sensors
Technical Note
Development of a New, High Sensitivity 2000 kg
Mechanical Balance
Jian Wang
Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China; [email protected];
Tel.: +86-10-6452-4609
Academic Editors: Thierry Bosch, Aleksandar D. Rakić and Santiago Royo
Received: 21 February 2017; Accepted: 28 March 2017; Published: 13 April 2017
Abstract: Mass measurement of more than 500 kg on an electronic mass comparator has no better
repeatability and linearity of measurement for meeting the calibration requirement of over class F1
weights from pharmacy and power generation plants. For this purpose, a new 2000 kg mechanical
balance was developed by the National Institute of Metrology (NIM). The advantages of measurement
of more than 500 kg on a new 2000 kg mechanical balance are introduced in the paper. In order to
obtain high measurement uncertainty, four vertical forces of two sides of beam are measured and used
as reference for adjustment of the beam position. Laser displacement sensors in the indication system
are more effective for decreasing reading errors caused by human vision. To improve the repeatability
and sensitivity of the equipment, a synchronous lifting control is designed for synchronously lifting
the beam ends along the vertical direction. A counterweight selection system is developed to get any
combination of weights in a limited space. The sensitivity of the new mechanical balance for 2000 kg
is more than 1.7 parts in 10−4 rad/g. The extended uncertainties for the mechanical balance of 500 kg,
1000 kg and 2000 kg are 0.47 g, 1.8 g and 3.5 g respectively.
Keywords: sensitivity; mechanical balance; laser displacement sensor; repeatability; synchronous
1. Introduction
The calibration requirement of high accuracy for big weights or loads like 500, 600 and 1000 kg is
increasing year by year in China. Electronic mass comparators are usually used for calibrating high
accuracy weights all over the world. The repeatability and linearity of electronic mass comparators are
good for meeting the calibration requirement of over class F1 weights, except for mass comparators
with a maximum capacity of more than 500 kg [1–3].
The repeatability and linearity of a mass comparator depends on its lever structure, the position
of the applied gravity force and the performance of its load cells. The lever structure in a mass
comparator, consisting of a pivot and metal beam, is used to amplify the force of gravity during the
mass measurement. The material and deformation of the metal beam are the factors that influence
and amplify the accuracy. The precision of the amplification on a small mass comparator is better than
that on a large mass comparator. For large electronic mass comparators based on lever structures it is
difficult to get better repeatability and linearity in the mass measurement process.
A weight placed on different position of the platform could result in a difference between two
adjacent measurements. This is more obvious for big weights over 100 kg in mass. For obtaining better
measurement result repeatability, the bottom position of the weight on the platform is usually marked.
This ensures the weight will be placed on the same position each time during the measurement process.
Due to the characteristics of load cells, electronic mass comparators with different maximum
capacities may be selected when used for measuring the masses of weights with the same accuracy
and different nominal values. It is necessary for the weights mentioned above to use several electronic
mass comparators for performing the corresponding measurements.
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and different nominal values. It is necessary for the weights mentioned above to use several
electronic mass comparators for performing the corresponding measurements.
The
mechanicalbalance
balancewith
withone
oneindicator
indicator
based
optical
principle
is commonly
The mechanical
based
onon
thethe
optical
principle
is commonly
usedused
all
all
over
the
world.
Usually
the
operator
participates
in
the
data
acquisition,
and
automatic
data
over the world. Usually the operator participates in the data acquisition, and automatic data
acquisition
acquisition is
is not
not available.
available. This
This method
method introduces
introduces some
some reading
reading uncertainty.
uncertainty.ItItcauses
causesan
anincrease
increasein
the
measurement
uncertainty
of
a
mechanical
balance
[4,5].
A
new
method
based
on
laser
displacement
in the measurement uncertainty of a mechanical balance [4,5]. A new method based on laser
sensors
is proposed
the to
problem
this
paper. in this paper.
displacement
sensorstoisresolve
proposed
resolvein
the
problem
Due
weight
of the
measured
weight,
the counterweights
are usually
not installed
Due to
tothe
thedifferent
different
weight
of the
measured
weight,
the counterweights
are usually
not
on
the
mechanical
balance.
When
used,
counterweights
are
selected
to
be
loaded
on
the
side
of
the
installed on the mechanical balance. When used, counterweights are selected to be loaded on the
mechanical
balance [6].balance
This is[6].
notThis
convenient
to operate
it affects
measurement
accuracy.
side of the mechanical
is not convenient
toand
operate
and itthe
affects
the measurement
To
resolve this
a special
designa with
counterweights
on the mechanical
accuracy.
To problem,
resolve this
problem,
special
design withmounted
counterweights
mounted balance
on the is
introduced
this paper.
mechanical in
balance
is introduced in this paper.
The beam of a mechanical
mechanical balance
balance has
has better
betterstiffness
stiffnessand
andless
lessdeformation
deformationthan
thanthat
thatofofanan
electronic
onon
thisthis
characteristic,
we have
developed
a newa mechanical
balance
electronic mass
masscomparator.
comparator.Based
Based
characteristic,
we have
developed
new mechanical
with
a
maximum
capacity
of
2000
kg.
The
sensitivity
of
the
mechanical
balance
for
2000
kg
is
more
balance with a maximum capacity of 2000 kg. The sensitivity of the mechanical balance for 2000 kg
is
−
4
−4
more1.7
than
1.7in
parts
10 rad/g.
The repeatability
for kg
2000
kg isthan
less0.15
thang.0.15
g. It measure
could measure
than
parts
10 inrad/g.
The repeatability
for 2000
is less
It could
weights
weights
with different
values
kg kg.
to 2000 kg.
with
different
nominal nominal
values from
100from
kg to100
2000
2. Structure of Mechanical
Mechanical Balance
Balance
The mechanical
balance isis composed
composed of
of beam
beamsystem,
system,middle
middleknife,
knife,side
sideknives,
knives,indicator,
indicator,
mechanical balance
counterweights,
selecting system,
system, weighing
weighing system,
system,motors
motorsand
andcontroller.
controller.The
Thestructure
structureofofthe
the
counterweights, selecting
mechanical balance is shown
shown in
in Figure
Figure 1.
1.
Figure 1. The structure of the mechanical balance.
Figure 1. The structure of the mechanical balance.
Figure 2 is a picture of mechanical balance. The height of the mechanical balance is 2.8 m. The
Figure
is a picture
mechanical
balance. The height of the mechanical balance is 2.8 m.
length
of the2balance
beam of
equals
2 m.
The length of the balance beam equals 2 m.
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Figure
Figure2.
2.The
Thepicture
pictureof
ofmechanical
mechanicalbalance.
balance.
Figure
2.
The
picture
of
mechanical
balance.
2.1.
2.1.Knives
Knivesof
ofMechanical
MechanicalBalance
Balance
2.1.
Knives
of
Mechanical
Balance
For
For supporting
supporting an
an approximate
approximate 777 ttt load,
load, TH10
TH10 high-speed
high-speed steel
steel is
is used
used as
as the
the material
material of
of the
the
For
supporting
an
approximate
load,
TH10
high-speed
steel
is
used
as
the
material
of
the
middle
knife
and
side
knives
after
a
special
heat
treatment
process
as
shown
in
Figure
3.
The
special
middleknife
knifeand
andside
sideknives
knivesafter
afteraaspecial
specialheat
heattreatment
treatmentprocess
processas
asshown
shownin
inFigure
Figure3.3. The
The special
special
middle
heat
treatment
process
includes
preheating
two
times
at
500–600
℃
and
800–850
℃,
respectively,
heat
treatment
process
includes
preheating
two
times
at
500–600
℃
and
800–850
℃,
respectively,
heat treatment process includes preheating two times at 500–600 °C and 800–850 °C, respectively,
quenching
quenching at
at 1200–1250
1200–1250 ℃,
℃, tempering
tempering three
three times
times at
at 550–570
550–570 ℃
℃ and
and aaa deep
deep cooling
cooling cycle
cycle down
down to
to
quenching
at
1200–1250
°C,
tempering
three
times
at
550–570
°C
and
deep
cooling
cycle
down
to
–120
℃
[7].
After
machining
the
knives
have
maintained
high
hardness
and
high
toughness
under
–120°C
℃ [7].
[7]. After
After machining
machining the
the knives
knives have
have maintained
maintained high
high hardness
hardness and
and high
high toughness
toughness under
under
–120
heavy
load
conditions
[8].
heavy
load
conditions
[8].
heavy load conditions [8].
Figure
Figure
3.
Heat
treatment
process
of
TH10.
Figure3.
3.Heat
Heattreatment
treatmentprocess
processof
ofTH10.
TH10.
2.2.
2.2.Indicators
Indicatorsof
ofMechanical
MechanicalBalance
Balance
2.2.
Indicators
of
Mechanical
Balance
The
includes
two
individual
indicators.
is an
The display
display device
device includes
includes two
two individual
individual indicators.
indicators. One
an indicator
indicator based
based on
on optical
optical
The
display
device
One is an
indicator
based
on
optical
principles.
It
is
composed
of
a
small
scale,
a
high
definition
camera
and
a
liquid
crystal
principles. It is composed of a small scale, a high
high definition
definition camera
camera and
and aa liquid
liquid crystal
crystal display
display
principles.
display
(LCD).
shown
in
Figure
4.4.AAmetal
(LCD).The
Thescale
scaleand
andthe
theLCD
LCDare
areshown
shownin
inFigure
Figure4.
metalthin
thinrod
rodfixed
fixedin
inthe
themiddle
middleof
ofbeam
beamis
(LCD).
The
scale
and
the
LCD
are
A metal
thin
rod
fixed
in
the
middle
of
beam
isis
perpendicular
to
the
beam.
The
scale
of
the
indicator
is
mounted
on
the
end
of
the
metal
thin
rod
perpendicularto
tothe
thebeam.
beam.The
Thescale
scaleofof
the
indicator
is mounted
of metal
the metal
rod
perpendicular
the
indicator
is mounted
on on
the the
endend
of the
thin thin
rod and
and
to the
The
between
the
knife-edge
and
the
isis 42
cm.
The
and parallel
parallel
the beam.
beam.
The distance
distance
between
the middle
middle
knife-edge
and
the scale
scale
42The
cm.scale
The
parallel
to thetobeam.
The distance
between
the middle
knife-edge
and the
scale
is
42 cm.
scale
with
the
of
beam
and
160
The
between
divisions
scaleswings
swings
with
theswing
swing
ofthe
theand
beam
andincludes
includes
160divisions.
divisions.
Theinterval
interval
between
divisions
swings
with the
swing
of the beam
includes
160 divisions.
The interval
between
divisions
of the
of
the
scale
is
equal
to
0.25
mm.
A
high
definition
camera
with
14
million
pixels
is
used
for
of the
scale is
equalmm.
to 0.25
mm.
A highcamera
definition
with
14 million
pixels
is used the
for
scale
is equal
to 0.25
A high
definition
withcamera
14 million
pixels
is used for
amplifying
amplifying
the
scale
and
displaying
it
on
the
LCD.
During
the
measurement,
the
operator
reads
the
amplifying
the
scale
and
displaying
it
on
the
LCD.
During
the
measurement,
the
operator
reads
the
scale and displaying it on the LCD. During the measurement, the operator reads the LCD readings.
LCD
readings.
LCDAnother
readings.includes two laser displacement sensors, a signal processor and acomputer.
Another
includes
two
sensors, aa signal
processor
and
Laser
includes
two laser
laser displacement
displacement
signal
processor
and asides
a computer.
computer.
Laser
LaserAnother
displacement
sensors
with
the
resolution sensors,
of 3 µm are
mounted
on both
of the beam.
displacement
sensors
with
the
resolution
of
3
m
are
mounted
on
both
sides
of
the
beam.
The
displacement
sensors
with
the
resolution
of
3
m
are
mounted
on
both
sides
of
the
beam.
The distance between the middle knife-edge and each laser displacement sensor is 42 The
cm.
distance
between
the
knife-edge
and
laser
sensor
is 42
The
distance
between
the middle
middle
knife-edge sensors
and each
each
laser displacement
displacement
sensor
42 cm.
cm.
The
The
installation
of two
laser
displacement
is shown
as
Figure 5. When
theisbeam
swings,
installation
of
displacement
sensors
as
When
beam
the
installation
of two
two laser
laser
displacement
sensors isis shown
shown
as Figure
Figureto5.5.equilibrium
When the
the position
beam swings,
swings,
the
the
laser displacement
sensor-L
gets the displacement
corresponding
on the left
laser
displacement
sensor-L
gets
the
displacement
corresponding
to
equilibrium
position
on
the
left
laser
displacement
sensor-L
gets
the
displacement
corresponding
to
equilibrium
position
on
the
left
side. Meanwhile the laser displacement sensor-R gets the displacement on the right side. The difference
side.
Meanwhile
the
laser
displacement
sensor-R
the
on
right
The
side.
Meanwhile of
the
laser
displacement
sensor-Rofgets
gets
the displacement
displacement
on the
right side.
side.
of
displacements
both
sides
is the displacement
the beam.
It can eliminate
the influence
of The
the
difference
of
displacements
of
both
sides
is
the
displacement
of
the
beam.
It
can
eliminate
difference of displacements of both sides is the displacement of the beam. It can eliminate the
the
influence
of
the
zero
drift
of
the
laser
displacement
sensor.
The
difference
is
processed
by
the
signal
influence of the zero drift of the laser displacement sensor. The difference is processed by the signal
processor
processorand
andsent
sentto
tothe
thecomputer.
computer.
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zero drift of the laser displacement sensor. The difference is processed by the signal processor and sent
to the 2017,
computer.
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(a)
(b)
(a)
(b)
(a)
(b)
Figure 4. (a)The scale and (b) the LCD.
Figure 4. (a) The scale and (b) the LCD.
Figure 4. (a)The scale and (b) the LCD.
Figure 4. (a)The scale and (b) the LCD.
Figure 5. The installation of two laser displacement sensors.
Figure 5. The installation of two laser displacement sensors.
Figure 5. The installation of two laser displacement sensors.
The indicator based on optical principle is used for adjusting the indicator with two laser
The indicator
based
onWhen
optical
is the
used
forisadjusting
the
with
displacement
sensors
[9,10].
theprinciple
pointer on
LCD
located on
theindicator
left end of
the two
scale,laser
the
The
indicator based
on
optical principle
principle is
used for
for adjusting
adjusting the
the indicator
indicator with
with two
two laser
laser
The
indicator
based
on
optical
is
used
displacement
[9,10].
thetopointer
on the LCD
is located
on the left
end of
pointer
in thesensors
computer
is When
adjusted
the minimum
position.
When
pointer
onthe
thescale,
LCDthe
is
displacement sensors
[9,10]. When
the
pointer
onon
thethe
LCD
is located
on thethe
leftleft
endend
of the
scale,
the
displacement
When
the
pointer
LCD
located
of
scale,
pointer on
in the
computer
to computer
the minimum
position.
Whentoon
the
onBased
thethe
LCD
is
located
thesensors
middle[9,10].
of is
theadjusted
scale, the
pointer
is is
adjusted
thepointer
middle.
on
the
pointer
in the
computer
is adjusted
to to
the
minimum
position.
When
the
pointer
on
the
LCD
is
the
pointer
in
the
computer
is
adjusted
the
minimum
position.
When
the
pointer
on
the
LCD
is
located
on
the
middle
of
the
scale,
the
computer
pointer
is
adjusted
to
the
middle.
Based
on
the
adjustments on these positions, the indicator with two laser displacement sensors can get
located
on
the
middle
of
the
scale,
the
computer
pointer
is
adjusted
to
the
middle.
Based
on
the
located
on
of
the scale,
computer
pointer
is
adjusted
to the middle.
Based
onas
the
adjustments
onmiddle
these automatically.
positions,
thetheThe
indicator
with
twotwo
laser
displacement
sensors
canused
get
the
readings
bythe
computer
indicator
with
laser
displacement
sensors
a
adjustments on
onthese
thesepositions,
positions,
the
indicator
with
two displacement
laser displacement
sensors
can readings
get the
adjustments
the
indicator
with
two
laser
sensors
can
get
the
readings
by
computer
automatically.
The
indicator
with
two
laser
displacement
sensors
used
as
reading system of the mechanical balance is available for decreasing reading errors caused bya
readings
by computer
automatically.
The indicator
with two
laser displacement used
sensors
as a
by
computer
automatically.
Thethe
indicator
with
two
displacement
ascaused
aused
reading
reading
system
of the 6mechanical
balance
isofavailable
for
decreasing sensors
reading
errors
by
human
vision.
Figure
shows
position
one laser
laser
displacement
sensor and
the
software
reading
system
of
the
mechanical
balance
is
available
for
decreasing
reading
errors
caused
by
system
of
the
mechanical
balance
is
available
for
decreasing
reading
errors
caused
by
human
vision.
human vision.
Figure 6 shows the position of one laser displacement sensor and the software
interface
of the indicator.
human6 vision.
Figure
6 shows
of onesensor
laser and
displacement
andofthe
software
Figure
position
of onethe
laserposition
displacement
the softwaresensor
interface
the indicator.
interfaceshows
of the the
indicator.
interface of the indicator.
(a)
(b)
(a)
(b)
(a)position of one sensor and (b) the software
(b) interface.
Figure 6. (a) The
Figure
interface.
Figure 6.
6. (a)
(a) The
The position
position of
of one
one sensor
sensor and
and (b)
(b) the
the software
software interface.
Figure
6.
(a)
The
position
of
one
sensor
and
(b)
the
software
interface.
2.3. Counter Weight Selecting System
2.3. Counter Weight Selecting System
2.3. Counter
System requirement of full range from 100 kg to 2000 kg in a limited
Weight
Selecting
According
to the
measurement
According
to the measurement
requirement
of full
range
from 100
kgcounterweight
to 2000 kg in aselection
limited
space,
a counterweight
selection system
is designed
and
produced.
The
requirement
According to the measurement requirement
of full range from 100 kg to 2000 kg in a limited
space, ashown
counterweight
selection
system
is designed
and
produced.
The
counterweight
selection
system
in
Figure
7
consists
of
one
stainless
steel
frame
with
three
layer
support,
nested
1, 2, 2,
space, a counterweight selection system is
is designed
designed and
and produced.
produced. The counterweight selection
system
shown
in
Figure
7
consists
of
one
stainless
steel
frame
with
three
layer
support,
nested
2, 2,
5system
ratio counterweights
the inside to the outside and three sets of selection modules with1,nine
shown in Figurefrom
2, 2,
2,
7 consists of one stainless steel frame with three layer support, nested 1, 2,
5 ratio counterweights
the inside toThe
the outside
and three
sets with
of selection
modules
withtop
nine
motors
for selecting thefrom
counterweights.
first selection
module
four motors
on the
of
5 ratio counterweights
from the inside to the outside and three sets of selection modules with nine
motors
for selecting
the counterweights.
The
selection
module
with
four
motors
on among
the top10,
of
the
counterweight
selection
system is used
forfirst
selecting
one
weightwith
or
one
set
of
weights
motors
for
module
four
motors
on on
the the
top top
of the
for selecting
selectingthe
thecounterweights.
counterweights.The
Thefirst
firstselection
selection
module
with
four
motors
of
the
counterweight
selection
system
is
used
for
selecting
one
weight
or
one
set
of
weights
among
10,
20,
20 and 50 kgselection
options. system
The second
onefor
is similar
as the
first
layer
selecting
one weight
counterweight
is used
selecting
oneone
weight
orstructure
one
set set
offor
weights
among
10, 10,
20,
the counterweight
selection system
is used
for
selecting
weight
or one
of weights
among
20,one
20 and
kg options.
The second
one
similar
first layer
structure
for selecting
oneand
weight
or
set 50
of weights
among
100, 200,
200isand
500as
kgthe
options.
There
is one 1000
kg weight
one
20, 20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight
or
one
set
of
weights
among
100,
200,
200
and
500
kg
options.
There
is
one
1000
kg
weight
and
one
set of selection modules with one motor in the third layer.
or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one
set of selection modules with one motor in the third layer.
set of selection modules with one motor in the third layer.
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20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight or
one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of
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of 12
12
selection
modules
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Figure 7.
7. Counterweight
Counterweight selection
selection system.
system.
Figure
Figure 7. Counterweight selection system.
2.4. Synchronous
Synchronous Lifting
Lifting Control
Control
2.4.
2.4. Synchronous Lifting Control
To improve
improve the
the repeatability
repeatability and
and sensitivity
sensitivity of
of the
the mechanical
mechanical balance,
balance, aa synchronous
synchronous lifting
lifting
To
To improve
the repeatability
and
sensitivity
of the
mechanical
balance, selection
a synchronous
lifting
control
is
developed
for
lifting
the
weighing
system
and
the
counterweight
system
along
control is developed for lifting the weighing system and the counterweight selection system along
control
is
developed
for
lifting
the
weighing
system
and
the
counterweight
selection
system
along
the
the vertical
vertical direction
direction synchronously
synchronously [11].
[11]. Four
Four motors
motors under
under the
the weighing
weighing system
system and
and four
four motors
motors
the
vertical
direction
synchronously
[11].
Four
motors
under
the
weighing
system
and
four
motors
under
under the
the counterweight
counterweight selection
selection system
system are
are driven
driven synchronously
synchronously for
for decreasing
decreasing the
the displacement
displacement
under
the
counterweight
selection system are driven synchronously for decreasing the displacement errors
errors
between
them.
errors between them.
between them.
2.5. Monitor
Monitor System for
for the Balance
Balance of
of the
the Beam
Beam
2.5.
2.5.
Monitor System
System for the
the Balance of
the Beam
After the
the weighing system
system and the
the counterweight selection
selection system are
are lifted synchronously,
synchronously, the
the
After
After
the weighing
weighing system and
and the counterweight
counterweight selection system
system are lifted
lifted synchronously, the
beam
including
the
middle
knife
and
side
knives
is
dropped.
The
middle
knife-edge
and
beam including
includingthethe
middle
andknives
side isknives
is The
dropped.
middleand
knife-edge
and
beam
middle
knifeknife
and side
dropped.
middleThe
knife-edge
corresponding
corresponding bearing
bearing block
block form
form the
the pivot
pivot to
to support
support everything.
everything. Four
Four force
force sensors
sensors are
are mounted
mounted
corresponding
bearing block form the pivot to support everything. Four force sensors are mounted at two sides of the
at two
two sides
sides of
of the
the beam.
beam. The
The installation
installation positions
positions are
are shown
shown in
in Figure
Figure 8.
8. When
When the
the beam
beam is
is
at
beam.
The installation
positions are
shown in Figure 8. When
the beam is
dropping,
the vertical
forces
dropping,
the
vertical
forces
of
four
points
on
the
beam
are
measured
to
judge
the
loading
dropping,
theonvertical
forces
of four points
beamsynchronization
are measured and
to judge
loading
of
four points
the beam
are measured
to judgeonthethe
loading
adjust the
the position
synchronization and
and adjust
adjust the
the position
position of
of the
the beam.
beam.
synchronization
of the beam.
Figure 8.
8. The
The force
force sensors
sensors installation
installation positions.
positions.
Figure
The
force
sensors
Figure
8.
installation
positions.
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66 of
3. Operational Principle
3. Operational Principle
The weighing system is located at the left of the mechanical balance, and the counterweight
The weighing
system
is located
at the aleft
of the mechanical
balance,
and the weight
counterweight
selection
system is on
the right
side. When
measurement
is started,
the reference
and the
selection
system
is
on
the
right
side.
When
a
measurement
is
started,
the
reference
weight
and
the test
test weight are place on the weighing system of the mechanical balance in turn. Meanwhile,
weight
areto
place
on the weighing
of weight,
the mechanical
balance in
according
according
the nominal
mass of system
reference
a counterweight
orturn.
a set Meanwhile,
of counterweights
are
to
the nominal
mass
of reference weight,
a counterweight
or a9 set
of counterweights
are selected on
selected
on the
counterweight
selection
system. Figure
shows
a general two-dimensional
the
counterweight
selection
system.balance
Figure showing
9 shows athe
general
two-dimensional
representation
of the
representation
of the
mechanical
characteristic
quantities
of the mechanical
mechanical
balance
characteristic
of theof
mechanical
balance.acts
Theatpoint
S’ is the
balance. The
point showing
S’ is the the
beam's
pivot. Thequantities
gravity force
beam mass
its center
of
beam's
pivot.
The
gravity
force
of
beam
mass
m
acts
at
its
center
of
gravity
S.
The
masses
m
and
m
S
R
gravity S. The masses
and
hang at points
L and R. The broken line connecting LL and R
hang
The
brokenline
linethrough
connecting
L and
R forms
an angle
α with the horizon
line
formsatanpoints
angleLαand
withR.the
horizon
point
S’, and
is divided
perpendicularly
through
S’
through
divided
perpendicularly
through S’ with the length a into the sections lL and lR .
with the point
lengthS’,aand
intoisthe
sections
and .



Figure 9. The general two-dimensional representation.
The lever
center
of gravity
withwith
a length
an angle
γ withγa.with
These
The
lever arm
armofofthe
thebalance's
balance's
center
of gravity
a lengthforms
lS forms
an angle
a.
torques
around
point
S’
are
neutralized
under
the
equilibrium
condition
[12].
With
the
gravitational
These torques around point S’ are neutralized under the equilibrium condition [12]. With the
accelerations accelerations
,
and gLin
three gravitational centers of the masses, the following expression
gravitational
, gthe
R and gS in the three gravitational centers of the masses, the following
is
valid:
expression is valid:
(1)
cos + sin =
cos − sin +
sin −
mR gR (lL cos α + a sin α) = mL gL (lL cos α − a sin α) + mS gS lS sin(γ − α)
(1)
=
=
= , the sensitivity of the mechanical balance is defined
It is assumed that
It is assumed
that g(1)
according
to Equation
asgfollows:
L =
R = gS = g, the sensitivity of the mechanical balance is defined according
to Equation (1) as follows:
∂α
cos − sin
=
(2)
sin + cos +
+
cos −
∂α ∂
lL coscos
α − a−sinsin
α
=
(2)
α) + mR=( a0,cos
α − lR sin
+ mS lS cos
− α)
In the case∂m
ofL = m
0,L (lL=sin α=+, a cos
= 0and
formula
(1) αis) changed
as(γ
follows:
= Equation (1) is changed as follows:
In the case of a = 0, lL = lR = l, γ = 0 and=α = 0,
The sensitivity of mechanical balance is modified as follows:
mL = mR = m
∂α
=
∂
The sensitivity of mechanical balance is modified as follows:
(3)
(3)
(4)
The sensitivity is independent of load, depending only on the mass of the beam and the position
l
∂α
of the center of gravity. = 0 means that the mechanical
balance is symmetrical. The beam of(4)a
=
∂mL
m S lS
symmetrical balance is horizontal only if the masses of the ends of beam are equal. = 0, = 0
means
that
the pivots
are on one level.
The
sensitivity
is independent
of load, depending only on the mass of the beam and the position
onofthe
principle
above,
production
and assembly
of one long
of theBased
center
gravity.
γ =mentioned
0 means that
thethe
mechanical
balance
is symmetrical.
The beam
beamwith
of a
knives and bearing
blocks
is very
important
for improving
repeatability
of a
symmetrical
balance is
horizontal
only
if the masses
of the ends the
of beam
are equal.and
a =sensitivity
0, α = 0 means
mechanical
balance.
coordinate measurements and adjusting technology is used for adjusting
that
the pivots
are onThree
one level.
the straightness,
and flatness
between
the middle and
knifeassembly
and sideof
knives
to bebeam
mounted
Based on theparallelism
principle mentioned
above,
the production
one long
with
on the beam.
The parallelism
flatness between
middlethe
knife-edge
and side
knives
and bearing
blocks is and
verythe
important
for improving
repeatability
and knife-edges
sensitivity ofare
a
less
than
20
m.
The
straightness
of
each
knife-edge
is
also
less
than
20
m.
mechanical balance. Three coordinate measurements and adjusting technology is used for adjusting
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the straightness, parallelism and flatness between the middle knife and side knives to be mounted on
the beam. The parallelism and the flatness between middle knife-edge and side knife-edges are less
than 20 µm. The straightness of each knife-edge is also less than 20 µm.
4. Mechanical Balance Experiments
4.1. Mechanical Balance Results
Class E2 weights of 5, 10 and 20 g are used as sensitivity weights from no load to full load.
Ten pieces of class E2 50 kg weights are used as the reference weight of 500 kg. One hundred pieces of
class F1 20 kg weights are used as the reference weights for 1000 kg or 2000 kg. The steps of balance
calibration are shown as follows:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
Under no loading conditions, one uses the small counterweights to adjust the balance of the beam.
Record the indication of the balance.
Add a sensitivity weight of 5 g on the left side.
Record the indication of the balance.
Remove the sensitivity weight of 5 g.
Load the reference weights of 2000 kg on the left side and the 2000 kg counterweight on the
right side.
Increase or decrease the small counterweights until the beam is balanced.
Record the indication of the balance.
Add a sensitivity weight of 20 g on the left side.
Record the indication of the balance.
Remove the sensitivity weight of 20 g.
Unload the reference weights of 2000 kg on both sides.
Use the small counterweights to adjust the balance of the beam.
Record the indication of the balance.
Add a sensitivity weight of 5 g on the right side.
Record the indication of the balance.
Remove the sensitivity weight of 5 g.
Repeat (6) and (7).
Record the indication of the balance.
Add a sensitivity weight of 20 g on the right side.
Record the indication of the balance.
The sensitivities of no load and full load are shown as Table 1. The full load sensitivity is
more than 1.7 part in 10−4 rad/g. The standard deviations of no load and full load are shown in
Tables 2 and 3, respectively.
Table 1. Sensitivity measurements of the mechanical balance.
Left Side
Right Side
Results (Division)
Sensitivity (10−4 rad/g)
No load
Sensitivity weight 5 g
No load
No load
15.381
32.072
7.3
Full load
Sensitivity weight 20 g
Full load
Full load
18.694
34.130
1.7
No load
No load
No load
Sensitivity weight 5 g
15.803
−4.177
7.3
Full load
Full load
Full load
Sensitivity weight 20 g
18.838
3.298
1.7
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Table 2. Standard deviation of no load.
Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
15.394
15.515
15.637
15.714
15.452
15.546
7.3
7.3
7.3
7.3
7.3
7.3
0.04
Table 3. Standard deviation of full load.
Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
18.765
18.783
18.888
19.026
18.896
18.954
1.7
1.7
1.7
1.7
1.7
1.7
0.13
After the indicator based on laser displacement sensors is adjusted, the reading comparisons
between indicators based on optical principles and laser displacement sensors at 500 kg are shown as
Table 4 and Figure 10. The comparison steps between indicators are as follows:
(1)
(2)
(3)
(4)
(5)
Place the 500 kg weight on the weighing pan (left side of the mechanical balance) and select a
500 kg counterweight on the right side of the mechanical balance.
Read the first divisions from the two indicators, respectively, after reaching balance.
Place a sensitivity weight of 5 g on the top of the counterweights or the weighing pan.
Read the second divisions, respectively.
Divide 5 g into the difference between the first divisions and the second divisions. The mass
against one division that represents the sensitivity of the mechanical balance at 500 kg could
be known.
The values of the first column in the Table 4 are the readings based on the optical principle, and
the values of the second column are the sensitivities corresponding to the readings. The values of the
third column in the Table 4 are the readings based on two laser displacement sensors. The values of the
last column are the sensitivities corresponding to the readings based on two laser displacement sensors.
The maximum difference between readings based on optical principle and two laser displacement
sensors is from the eighth row. It is 0.336 divisions. The mass corresponding to the divisions is 0.2 g,
i.e., very small and it can be ignored. The results show the readings between two indicators coincide.
Table 4. Reading comparisons between indicators based on optical principle and laser displacement
sensors at 500 kg.
Optical Principle
Results (Division)
17.925
18.450
18.225
18.050
18.275
18.250
18.250
18.300
18.075
18.200
Laser Displacement Sensors
Sensitivity
(10−4
3.75
3.69
3.64
3.54
3.61
3.63
3.64
3.62
3.76
3.65
rad/g)
Results (Division)
Sensitivity (10−4 rad/g)
17.710
18.193
17.943
17.978
18.097
18.116
17.953
17.964
17.856
18.046
3.73
3.60
3.55
3.50
3.54
3.57
3.55
3.54
3.74
3.58
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18.6
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18.6
18.2
Optical
Principle
18.4
18
Reading（divisions）
Reading（divisions）
18.4
18.2
Optical
Principle
Laser
17.8 18
Displacement
Sensors
Laser
Displacement
Sensors
17.6
17.8
17.4
17.6
17.4
17.2
17.2
1
2
1
3
4
5
6
7
8
9
3Number
4 of
5 Measurement
6
7
8
2
9
10
10
Number of Measurement
Figure 10. Reading results of two indicators.
Figure 10. Reading results of two indicators.
Figure 10. Reading results of two indicators.
The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11. The
The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11.
Thevalue
resultsisregarding
the measurement
of beam
stability
at 2000
are shown
in Figure
The
maximum
7.201 divisions,
and the
minimum
value
is kg
7.329
divisions.
The11.difference
The maximum value is 7.201 divisions, and the minimum value is 7.329 divisions. The difference
maximum
value is 7.201
divisions, and
the minimum
value
is 7.329 divisions. The difference
between
the maximum
andand
minimum
values
divisions.
between
the maximum
minimum
valuesisisonly
only 0.118
0.118 divisions.
between the maximum and minimum values is only 0.118 divisions.
7.4
7.4
7.35
7.35
7.3
7.3
Reading
Reading
7.25
7.25
(divisions)
(divisions)
7.2
7.2
7.15
7.15
7.1
7.1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
Number of measurement
8
9
9
10
11
10
11
Number of measurement
Figure
11.11.
Measurement
ofof
beam
stability.
Figure
Measurement
beam
stability.
Figure 11. Measurement of beam stability.
Figure 12 shows the results of 500, 1000 and 2000 kg. The sensitivity for 500 kg is more than
Figure 12−4shows the results of 500, 1000 and 2000 kg. The sensitivity for 500
kg is more than
3.6
parts12
in shows
10 rad/g,
the sensitivity
1000
kg2000
is more
2.7 parts infor
10−4500
rad/g,
and
the than
Figure
the results
of 500,for
1000
and
kg. than
The sensitivity
kg is
more
3.6 parts in 10−4 rad/g, the sensitivity for 1000−4 kg is more than 2.7 parts in 10−4 rad/g, and the
−4
−4
for 2000
kg is more
than 1.7 parts
in 10 kg
rad/g.
Figurethan
13 showsparts
the relationship
between
3.6 sensitivity
parts
in 10
sensitivity
for 1000
is more
in 10 rad/g,
and the
sensitivity
for rad/g,
2000 kgthe
is more
than 1.7 parts
in 10−4 rad/g.
Figure 13 2.7
shows the relationship
between
the
sensitivity
and
the
load.
As
the
load
changes,
the
sensitivity
becomes
worse.
−4
sensitivity
for 2000and
kg the
is more
1.7
parts
in 10 the
rad/g.
Figure
13 shows
the relationship between
the sensitivity
load. than
As the
load
changes,
sensitivity
becomes
worse.
the sensitivity and the load. As the load changes, the sensitivity becomes worse.
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18
18
16
16
14
14
12
12
Reading 10
(divisions)
Reading 108
(divisions) 8
6
64
500 kg
500
kgkg
1000
1000
2000kg
kg
2000 kg
42
20
1
1
0
2
2
3
4
5
6
7
8
3 Number
4
5 measurement
6
7
8
of
9
9
10
10
Number of measurement
Sensitivity(rad/g)
Sensitivity(rad/g)
Figure
12.12.
The
results
1000kg
kgand
and2000
2000
Figure
The
resultsfor
for500
500 kg,
kg, 1000
kg.kg.
Figure 12. The results for 500 kg, 1000 kg and 2000 kg.
0.0008
0.0008
0.0006
0.0006
0.0004
0.0004
0.0002
0.0002
0
0 0
0
500
1000
500Load(kg)
1000
2000
2000
Load(kg)
Figure 13. The relationship between the sensitivity and the load.
Figure 13. The relationship between the sensitivity and the load.
Figure
13. The
relationship between the sensitivity and the load.
4.2. Uncertainties of
Mechanical
Balance
4.2. Uncertainties of Mechanical Balance
According to the operational principle of the mechanical balance, the expression of indication
4.2. Uncertainties of Mechanical Balance
According
to thetooperational
principle
mechanical balance, the expression of indication
error with respect
the mechanical
balanceof
is the
as follows:
to the
operational
principle
mechanical balance, the expression of indication
errorAccording
with respect
to the
mechanical
balanceof
is the
as follows:
E
=
I
−L
(5)
error with respect to the mechanical balance is as follows:
(5)
= −
where E is the error between the indication of the
balance and the applied load, I is the (5)
= mechanical
−
where E is the error between the indication of the mechanical balance and the applied load, I is the
indication of mechanical balance regarding applied load and L is the applied load [13–15].
where
E isThe
theuncertainty
error between
indication
of the
mechanical
and the
applied
load, I is the
indication
of
mechanical
regarding
applied
load
and Lbalance
is the applied
load
[13–15].
ofbalance
the the
mechanical
balance
is as
follows:
indication
of mechanical
balance
regarding
applied
and L is the applied load [13–15].
The uncertainty
of the
mechanical
balance
is asload
follows:
2
d2
The uncertainty of the mechanical
balance is asd follows:
u2 ( E ) = s2 ( I ) + 0 + L + u2 ( L )
(6)
(6)
=
+ 12 + 12 +
12 12
+
+
+of the mechanical balance corresponding (6)
where u( E) is the uncertainty of error, s(=
I ) is the repeatability
12 the12repeatability
where
is the uncertainty of error,
is
of the mechanical balance
to the applied load, d0 is the no load sensitivity, dL is the applied load sensitivity, u( L) is the uncertainty
where
is
the
uncertainty
of
error,
is
the
repeatability
of
mechanical
balance
is the no load sensitivity,
is thethe
applied
load sensitivity,
corresponding
to the applied load,
deriving from the reference weight including the air buoyancy correction. The uncertainties of 500,
is the
no loadweight
sensitivity,
is the air
applied
load sensitivity,
corresponding
to the
applied
load,
is the
deriving
from5.the
reference
including
buoyancy
correction.
1000
anduncertainty
2000
kg are
shown
in Table
is the uncertainty
reference
the air buoyancy correction.
The uncertainties
of 500,deriving
1000 andfrom
2000the
kg are
shownweight
in Tableincluding
5.
The uncertainties of 500, 1000 and 2000 kg are shown in Table 5.
Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load
(kg)
Load
(kg)
500
1000
500
2000
Standard
Uncertainty
Standardof the
Weighing
Process
Uncertainty
of the(g)
Standard
Uncertainty
Due to
Standard
the Sensitivity
Uncertainty
Due(g)
to
Standard Uncertainty of the
Reference
Weight with
Standard
Uncertainty
of Air
the
BuoyancyWeight
Correction
Reference
with (g)
Air
Combined
Standard
Combined
Uncertainty
Standard (g)
Extended
Uncertainty
Extended
(k = 2, g)
Uncertainty
0.072
Weighing
Process (g)
0.176 (g)
the Sensitivity
Buoyancy0.134
Correction (g)
0.232 (g)
Uncertainty
(k 0.47
= 2, g)
0.028
0.072
0.117
0.236
0.176
0.469
0.833
0.134
1.667
0.867
0.232
1.736
1.8
0.47
3.5
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Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load (kg)
Standard Uncertainty
of the Weighing
Process (g)
Standard
Uncertainty Due to
the Sensitivity (g)
Standard Uncertainty
of the Reference Weight
with Air Buoyancy
Correction (g)
Combined
Standard
Uncertainty (g)
Extended
Uncertainty
(k = 2, g)
500
1000
2000
0.072
0.028
0.117
0.176
0.236
0.469
0.134
0.833
1.667
0.232
0.867
1.736
0.47
1.8
3.5
5. Conclusions
The establishment of a new 2000 kg mechanical balance is important for traceability of class F1
weights from 500 kg to 2000 kg used in industrial processes. To develop a mechanical balance with
high accuracy and a wide measurement range for measurement of class F1 weights over 500 kg, a new
heat treatment method of metal material, three coordinate measurement and adjustment technology,
dynamic monitoring with regards to the balance of the beam and synchronous lifting control are
used to improve the repeatability and sensitivity of the mechanical balance. For the realization of any
combinations of counterweights in a limited space, a new counter-weight selection system is designed
and its construction accomplished. The sensitivity of the new 2000 kg mechanical balance is more than
1.7 parts in 10−4 rad/g. The extended uncertainties of 500, 1000 and 2000 kg for the mechanical balance
are 0.47 g, 1.8 g and 3.5 g, respectively. The results show the performance of the new mechanical
balance is better than that of electronic mass comparators used in commerce.
Acknowledgments: This work was supported in part by the National Science and Technology Support Program
under Grant 2011BAK15B06, in part by the Special-Funded Program through the National Key Scientific
Instruments and Equipment Development under Grant 2012YQ090208, and in part by National Key Research and
Development Program for National Quality Infrastructure under Grant 2016YFF0200103.
Conflicts of Interest: We declare that we have no conflict of interest.
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