an embodiment, with reference to FIG. 9,
dual diameter wheel 202 includes bi-spherical air bearing
spindle 254 and bi-spherical air bearing 260. Bi-spherical air
bearing spindle 254 provides an alternative balance fulcrum
203 and is comprised of two hemispherical pieces with
smooth surface finishes which are rigidly mounted against
one another residing inside a matching shaped bi-spherical
air bearing 260

In an embodiment, pivot contactor 227 includes knife
edge 222, pin point 224, or ball 225 in contact with bulkhead

5 223. In an embodiment, pivot contactor 227 further includes

contact mount 228 and pin 226 disposed on contact mount
228, wherein pin 226 includes pin point 224, In an embodi-


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(10) Patent No.:

US 11,187,571 B2

Chao et al. (45) Date of Patent: Nov. 30, 2021
(54) ABSOLUTE MASS BALANCE (58) Field of Classification Search
CPC veesssees GOIG 1/18; GOIG 1/185; GOIG 7/00-
(71) Applicant: Government of the United States of 71045; GOIG 23/01; GO1G 23/10
America, as represented by the See application file for complete search history.
Secretary of Commerce, Gaithersburg, (55) References Cited
(72) Inventors: Leon Shih Chao, Gaithersburg, MD U.S. PATENT DOCUMENTS
(US): Jon Robert Pratt, Clarksburg. 1,770,610 A * 7/1930 Gilbert GOIG L/18
MD (US) 177/195
1,880,563 A * 10/1932 Weckerly GO1G 7/04
(73) Assignee: GOVERNMENT OF THE UNITED 177/21 OR
STATES OF AMERICA, AS (Continued)
REPRESENTED BY THE
SECRETARY OF COMMERCE, OTHER PUBLICATIONS
Gaithersburg, MD (US)
Rothleitner, C., et al., “The Planck-Balance—a Self-Calibrating
(*) Notice: Subject to any disclaimer, the term of this Precision Balance for Industrial Applications”, 59th Ilmenau Col-
patent is extended or adjusted under 35 loquium, 2017.
U.S.C, 154(b) by 59 days. (Continued)
(21) Appl. No.: 16/706,011 Primary Examiner — Randy W Gibson
(74) Attorney, Agent, or Firm — Office of Chief Counsel
(22) Filed: Dec. 6, 2019 for National Institute of Standards and Technology
(57) ABSTRACT
(65) Prior Publication Data An absolute mass balance determines an absolute mass of an
US 2020/0182682 Al Jun. 11, 2020 object and includes: a dual diameter wheel including: a
balance fulcrum; and a balance beam disposed on the
balance fulcrum and including: a main mass arm and a
Related U.S. Application Data counter mass arm: a main mass receiver that receives the
(60) Provisional application No. 62/777,274, filed on Dee. object; a main magnet system including: a first main coil that
10, 2018. produces a first magnetic field; a second main coil that
produces a second magnetic field; and a permanent magnet
(51) Int. Ch. that produces a third magnetic field that interacts with the
G0IG 7/02 (2006.01) first magnetic field and the second magnetic field; a dis-
GOIG 1/18 (2006.01) placement measuring system that provides a null position of
(Continued) the dual diameter wheel and measures a velocity of the main
(52) magnet system; and a driving motor including: an eddy

GO1G 7/02 (2013.01); GOIG 1/18

(2013.01); GIG 23/01 (2013.01); GOIG
23/10 (2013.01)

current damper that provides a constant velocity of the main
mass receiver; and a counter mass magnet system.

15 Claims, 31 Drawing Sheets

Saag meee



US 11,187,571 B2

29

performing a velocity sweep by synchronously moving,
at a selected velocity, the object, the main mass arm,
the first main coil, and the second main coil relative
to the permanent magnet in:

a first direction that is along a direction perpendicu-
lar to a magnetic field of the permanent magnet;
and

a second direction, after moving in the first direction,
wherein the second direction opposes the first
direction;

determining a first voltage produced from synchro-
nously moving the first main coil, and the second
main coil in the magnetic field of the permanent
magnet in the first direction and the second direction;
and

determining a velocity mode product BL from the

velocity and the first voltage reading, wherein B is a

magnetic field strength and L is a length of wire of

the first main coil and the second main coil;
operating the absolute mass balance in a force mode by:
performing an object-on measurement by:

moving the first main coil and the second main coil
to a weighing position;

removing the object from the absolute mass balance;

performing hysteresis erasing of the balance ful-
crum;

flowing a first force mode current through a mea-
surement resistor in electrical communication
with the first main coil and the second main coil;
and

10

20

30

determining a first force mode voltage produced
from flowing the force mode current through the
measurement resistor with the object removed
from the absolute mass balance;
performing an object-off measurement by:
re-disposing the object on the absolute mass balance
in mechanical communication with the main mass
arm via the first main coil and the second main
coil;
performing hysteresis erasing of the balance ful-
crum;
flowing a second force mode current through the
measurement resistor in electrical communication
with the first main coil and the second main coil;
and
determining a second force mode voltage produced
from flowing the force mode current through the
measurement resistor with the object disposed on
the absolute mass balance;
converting the first force mode voltage and the second
force mode voltage by weighting the first force mode
voltage and the second force mode voltage with the
velocity mode product BL to produce an intermediate
value; and
normalizing the intermediate value with respect to a
resistance of the measurement resistor to determine the
absolute mass of an object.

+ * RR Oe


U.S. Patent Nov. 30, 2021 Sheet 10 of 31 US 11,187,571 B2

Magnet shimming

no
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Magnet System
Cross Sectional View

Original state:

B

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209 at ‘ lower a
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FIG. 10


U.S. Patent Nov. 30, 2021 Sheet 9 of 31 US 11,187,571 B2

To 202

Wheel

FIG. 9


US 11,187,571 B2

21

for j=1 . . . 8, wherein odd values of j were mass-off
measurements, and even values were mass-on measure-
ments. The balance offset was such that V,,,,=-V_. The mass
imbalance for the mass-on and mass-off measurement was
approximately half the mass to be measured. The imbalance
was adjusted by adding or removing wire masses on the
CMS before the measurement campaign. The BL value used
in each term in equation 6 was a time-specific interpolated
value coinciding with each mass-on or mass-off measure-
ment, occurring once every 180 seconds. The A-B-A tech-
nique removed linear drifts of the BL caused by temperature
changes of the magnet. The average value for a set of mass
calculations was one mass determination:

AEH, to)

wherein k represented the mass determination set number
inside the full measurement run. A full measurement run of
5 g and 1 g mass determinations are shown in FIG. 31 and
FIG, 32.

The final value for the 5 g and 1 g mass were calculated
by the unweighted mean of the mass determinations:

(8)

wherein n=27 for the 5 g value and n=41 for the 1 g value.
‘Their corresponding statistical uncertainties were calculated
as the standard deviation of the mean:

XC — fina)”
ohm = ae
feet i nl

With regard to uncertainty analysis, final uncertainty
budgets are listed in Table 2. With regard to interferometer
readout, as used in Table 2, “laser stability and accuracy”
refers to uncertainty associated with knowing the vacuum
wavelength of the laser source. This error is based on the
difference between the original wavelength measurement of
the laser conducted by NIST in 2012 and a new measure-
ment conducted in 2018. The relative difference was deter-
mined to be 5x10. As used in Table 2, “deadpath error”
refers to uncertainty associated with calculating the change
in the differential optical path length between the reference
and measurement arms of the interferometer. This differen-
tial change was caused by refractive index fluctuations and
has a negligible effect. As used in Table 2, “optics thermal
drift” refers to uncertainty associated with knowing the
change in geometry of the optical components due to finite
coefficients of thermal expansion caused by thermal fluc-
tuations. This effect can be negligible. As used in Table 2,
“electronics error” refers to uncertainty associated with
frequency variations at a fixed temperature of the optical
receiver for plane mirror optics. This effect was 0.1x10~°
based on performance specifications. As used in Table 2,
“Abbe error” refers to uncertainty associated with knowing
angular deviation caused by a horizontal separation between
the measurement reflector and the trajectory axis of the air
bearing. Since the mirror mount was centered on the air
bearing within machining tolerances and the laser spot was
centered on the mirror surface, this effect is negligible. As
used in Table 2, “off axis motions” refers to uncertainty
associated with parasitic movements due to unwanted com-

)

0

40

&

0

22

pliance in all DOFs except Z. Horizontal displacement
variations in X and Y were measured to be about 0.09 m and
0.17 m over the complete travel range, respectively. Rotation
about Y and Z were measured during mass on and mass off
weighings to be about 10 rad and 5 rad, respectively.
Rotation about Z indicated a 20 rad jumped between force
mode and velocity. As reference, a cosine error between
force mode and velocity mode of 1700 rad yielded 1.4x10°°
error. The square air bearing provided nearly zero-friction,
single degree of freedom motion, and off-axis errors were
deemed negligible. As used in Table 2, “cosine error” refers
to uncertainty associated with the deviation of the interfer-
ometer beam from vertical. An alcohol pool was a reference
surface for this alignment. Angular deviations were ampli-
fied by an optical lever of 4.3 m, and the interferometer laser
spot was aligned to the alcohol pool spot to within 3 mm and
provided a cosine error of 0.1x10°°.

As used in Table 2, “timing jitter term” refers to uncer-
tainty associated with fluctuations in timekeeping by the
TIA and its contribution was determined to be negligible
based on the worst case scenario found in the performance
specifications thereof. As used in Table 2, “wavelength
compensation” term refers to uncertainty associated with
calculating the index of refraction correction of air. The
correction has a value of approximately 264x107° and was
calculated by a modified Edlen equation:

NM y=[(292.75I(W/4273.15)]{GiPa) [3.7345-0.0401x

(oim)Px10-!° (10)

wherein n,,, is the standard air refractivity; t is the tempera-
ture: fis the partial pressure of water vapor expressed in Pa,
and a is the vacuum wave number expressed in mTM'. Here,
fis a function of relative humidity and the saturation vapor
pressure p,, calculated from air temperature.

The lab was held at standard room temperature, around 24
degrees C., 100 kPa, and 37% RH. Fluctuations on these
three values were measured to be about 0.03, 2 Pa, and
0.05% RH during one set of velocity sweeps over a span of
a few minutes. This yielded a change in refractive index of
approximately 0.02x10-°. However, uncertainty in deter-
mining the absolute index of refraction was dominated by
the combined uncertainties associated with the environmen-
tal sensor’s accuracy in measuring temperature, pressure,
and humidity. 0.5x10° relative uncertainty on the refractive
index was calculated as a worst case scenario based on the
performance specifications. Conducting a Monte Carlo
analysis on the modified Edlen equation with the three
inputs, each with 10,000 measured data points, reduces the
uncertainty to 0.2x10-°

With regard to coil Z-position, as used in Table 2, “field
gradient” refers to uncertainty associated with a change in
magnetic flux density as a function of Z position. The
measured BL profile of the MMS magnet system was
determined to have a 0.7x10~/m slope around Z=0. Since
the position feedback controls held the weighing position to
within 0.06 m, the BL at Z=0 had an uncertainty of 0.04x
10°.

As used in Table 2, “material thermal expansion” refers to
uncertainty associated with length fluctuations of the sus-
pended components below the measurement reflector. The
weighing position was servoed to Z=0 with respect to the
reflector so temperature fluctuations combined with the
finite thermal expansion coeflicient of the coil former lead to
a change in distance between the location of the coil and the
measurement position. Hence, such a length change can be
undetectable with the interferometer. Given the temperature
variations in the room, the coil’s position can be known to


US 11,187,571 B2

Sheet 30 of 31

Nov. 30, 2021

U.S. Patent

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US 11,187,571 B2

Sheet 20 of 31

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US 11,187,571 B2

11

of the PID controller, and the like. In an embodiment,
controller system 252 includes a closed loop controller using
a fast sampling data acquisition (DAQ) system embedded
inside of the computer in electrical communication with
electrical system 250 and electronics system 251

Absolute mass balance 200 and processes disclosed
herein have numerous beneficial uses, including a fully
tabletop instrument capable of operation without a vacuum
environment and absolute determination of mass in an
absence of comparison to reference mass standards. Advan-
tageously, absolute mass balance 200 overcomes limitations
of technical deficiencies of conventional processes such as
conventional mass dissemination, wherein determination of
small masses relies on the careful traceability scaled from
the 1 kg artifact standard, represented by a series of tedious
inter-comparisons ultimately tracing back to primary mass
laboratories.

Absolute mass balance 200 and processes herein stream-
line the dissemination chain by removing mass inter-com-
parisons upstream of the gram-level. Moreover, absolute
mass balance 200 provides an alternate traceability chain to
electrical standards rather than the traditional mass standards
and provides industrial laboratories with direct realization of
small masses.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting

EXAMPLES

Example 1. Design and Development of an
Absolute Mass Balance

The unit of mass, the kilogram, is a fixed value of the
Planck constant h, and an absolute mass balance, also

referred to herein as a Kibble balance (KB), tabletop Kibble 3

balance, or tabletop-sized Kibble balance (KIBB-g1), pro-
vides determination of a mass of an object. Upon fixing the
Planck constant, mass is directly realized, relinquishing a
physical kilogram standard as a historically artifact. At the
National Institute of Standards and Technology (NIST), the
absolute mass balance was operated at a gram-level range
with uncertainties on the order of a few parts in 10°.

Amaximum permitted uncertainty for International Orga-
nization of Legal Metrology (OIML) class E, calibration
weights ranging from 1 g to 10 g is on the order of a few g,
limited by accrued uncertainties associated with repeatabil-
ity of balances used within the traceability chain to the IPK
and the stability of the artifacts. With the revised SI, mass
can be directly realized at any scale point (i.e. milligram,
gram, kilogram, etc.). Instrument manufacturers and phar-
maceutical companies have interest in directly measuring
small masses. The absolute mass balance realizes mass with
the same level of uncertainties associated with a set of
calibration weights that replace such a set. Operating at this
level of relative uncertainty removes demand for quantum
electrical standards, gravimeters, and high vacuum environ-
ments. Here, the absolute mass balance—KIBB-gl, or
(KIB)ble (B)alance at the (g)ram level—achieved uncertain-
ties on the order of a few g.

The absolute mass balance is different than a conventional
equal-arm beam balance. A conventional beam balance
makes relative measurements, comparing a weight of an
object to that of a calibrated mass. The absolute mass
balance makes absolute measurements, comparing the
weight of an object to a frequently calibrated electromag-
netic force determined by electrical quantities. The absolute
mass balance includes two modes of operation, velocity

40

g

12

mode and force mode. Velocity mode is based on the
principle of Faraday’s law of induction. A coil (wire length
L) is moved at a velocity v through a magnetic field (flux
density B) so that a voltage V is induced. The induced
voltage is related to the velocity through the flux integral
BL:

V=BLy. a
Force mode is based on Lorentz forces. The gravitational
force on a mass m is counteracted by an upward electro-
magnetic force F generated by the now current-carrying coil
in a magnetic field:

F=BLI-mg Q)

where g is the local gravitational acceleration and I is the
current in the coil.

By combining Eqs. (1) and (2), canceling out the BL
factor common to both equations, and rearranging the vari-
ables, expressions for electrical and mechanical power are
equated and a solution for mass is obtained:

fo)

Vi=mgv>m

ry

The equation above relates mechanical power to electrical
power and provides a means to relate mass to electrical
quantities. The relationship equates “virtual” power, in the
sense that the factors of each product, V and I or mg and v,
are not measured simultaneously, but separately in the two
modes. The “power” only exists virtually, ie., as a math-
ematical product.

Since absolute mass balance provides relative uncertain-
ties on the order of a few parts in 10°, the Planck constant
makes a subtle appearance for absolutely calibrating hard-
ware for electrical quantities.

The absolute mass balance provides industrial laborato-
ries to directly realize mass units at the gram level on-site.
The absolute mass balance can include a form factor that is
a tabletop-sized instrument; have low-cost that can be less
than 50,000 USD; can determine a mass absolutely, e.g.,
from 1 g to 10 g, can obtain a relative uncertainty that
is ~10~%; can be operated in conveniently in air in an absence
of vacuum around the absolute mass balance.

Here, the absolute mass balance was constructed and
measured 57 cm tall and 30 cm in diameter and included: a
“main mass side’ (MMS) that included components relevant
to velocity and force mode; and a ‘counter mass side’ (CMS)
that included a driving motor, as shown in FIG. 14, wherein
a cross-sectional view magnets and coils are shown for the
absolute mass balance. The main mass side includes features
to the left of the knife points, and the counter mass side
includes features to the right of the knife points.

With reference to FIG. 14 and FIG. 15, starting from the
top of the absolute mass balance, a dual-diameter truncated
wheel pivots about a two-point contact, forming a line
contact, referred to as “knife points.” The two pivot points
are nonmagnetic alloy points, and each knife point rests on
a polished sapphire disk. The simple design of the two knife
points provide a straight-line contact without a precision
knife edge.

The truncated wheel looks like a beam but behaves as a
wheel. The motion of the hanging coils along the Z-axis is
constrained by rotation of the wheel about the Y-axis. The
MMS beam are has a smooth, curved surface with a radius
1.4 times that of the CMS are where both arcs are concentric.


US 11,187,571 B2

13

This radius mismatch allows for increased space on the
MMS without increasing the form factor of the entire
apparatus. Each knife point is rigidly attached to the end of
a screw inserted through the center of the balance beam.
Adjusting the depth of each screw allows aligning the
rotational degree of freedom (DOF) about the X-axis and
translational DOF in the Z-axis. This adjusts a location of the
truncated wheel’s center of gravity as well as aligning its
geometric center to the rotation center of the knife points.

The MMS electromagnet system includes two coils with
3253 turns and mean diameter of 73 mm, wherein each is
wound from magnet wire with a diameter of 0.06 mm. The
MMS permanent magnet includes a single SmCo magnet
disk, wherein a magnetic flux is guided by a mild steel yoke
The magnetic flux is guided radially through two air gaps for
interaction with the two coils. The magnetic flux density
through the air gaps are measured to be about 0.4 T.

The coil is rigidly connected to two parallel ceramic
coated aluminum shafts and is suspended from the MMS of
the beam via a titanium wire. One of the parallel shafts is
guided by an air bearing operating at about 240 kPa above
atmosphere. Air bearings for both shafts can be included but
parallelism alignment should overcome effects of over con-
straining. Two shielding plates were bolted above and below
the air bearing to reduce noise from the exhaust. A force
mode measurement was performed with varying input pres-
sures ranging from 240-700 kPa. Although higher pressures
resulted in an increase in noise, the overall mass determi-

nation for each pressure level was consistent. Air exhaust is 3

a constant offset force common in both the mass on and mass
off states during force mode. A vertical tube shielded laser
paths from small refractive index fluctuations caused by
exhaust air. The lab temperature, humidity, and pressure

fluctuations were measured by an environmental sensor 3

placed next to the magnet for buoyancy and refractive index
corrections, and the effect of each contributed relatively less
than 1x10-®. Suspended from the bottom of the coil was a
mass pan gimbal, and a piston loaded and unloaded the test
mass.

‘The CMS included a coil mounted below a copper tube (a
dead mass to account for the mass on the MMS), suspended
by two filaments of the same wire as the MMS. NdFeB
magnets interacted with the copper tube and were eddy
current dampers that suppressed pendulum modes of the
CMS hanging assembly. The CMS coil hung inside a
closed-circuit NeFeB/mild steel magnet system.

‘A dual frequency 2.83 MHz Zeeman-split laser was a light
source for the Michelson heterodyne interferometer that
measured and controlled displacement of the main coil along
Z. The measurement laser beam of the interferometer proj-
ects onto a flat mirror mounted and centered on a top surface
of the coil former adjustable in angle about X and Y. Because
the angular degrees of freedom of the coil were constrained
by the air bearings, a simple flat mirror was chosen instead
of a retroreflector. The reference arm projected onto a
similar mirror system mounted to the top edge of the
magnet. This location minimized the optical path difference
between the two arms and provided common mode rejection
of mechanical vibration between the coil and magnet. The
interferometer signals were read through two time interval
analyzers (TIA). One TIA provide continuous position and
time readout, and the second TIA provided the measurement
readout for velocity when triggered. A horizontal displace-
ment sensor (HDS) included a separate laser beam that
reflected from a corner cube mounted off-center of the coil
former onto a 2D position sensor for monitoring parasitic X

10

0

0

0

14

and Y motions of the coil during the velocity trajectory and
as an aid for aligning the trajectory to gravity.

The coils of the absolute mass balance were connected to
a 26-bit current source through a relay box ultimately
controlled by a data acquisition unit. In velocity mode, the
induced voltage is measured with an voltmeter. In force
mode, the full voltage drop produced by the weighing
current traversing a 1 kQ calibrated resistor was measured.
Measurement and timing triggers were controlled by a field
programmable gate array (FPGA). A global positioning
system (GPS) receiver produced a 10 MHz signal as a timing
source for the FPGA and TIAs.

With regard to magnets, the magnet system for the abso-
lute mass balance included a single SmCo disk with a
12.7-mm height and 50.8-mm diameter as a source of the
magnetic circuit. Two mild steel cylinders sandwiched the
magnet and were concentrically constrained by an aluminum
sleeve as shown in FIG. 3. The inner yoke included these
three components. Two symmetric tubes made from the
same steel were stacked and locked to each other via three
dowel pins and were the outer yoke assembly. Both the inner
and outer yoke assemblies were bolted to an aluminum base
as a bulkhead that provided tip, tilt, and vertical translation.

The upper and lower 7.6 mm wide and 35.6 mm tall air
gaps contained the radial magnetic field and guided linearly
increasing or decreasing magnetic flux densities with respect
to Z as seen in FIG. 16 and FIG. 17. The combined magnetic
flux density curve was uniform in the neighborhood of Z=0.

The magnet can include a monolithic tube as the outer
yoke. Due to manufacturing and assembly procedure asym-
metries of both the magnet and the coils, the combined field
profile had a slope of 0.075 Tm/mm. Mass determinations
can be sensitive to deviations about the weighing position.
To achieve a flat spot in the profile, a different outer yoke
was fabricated as two separate pieces, wherein the assembly
procedure was symmetric, and no yoke pieces were mag-
netized more than once. Another attempt was altering the
reluctance of the bottom half of the outer yoke with an
external magnetic field. A flat field near Z=0 was provided
by shimming the height of the inner yoke assembly by 2mm
relative to the outer yoke. This led to a measured magnetic
field profile shown in FIG. 19, wherein the slope was less
than 0.004 Tm/mm or in relative terms was 2.3x10-*/m near
Z=0. The balance controls held a weighing position at
Z-0+0.5 m.

The open top/bottom magnet system may magnetic flux
near the unguided regions. The test mass can experience a
systematic force from the stray magnetic field and its
gradient. The mass pan hung approximately 50 mm below
the bottom surface of the magnet. An OIML class E, 10-g
stainless steel mass could experience a force equivalent of a
12 mg mass due to magnetic susceptibility of the material
A field cancellation procedure included adding a 5-DOF
adjustable magnet underneath the mass pan to negate the
field at the mass location and reduced the magnetic field
gradient to zero.

To align the absolute mass balance, verticality of the
absolute mass balance, HDS, and interferometer was
achieved. The magnet, which can be independently tilted,
was aligned to be vertical. The direction of the interferom-
eter and the HDS laser beams were aligned to be vertical,
defined by g, with reference to an alcohol pool. The verti-
cality of the measurement laser of the interferometer was
adjusted to be within 200 rad due to the length of the optical
lever. The trajectory of the coil was made vertical by
adjusting the absolute mass balance and HDS to align tog.



U.S. Patent Nov. 30, 2021 Sheet 26 of 31 US 11,187,571 B2

MM Coil

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CM Co

Resistor
FIG. 26

Current Source
ee



U.S. Patent Nov. 30, 2021 Sheet 2 of 31 US 11,187,571 B2

Tabletop Kibble Balance

205 206

217

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FIG. 2


US 11,187,571 B2

27

a balance beam disposed on the balance fulcrum and
that pivots about the balance fulcrum, the balance
beam comprising:

a main mass arm in mechanical communication with
the balance fulcrum; and

a counter mass arm laterally disposed proximate to
the main mass arm and in mechanical communi-
cation with the balance fulcrum;
a main mass receiver in mechanical communication with
the main mass arm and that receives the object and that
moves with the main mass arm;
a main magnet system comprising:
a first main coil in mechanical communication with the
main mass receiver and the main mass arm, inter-
posed between the main mass receiver and the dual
diameter wheel, and that produces a first magnetic
field and that moves with the main mass arm;
a second main coil in mechanical communication with
the main mass receiver and the main mass arm,
interposed between the main mass receiver and the
first main coil, and that produces a second magnetic
field, the second main coil being in electrical com-
munication with the first main coil and that moves
with the main mass arm; and
permanent magnet disposed between the first main
coil and the second main coil and that produces a
third magnetic field that interacts with the first mag-
netic field and the second magnetic field;
a displacement measuring system in mechanical commu-
nication with the permanent magnet such that displace-
ment measuring system provides a null position of the
dual diameter wheel and measures a velocity of the
main magnet system: and
a driving motor in mechanical communication with the
counter mass arm and comprising:
an eddy current damper in mechanical communication
with the counter mass arm that moves with the
counter mass arm, that provides a constant velocity
of the main mass receiver, and that suppresses a
pendulum mode of the driving motor; and

a counter mass magnet system in mechanical commu-
nication with the eddy current damper,

wherein the absolute mass balance determines the abso-
lute mass of the object by comparing a weight of the
object to a calibrated electromagnetic force.

2. The absolute mass balance of claim 1, further com-
prising a main mass tether in mechanical communication
with the main mass arm and the main mass receiver.

3. The absolute mass balance of claim 1, further com-
prising a counter mass tether in mechanical communication
with the counter mass arm and the eddy current damper.

4. The absolute mass balance of claim 1, further com-
prising a linear motion member in mechanical communica-
tion with the main mass arm and the main magnet system
and that provides linear motion between the main mass arm
and the first main coil and the second main coil.

5. The absolute mass balance of claim 4, wherein the
linear motion member comprises:

a linear bearing in mechanical communication with the
main mass arm and the main magnet system; and

a linear bearing disposed around the linear shaft.

6. The absolute mass balance of claim 1, wherein the
balance beam further comprises a center-of-mass adjuster.

7. The absolute mass balance of claim 1, wherein the
balance fulcrum further comprises a pivot contactor dis-
posed ona bulkhead, wherein the dual diameter wheel pivots
about the pivot contactor relative to the bulkhead.

»

28

8. The absolute mass balance of claim 7, wherein the pivot
contactor comprises a knife edge, a pin point, or a ball in
contact with the bulkhead.

9. The absolute mass balance of claim 8, wherein the pivot

5 contactor further comprises a contact mount and a pin
disposed on the contact mount, wherein the pin comprises
the pin point.

10. The absolute mass balance of claim 8, wherein the
pivot contactor further comprises a contact mount, wherein

10 the ball is disposed on the contact mount.

11. The absolute mass balance of claim 1, wherein the
main mass receiver comprises:

a mass pan on which receives the object; and

a mass pan gimbal interposed between the mass pan and

the main magnet system.

12. The absolute mass balance of claim 1, wherein the
counter mass magnet system comprises:

a counter mass coil in mechanical communication with

the eddy current damper; and

a counter mass magnet in which the counter mass coil is

disposed.

13. The absolute mass balance of claim 1, wherein the
main magnet system comprises:

a housing in mechanical communication with a bulkhead:

a coil former on which the first main coil and the second

main coil are disposed and that is disposed in the

housing and that moves with the main mass arm and the
main mass receiver;

a first yoke disposed in the housing and in mechanical
30 communication with the housing; and

a second yoke disposed in the housing and in mechanical

communication with the housing and the first yoke,

such that the permanent magnet is disposed on and
interposed between the first yoke and the second yoke.
14. The absolute mass balance of claim 1, wherein the
displacement measuring system comprises:
a Michelson heterodyne interferometer comprising:
a laser that produces source light;
a reference mirror disposed on the housing in optical
communication with the laser and that receives the
source light from the laser and produces reference
light from the source light;
a displacement mirror disposed on the linear bearing in
optical communication with the laser and that
receives the source light from the laser and produces
displacement light from the source light;
reference photodetector in optical communication
with the laser and that receives the source light from
the laser and produces a reference signal from the
source light; and
a measurement photodetector in optical communication
with the reference mirror and the displacement mir-
ror and that:
receives the reference light from the reference mir-
ror,

receives the displacement light from the displace-
ment mirror; and

produces an interference signal from the reference
light and the displacement light.

15. A process for determining an absolute mass of an
object with the absolute mass balance of claim 1, the process
comprising:

disposing the object in mechanical communication with

the main mass arm via the first main coil and the second

main coil;

operating the absolute mass balance in a velocity mode

by:

20

25

45

2

60


US 11,187,571 B2

23

0.6 m which, combined with the magnetic field gradient,
leads to a relative uncertainty of 0.4x10-°.

As used in Table 2, “statistical” refers to uncertainty
associated with the data analysis procedure. The final mass
determination was the average value of the whole set of
force mode mass determinations and had an uncertainty
equal to the standard deviation of the mean. An Allan
variance analysis was conducted to verify that the data was
Gaussian. Each individual force mode mass determination
was the average value of a group of mass calculations
bracketed by two velocity mode BL determinations. The
uncertainty of each mass determination was the standard
deviation of the mean of each group of mass calculations
then added in quadrature to the uncertainty of the bracketing
velocity mode measurements. These uncertainties were 0.7
10°© and 2.8x10-° for the 5 g and 1 g determinations,
respectively.

With regard to profile fitting, as used in Table 2, “BL.
interpolation” refers to uncertainty associated with the cal-
culated BL value for each force mode measurement. Both a
linear interpolation per every neighboring pair of BL deter-
minations and a nTM order fit interpolation for the entire
measurement were implemented and compared. The fit
order was chosen depending on the drift shape of the entire
measurement. A fifth order fit was selected for the 5 g data
set as shown in FIG. 30. The difference in the overall mass
determination was 0.2x107° between the two methods.

As used in Table 2, “individual BL profile” refers to
uncertainty associated with the variation of the BL profile

shape caused by using different fit orders per velocity mode 3

measurement. The individual BL profiles were fitted with
both second and third order polynomials. The variation of
the BL at Z=0 was 0.7x10~°.

As used in Table 2, “resistor” refers to uncertainty asso-

ciated with knowing the absolute resistance value of a 1 kQ: 3

reference resistor that was calibrated against the NIST
Graphene Quantum Hall Resistor QHR) approximately one
month prior to the blind measurements. The resistor was
calibrated frequently over the past few years and its history
indicated a relative drift of approximately 0.5x10-‘/year.
Taking into account drift rate and the recent calibration, a
conservative uncertainty of 0.1x10-° was assigned for the
resistor value.

As used in Table 2, “DVM” refers to uncertainty associ-
ated with voltage measurements by a multimeter. Following
best metrological practices, the DMM used for this mea-
surement was characterized by a programmable josephson
voltage system (PJVS). The performance of the 1 V range
was measured and had a 0.4x10°° gain error and 0.02x10-°
offset.

With regard to forces on the mass, as used in Table 2,
“magnetic susceptibility of mass” refers to uncertainty asso-
ciated with a magnetic force between the test mass and the
ambient magnetic field. This was calculated to have a
relative effect of 0,02x10"°. As used in Table 2, “balance
sensitivity” refers to uncertainty associated with a torque
caused by the separation between the center of mass of the
wheel and its rotational axis. The torque varied as a function
of wheel angle, therefore Z position of the coil. By adjusting
the mass distribution of the wheel, this separation was
adjusted such that the torque was constant near the weighing
position. This alignment was not performed here, and the
absolute mass balance had a 50 g/m slope near the weighing
position. Sensitivity of the absolute mass balance came into
effect if the wheel position differed between a mass-on
measurement and a mass-off measurement. This measured
difference was on average 0.4 nm, due to the imperfect knife

0

2

40

50

0

24

edge hysteresis erasing procedure so a relative uncertainty of
4x10°° and 2x10-* was assigned to the 5 g and 1 g mea-
surements, respectively.

‘As used in Table 2, “buoyancy” refers to uncertainty
associated with calculated air buoyancy correction (i.e.,
density of air) for a copper mass of density 8.9 g/cm. The
correction was approximately 131x10-° with respect to lab
environmental parameters. The lab was held at standard
room temperature, around 24 degrees C., 100 kPa, and 37%
RH. Similar to wavelength compensation, uncertainty in
determining the absolute density of air was included in
combined uncertainties associated with the environmental
sensor’s accuracy in measuring temperature, pressure, and
humidity. Here, 0.3x10-° relative uncertainty on the air
density was calculated as a scenario based on the perfor-
mance specifications. Conducting a Monte Carlo analysis on
the air density equation with the three inputs, each with
10,000 measured data points, reduced the uncertainty to
0.1x10°°.

As used in Table 2, “balance mechanics” refers to uncer-
tainty associated with mechanical hysteresis of the knife
edge and was measured by monitoring repeatability of
weighing mode current before and after intentional knife
edge excursions caused by a 5 g mass exchange. The
remaining knife edge hysieresis effects after an erasing
procedure was about 1 g. Relative uncertainties were 0.2x
10-6 and 1x10-° for the 5 g and 1 g measurements, respec-
tively.

As used in Table 2, “gravity” refers to uncertainty asso-
ciated with knowing a local acceleration of gravity at a
location of the test mass. The value was measured with an
FG-5 absolute gravimeter next to the absolute mass balance
with an uncertainty of 0.1x10-®, in agreement with the
online Surface Gravity Prediction software value calculated
by the National Oceanic and Atmospheric Administration
(NOAA) gravity survey. However, since the FG-5 measure-
ment was a single point determination and does not account
for earth’s tidal changes, the uncertainty of g was 0.3x10"°.

As used in Table 2, “magnet nonlinearity” refers to
uncertainty associated with the level of weighing asymmetry
before the start of a measurement. A weighing current-
dependent offset force observed in the MMS electromagnet
has a 38x10~%/g effect. For example, if BL/g(IIgg!=lI,,1)=1
g, then the determination would be 38x10~° lower than the
true value. Prior to the start of a measurement, an iterative
balancing procedure reduces the asymmetry to within 10
mg, or a relative uncertainty of 0.4x10~°.

‘As used in Table 2, “air bearing pressure” refers to
uncertainty associated with input pressure dependent air
bearing exhaust forces. A digital pressure gauge was con-
nected to the intake with a resolution of 69 Pa. Pressure data
taken over 27 hours was analyzed and determined that the
fluctuations coherent with the mass exchanges are limited to
have a 1.1x10°° uncertainty on the 5 g mass and 5.4x10~° on
the 1 g mass.

With regard to an uncertainty budget for the absolute mass
balance, sources of uncertainty and their relative magnitudes
for a nominally 5-g and 1-g mass are listed in Table 2. A
source of uncertainty entered with a value of 0.0 indicates
that such uncertainty is less than 0.05x107°.

TABLE 2

5_g measurement

1_g measurement

Source Item Subtotal Item Subtotal
Laser Stability/Accuracy 0.0 0.0
Deadpath Error 0.0 0.0


U.S. Patent Nov. 30, 2021 Sheet 13 of 31 US 11,187,571 B2

Square shaft air

bearing
(A) 218
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plan view 90 prewee4 Y - Yi r-4 Oy f------>
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(B) 218

cross sectional view

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208—

FIG. 18


US 11,187,571 B2

Sheet 15 of 31

Nov. 30, 2021

U.S. Patent

FIG. 15


U.S. Patent Nov. 30, 2021 Sheet 1 of 31 US 11,187,571 B2

200
228
2
207 “8
222
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7 I 206
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FIG. 1


US 11,187,571 B2

9

coil 231 is disposed. Here, counter mass coil 231 can include
conductive wire forming one or more loops. Exemplary
counter mass coils 231 include insulated circular cross-
section copper wire forming over 500 turns, and the like. A
height of counter mass coil 231 can be from 1 mm to 30 mm,
specifically from 3 mm to 20 mm, and more specifically
from 5 mm to 10 mm. A diameter of counter mass coil 231
can be from 1 mm to 150 mm, specifically from 10 mm to
100 mm, and more specifically from 20 mm to 50 mm. In an
embodiment, counter mass coil 231 is in mechanical com-
munication with eddy current damper 214 and electrical
communication with the electrical system 250 and electron-
ics system 251.

Further, eddy current damper 214 can include a metallic,
nonmagnetic, smooth surface for which permanent magnets
can interface without mechanical contact. Exemplary eddy
current dampers 214 include a copper hollow cylinder
surrounded by permanent magnets, and the like. Moreover,
eddy current damper 214 is suspended from counter mass
tether 216 and is surrounded by neodymium magnets to
reduce the pendular motions of eddy current damper 214. In
an embodiment, eddy current damper 214 is in mechanical
communication with counter mass tether 216 and counter
mass coil 231 and in magnetic communication with external
neodymium magnets in mechanical communication with
bulkhead 223.

Absolute mass balance 200 includes displacement mea-
suring system 211 for tracking the displacements of main
coil 208 with respect to main magnet system 212. In an

embodiment, with reference to FIG. 1, displacement mea- 3

suring system 211 includes a Michelson heterodyne inter-
ferometer that includes laser 233 that produces source light
234, Here, reference mirror 239 is disposed on housing 237
in optical communication with laser 233. Reference mirror

239 receives source light 234 from laser 233 and produces 3

reference light 240 from source light 234. Displacement
mirror 238 is disposed on linear bearing 219 in optical
communication with laser 233, receives source light 234
from laser 233, and produces displacement light 241 from
source light 234. Reference photodetector 242 is in optical
communication with laser 233, receives source light 234
from laser 233, and produces reference signal 244 from
source light 234. Displacement measuring system 211 also
includes measurement photodetector 243 that is in optical
communication with reference mirror 239 and displacement
mirror 238. Source light 234 receives reference light 240
from reference mirror 239, receives displacement light 241
from displacement mirror 238, and produces interference
signal 245 from reference light 240 and displacement light
241.

Absolute mass balance 200 has numerous advantageous
and unexpected benefits and uses. In an embodiment, with
reference to FIG. 25, FIG. 26, Example 1, and Example 2,
a process for determining an absolute mass of object 201
with absolute mass balance 200 includes: disposing object
201 in mechanical communication with main mass arm 205
via first main coil 208.1 and second main coil 208.2 by
disposing object 201 on main mass receiver 207; operating
absolute mass balance 200 in velocity mode. Velocity mode
includes performing a velocity sweep by synchronously
moving, at a selected velocity, object 201, main mass arm
205, first main coil 208.1, and second main coil 208.2
relative to permanent magnet 209 in a first direction that is
along a direction perpendicular to a magnetic field of
permanent magnet 209 and in a second direction, after
moving in the first direction, wherein the second direction
opposes the first direction; determining a first voltage pro-

S

2

40

&

50

10

duced from synchronously moving first main coil 208.1, and
second main coil 208.2 in the magnetic field of permanent
magnet 209 in the first direction and the second direction;
and determining a velocity mode product BL from the
velocity and the first voltage reading, wherein B is a
magnetic field strength and L is a length of wire of first main
coil 208.1 and second first main coil 208.2. The process for
determining the absolute mass of object 201 with absolute
mass balance 200 also includes operating absolute mass
balance 200 in a force mode. Force mode includes perform-
ing an object-on measurement by: moving first main coil
208.1 and second main coil 208.2 to a weighing position;
removing object 201 from absolute mass balance 200;
performing hysteresis erasing of balance fulcrum 203; flow-
ing a first force mode current through measurement resistor
248 in electrical communication with first main coil 208.1
and second main coil 208.2; and determining a first force
mode voltage produced from flowing the force mode current
through measurement resistor 248 with object 201 removed
from absolute mass balance 200. Force mode further
includes performing an object-off measurement by: re-dis-
posing object 201 on absolute mass balance 200 in mechani-
cal communication with main mass arm 205 via first main
coil 208.1 and second main coil 208.2; performing hyster-
esis erasing of balance fulcrum 203; flowing a second force
mode current through measurement resistor 248 in electrical
communication with first main coil 208.1 and second main
coil 208.2; and determining a second force mode voltage
produced from flowing the force mode current through
measurement resistor 248 with object 201 disposed on
absolute mass balance 200. The process for determining the
absolute mass of object 201 with absolute mass balance 200
also includes converting the first force mode voltage and the
second force mode voltage by weighting the first force mode
voltage and the second force mode voltage with the velocity
mode product BL to produce an intermediate value; and
normalizing the intermediate value with respect to a resis-
tance of measurement resistor 248 to determine absolute
mass of an object 201

In an embodiment, with reference to FIG. 4, absolute
mass balance system 249 that includes absolute mass bal-
ance 200, electrical system 250 in electrical communication
with absolute mass balance 200, electronics system 251 in
electrical communication with absolute mass balance 200,
and controller system 252 in electrical communication with
electronics system 251. In an embodiment, electronics sys-
tem 251 includes a digital voltmeter, time interval analyzers,
field programmable gate array, GPS receiver, and clock used
for the precision measurement of voltage and time where the
triggering of the measurements is provided by the field
programmable gate array. Moreover, electronics system 251
is in electrical communication with electrical system 250,
absolute mass balance 200, optical system 211, and control-
ler system 252, e.g., a computer. In an embodiment, elec-
trical system 250 includes main coil 208, resistor, and
current source in electrical communication, e.g., through a
communication bus, as seen in FIG. 26. Exemplary electri-
cal system 250 includes main coil 208, a commercial pre-
cision resistor, a Vernier current source, and the like. More-
over, electrical system 250 provides the electrical current for
velocity mode and force mode operation. In an embodiment,
electrical system 250 includes a high stability 1000 Ohm
resistor, Vernier current source with 26 bits of resolution and
a range of +1 mA. In an embodiment, controller system 252
includes a digital proportional-integral-derivative (PID)
closed loop controller. Exemplary controller system 252
includes custom programmed software for implementation


US 11,187,571 B2

Sheet 24 of 31

Nov. 30, 2021

U.S. Patent

af

FIG. 24


US 11,187,571 B2

Page 2
(51) Int. CL
GOIG 23/10 (2006.01)
GOIG 23/01 (2006.01)
(56) References Cited
U.S. PATENT DOCUMENTS
3,519,095 A * 7/1970 Tomes GOIG 7/04
177/21 OR
3,967,691 A * 7/1976 Wirth GOIG 1/18
177/230
3,973,636 A * 8/1976 Uchida GOIG 1/18
177/132
4,153,124 A * 5/1979 Knothe GO1G 7/04
177/21 OEM
4,354,563 A * 10/1982 Luchinger GO1G 7/04
177/21 OEM
4,489,800 A * 12/1984 Nufer GO1G 7/04
177/21 OEM.
5,998,742 A * 12/1999 Liu GO1G 7/02
177/184
7,690,273 B2* 4/2010 Reber GOIG 7/04
73/862.69

OTHER PUBLICATIONS

Rothleitner, C., et al., “The Planck-Balance—asing a fixed value of
the Planck constant to calibrate E1/E2-weights”. Measurement
Science and Technology, 2018, 074003, vol. 29.
Rothleitner, C., et al., “First results using the Planck-Balance”, 2018
Conference on Precision Electromagnetic Measurements (CPEM.

2018), 2018.

* cited by examiner


US 11,187,571 B2

1
ABSOLUTE MASS BALANCE

CROSS REFERENCE TO RELATED
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/777,274 filed Dec. 10, 2018, the
disclosure of which is incorporated herein by reference in its
entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce. The Government has certain rights in the
invention. Licensing inquiries may be directed to the Tech-
nology Partnerships Office, NIST, Gaithersburg, Md.,
20899; voice (301) 301-975-2573; email tpo@nist.gov; ref-
erence NIST Docket Number 19-016US1

BRIEF DESCRIPTION

Disclosed is an absolute mass balance for determining an
absolute mass of an object, the absolute mass balance
comprising: a dual diameter wheel comprising: a balance
fulcrum on which the dual diameter wheel pivots; and a
balance beam disposed on the balance fulcrum and that

pivots about the balance fulcrum, the balance beam com- 3

prising: a main mass arm in mechanical communication with
the balance fulcrum; and a counter mass arm laterally
disposed proximate to the main mass arm and in mechanical
communication with the balance fulcrum; a main mass

receiver in mechanical communication with the main mass 3

arm and that receives the object and that moves with the
main mass arm; a main magnet system comprising: a first
main coil in mechanical communication with the main mass
receiver and the main mass arm, interposed between the
main mass receiver and the dual diameter wheel, and that
produces a first magnetic field and that moves with the main
mass arm; a second main coil in mechanical communication
with the main mass receiver and the main mass arm,
interposed between the main mass receiver and the first main
coil, and that produces a second magnetic field, the second
main coil being in electrical communication with the first
main coil and that moves with the main mass arm; and a
permanent magnet disposed between the first main coil and
the second main coil and that produces a third magnetic field
that interacts with the first magnetic field and the second
magnetic field; a displacement measuring system in
mechanical communication with the permanent magnet such
that displacement measuring system provides a null position
of the dual diameter wheel and measures a velocity of the
main magnet system; and a driving motor in mechanical
communication with the counter mass arm and comprising:
an eddy current damper in mechanical communication with
the counter mass arm that moves with the counter mass arm,
that provides a constant velocity of the main mass receiver,
and that suppresses a pendulum mode of the driving motor;
and a counter mass magnet system in mechanical commu-
nication with the eddy current damper, wherein the absolute
mass balance determines the absolute mass of the object by
comparing a weight of the object to a calibrated electro-
magnetic force.

Disclosed is a process for determining an absolute mass of
an object with an absolute mass balance, the process com-

2

40

6:

2

prising: disposing the object in mechanical communication
with the main mass arm via the first main coil and the second
main coil; operating the absolute mass balance in a velocity
mode by: performing a velocity sweep by synchronously
moving, at a selected velocity, the object, the main mass
arm, the first main coil, and the second main coil relative to
the permanent magnet in: a first direction that is along a
direction perpendicular to a magnetic field of the permanent
magnet; and a second direction, after moving in the first
direction, wherein the second direction opposes the first
direction; determining a first voltage produced from syn-
chronously moving the first main coil, and the second main
coil in the magnetic field of the permanent magnet in the first
direction and the second direction; and determining a veloc-

S ity mode product BL from the velocity and the first voltage

reading, wherein B is a magnetic flux density and L is a
length of wire of the first main coil and the second main coil;
operating the absolute mass balance in a force mode by:
performing an object-off measurement by: moving the first
main coil and the second main coil to a weighing position;
removing the object from the absolute mass balance; per-
forming hysteresis erasing of the balance fulcrum; flowing a
first force mode current through a measurement resistor in
electrical communication with the first main coil and the

S- second main coil; and determining a first force mode voltage

produced from flowing the force mode current through the
measurement resistor with the object removed from the
absolute mass balance; performing an object-on measure-
ment by: re-disposing the object on the absolute mass
balance in mechanical communication with the main mass
arm via the first main coil and the second main coil;
performing hysteresis erasing of the balance fulcrum; flow-
ing a second force mode current through the measurement
resistor in electrical communication with the first main coil
and the second main coil; and determining a second force
mode voltage produced from flowing the force mode current
through the measurement resistor with the object disposed
on the absolute mass balance; converting the first force
mode voltage and the second force mode voltage by weight-
ing the first force mode voltage and the second force mode
voltage with the velocity mode product BL to produce an
intermediate value; and normalizing the intermediate value
with respect to a resistance of the measurement resistor to
determine the absolute mass of an object.

BRIEF DESCRIPTION OF THE DRAWINGS.

The following description should not be considered lim-
iting in any way. With reference to the accompanying
drawings, like elements are numbered alike

FIG. 1 shows an absolute mass balance, wherein a cross-
sectional view of magnets and coils are shown;

FIG. 2 shows an absolute mass balance;

FIG. 3 shows a cross-section of a magnet system, wherein
two coils wound on a coil former are with their windings
connected in series opposition, and two halves of an outer
yoke is shown as a single member;

FIG. 4 shows an absolute mass balance system;

FIG. 5 shows a dual diameter wheel;

FIG. 6 shows a dual diameter wheel;

FIG. 7 shows a dual diameter wheel in panel A and pivot
contactors in panels B, C, and D;

FIG. 8 shows a perspective view of a dual diameter wheel
in panel A and a side view of the dual diameter wheel in
panel B;

FIG. 9 shows a side view of a dual diameter wheel with
a bi-spherical air bearing spindle;


US 11,187,571 B2

19

The open top and bottom magnet system can leak mag-
netic flux near the unguided regions. A test mass could be
susceptible to a systematic force from a stray magnetic field
and its gradient along Z. The mass pan was hung and
disposed approximately 50 mm below the bottom surface of
the magnet. An OIML class E, 10 g stainless steel mass
disposed on the mass pan experienced an additional force
equivalent to a 12 mg mass due to magnetic susceptibility of
the material. This effect was characterized by two magnetic
force terms as:

by 4)
1 = Bo.
1 = xBo.T

bY ©)
2 = Ho ——

Ho

wherein x, is a volume magnetic susceptibility of the mass;
B,, is an absolute magnetic flux density; 1, is free space
permeability; M_ is permanent axial magnetization; b_ is the
field gradient along Z, and V is volume of the mass. The
overall force is the sum, ¢, +e.

The absolute magnetic field and the field gradient were
measured at the mass pan to be 4.1 mT and 100 T/mm,
respectively. A field cancellation procedure of adding a
5-DOF adjustable permanent magnet underneath the mass
pan to negate the field at the mass location was successful
and reduced the magnetic field gradient to zero, reducing

both ¢, and e, to zero. A strong magnet can be disposed °

proximate to the mass pan. Here, measurements were made
with masses made from copper, wherein magnetic forces are
negligible.

With regard to determining the mass of the object and data

analysis, a blind measurement was conducted with two ”

weights having nominal masses of 5 g and 1 g. The widths
were calibrated by comparison with standards traceable to
the SI definition of mass. True mass was determined for each
weight, meaning that the raw mass readings of each weight,
or apparent mass, was corrected for the effects of air
buoyancy. Furthermore, each of the weights was calibrated
using a weighing design in which the unknown weight was
compared with three other weights that had the same nomi-
nal mass. The three other weights included a first weight as
a restraint or standard mass, a second weight as a check
standard, and a third weight whose mass was unknown.
Each weight in the design was compared with every other
weight so six comparisons (mass differences) were available
as listed in Table 1

TABLE 1
Wi w2 w3 wa
1 -1 0 °
1 0 -1 0
1 0 0 -1
0 1 -1 °
0 1 0 -1
0 0 1 -1

wherein W1=standard weight (restraint), W2=check stan-
dard weight, W3=unknown weight #1, and W4=unknown
weight #2. The six mass comparisons listed Table 1 form a
set of six equations with two unknowns that can be solved
using linear algebra. Uncertainties in the restraint and check
standard can be incorporated into the design along with the
uncertainties in the mass comparator and air buoyancy

2

&

50

3!

60

20

corrections. The result of the calculation was a mass value
for each of the unknowns along with Type A (statistical) and
Type B (non-statistical) uncertainties. By incorporating a
check standard, statistical tests on the measurement process
and results can be performed that provide a measure of
confidence.

‘An acrylic dome was disposed over the absolute mass
balance to shield the instrument from air currents. A small
hole in the dome provided communication for the interfer-
ometer laser beam. An environmental sensor next to the
absolute mass balance measured temperature, pressure, and
relative humidity for calculating corrections for index of
refraction and buoyancy variations.

Velocity mode operated with the measurement mass rest-
ing on the mass pan and the MMS heavier by an amount
equal to half the measurement mass. The measurement
started with 3 up and 3 down velocity sweeps at a constant
velocity of 1 mm/s while sampling the DVM every 1 power
line cycle (NPLC) or 33 ms with an auto zero between each
sampling aperture. These parameter values were chosen
based on examining the power spectrum of velocity noise
and a separate parametric study between differing NPLC and
velocity values. The FPGA triggered the sampling of the
TIA and DVM. Each voltage measurement was bracketed by
17 position and time readings, wherein each set was aver-
aged down to a single position and time. The velocity during
the voltage measurement was determined by difference of
two consecutive position readings divided by the sample
time. From the voltage and velocity data pairs, the quotient
was calculated as BL. Each sweep included 60 BL measure-
ments ranging between Z=+2.2 mm and was fitted with a
second order polynomial as shown in FIG. 29. A mean and
standard was calculated for each set of velocity sweeps at
Z=0, represented by markers shown in FIG. 30. The mea-
surement of BL determinations was fitted with a fifth order
polynomial for which the interpolated values were used in
force mode calculations.

Between sets of velocity mode measurements, the system
toggled to force mode, and coil position was servo con-
trolled to Z=0, i.e., the weighing position. A motorized
translation stage first removed the mass while the balance
was controlled. The excursion of the balance beam from the
nominal position was suppressed with large control gains
As reference, the balance excursion was approximately +40
m for a 5 g exchange. The absolute mass balance was then
subjected to a knife-edge hysteresis erasing procedure,
wherein the absolute mass balance followed a decaying
sinusoidal trajectory with an initial amplitude larger than
that of the perturbation caused by the mass removal because
the knife edge was not an ideal, frictionless surface and
incurred a bias restoring force depending on the direction
and amplitude of the excursion from mass exchanges. After
a 30-second settling time, 200 voltage readings from the
weighing current across the measurement resistor once
every 100 ms were acquired. The process was repeated for
a mass on measurement. In total, 5 mass-on and 5 mass-off
measurements were taken per force mode set.

The set of force mode voltage measurements were con-
verted to 8 mass calculations via an interpolated BL value
from bracketing velocity mode sets. Referred to as A-B-A
measurements, the mass calculations were:

1 / Bl Vil + Bl jealVal ©
ae 7

+ BljalV yal)


U.S. Patent Nov. 30, 2021 Sheet 27 of 31 US 11,187,571 B2

Ol X TH/ (1 LF9E R91 — TZ)

iJ o 2

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2
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U.S. Patent Nov. 30, 2021 Sheet 11 of 31 US 11,187,571 B2

Magnet shimming

212 Shimmed state:
236.1
T
2081—-+-F--O Ly — $208.1
ae | 208.1
236.2— a
208.2; ~O EG oO 208.2
237—- WH Shim | “P—237
255 YY [~~ 2mm
z
Y
dB
az
B
total =0

FIG. 11


U.S. Patent Nov. 30, 2021 Sheet 14 of 31 US 11,187,571 B2

Two knife Qual diameter wheel

points
Custom
heterodyne
interferometer
© bt
I
Cerami¢-——
coated Al
shafts Linear air—+--7 |
bearing

a

Main a r | S

SmCo Magnet" ( Driving motor
System

L.,

M