THE 9th INTERNATIONAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTR ICAL ENGINEERING [603461]

THE 9th INTERNATIONAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTR ICAL ENGINEERING
May 7-9, 2015
Bucharest, Romania

978-1-4799-7514-3/15/$31.00 ©2015 IEEE Xi Yi
Weighing instrument Between Parallel Mirrors – An Electronic Weighing
Instrument

Adriana Vâlcu
Mass Laboratory, National Institute of Metrology
Șos. Vitan Bârze ști nr. 11, sect. 4, Bucharest, Romania
e-mail: [anonimizat] ; [anonimizat]

Abstract – The paper presents the assessment way of electronic
weighing instruments according to their use. Thus, in mass
measurements there are two ways to use a weighing instrument:
as a mass comparator, in the dissemination of mass unit from
national mass standard to standards of the lowest accuracy and as a direct weighing instrument, a common balance, used in
different applications. Even if, in term of constructive and
functional points of view the two type of weighing instruments are not different, their use differs and hence, the need to
approach different assessment methods. In the paper, it is
highlighted the difference between determination of measurable properties by calibration, for both, mass comparators and a
common balance (non-automatic weighing instruments –
NAWI), making a parallel between them.
Keywords : electronic weighing instrument, EMFC principle,
mass comparator, error of indication.
I. INTRODUCTION
Determination of bodies mass, weighing, aims to obtaining
measurement information, i.e. information of a particular type, that tell us how many times the examined body mass is greater or less than the mass of a given body, adopted as the measurement unit.
Since this information is obtained through appropriate
technical means, before presenting the actual weighing operation is required a presentation of the basic principle of a weighing instrument.
Any weighing instrument, regardless of its operating
principle or its destination, can be considered as a black box, represented as in the Figure 1.

Fig. 1 Schematic representation of a weighing instrument

The adjective "black" emphasizes that the concrete
solutions which underlying instrument construction are ignored. When the operating principle of a device is highlighted, it can be said that this box will be lighted.
The black box has a pan on which is placed an object, an
indicator that reads "zero" when the pan is empty and other figures when the object is placed on the pan.
An "ideal" balance should have the following
characteristics [1]: • when the same object is weighted, the indicator should
indicate the same value under the same conditions of temperature, humidity, atmospheric pressure, etc;
• when two objects are placed on the pan at the same time,
the balance indication should be equal to the sum of the indications corresponding to each object individually placed
on the pan.
The first characteristic refers to the repeatability of the
balance and the second one to its linearity.
II. U
SE OF THE WEIGHING INSTRUMENT
The same weighing instrument can be used in two ways:
¾ As a mass comparator (standard balance), in the
dissemination of mass unit from national mass standard (with values derived from the International Prototype of the Kilogram) to the standards in routine use. For this purpose, the following parameters of the mass comparator are determined: sensitivity and/or the mass value of the smallest scale interval, measurement repeatability results (determined according to measurement cycle used, ABBA or ABA [2]) and, if necessary, the effect of the loads eccentrically placed (eccentricity). The mass comparator gives the difference of mass values between two weights, mass standard and test weight using a differential weighing method.
In turn, mass comparators are classified in three main
categories, namely manual, automatic and robotic:
– manual comparators require human operation for loading,
unloading of the mass standards and recording of readings;
– automatic comparators minimize the need for human
intervention so that, errors due to operator during the determinations are practically eliminated;
– robotic comparators (fully automated mass comparisons),
having up to 4 arms work.
Depending on the type of construction, the comparators
may have a restricted weighing range or a whole weighing range, from zero to Max.
¾ As a direct weighing instrument, a common balance,
known as non-automatic weighing instrument, whose measurable properties are repeatability of indications, the error of indication for the whole range of display scale and, if necessary, the effect of the loads eccentrically placed. The balance indicates the mass of a body placed on its pan, without having recourse to mass standards [3].

1/3 Max= 150 g
I (g) E (g)
A 0.000 0
B 0.000 1 0.000 1
C 0.000 0 0.000 0
D 0.000 0 0.000 0
E 0.000 0 0.000 0
ΔIec ci (g) 0.000 1
ΔIecci (i n mg) 0.10
uEc c (mg) 0.058
UEc c (m g) 0.115
No. Load applied Indication The average of Difference
on the pan indications
I
g g g mg
1 0 0,000 0
2 L= 500 499.999 9
3 500+ k =10 g 509.999 9
4 500 A 499.999 8
5 500 B 499.999 8
6 500 B 499.999 7 499.999 75 -0.15
7 500 A 500.000 0 499.999 90
8 500 A 499.999 8
9 500 B 499.999 7
10 500 B 499.999 7 499.999 7 -0.15
11 500 A 499.999 9 499.999 9
12 500 A 499.999 8
13 500 B 499.999 7
14 500 B 499.999 7 499.999 7 -0.20
15 500 A 500.000 0 499.999 9
16 500 A 500.000 0
17 500 B 499.999 9
18 500 B 499.999 8 499.999 9 -0.10
19 500 A 499.999 9 500.000 0
20 500 A 499.999 9
21 500 B 499.999 8
22 500 B 499.999 8 499.999 8 -0.15
23 500 A 500.000 0 500.000 0
24 500 A 500.000 0
25 500 B 499.999 8
26 500 B 499.999 8 499.999 8 -0.20
27 500 A 500.000 0 500.000 0
An Bn n I I I − = ΔIII. OPERATING PRINCIPLE OF AN ELECTRONIC WEIGHING
INSTRUMENT
A high resolution of a weighing instrument can only
achieved with electromagnetic force compensation principle which represents the state of the art with respect to accuracy in mass metrology, being the most favorable principle for a correct weighing in an extended measuring range.
The operating principle scheme of an electronic weighing
instrument is shown in Figure 2 [4].

Fig. 2 Schematic representation of an EMFC principle

Such electronic balance uses a feedback circuit to compare
the electrical output to the force input 1. The force applied by the mass of an object is compensated by the magnetic force of a coil 2. Through the compensation coil (inserted in a permanent magnetic field 3) a permanent current flows which generates a restoring force in opposition to the applied force. With the aid of an electronic position sensor 4 and servo amplifier 5, the coil position is controlled. When the balance is loaded, vertical positional changes are recorded. The current is directly proportional to the loaded weight and is measured by a precision resistor 6. The signal is transmitted to the analog-to digital converter A/D. With the aid of a microprocessor, the digital signal is processed and shown on the balance display 7.
IV. A
SSESSMENT OF ELECTRONIC MASS COMPARATORS
1. Determination of metrological characteristics
For electronic mass comparators, the following
metrological characteristics are determined:
– the value of the scale interval (division); – repeatability of the measurements; – the effect of the loads eccentrically placed (eccentricity). An example of calibration for electronic mass comparators
is presented in the Table I.
TABLE I
A CALIBRATION MODEL FOR ELECTRONIC MASS COMPARATORS
Determination of the scale interval, repeatability of the measurements and
eccentricity

In the Table I: m
L= 500000.26 mg with umL= 0.125 mg
mk= 10000.001 mg with umk= 0.01 mg
From the Table I, the next metrological characteristics are
calculated:
A. The value of the scale interval
A1. If the balance has a restricted domain:
– an overload k having a mass mk equal to maximum
capacity of the restricted domain it’s applied on the balance.
The value of the scale interval is calculated as follows:
d = mk / |I3-I2|= mk /ΔIs= 0.10 mg (1)
A2. For balances where the maximum capacity of the
domain corresponds to the maximum capacity of the balance:
– the mass of the overload mL can be considered just
this maximum value L of the comparator. The value of the
scale interval can be calculated as follows:
d = m L / |I 2-I1| = mL /ΔIs= 0.10 mg (2)
I1, I2 and I3 are the indications of the balance, in scale
divisions.
ΔIs represents the modification of the balance indication
(written in general form) after applying a surcharge.
In the Table I, are presented the both cases: A1 and A2. A BC
D
Ed2

mgILL
dd
Uecc
ecci
ecci
ecc 8.5
32 =Δ⋅ ⋅
=mg II I where I IA i ecci ecci ecci 10.0} : , max{ = −= Δ Δ = ΔmgnI I
sn
ii
04.01) (
12
=−Δ−Δ
=∑
=B. Repeatability of the measurements
Repeatability is determined by calculating standard
deviation s, performed for n = min. six “ABBA” cycles:
(3)
C. The effect of the load eccentrically placed
A load L
ecc ≈ 1/3 Max is applied in an arbitrary order on the
pan in the positions A, B, C, D, E, indicated in the Table I, in order to check the influence of asymmetric placement of the loads on the measurement.
From the indications I
i obtained for different positions of
the load, is calculated the difference ΔIecci:
(4)

2. Measurement uncertainty obtained in determination
of metrological characteristics of mass comparators
A. Uncertainty associated to the scale interval (division) [2]
(5) U
d = 3.1×10-6 for the case A1
Ud = 5.1×10-8 for the case A2
where: d is the value of the scale division (interval);
m
(k,L) mass of the overload k or L;
um(k,L) uncertainty of mk (or mL);
u (ΔIs) uncertainty of the difference ΔIs.
B. Variance of repeatability
Variance of repeatability is given by standard deviation s
calculated for n “ABBA” (or “ABA”) measurements cycles.
u r 2
= s2=0.0016 mg (6)
C. Uncertainty associated to the effect of the loads eccentrically
placed (eccentricity).
This component is calculated on the one hand, depending on the actual load L
i and distance from the center of the pan di and, on the
other hand, using the value of the load Lecc and the distance decc used
at the eccentricity test:
(7)
When we calibrate the mass comparators, d
i=decc and
Lecc=Li, but are different in the calibration of the weights.
3. Areas of application of mass comparators
Generally, it is recommended that the ratio between
standard deviation of the mass comparator and calibration uncertainty be 1/3. For the weights classified in accuracy classes E
2, F 1, F 2, M 1, M 2, and M 3 it is required that the
calibration uncertainty be less than or equal to one third of the maximum permissible errors ( E
T) of the weights.
Consequently, it is recommended that: 10 s ≤ E
T (8) For this reason is not established a minimum capacity of
the mass comparator (standard balance) but are given in tabular form, information on weights (nominal values and accuracy classes) that can be calibrated using the respective comparator.
Example : It was performed the calibration of the mass
comparator according to the Table I, with following characteristics: Max 510 g and d = 0.1 mg. The standard deviation s obtained from six ABBA cycles was s = 0.04 mg.
Therefore, the mass comparator can be used for calibration of weights having nominal mass up to 500 g and maximum permissible error MPE ≥0.4 mg. In the Table II are the
MPE (s) of the weights and in the Table III are listed the
nominal values of the weights that can be calibrated using this mass comparator.
TABLE II
MPE (S) OF THE WEIGHTS

TABLE III
A
REAS OF APPLICATION OF THE MASS COMPARATOR
Nominal
Values

Class
E2 Class
F1 Class
F2 Class
M1
500 g Yes Yes Yes Yes
(200…100) g NO Yes Yes Yes
(50…2) g NO NO Yes Yes
1 g NO NO NO Yes
(0.5…0.1) g NO NO NO Yes
0.05 g NO NO NO Yes
V. ASSESSMENT OF ELECTRONIC NON -AUTOMATIC
WEIGHING INSTRUMENTS
1. Determination of metrological characteristics
The calibration of the non automatic weighing instrument
(NAWI) consists in:
– applying test loads to the instrument under specified conditions; – determining the errors of the indication and uncertainty of measurement attributed to the results; – evaluating the uncertainty of measurement to be attributed to the results.
The next measurable proprieties are determined:
– repeatability of indications, ()2 2
(,)
22
(,)2s
dd
smkL
kLu uIUk u d
mI⎛⎞ Δ⎜⎟ =⋅ = × +⎜⎟ Δ⎝⎠
1.0
0.3
0.10
0.030 1 g
0.8
0.25
0.08
0.025 0.5 g
0.6
0.20
0.06
0.020 0.2 g
0.5
0.15
0.05
0.015 0.1 g
0.4
0.12
0.04
0.012 0.05 gNominal
ValuesClass
E2Class
F1Class
F2Class
M1
500 g
0.8
2.5
8.0
25
200 g
0.3
1.0
3.0
10
100 g
0.16
0.5
1.6
5.0
50 g
0.10
0.3
1.0
3.0
20 g
0.08
0.25
0.8
2.5
10 g
0.06
0.20
0.6
2.0
5 g
0.05
0.16
0.5
1.6
2 g
0.04
0.12
0.4
1.2
1 g
0.03
0.10
0.3
1.0
2 g
0.04
0.12
0.4
1.2
1.0
0.3
0.10
0.030 1 g
0.8
0.25
0.08
0.025 0.5 g
0.6
0.20
0.06
0.020 0.2 g
0.5
0.15
0.05
0.015 0.1 g
0.4
0.12
0.04
0.012 0.05 gNominal
ValuesClass
E2Class
F1Class
F2Class
M1
500 g
0.8
2.5
8.0
25
200 g
0.3
1.0
3.0
10
100 g
0.16
0.5
1.6
5.0
50 g
0.10
0.3
1.0
3.0
20 g
0.08
0.25
0.8
2.5
10 g
0.06
0.20
0.6
2.0
5 g
0.05
0.16
0.5
1.6
2 g
0.04
0.12
0.4
1.2
1 g
0.03
0.10
0.3
1.0
2 g
0.04
0.12
0.4
1.2

Repeatability
500 g 1500 g
div div
1 -1.0 -6 .0
2 -2.0 -6 .0
3 -2.0 -6 .0
4 -2.0 -6 .0
5 -2.0 -6 .0
6 -2.0 -6 .0
7 -2.0 -6 .0
8 -2.0 -6 .0
9 -2.0 -6 .0
10 -2.0 -7 .0
sp[div]= 0.316 0.316
sp[mg]= 3.162 3.162
Eccentri city
1/3 Max= 500.0002 g U Et 0.300
I[ g] E [ mg] E c[mg]
0 0.00 0.00
A 499.98 -2 0.02 -2 0.02
B 499.97 -3 0.02 -1 0.00
C 499.97 -3 0.02 -1 0.00
D 499.98 -2 0.02 0.00
E 499.98 -2 0.02 0.00

ΔIecci max = 10.00 mg
ET AL ON AR E u = 2.887 mg
U = 5.774 mg
Error of indication at:
Load
Indication Error Corrected Um st
error from CC uE U E
L I E Ec U
g g mg mg mg mg mg

0.000 000 0.00 0.00 0.00 0.00 4.28 8.56
0.499 981 0.50 0.02 0.02 0.02 5.16 10.33
10.000 002 10.00 0.00 0.00 0.04 5.16 10.33
49.999 944 50.00 0.06 0.06 0.06 5.17 10.34
99.999 830 100.00 0.17 0.17 0.10 5.20 10.39
199.999 970 200.00 0.03 0.03 0.50 5.31 10.61
299.999 800 300.00 0.20 0.20 0.70 5.47 10.95
500.000 020 499.99 -10.02 -10.02 0.30 5.92 11.84
699.999 990 699.98 -19.99 -19.99 0.80 6.59 13.17
999.999 800 999.96 -39.80 -39.80 0.60 7.76 15.52
1199.9997 70 1199.95 -49.77 -49.77 1.10 8.68 17.36
1499.9998 20 1499.94 -59.82 -59.82 0.90 10.11 20.21
1509.9998 22 1509.94 -59.82 -59.82 1.00 10.16 20.32
– errors of indications,
– effect of a load eccentrically placed.
An example of calibration for a NAWI with Max 1510 g
and d =10 mg is presented in the Table IV.
TABLE IV
EXAMPLE OF CALIBRATION FOR NAWI

A.
Repeatability of indications
Repeatability consists in the repeated deposition of the
same load on the load recepto r under repeatability conditions.
Usually, repeatability is performed at two loads approximately equal to 0.5 Max and Max. For each chosen load j, the repeatability is expressed as standard deviation s:
w i t h ( 9 )
where:
n is the number of the indications I
ji (which can be replaced
with error of indications Eji).
B. Error of indication
For a load j applied on the pan in an ascending, descending,
or in combination way, the error of indication is calculated as follows [6]:
E
j = Ij – mstj (10)
where Ij is the indication of the balance and mstj is the mass
value of the standard weight from the calibration certificate.
The minimum number of the different loads applied for this
test is 5 (the loads should be distributed fairly evenly over the normal weighing range [6]). If a weighing instrument is used only over a part of its capacity, the calibration may be restricted to this part of the measuring range [7]. C.
Eccentricity test
The eccentricity test is performed in the same manner as
for mass comparators. The difference ΔIecci is calculated as in
formula (4).
The results obtained for tests A, B and C are shown in the
Table IV.
2. Standard uncertainty associated to error of indication
Starting from the equation (11), by derivation, it can be
obtained the standard uncertainty of the error [5, 6].
22() ( ) ( )st uE u I u m =+ (11)
where: u(E) is standard uncertainty of the error of indication;
u(I) standard uncertainty of the indication;
u(m
st) standard uncertainty of the standard weight from de
calibration certificate.
The expanded uncertainty of the error can be calculated as
follows [5, 6]: (12)
where:
– d
0 is the resolution of the balance at no-load indication;
– dL the resolution of the balance at load ;
– s(I) uncertainty due to repeatability of the indication,
given by standard deviation of several weighing results;
– u(mst) is standard uncertainty of the mass standard from
the calibration certificate.
-()ˆecc wIδ relative uncertainty associated to the effect of
the load Lecc eccentrically placed [6]:

(13)

This value is multiplied by the balance indication, yielding
to uncertainty value for each load.
The uncertainty values associated to errors of indication
obtained for each load are shown in the Table IV.
All the uncertainty components can be graphically
represented in an Ishikawa (Fishbone) diagram, as shown in Figure 3, [5].

Fig. 3 Ishikawa diagram of uncertainty components for NAWI calibration ()2
1
1()n
ji j
i
jII
sIn=−
=−∑
11n
j ji
iI In ==⋅∑22 2 2 2 2
0ˆ () 2 () 2 / 1 2 / 1 2 ( ) ( ) ( )Le c c s t UE uE d d s I w I I u m δ == ++ + +
(),maxˆ 0.0000058
23ecc i
ecc
eccI
wI
LδΔ
==
A BC
D
Ed2

VI. PARALLEL BETWEEN MEASURABLE PROPERTIES OF
WEIGHING INSTRUMENTS
In the Table V is presented a parallel between determined
characteristics of the two type of weighing instruments. From the table, it can see that only the eccentricity error
ΔIecc is calculated in the same way for both weighing
instruments.

TABLE V
PARALLEL BETWEEN MEASURABLE PROPERTIES OF WEIGHING INSTRUMENTS
Determined characteristics

Mass comparators NAWI

Repeatability of measurements
Std. dev. of min. 6 ABBA cycles:

Repeatability of indications
Std dev. of indications, the load is applied at least 5 times:

The value of the balance scale interval

d = m k / |I n-In-1|= m k /ΔIs

The error of indication

Ej = Ij – mrefj
22() ( ) ( )ref uE u I u m =+
Eccentricity

32ecc
ecci
ecci
eccILL
dd
UΔ⋅ ⋅
=
Eccentricity

VII. CONCLUSION
The paper describes the assessment way of electronic
weighing instruments according to their use.
Even if, in term of constructive and functional points of
view the two type of electronic weighing instruments are not different, their use differs and hence, the need to approach different assessment methods.
In the paper, it is highlighted the difference between
determination of measurable properties by calibration, for both, mass comparator and a common balance, making a parallel between them.
Thus, it can be seen that for the mass comparators,
repeatability is calculated from min. 6 ABBA measuring cycles, whereas for NAWI is determined using the direct indication of the balance.
Also, for mass comparators is determined the value of the
scale interval (division) which is a main characteristic in the calibration of the weights, whereas for NAWI, is determined the indication error which is very important for different applications. Thus, the accurate determination of mass influences a vast range of activities being an important source of measurement uncertainty in any analysis.
From the Table I and Table IV it can be seen that only the
eccentricity error ΔI
ecc is calculated in the same way for both
weighing instruments but, uncertainty calculation differs.
So, before the calibration of an electronic weighing
instrument it is very important to know its destination, in order to perform a correct assessment.
R
EFERENCES
[1] R. Davis and K. Jaeger, “A primer for mass metrology,” NBS Special
Publication 700-1, 1984.
[2] OIML, International Recommendation No 111, “Weights of classes E1,
E2, F1, F2, M1, M2, M3,” 2004, pp. 5-71.
[3] R. Schwartz, “Guide to mass determination with high accuracy,” PTB
MA-40, 1995 , p. 3 and pp. 54-58
[4] http://www.weighing-systems.com/TechnologyCentre/Balances.html [5] A.Vâlcu, F. Iacobescu “The Provision of Mass Calibrations for
Micro/Nano Force Measurements”, Proceedings of ICQNM IARIA,
2013.
[6] EURAMET cg-18, Version 3.0., “Guidelines on the Calibration of
Non-Automatic Weighing Instruments”, 2011.
[7] A.Vâlcu, “Etalonarea aparatelor de cânt ărit cu func ționare neautomat ă
utilizate în laboratoarele farmaceutice”/ “Calibration of non-automatic weighing instruments used in pharmaceutical laboratories”, Metrologie,
no.2/2005, Vol. LI , pp.43-49.
2
1
1n
imed i
i
( ABBA )()
sn=Δ− Δ
=−∑
()2
1
1()n
ji j
i
jII
sIn=−
=−∑
()2 2
222s
dd
smk
kuI uUk u d
mI⎛⎞ Δ⎜⎟ =⋅ = × +⎜⎟ Δ⎝⎠
{ } max , :ecc ecci ecci i AI Iw h e r e I I I Δ= Δ Δ = −
(),max
23ecc i
ecc
eccI
uI I
LδΔ
={ } max , :ecc ecci ecci i AI Iw h e r e I I I Δ= Δ Δ = −