ISO/TR 6057:2023
(Main)Hydraulic fluid power — Sample calculations for ISO 11171
Hydraulic fluid power — Sample calculations for ISO 11171
This document shows how to use the normative mathematical formulae and tools of ISO 11171. Examples are used to demonstrate their use for calibrating automatic particle counters (APCs).
Transmissions hydrauliques — Calculs des échantillons pour l'ISO 11171
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Standards Content (Sample)
TECHNICAL ISO/TR
REPORT 6057
First edition
2023-04
Hydraulic fluid power — Sample
calculations for ISO 11171
Transmissions hydrauliques — Calculs des échantillons pour l'ISO
11171
Reference number
ISO/TR 6057:2023(E)
© ISO 2023
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ISO/TR 6057:2023(E)
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ISO/TR 6057:2023(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Example 1: Selection of threshold voltage settings . 1
5 Example 2: Evaluating data quality . 3
6 Example 3: Dilution of samples .5
7 Example 4: Relating particle size to threshold voltage setting for particles 30 µm(c)
and smaller . 7
8 Example 5: Relating particle size to threshold voltage setting for primary
calibration of sizes larger than 30 µm(c) . 9
9 Example 6: Construction of calibration curve .11
10 Example 7: Calculation of coefficient variation for volume measurement using
ISO 11171:2022, Clause A.8 .12
11 Example 8: Determination of coincidence error limit .13
12 Example 9: Determination of flow rate limits using ISO 11171:2022, Annex C .14
13 Example 10: Determination of resolution using ISO 11171:2022, Annex D .17
14 Example 11: Verification of counting accuracy and secondary calibration
suspensions using ISO 11171:2022, Clause E.1 .18
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ISO/TR 6057:2023(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee
SC 6, Contamination control.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/TR 6057:2023(E)
Introduction
ISO 11171:2022, like its predecessors, retains traceability to the internationally accepted definition
of a metre and reports particle size in units of µm(c). The methods for determining data acceptance
criteria, coincidence error limit, working flow rate and resolution remain unchanged, but mathematical
calculations and tools were first introduced in ISO 11171:2020 to ensure consistency in terms of how
automatic particle counter (APC) calibration curves are created and used. For example, mathematical
techniques have been introduced to determine the APC threshold settings used to obtain calibration
data and a tool provided to generate calibration curves. Other mathematical equations to estimate
the standard error of the calibration, to calculate normalized concentrations for diluted samples, and
to calibrate at particle sizes larger than 30 µm(c) were first introduced in 2020. This document uses
example calculations that fully conform to ISO 11171.
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TECHNICAL REPORT ISO/TR 6057:2023(E)
Hydraulic fluid power — Sample calculations for ISO 11171
1 Scope
This document shows how to use the normative mathematical formulae and tools of ISO 11171.
Examples are used to demonstrate their use for calibrating automatic particle counters (APCs).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 11171, Hydraulic fluid power — Calibration of automatic particle counters for liquids
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11171 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Example 1: Selection of threshold voltage settings
The method of selecting threshold voltages for particle sizing calibration is specified in ISO 11171:2022,
6.3, which requires that:
— a minimum of 12 different threshold settings be used to construct a calibration curve;
— the first (lowest) threshold setting, J, be 1,5 times the threshold noise level of the APC;
— the highest threshold setting, H, corresponds to a particle size of approximately 30 μm(c) or smaller
for primary calibrations and corresponds to a size that does not exceed the largest reported particle
size that is in conformance with ISO 11171:2022, Annex F, for secondary calibrations;
— intermediate threshold settings be logarithmically spaced such that the value of each channel is K
times greater than its preceding channel, where K is a constant defined by Formula (1):
()loglHJ− og /()G−1
K =10 (1)
where G is the number of threshold settings used to construct the calibration curve and is greater
than or equal to 12.
This example considers an APC with eight threshold settings that can be adjusted in 1 mV increments.
The threshold noise level of the APC was determined to be 5 mV and its manufacturer indicated that
30 μm(c) is expected to correspond to a threshold voltage setting of about 2 600 mV.
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ISO/TR 6057:2023(E)
The calibration curve will be determined using 12 threshold voltage settings, the minimum number
permitted by ISO 11171. Thus, the value of H is 2 600 mV and the value of G is 12. The value of J is
determined by Formula (2):
J =×15,,57= 5 (2)
Since this APC can only be adjusted in 1 mV increments, the value of J is rounded up to 8 mV for
calibration. Using the values of G, H and J, the value of K can be calculated by Formula (3):
(logHJ−−log)/(G 12)(log( 600)l−−og()81)/()21
K ==10 10 =1,692 (3)
The threshold settings for the 10 intermediate channels are set at values corresponding to 1,692 times
the value of each preceding channel as shown in Table 1.
Table 1 — Threshold voltage settings for APC in Example 1
a
Threshold setting number Calculation Threshold voltage setting
1 1,5 × 5 mV = 8 mV
2 1,692 × 8 mV = 14 mV
3 1,692 × 14 mV = 23 mV
4 1,692 × 23 mV = 39 mV
5 1,692 × 39 mV = 66 mV
6 1,692 × 66 mV = 111 mV
7 1,692 × 111 mV = 188 mV
8 1,692 × 188 mV = 317 mV
9 1,692 × 317 mV = 537 mV
10 1,692 × 537 mV = 908 mV
11 1,692 × 908 mV = 1 537 mV
12 1,692 × 1 537 mV = 2 600 mV
a
Threshold voltage settings rounded off to the nearest mV based upon the capabilities of the APC in the example.
This APC only has the minimum number of channels required in ISO 11171:2022, 6.4 (eight channels),
but ISO 11171:2022, 6.3, requires data from twelve or more threshold settings to construct a calibration
curve. ISO 11171:2022, 6.8, requires that data from at least two different samples be obtained for each of
the threshold voltage settings (refer to ISO 11171:2022, 6.8) and that the channels used for a particular
sample be distributed over the entire range to the extent possible. To meet these requirements in
this example, eight different threshold settings chosen from the list of twelve can be used for the first
sample and different combinations of eight threshold settings used for each of the other two samples.
An example of how to allocate threshold settings among the eight channels is shown in Table 2, where
the first column lists the twelve required threshold voltage settings and columns 2, 3 and 4 show the
channels used to collect data at these settings for the indicated sample. The last column in Table 2
shows the number of samples for which data are obtained for each threshold setting, confirming these
requirements have been met.
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ISO/TR 6057:2023(E)
Table 2 — Allocation of threshold voltage settings among the eight channels
of the Example 1 APC
Channel number corresponding to indicated threshold Number of samples
Threshold
voltage setting and sample at indicated thresh-
voltage
a old voltage setting
setting mV
Sample A Sample B Sample C
8 1 1 2
14 1 2 2
23 2 3 2
39 3 2 2
66 3 4 2
111 4 5 2
188 5 4 2
317 5 6 2
537 6 7 2
908 7 6 2
1 537 7 8 2
2 600 8 8 2
a
Threshold voltage settings determined in Table 1.
5 Example 2: Evaluating data quality
ISO 11171:2022, 6.6, specifies how to verify the acceptability of particle count data for APC calibration
purposes. In brief, the process involves:
— calculation of the total number of particles, N, counted for a given APC channel and sample;
— calculation of the data quality factor, D ;
Q
— identification of potential outliers among the data if the D is unacceptable.
Q
This process is used throughout ISO 11171 to ensure the integrity of data used for APC calibration. This
example uses a calibration suspension sample analysed as described in ISO 11171:2022, 6.5 and 6.6,
using a sample volume, V, of 10 mL. Unless otherwise noted, the term “particle concentration” refers to
cumulative particle concentration throughout this document. Particle concentrations of 26 068
particles/mL, 25 757 particles/mL, 25 802 particles/mL, 31 771 particles/mL and 25 834 particles/mL
were obtained. The mean particle concentration, X , for these five counts is 27 046. The mean observed
number of particles counted for the five particle counts, X, is given by Formula (4):
XV ==X 27 046×= 10 270460 (4)
The total number of particles, N, counted for the sample is calculated using Formula (5):
NX==5 270 460×=51352300 (5)
This value is greater than 1 000, as required by ISO 11171:2022, 6.6, hence is sufficiently high for
calibration purposes.
Using ISO 11171:2022, Table C.2, and the value of X previously calculated, the maximum allowable D
Q
for the data can be determined. Referring to the first two columns of the table, a value of 270 460 for X
corresponds to the first row of the table, i.e. X greater than or equal to 10 000. The maximum allowable
D can be found in the third column, which is used for ISO 11171:2022, 6.6, 6.13, B.5, C.9, D.4, D.9, E.6
Q
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ISO/TR 6057:2023(E)
and F.5. Thus, the maximum allowable D is 11,0 for this example. The value of D expressed as a
Q Q,
percentage, for the data in this example is calculated using Formula (6):
XX−
31 771−25757
maxmin
D = ×=100 ×=100 22,24 (6)
Q
X 27 046
where
X is the maximum number of counts observed among the five particle counts or 31 771;
max
X is the minimum number of counts observed among the five particle counts or 25 757.
min
Since the value of D is greater than the maximum allowable D , the data are unacceptable for
Q Q
calibration purposes and can be examined for possible outliers.
The outlier test parameter, D , for the data in this example is calculated using Formula (7):
0
XX−
31771 −25757
maxmin
D = = =10, 5 (7)
0
XX− 31771 −26068
0 N
where
X is the observed particle concentration of suspected data outlier (either X or X ), 31 771
0 max min
particles/mL;
X is the observed particle concentration closest in value to the suspected outlier, 26 068
N
particles/mL.
If the value of D is less than 1,44, as in this example, X can be discarded as a statistical outlier. In
0 0
Example 2, D was found to be 1,05, well below 1,44, hence the suspect data point, 31 771, can be
0
discarded as an outlier. The remaining four data points are used to recalculate X , giving a value of
25 865 particles/mL, which will be used in constructing the calibration curve.
In another example, data from a different channel setting is considered for the same calibration
suspension sample analysed in the previous example. For this channel setting, particle concentrations
of 810 particles/mL, 802 particles/mL, 800 particles/mL, 805 particles/mL and 803 particles/mL were
obtained.
The mean particle concentration, X , for these five counts is 804. The mean observed number of
particles counted for the five particle counts, X, is given by Formula (8):
XV ==X 804 ×=10 8040 (8)
The total number of particles, N, counted for the sample is calculated using Formula (9):
NX==58 040×=540200 (9)
This value is greater than 1 000, as required by ISO 11171:2022, 6.6, hence is sufficiently high for
calibration purposes.
Using ISO 11171:2022, Table C.2, and the value of X previously calculated, the maximum allowable D
Q
for the data can be determined. Referring to the first two columns of the table, a value of 8 040 for X
corresponds to the second row of the table, i.e. X greater than or equal to 5 000 but less than 10 000.
The maximum allowable D can be found in the third column, which is used for ISO 11171:2022, 6.6,
Q
6.13, B.5, C.9, D.4, D.9, E.6 and F.5. Thus, the maximum allowable D is 11,3 for this example. The value of
Q
D , expressed as a percentage, for the data in this example is calculated using Formula (10):
Q
XX−
810−800
maxmin
D = ×=100 ×=100 12, 0 (10)
Q
X 804
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ISO/TR 6057:2023(E)
where
X is the maximum number of counts observed among the five particle counts or 810;
max
X is the minimum number of counts observed among the five particle counts or 800.
min
Since the value of D is less than the maximum allowable D , the data are acceptable for calibration
Q Q
purposes and can be used in constructing the calibration curve.
6 Example 3: Dilution of samples
To facilitate calibration at small particle sizes, ISO 11171:2022, Annex G, provides a standardized
procedure for diluting calibration suspensions and ISO 11171:2022, 6.7, specifies a method for
normalizing the resultant particle count data. To use this procedure, it is necessary to know the
coincidence error limit of the APC and the approximate size of the smallest particles that it can count.
In this example, the APC is capable of counting particles as small as 2 µm(c) and has a coincidence error
limit, X , of 12 713 particles/mL. The certified particle size distribution of the calibration samples is
A
shown in Table 3.
Table 3 — Certified particle size distribution of calibration sample for Example 3
Certified particle
Certified particle size
concentration
µm(c)
particles/mL
2 33 066
3 17 714
4 10 865
5 6 637,0
6 4 210,0
7 2 886,4
8 2 007,2
9 1 478,7
10 1 114,9
11 847,55
12 649,63
13 502,37
14 389,25
15 299,27
16 230,39
17 180,38
18 142,77
19 114,53
20 93,176
21 77,445
22 65,134
23 55,040
24 46,831
25 40,194
26 34,678
27 29,990
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ISO/TR 6057:2023(E)
TTaabblle 3 e 3 ((ccoonnttiinnueuedd))
Certified particle
Certified particle size
concentration
µm(c)
particles/mL
28 26,006
29 22,665
30 19,697
The expected number concentration of particles in the diluted calibration suspension samples at the
smallest particle size, X , is calculated as shown in Formula (11):
D
X 12 713
A
X == =9 779 (11)
D
13,,13
The smallest size that the APC can count is 2 µm(c). Referring to Table 3, the certified particle
concentration at this size, X , is 33 066 particles/mL. The minimum dilution ratio, D , that is required
C RR
to achieve X can be estimated using Formula (12):
D
X 33 066
C
D == =33, 8 (12)
RR
X 9 779
D
ISO 11171:2022, Annex G, permits either volumetric or mass dilution. In this example, it can be
assumed that diluted calibration suspension samples were prepared by mixing 100,0 mL of calibration
suspension weighing 86,0 g with 300,0 mL of dilution fluid weighing 258,0 g. Both sample and fluid
have a density of 0,86 g/mL. If volumetric dilution is used, the actual dilution ratio, D , is given by
R
Formula (13):
vv+
300,,0+100 0
0 S
D = = =40, 0 (13)
R
v 100,0
S
where
v is the volume of dilution fluid = 300,0 mL;
0
v is the volume of sample fluid = 100,0 mL.
S
If mass dilution is used for the same sample, the actual dilution ratio, D , is given by Formula (14):
R
MM− M
344,,08− 60 86,0
t s s
+
+
ρρ
08, 6 08, 6
d s
D = = =40, 0 (14)
R
M 86,0
s
08, 6
ρ
s
where
M is the total mass of diluted sample = 344,0 g;
t
M is the mass of sample = 86,0 g;
s
ρ is the density of dilution fluid = 0,86 g/mL;
d
ρ is the density of sample = 0,86 g/mL.
s
Since D is 4,00, greater than D , the actual diluted samples will have particle concentrations below
R RR
the coincidence error limit of the APC and can be used for calibration.
Continuing the example, the diluted sample was analysed and a mean particle concentration, X , of
7 041,6 particles/mL obtained. This is below the coincidence error limit of 12 713 particles/mL hence
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ISO/TR 6057:2023(E)
the data are not in coincidence error. Formula (15) can be used to calculate the particle concentration in
the undiluted sample, X :
N
XX= D =×7 041,,64 00 =28166 (15)
N R
where D is 4,00 as calculated in Formula (14). Thus, the value of X , 28 166, is used for this threshold
R N
setting when constructing the calibration curve for this APC.
7 Example 4: Relating particle size to threshold voltage setting for particles
30 µm(c) and smaller
Once acceptable particle count data are obtained, particle size data can be related to threshold voltage
1)
setting. ISO 11171:2022, 6.9, provides a link to an Excel spreadsheet tool that uses the constrained
cubic spline interpolation method for this purpose.
This example uses the same APC and calibration suspensions used in the previous examples. Table 2
lists the twelve threshold settings used and how they were allocated among the eight channels of the
APC for each of the three samples. Table 3 is the certified particle size distribution for the secondary
calibration suspensions. Table 4 shows the threshold settings and corresponding particle count data for
the three calibration suspension samples in the first four columns of the completed worksheet from
ISO 11171:2022, 6.9, for this example. The values for all twelve of the threshold settings are entered
consecutively in the first column in order of decreasing value (highest to lowest). No empty cells are
permitted in the first column between the maximum and minimum threshold settings. Mean normalized
particle concentrations, X , for the eight channel settings used for sample 1 are entered in the second
N
column adjacent to their corresponding threshold settings. Similarly, X for the eight channels of
N
sample 2 are entered in the third column and for sample 3 in the fourth column. Each row contains data
from at least two different calibration samples. If a threshold setting was not used for a particular
sample, the corresponding normalized particle concentration data cell in the spreadsheet is left empty.
The mean X for the samples for each threshold setting is automatically calculated and displayed in
N
yellow column 5. A value of #DIV/0! is displayed in column 5 for any threshold setting lacking particle
count data. A numerical value for the mean X is displayed for each threshold setting before proceeding.
N
All particle size and corresponding concentration data obtained from the certificate of analysis for
the calibration samples, given in Table 3 for this example, are entered in blue columns 6 and 7. The
corresponding interpolated threshold voltage setting for each size is automatically displayed in yellow
column 8. A value of 0 is displayed for any particle size whose concentration lies outside the range of
the particle concentrations shown in column 5, or if no particle concentration is entered. The particle
size values shown in blue column 6 and corresponding threshold settings in yellow column 8 relate
particle size to threshold setting, e.g. a particle size of 2 µm(c) corresponds to 10 mV in the example.
These values will later be used to construct the calibration curve.
1) Excel is the trademark of a product supplied by Microsoft. This information is given for the convenience of users
of this document and does not constitute an endorsement by ISO of the product named. Equivalent products may be
used if they can be shown to lead to the same results.
7
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ISO/TR 6057:2023(E)
8
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Table 4 — Output from the worksheet from ISO 11171:2022, 6.9, for Example 4
Enter all of the threshold settings determined in 6.3 in column A in order of decreasing value of The particle size and concentration data from the particle
size calibration summary portion of Table 4 are entered in
threshold setting. For each calibration suspension sample, enter the Values of X obtained for
N
columns F and G. The corresponding interpolated threshold
each threshold setting actually used for a sample in the appropriate cells of columns B, C or D. If a
voltage setting displayed in column H of this worksheet is
threshold setting was not used for a particular sample, leave the cell for that sample blank
entered in Table 4.
Interpolated
Threshold X for first X for second X for third Particle
N N N
Particle size threshold voltage
Mean X
N
voltage setting concentration
sample sample sample
setting
particles per particles per particles per particles per particles per
mV µm(c) mV
millilitre millilitre millilitre millilitre millilitre
2 600 19, 63 19,72 19,675 2 33 066 10
1 537 386,06 308,99 347,52 3 17 714 28
908 1 041,32 1 024,9 1 033,1 4 10 865 83
537 2 261,0 2 341,4 2 301,2 5 6 637,0 190
317 3 932,2 4 128,8 4 030,5 6 4 210,0 305
188 6 397,2 6 980,3 6 688,9 7 2 886,4 442
111 9 043,8 9 707,1 9 375,4 8 2 007,2 595
66 11 980 12 272 12 126 9 1 478,7 738
39 15 553 15 442 15 498 10 1 114,9 873
23 19 741 19 219 19 480 12 649,63 1 176
14 25 369 28 675 27 022 14 389,25 1 479
8 35 784 36 508 36 146 16 230,39 1 805
18 142,77 2 105
21 77,445 2 362
25 40,194 2 515
30 19,697 2 600
0
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ISO/TR 6057:2023(E)
ISO 11171:2022, 6.9, defines how the standard uncertainty in X is calculated for each threshold
N
setting. By way of illustration, this example uses cumulative particle count data at 14 mV and the
previous dilution ratio, D , of 4,0 as in Example 1. In an actual calibration, these data would be taken
R
from ISO 11171:2022, Table 2.
To calculate the standard uncertainty, the total number of acceptable particle counts, N , and the
C
standard deviation of the particle concentrations for all the acceptable counts for all the samples is
calculated. Referring to Table 5, the total number of acceptable particle counts is ten, i.e. five counts
obtained for each of two different samples, in the example. The standard deviation, s, is calculated using
the individual particle concentration data, X , for the ten counts shown in Table 5. In this example, the
i
standard deviation, s, for the ten counts is 466,6 particle/mL. The standard uncertainty, s , for the
N
14 mV threshold setting is given by Formula (16):
sD 466,,64× 00
R
s == =590,3 (16)
N
N 10
C
Table 5 — Particle concentration data for secondary calibration samples
Sample 1 X Sample 2 X
i i
Count
particles/mL particles/mL
1 6 376 7 312
2 6 220 7 186
3 6 507 6 866
4 6 288 7 444
5 6 321 7 036
8 Example 5: Relating particle size to threshold voltage setting for primary
calibration of sizes larger than 30 µm(c)
Latex spheres are used for primary calibrations at particle sizes larger than 30 µm(c). Selection criteria
for the sizes of latex to be used are specified in ISO 11171:2022, 6.11. The settings for the first four
channels of the APC are defined in ISO 11171:2022, 6.12, while ISO 11171:2022, 6.14, specifies how to
use the particle count data from these channels to determine the threshold setting corresponding to
the particle size of the latex.
This example uses the same hypothetical APC used in previous examples and assumes the intention
to calibrate to 50 µm(c). ISO 11171:2022, 6.11, states that the smallest polystyrene latex particle size
“shall be between 35 µm and 45 µm”. In this example, commercially available 39,33 µm latex particles,
with a standard deviation of 0,5 µm, are used to meet this requirement. The next size of latex, D, “shall
be approximately equal to the size of the [previous] smaller latex sphere [L] times a constant with a
value between 1,1 and 1,5”. Thus, its value of D is within the range given by Formula (17):
11,, ×≤LD ≤×15 L (17)
In this example, L is 39,33 µm, hence D for the second size of latex will be between 43,3 µm and 59,0 µm.
A commercially available latex with particle size of 50,2
...
© ISO 2022 – All rights reserved
ISO/FDTR DTR 6057:2022 -10(E)
Date: 2022-12-23
ISO TC 131/SC 6/WG 1
Secretariat: BSI
Hydraulic fluid power — Sample calculations for ISO 11171
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TECHNICAL REPORT ISO/DTR 6057:2022(E)
© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of
this publication may be reproduced or utilized otherwise in any form or by any means, electronic or
mechanical, including photocopying, or posting on the internet or an intranet, without prior written
permission. Permission can be requested from either ISO at the address below or ISO's member body in the
country of the requester.
ISO Copyright Office
CP 401 • CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland.
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ISO/DTR 6057:2022(E)
Contents
Foreword .iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Example 1: Selection of threshold voltage settings . 1
5 Example 2: Evaluating data quality . 3
6 Example 3: Dilution of samples . 5
7 Example 4: Relating particle size to threshold voltage setting for particles 30 µm(c)
and smaller . 8
8 Example 5: Relating particle size to threshold voltage setting for primary calibration
of sizes larger than 30 µm(c) . 11
9 Example 6: Construction of calibration curve . 13
10 Example 7: Calculation of coefficient variation for volume measurement using
ISO 11171:2022, Clause A.8 . 15
11 Example 8: Determination of coincidence error limit . 15
12 Example 9: Determination of flow rate limits using ISO 11171:2022, Annex C . 17
13 Example 10: Determination of resolution using ISO 11171:2022, Annex D . 20
14 Example 11: Verification of counting accuracy and secondary calibration suspensions
using ISO 11171:2022, Clause E.1 . 21
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ISO/DTR 6057:2022(E)
Foreword
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ISO/DTR 6057:2022(E)
Introduction
ISO 11171:2022, like its predecessors, retains traceability to the internationally accepted definition of a
metre and reports particle size in units of µm(c). The methods for determining data acceptance criteria,
coincidence error limit, working flow rate, and resolution remain unchanged, but mathematical
calculations and tools were first introduced in ISO 11171:2020 to ensure consistency in terms of how
automatic particle counter (APC) calibration curves are created and used. For example, mathematical
techniques have been introduced to determine the APC threshold settings used to obtain calibration data
and a tool provided to generate calibration curves. Other mathematical equations to estimate the
standard error of the calibration, to calculate normalized concentrations for diluted samples, and to
calibrate at particle sizes larger than 30 µm(c) were first introduced in 2020. This document uses
example calculations that are in full compliance withfully conform to ISO 11171.
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DRAFT TECHNICAL REPORT ISO/DTR 6057:2022(E)
Hydraulic Fluid Powerfluid power — Sample
calculationcalculations for ISO 11171
1 Scope
This document shows how to use the normative mathematical equationsformulae and tools of ISO 11171.
Examples are used to demonstrate their use for calibrating automatic particle counters (APCAPCs).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 11171, Hydraulic fluid power — Calibration of automatic particle counters for liquids
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11171, Hydraulic fluid power —
Calibration of automatic particle counters for liquids apply.
ISO and IEC maintain terminologicalterminology databases for use in standardization at the following
addresses:
IEC Electropedia: available at — ISO Online browsing platform: available at
https://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/
4 Example 1: Selection of threshold voltage settings
Throughout this technical report, any cited clauses or annexes refer to the corresponding clause or annex
in ISO 11171. The method of selecting threshold voltages for particle sizing calibration is specified in
ISO 11171 clause:2022, 6.3. This clause, which requires that:
— a minimum of 12 different threshold settings be used to constructingconstruct a calibration curve;
— the first (lowest) threshold setting, J, be 1,5 times the threshold noise level of the APC;
— the highest threshold setting, H, corresponds to a particle size of approximately 30 μm(c) or smaller
for primary calibrations and mustcorresponds to a size that does not exceed the largest reported
particle size that is in conformance with ISO 11171:2022, Annex F, for secondary calibrations; and
— intermediate threshold settings be logarithmically spaced such that the value of each channel is K
times greater than its preceding channel, where K is a constant defined by Formula (1):
(log H−−log JG)/( 1)
K = 10
(1)
where G is the number of threshold settings used to construct the calibration curve and must beis
greater than or equal to 12.
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ISO/DTR 6057:2022(E)
This example considers an APC with 8eight threshold settings that can be adjusted in 1 mV increments.
The threshold noise level of the APC was determined to be 5 mV and its manufacturer indicated that
30 μm(c) is expected to correspond to a threshold voltage setting of about 2 600 mV.
The calibration curve will be determined using 12 threshold voltage settings, the minimum number
permitted by ISO 11171. Thus, the value of H is 2 600 mV and the value of G is 12. The value of J is
determined by Formula (2):
J 1,5×=5 7,5
𝐽𝐽 = 1,5 × 5 𝑚𝑚𝑚𝑚 = 7,5 (2)
Since this APC can only be adjusted in 1 mV increments, the value of J is rounded up to 8 mV for
calibration. Using the values of G, H and J, the value of K can be calculated by formula Formula (3):
(log H−−log J )/(G 1) (log(2600)−log(8))/(12−1)
K 10 10 1,692
(3)
The threshold settings for the 10 intermediate channels are set at values corresponding to 1,692 times
the value of each preceding channel as shown in Table 1.
Table 1 — Threshold voltage settings for APC in Example 1
Threshold setting Calculation Threshold voltage
1 a
number setting setting
1 1,5 x × 5 mV = 8 mV
2 1,692 x × 8 mV = 14 mV
3 1,692 x × 14 mV = 23 mV
4 1,692 x × 23 mV = 39 mV
5 1,692 x × 39 mV = 66 mV
6 1,692 x × 66 mV = 111 mV
7 1,692 x × 111 mV = 188 mV
8 1,692 x × 188 mV = 317 mV
9 1,692 x × 317 mV = 537 mV
10 1,692 x × 537 mV = 908 mV
11 1,692 x × 908 mV = 1 537 mV
12 1,692 x × 1 537 mV = 2 600 mV
1a
Threshold voltage settings rounded off to the nearest mV based upon the capabilities of the APC in the example.
This APC only has the minimum number of channels required in ClauseISO 11171:2022, 6.4 (8eight
channels), but ClauseISO 11171:2022, 6.3, requires data from 12twelve or more threshold settings to
construct a calibration curve. ClauseISO 11171:2022, 6.8, requires that data from at least 2two different
samples be obtained for each of the threshold voltage settings (refer to clauseISO 11171:2022, 6.8) and
that the channels used for a particular sample be distributed over the entire range to the extent possible.
To meet these requirements in this example, 8eight different threshold settings chosen from the list of
12twelve can be used for the first sample and different combinations of 8eight threshold settings used
for each of the other two samples.
An example of how to allocate threshold settings among the 8eight channels is shown in Table 2, where
the first column lists the twelve required threshold voltage settings and columns 2, 3, and 4 show the
channels used to collect data at these settings for the indicated sample. The last column in Table 2 shows
the number of samples for which data isare obtained for each threshold setting, confirming these
requirements have been met.
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ISO/DTR 6057:2022(E)
Table 2 — Allocation of threshold voltage settings among the 8eight channels
of the Example 1 APC
Channel number corresponding to indicated threshold Number of
Threshold
voltage setting and sample samples at
voltage
indicated
setting
threshold
1 a
Sample A Sample B Sample C
mV mV
voltage setting
8 1 1 2
14 1 2 2
23 2 3 2
39 3 2 2
66 3 4 2
111 4 5 2
188 5 4 2
317 5 6 2
537 6 7 2
908 7 6 2
1 537 7 8 2
2 600 8 8 2
1a
Threshold voltage settings determined in Table 1.
5 Example 2: Evaluating data quality
ClauseISO 11171:2022, 6.6, specifies how to verify the acceptability of particle count data for APC
calibration purposes. In brief, the process involves:
— calculation of the total number of particles, N, counted for a given APC channel and sample,;
, and
— calculation of the data quality factor, D ;
Q
— identification of potential outliers among the data if the D is unacceptable.
Q
This process is used throughout ISO 11171 to ensure the integrity of data used for APC calibration. This
example uses a calibration suspension sample analysed as described in ClausesISO 11171:2022, 6.5 and
6.6, using a sample volume, V, of 10 mL ml. Unless otherwise noted, the term “particle concentration” will
referrefers to cumulative particle concentration throughout this document. Particle concentrations of
26 068 particles/ml, 25 757 particles/ml, 25 802 particles/ml, 31 771, particles/ml and 25 834
particles/mLml were obtained. The mean particle concentration, X , for these five counts is 27 046. The
mean observed number of particles counted for the five particle counts, X, is given by Formula (4):
X = XV = 27 046 × 10 = 270 460
(4)
The total number of particles, N, counted for the sample is calculated using Formula (5):
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ISO/DTR 6057:2022(E)
N 5X 270 460×=5 1 352300 (5)
This value is greater than 1 000, as required by ISO 11171:2022, 6.6, hence is sufficiently high for
calibration purposes.
Using ISO 11171:2022, Table C.2 of ISO 11171, and the value of X previously calculated, the maximum
Table
allowable D for the data can be determined. Referring to the first two columns of the table, a value
Q
Table
of 270 460 for X corresponds to the first row of the table, i.e. X greater than or equal to 10 000. The
clauses
maximum allowable D can be found in the third column, which is used for ISO 11171:2022, 6.6,
Q
6.13, B.5, C.9, D.4, D.9, E.6 and F.5. Thus, the maximum allowable D is 11,0 for this example. The value of
Q
D expressed as a percentage, for the data in this example is calculated using Formula (6):
Q,
X − X
31 771−25 757 𝑋𝑋 −𝑋𝑋 31 771−25 757
max min 𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚𝑚𝑚
D 100 22,24𝐷𝐷 = × 100 = = 22,24 (6)
𝑄𝑄
Q
�
𝑋𝑋 27 046
X 27 046
where:
X is the maximum number of counts observed among the 5 particle counts or 31 771;
max
X is the minimum number of counts observed among the 5 particle counts or 25 757.
min
X is the maximum number of counts observed among the five particle counts or 31 771;
max
X is the minimum number of counts observed among the five particle counts or 25 757.
min
Since the value of D is greater than the maximum allowable D , the data isare unacceptable for
Q Q
calibration purposes and can be examined for possible outliers.
The outlier test parameter, D , for the data in this example is calculated using Formula (7):
0
X − X
31771 −25757
𝑋𝑋 −𝑋𝑋 31 771 −25 757
max min
𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚𝑚𝑚
D 1,05𝐷𝐷 = = = 1.05 (7)
0 0
|𝑋𝑋−𝑋𝑋 | |31 771 −26 068|
0 𝑁𝑁
XX− 31771 −26 068
0 N
where
X is the observed particle concentration of suspected data outlier (either X or X ),
0 max min 31 771
particles/mL;
X is the observed particle concentration closest in value to the suspected outlier, 26 068
N
particles/mL.
X is the observed particle concentration of suspected data outlier (either X or X ), 31 771
0 max min
particles/ml;
X is the observed particle concentration closest in value to the suspected outlier, 26 068
N
particles/ml.
If the value of D is less than 1,44, as in this example, X can be discarded as a statistical outlier. In example
0 0
Example 2, D was found to be 1,05, well below 1,44, hence the suspect data point, 31 771, can be
0
discarded as an outlier. The remaining 4four data points are used to recalculate X , giving a value of
25 865 particles/mLml, which will be used in constructing the calibration curve.
In another example, data from a different channel setting is considered for the same calibration
suspension sample analysed in the previous example. For this channel setting, particle concentrations of
810 particles/ml, 802 particles/ml, 800 particles/ml, 805 particles/ml and 803 particles/mLml were
obtained.
The mean particle concentration, X , for these five counts is 804. The mean observed number of particles
counted for the five particle counts, X, is given by Formula (8):
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ISO/DTR 6057:2022(E)
X = XV = 804 × 10 = 8 040
(8)
The total number of particles, N, counted for the sample is calculated using Formula (9):
N 5X 8 040×=5 40 200 N =5X = 8 040 x 5 = 40 200 (9)
This value is greater than 1 000, as required by Clause 6.6 of ISO 11171:2022, 6.6, hence is sufficiently
high for calibration purposes.
Using Table C.2 of ISO 11171:2022, Table C.2, and the value of X previously calculated, the maximum
Table
allowable D for the data can be determined. Referring to the first two columns of the table, a value
Q
of 8 040 for X corresponds to the second row of the Tabletable, i.e. X greater than or equal to 5 000 but
less than 10 000. The maximum allowable D can be found in the third column, which is used for
Q
clauses
ISO 11171:2022, 6.6, 6.13, B.5, C.9, D.4, D.9, E.6 and F.5. Thus, the maximum allowable D is 11,3
Q
for this example. The value of D , expressed as a percentage, for the data in this example is calculated
Q
using Formula (10):
X − X
810− 800 𝑋𝑋 −𝑋𝑋 810 −800
max min 𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚𝑚𝑚
D = ×=100 = 1,20𝐷𝐷 = × 100 = = 1,20 (10)
𝑄𝑄
Q
�
𝑋𝑋 804
X 804
where
X is the maximum number of counts observed among the 5 particle counts or 810
max
X is the minimum number of counts observed among the 5 particle counts or 800.
min
X is the maximum number of counts observed among the five particle counts or 810;
max
X is the minimum number of counts observed among the five particle counts or 800.
min
Since the value of D is less than the maximum allowable D , the data isare acceptable for calibration
Q Q
purposes and can be used in constructing the calibration curve.
6 Example 3: Dilution of samples
To facilitate calibration at small particle sizes, ISO 11171:2022, Annex G of ISO 11171, provides a
standardized procedure for the diluting calibration suspensions and ClauseISO 11171:2022, 6.7, specifies
a method for normalizing the resultant particle count data. To use this procedure, one needsit is
necessary to know the coincidence error limit of the APC and the approximate size of the smallest
particles that it can count. In this example, the APC is capable of counting particles as small as 2 µm(c)
and has a coincidence error limit, X , of 12 713 particles/mLml. The certified particle size distribution of
A
the calibration samples is shown in Table 3.
Table 3 — Certified particle size distribution of calibration sample for Example 3
Certified Particle
Concentration
Certified Particle Size
particle size
particle
µm(c)
concentration particles/mL
ml
2 33 066
3 17 714
4 10 865
5 6 637,0
6 4 210,0
7 2 886,4
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ISO/DTR 6057:2022(E)
Certified Particle
Concentration
Certified Particle Size
particle size
particle
µm(c)
concentration particles/mL
ml
8 2 007,2
9 1 478,7
10 1 114,9
11 847,55
12 649,63
13 502,37
14 389,25
15 299,27
16 230,39
17 180,38
18 142,77
19 114,53
20 93,176
21 77,445
22 65,134
23 55,040
24 46,831
25 40,194
26 34,678
27 29,990
28 26,006
29 22,665
30 19,697
The expected number concentration of particles in the diluted calibration suspension samples at the
smallest particle size, X , is calculated as shown in Formula (11):
D
X
12 713 𝑋𝑋 12 713
A 𝐴𝐴
X = = =9 779𝑋𝑋 = = = 9 779 (11)
𝐷𝐷
D
1,3 1,3
1,3 1,3
The smallest size that the APC can count down is 2 µm(c). Referring to Table 3, the certified particle
concentration at this size, X , is 33 066 particles/mLml. The minimum dilution ratio, D , that is required
C RR
to achieve X can be estimated using Formula (12):
D
X
33 066
C
D 3,38 (12):)
RR
X 9 779
D
𝑋𝑋 33 066
𝐶𝐶
(12)
𝐷𝐷 = = = 3,38
𝑅𝑅𝑅𝑅
𝑋𝑋 9 779
𝐷𝐷
ISO 11171:2022, Annex G, permits either volumetric or mass dilution. In this example, assumeit can be
assumed that diluted calibration suspension samples were prepared by mixing 100,0 mL ml of calibration
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ISO/DTR 6057:2022(E)
suspension weighing 86,0 g with 300,0 ml of dilution fluid weighing 258,0 g. Both sample and fluid have
mL
a density of 0,86 g/ ml. If volumetric dilution is used, the actual dilution ratio, D , is given by
R
Formula (13):
vv+
300,0+ 100,0
𝑣𝑣+𝑣𝑣 300,0+100,0
0 S 0 𝑆𝑆
D 4,00𝐷𝐷 = = = 4,00 (13)
R 𝑅𝑅
𝑣𝑣 100,0
𝑆𝑆
v 100,0
S
where
v is the volume of dilution fluid = 300,0 mL
0
v is the volume of sample fluid = 100,0 mL
S
v is the volume of dilution fluid = 300,0 ml;
0
v is the volume of sample fluid = 100,0 ml.
S
If mass dilution is used for the same sample, the actual dilution ratio, D , is given by formula
R
Formula (14):
MM− M
t ss 344,0− 86,0 86,0
+
𝑀𝑀 −𝑀𝑀 𝑀𝑀
+ 𝑡𝑡
𝑆𝑆 𝑆𝑆 344,0−86,0 86,0
+
+
ρρ
0,86 0,86 𝜌𝜌 𝜌𝜌
0,86 0,86
ds 𝑑𝑑 𝑆𝑆
D 4,00𝐷𝐷 = = = 4,00 (14)
86,0
𝑅𝑅 𝑀𝑀
R
𝑆𝑆
M 86,0
s 0,86
𝜌𝜌
𝑆𝑆
0,86
ρ
s
where
M is the total mass of diluted sample = 344,0 g
T
ρ is the density of dilution fluid = 0,86 g/mL
d
ρ is the density of sample = 0,86 g/mL
S
M is the total mass of diluted sample = 344,0 g
T
M is the total mass of diluted sample = 344,0 g;
t
ρ is the density of dilution fluid = 0,86 g/ml;
d
ρ is the density of sample = 0,86 g/ml.
s
Since D is 4,00, greater than D , the actual diluted samples will have particle concentrations below the
R RR
coincidence error limit of the APC and can be used for calibration.
Continuing the example, the diluted sample was analysed and a mean particle concentration, X , of
7 041,6 particles/mLml obtained. This is below the coincidence error limit of 12 713 particles/mLml
hence the data isare not in coincidence error. Formula (15) can be used to calculate the particle
concentration in the undiluted sample, X :
N
� �
X =XD =7 041,6×=4,00 28 166𝑋𝑋 = 𝑋𝑋𝐷𝐷 = 7 041,6 × 4,00 = 28 166 (15)
𝑁𝑁 𝑅𝑅
N R
where D is 4,00 as calculated in Formula (14). Thus, the value of X , 28 166, is used for this threshold
R
N
setting when constructing the calibration curve for this APC.
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ISO/DTR 6057:2022(E)
7 Example 4: Relating particle size to threshold voltage setting for particles
30 µm(c) and smaller
Once acceptable particle count data isare obtained, particle size data can be related to threshold voltage
1
setting. ClauseISO 11171:2022, 6.9, provides a link to an Excel spreadsheet tool that uses the constrained
cubic spline interpolation method for this purpose.
This example uses the same APC and calibration suspensions used in the previous examples. Table 2 lists
the 12twelve threshold settings used and how they were allocated among the 8eight channels of the APC
for each of the 3three samples. Table 3 is the certified particle size distribution for the secondary
calibration suspensions. Table 4 shows the threshold settings and corresponding particle count data for
the 3three calibration suspension samples in the first 4four columns of the completed 6.9 worksheet from
ISO 11171:2022, 6.9, for this example. The values for all 12twelve of the threshold settings are entered
consecutively in the first column in order of decreasing value (highest to lowest). No empty cells are
permitted in the first column between the maximum and minimum threshold settings. Mean normalized
particle concentrations, X , for the 8eight channel settings used for sample 1 are entered in the second
N
column adjacent to their corresponding threshold settings. Similarly, X for the 8eight channels of
N
sample 2 are entered in the third column and for sample 3 in the fourth column. Each row contains data
from at least 2two different calibration samples. If a threshold setting was not used for a particular
sample, the corresponding normalized particle concentration data cell in the spreadsheet is left empty.
The mean X for the samples for each threshold setting is automatically calculated and displayed in
N
yellow column 5. A value of #DIV/0! is displayed in column 5 for any threshold setting lacking particle
count data. A numerical value for the mean X must be is displayed for each threshold setting before
N
proceeding.
All particle size and corresponding concentration data obtained from the certificate of analysis for the
calibration samples, given in Table 3 for this example, are entered in blue columns 6 and 7. The
corresponding interpolated threshold voltage setting for each size is automatically displayed in yellow
column 8. A value of 0 is displayed for any particle size whose concentration lies outside the range of the
particle concentrations shown in column 5, or if no particle concentration is entered. The particle size
values shown in blue column 6 and corresponding threshold settings in yellow column 8 relate particle
size to threshold setting, e.g. a particle size of 2 µm(c) corresponds to 10 mV in the example. These values
will later be used to construct the calibration curve.
1
Excel is the trademark of a product supplied by Microsoft. This information is given for the convenience of users
of this document and does not constitute an endorsement by ISO of the product named. Equivalent products may
be used if they can be shown to lead to the same results.
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ISO/DTR 6057:2022(E)
Table 4 — Output from the worksheet from ISO 11171 Clause:2022, 6.9 worksheet, for Example 4
Enter allAll of the threshold settings determined in 6.3ISO 11171:2022, 6.9, in column A are Enter theThe particle size and concentration data from the
entered in order of decreasing value of threshold setting. For each calibration suspension particle size calibration summary portion of Table 4 4 are
entered in columns F and G. Enter in Table 4 theThe
sample, enter the Valuesvalues of X obtained for each threshold setting actually used for a
N
corresponding interpolated threshold voltage setting
sample are entered in the appropriate cells of columns B, C or D. If a threshold setting was not
displayed in column H of this worksheet is entered in
used for a particular sample, leave the cell for that sample is left blank.
Table 4.
X for
N
X for X for
Threshold Interpolated
N N
Particle
Secondse
voltage Mean X Particle size threshold
Firstfirst Thirdthir N
concentration
cond
setting voltage setting
sample d sample
sample
particles particles particles particles
µm particles per
mV per per per per mV
(c) millilitre
millilitre millilitre millilitre millilitre
2 600 19, 63 19,72 19,675 2 33 066 10
1 537 386,06 308,99 347,52 3 17 714 28
908 1 041,32 1 024,9 1 033,1 4 10 865 83
537 2 261,0 2 341,4 2 301,2 5 6 637,0 190
317 3 932,2 4 128,8 4 030,5 6 4 210,0 305
188 6 397,2 6 980,3 6 688,9 7 2 886,4 442
111 9 043,8 9 707,1 9 375,4 8 2 007,2 595
66 11 980 12 272 12 126 9 1 478,7 738
39 15 553 15 442 15 498 10 1 114,9 873
23 19 741 19 219 19 480 12 649,63 1 176
14 25 369 28 675 27 022 14 389,25 1 479
8 35 784 36 508 36 146 16 230,39 1 805
18 142,77 2 105
21 77,445 2 362
25 40,194 2 515
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ISO/DTR 6057:2022(E)
30 19,697 2 600
0
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ISO/DTR 6057:2022(E)
ClauseISO 11171:2022, 6.9, defines how the standard uncertainty in X is calculated for each threshold
N
setting. By way of illustration, this example uses cumulative particle count data at 14 mV and the previous
dilution ratio, D , of 4,0 as in Example 1. In an actual calibration, these data would be taken from
R
ISO 11171:2022, Table 2 of ISO 11171.
Table 5 — Particle concentration data for secondary calibration samples
Sample 1 X Sample 2 X
i i
Count
Particles/mL Particles/mL
1 6 376 7 312
2 6 220 7 186
3 6 507 6 866
4 6 288 7 444
5 6 321 7 036
To calculate the standard uncertainty, the total number of acceptable particle counts, N , and the
C
standard deviation of the particle concentrations for all the acceptable counts for al
...
FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 6057
ISO/TC 131/SC 6
Hydraulic fluid power — Sample
Secretariat: BSI
calculations for ISO 11171
Voting begins on:
2023-01-06
Voting terminates on:
2023-03-03
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/DTR 6057:2023(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
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ISO/DTR 6057:2023(E)
FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 6057
ISO/TC 131/SC 6
Hydraulic fluid power — Sample
Secretariat: BSI
calculations for ISO 11171
Voting begins on:
Voting terminates on:
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NATIONAL REGULATIONS. © ISO 2022
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ISO/DTR 6057:2022(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Example 1: Selection of threshold voltage settings . 1
5 Example 2: Evaluating data quality . 3
6 Example 3: Dilution of samples .5
7 Example 4: Relating particle size to threshold voltage setting for particles 30 µm(c)
and smaller . 7
8 Example 5: Relating particle size to threshold voltage setting for primary
calibration of sizes larger than 30 µm(c) . 9
9 Example 6: Construction of calibration curve .11
10 Example 7: Calculation of coefficient variation for volume measurement using
ISO 11171:2022, Clause A.8 .12
11 Example 8: Determination of coincidence error limit .13
12 Example 9: Determination of flow rate limits using ISO 11171:2022, Annex C .14
13 Example 10: Determination of resolution using ISO 11171:2022, Annex D .17
14 Example 11: Verification of counting accuracy and secondary calibration
suspensions using ISO 11171:2022, Clause E.1 .18
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ISO/DTR 6057:2022(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
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www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee
SC 6, Contamination control.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/DTR 6057:2022(E)
Introduction
ISO 11171:2022, like its predecessors, retains traceability to the internationally accepted definition
of a metre and reports particle size in units of µm(c). The methods for determining data acceptance
criteria, coincidence error limit, working flow rate and resolution remain unchanged, but mathematical
calculations and tools were first introduced in ISO 11171:2020 to ensure consistency in terms of how
automatic particle counter (APC) calibration curves are created and used. For example, mathematical
techniques have been introduced to determine the APC threshold settings used to obtain calibration
data and a tool provided to generate calibration curves. Other mathematical equations to estimate
the standard error of the calibration, to calculate normalized concentrations for diluted samples, and
to calibrate at particle sizes larger than 30 µm(c) were first introduced in 2020. This document uses
example calculations that fully conform to ISO 11171.
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TECHNICAL REPORT ISO/DTR 6057:2022(E)
Hydraulic fluid power — Sample calculations for ISO 11171
1 Scope
This document shows how to use the normative mathematical formulae and tools of ISO 11171.
Examples are used to demonstrate their use for calibrating automatic particle counters (APCs).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 11171, Hydraulic fluid power — Calibration of automatic particle counters for liquids
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11171 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Example 1: Selection of threshold voltage settings
The method of selecting threshold voltages for particle sizing calibration is specified in ISO 11171:2022,
6.3, which requires that:
— a minimum of 12 different threshold settings be used to construct a calibration curve;
— the first (lowest) threshold setting, J, be 1,5 times the threshold noise level of the APC;
— the highest threshold setting, H, corresponds to a particle size of approximately 30 μm(c) or smaller
for primary calibrations and corresponds to a size that does not exceed the largest reported particle
size that is in conformance with ISO 11171:2022, Annex F, for secondary calibrations;
— intermediate threshold settings be logarithmically spaced such that the value of each channel is K
times greater than its preceding channel, where K is a constant defined by Formula (1):
()loglHJ− og /()G−1
K =10 (1)
where G is the number of threshold settings used to construct the calibration curve and is greater
than or equal to 12.
This example considers an APC with eight threshold settings that can be adjusted in 1 mV increments.
The threshold noise level of the APC was determined to be 5 mV and its manufacturer indicated that
30 μm(c) is expected to correspond to a threshold voltage setting of about 2 600 mV.
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ISO/DTR 6057:2022(E)
The calibration curve will be determined using 12 threshold voltage settings, the minimum number
permitted by ISO 11171. Thus, the value of H is 2 600 mV and the value of G is 12. The value of J is
determined by Formula (2):
J =×15,,57= 5 (2)
Since this APC can only be adjusted in 1 mV increments, the value of J is rounded up to 8 mV for
calibration. Using the values of G, H and J, the value of K can be calculated by Formula (3):
(logHJ−−log)/(G 12)(log( 600)l−−og()81)/()21
K ==10 10 =1,692 (3)
The threshold settings for the 10 intermediate channels are set at values corresponding to 1,692 times
the value of each preceding channel as shown in Table 1.
Table 1 — Threshold voltage settings for APC in Example 1
a
Threshold setting number Calculation Threshold voltage setting
1 1,5 × 5 mV = 8 mV
2 1,692 × 8 mV = 14 mV
3 1,692 × 14 mV = 23 mV
4 1,692 × 23 mV = 39 mV
5 1,692 × 39 mV = 66 mV
6 1,692 × 66 mV = 111 mV
7 1,692 × 111 mV = 188 mV
8 1,692 × 188 mV = 317 mV
9 1,692 × 317 mV = 537 mV
10 1,692 × 537 mV = 908 mV
11 1,692 × 908 mV = 1 537 mV
12 1,692 × 1 537 mV = 2 600 mV
a
Threshold voltage settings rounded off to the nearest mV based upon the capabilities of the APC in the example.
This APC only has the minimum number of channels required in ISO 11171:2022, 6.4 (eight channels),
but ISO 11171:2022, 6.3, requires data from twelve or more threshold settings to construct a calibration
curve. ISO 11171:2022, 6.8, requires that data from at least two different samples be obtained for each of
the threshold voltage settings (refer to ISO 11171:2022, 6.8) and that the channels used for a particular
sample be distributed over the entire range to the extent possible. To meet these requirements in
this example, eight different threshold settings chosen from the list of twelve can be used for the first
sample and different combinations of eight threshold settings used for each of the other two samples.
An example of how to allocate threshold settings among the eight channels is shown in Table 2, where
the first column lists the twelve required threshold voltage settings and columns 2, 3 and 4 show the
channels used to collect data at these settings for the indicated sample. The last column in Table 2
shows the number of samples for which data are obtained for each threshold setting, confirming these
requirements have been met.
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ISO/DTR 6057:2022(E)
Table 2 — Allocation of threshold voltage settings among the eight channels
of the Example 1 APC
Channel number corresponding to indicated threshold Number of samples
Threshold
voltage setting and sample at indicated thresh-
voltage
a old voltage setting
setting mV
Sample A Sample B Sample C
8 1 1 2
14 1 2 2
23 2 3 2
39 3 2 2
66 3 4 2
111 4 5 2
188 5 4 2
317 5 6 2
537 6 7 2
908 7 6 2
1 537 7 8 2
2 600 8 8 2
a
Threshold voltage settings determined in Table 1.
5 Example 2: Evaluating data quality
ISO 11171:2022, 6.6, specifies how to verify the acceptability of particle count data for APC calibration
purposes. In brief, the process involves:
— calculation of the total number of particles, N, counted for a given APC channel and sample;
— calculation of the data quality factor, D ;
Q
— identification of potential outliers among the data if the D is unacceptable.
Q
This process is used throughout ISO 11171 to ensure the integrity of data used for APC calibration. This
example uses a calibration suspension sample analysed as described in ISO 11171:2022, 6.5 and 6.6,
using a sample volume, V, of 10 ml. Unless otherwise noted, the term “particle concentration” refers to
cumulative particle concentration throughout this document. Particle concentrations of 26 068
particles/ml, 25 757 particles/ml, 25 802 particles/ml, 31 771 particles/ml and 25 834 particles/ml
were obtained. The mean particle concentration, X , for these five counts is 27 046. The mean observed
number of particles counted for the five particle counts, X, is given by Formula (4):
XV ==X 27 046×= 10 270460 (4)
The total number of particles, N, counted for the sample is calculated using Formula (5):
NX==5 270 460×=51352300 (5)
This value is greater than 1 000, as required by ISO 11171:2022, 6.6, hence is sufficiently high for
calibration purposes.
Using ISO 11171:2022, Table C.2, and the value of X previously calculated, the maximum allowable D
Q
for the data can be determined. Referring to the first two columns of the table, a value of 270 460 for X
corresponds to the first row of the table, i.e. X greater than or equal to 10 000. The maximum allowable
D can be found in the third column, which is used for ISO 11171:2022, 6.6, 6.13, B.5, C.9, D.4, D.9, E.6
Q
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ISO/DTR 6057:2022(E)
and F.5. Thus, the maximum allowable D is 11,0 for this example. The value of D expressed as a
Q Q,
percentage, for the data in this example is calculated using Formula (6):
XX−
31 771−25757
maxmin
D = ×=100 =22,24 (6)
Q
X 27 046
where
X is the maximum number of counts observed among the five particle counts or 31 771;
max
X is the minimum number of counts observed among the five particle counts or 25 757.
min
Since the value of D is greater than the maximum allowable D , the data are unacceptable for
Q Q
calibration purposes and can be examined for possible outliers.
The outlier test parameter, D , for the data in this example is calculated using Formula (7):
0
XX−
31771 −25757
maxmin
D = = =10, 5 (7)
0
XX− 31771 −26068
0 N
where
X is the observed particle concentration of suspected data outlier (either X or X ), 31 771
0 max min
particles/ml;
X is the observed particle concentration closest in value to the suspected outlier, 26 068
N
particles/ml.
If the value of D is less than 1,44, as in this example, X can be discarded as a statistical outlier. In
0 0
Example 2, D was found to be 1,05, well below 1,44, hence the suspect data point, 31 771, can be
0
discarded as an outlier. The remaining four data points are used to recalculate X , giving a value of
25 865 particles/ml, which will be used in constructing the calibration curve.
In another example, data from a different channel setting is considered for the same calibration
suspension sample analysed in the previous example. For this channel setting, particle concentrations
of 810 particles/ml, 802 particles/ml, 800 particles/ml, 805 particles/ml and 803 particles/ml were
obtained.
The mean particle concentration, X , for these five counts is 804. The mean observed number of
particles counted for the five particle counts, X, is given by Formula (8):
XV ==X 804 ×=10 8040 (8)
The total number of particles, N, counted for the sample is calculated using Formula (9):
NX==58 040×=540200 (9)
This value is greater than 1 000, as required by ISO 11171:2022, 6.6, hence is sufficiently high for
calibration purposes.
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ISO/DTR 6057:2022(E)
Using ISO 11171:2022, Table C.2, and the value of X previously calculated, the maximum allowable D
Q
for the data can be determined. Referring to the first two columns of the table, a value of 8 040 for X
corresponds to the second row of the table, i.e. X greater than or equal to 5 000 but less than 10 000.
The maximum allowable D can be found in the third column, which is used for ISO 11171:2022, 6.6,
Q
6.13, B.5, C.9, D.4, D.9, E.6 and F.5. Thus, the maximum allowable D is 11,3 for this example. The value of
Q
D , expressed as a percentage, for the data in this example is calculated using Formula (10):
Q
XX−
810−800
maxmin
D = ×=100 = 12, 0 (10)
Q
X 804
where
X is the maximum number of counts observed among the five particle counts or 810;
max
X is the minimum number of counts observed among the five particle counts or 800.
min
Since the value of D is less than the maximum allowable D , the data are acceptable for calibration
Q Q
purposes and can be used in constructing the calibration curve.
6 Example 3: Dilution of samples
To facilitate calibration at small particle sizes, ISO 11171:2022, Annex G, provides a standardized
procedure for the diluting calibration suspensions and ISO 11171:2022, 6.7, specifies a method
for normalizing the resultant particle count data. To use this procedure, it is necessary to know the
coincidence error limit of the APC and the approximate size of the smallest particles that it can count.
In this example, the APC is capable of counting particles as small as 2 µm(c) and has a coincidence error
limit, X , of 12 713 particles/ml. The certified particle size distribution of the calibration samples is
A
shown in Table 3.
Table 3 — Certified particle size distribution of calibration sample for Example 3
Certified particle
Certified particle size
concentration particles
µm(c)
ml
2 33 066
3 17 714
4 10 865
5 6 637,0
6 4 210,0
7 2 886,4
8 2 007,2
9 1 478,7
10 1 114,9
11 847,55
12 649,63
13 502,37
14 389,25
15 299,27
16 230,39
17 180,38
18 142,77
19 114,53
20 93,176
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ISO/DTR 6057:2022(E)
TTaabblle 3 e 3 ((ccoonnttiinnueuedd))
Certified particle
Certified particle size
concentration particles
µm(c)
ml
21 77,445
22 65,134
23 55,040
24 46,831
25 40,194
26 34,678
27 29,990
28 26,006
29 22,665
30 19,697
The expected number concentration of particles in the diluted calibration suspension samples at the
smallest particle size, X , is calculated as shown in Formula (11):
D
X 12 713
A
X == =9 779 (11)
D
13,,13
The smallest size that the APC can count down is 2 µm(c). Referring to Table 3, the certified particle
concentration at this size, X , is 33 066 particles/ml. The minimum dilution ratio, D , that is required
C RR
to achieve X can be estimated using Formula (12):
D
X 33 066
C
D == =33, 8 (12)
RR
X 9 779
D
ISO 11171:2022, Annex G, permits either volumetric or mass dilution. In this example, it can be assumed
that diluted calibration suspension samples were prepared by mixing 100,0 ml of calibration suspension
weighing 86,0 g with 300,0 ml of dilution fluid weighing 258,0 g. Both sample and fluid have a density of
0,86 g/ml. If volumetric dilution is used, the actual dilution ratio, D , is given by Formula (13):
R
vv+
300,,0+100 0
0 S
D = = =40, 0 (13)
R
v 100,0
S
where
v is the volume of dilution fluid = 300,0 ml;
0
v is the volume of sample fluid = 100,0 ml.
S
If mass dilution is used for the same sample, the actual dilution ratio, D , is given by Formula (14):
R
MM− M
344,,08− 60 86,0
t s s
+
+
ρρ
08, 6 08, 6
d s
D = = =40, 0 (14)
R
M 86,0
s
08, 6
ρ
s
where
M is the total mass of diluted sample = 344,0 g;
t
ρ is the density of dilution fluid = 0,86 g/ml;
d
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ISO/DTR 6057:2022(E)
ρ is the density of sample = 0,86 g/ml.
s
Since D is 4,00, greater than D , the actual diluted samples will have particle concentrations below
R RR
the coincidence error limit of the APC and can be used for calibration.
Continuing the example, the diluted sample was analysed and a mean particle concentration, X , of
7 041,6 particles/ml obtained. This is below the coincidence error limit of 12 713 particles/ml hence
the data are not in coincidence error. Formula (15) can be used to calculate the particle concentration in
the undiluted sample, X :
N
XX= D =×7 041,,64 00 =28166 (15)
N R
where D is 4,00 as calculated in Formula (14). Thus, the value of X , 28 166, is used for this threshold
R N
setting when constructing the calibration curve for this APC.
7 Example 4: Relating particle size to threshold voltage setting for particles
30 µm(c) and smaller
Once acceptable particle count data are obtained, particle size data can be related to threshold voltage
1)
setting. ISO 11171:2022, 6.9, provides a link to an Excel spreadsheet tool that uses the constrained
cubic spline interpolation method for this purpose.
This example uses the same APC and calibration suspensions used in the previous examples. Table 2
lists the twelve threshold settings used and how they were allocated among the eight channels of the
APC for each of the three samples. Table 3 is the certified particle size distribution for the secondary
calibration suspensions. Table 4 shows the threshold settings and corresponding particle count data for
the three calibration suspension samples in the first four columns of the completed worksheet from
ISO 11171:2022, 6.9, for this example. The values for all twelve of the threshold settings are entered
consecutively in the first column in order of decreasing value (highest to lowest). No empty cells are
permitted in the first column between the maximum and minimum threshold settings. Mean normalized
particle concentrations, X , for the eight channel settings used for sample 1 are entered in the second
N
column adjacent to their corresponding threshold settings. Similarly, X for the eight channels of
N
sample 2 are entered in the third column and for sample 3 in the fourth column. Each row contains data
from at least two different calibration samples. If a threshold setting was not used for a particular
sample, the corresponding normalized particle concentration data cell in the spreadsheet is left empty.
The mean X for the samples for each threshold setting is automatically calculated and displayed in
N
yellow column 5. A value of #DIV/0! is displayed in column 5 for any threshold setting lacking particle
count data. A numerical value for the mean X is displayed for each threshold setting before proceeding.
N
All particle size and corresponding concentration data obtained from the certificate of analysis for
the calibration samples, given in Table 3 for this example, are entered in blue columns 6 and 7. The
corresponding interpolated threshold voltage setting for each size is automatically displayed in yellow
column 8. A value of 0 is displayed for any particle size whose concentration lies outside the range of
the particle concentrations shown in column 5, or if no particle concentration is entered. The particle
size values shown in blue column 6 and corresponding threshold settings in yellow column 8 relate
particle size to threshold setting, e.g. a particle size of 2 µm(c) corresponds to 10 mV in the example.
These values will later be used to construct the calibration curve.
1) Excel is the trademark of a product supplied by Microsoft. This information is given for the convenience of users
of this document and does not constitute an endorsement by ISO of the product named. Equivalent products may be
used if they can be shown to lead to the same results.
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ISO/DTR 6057:2022(E)
8
© ISO 2022 – All rights reserved
Table 4 — Output from the worksheet from ISO 11171:2022, 6.9, for Example 4
All of the threshold settings determined in ISO 11171:2022, 6.9, in column A are entered in order The particle size and concentration data from the particle
size calibration summary portion of Table 4 are entered in
of decreasing value of threshold setting. For each calibration suspension sample, the values of X
N
columns F and G. The corresponding interpolated threshold
obtained for each threshold setting actually used for a sample are entered in the appropriate cells
voltage setting displayed in column H of this worksheet is
of columns B, C or D. If a threshold setting was not used for a particular sample, the cell for that
entered in Table 4.
sample is left blank.
Interpolated
X for first X for second X for third
Threshold Particle
N N N
Mean X Particle size threshold voltage
N
voltage setting concentration
sample sample sample
setting
particles per particles per particles per particles per particles per
mV µm(c) mV
millilitre millilitre millilitre millilitre millilitre
2 600 19, 63 19,72 19,675 2 33 066 10
1 537 386,06 308,99 347,52 3 17 714 28
908 1 041,32 1 024,9 1 033,1 4 10 865 83
537 2 261,0 2 341,4 2 301,2 5 6 637,0 190
317 3 932,2 4 128,8 4 030,5 6 4 210,0 305
188 6 397,2 6 980,3 6 688,9 7 2 886,4 442
111 9 043,8 9 707,1 9 375,4 8 2 007,2 595
66 11 980 12 272 12 126 9 1 478,7 738
39 15 553 15 442 15 498 10 1 114,9 873
23 19 741 19 219 19 480 12 649,63 1 176
14 25 369 28 675 27 022 14 389,25 1 479
8 35 784 36 508 36 146 16 230,39 1 805
18 142,77 2 105
21 77,445 2 362
25 40,194 2 515
30 19,697 2 600
0
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ISO/DTR 6057:2022(E)
ISO 11171:2022, 6.9, defines how the standard uncertainty in X is calculated for each threshold
N
setting. By way of illustration, this example uses cumulative particle count data at 14 mV and the
previous dilution ratio, D , of 4,0 as in Example 1. In an actual calibration, these data would be taken
R
from ISO 11171:2022, Table 2.
To calculate the standard uncertainty, the total number of acceptable particle counts, N , and the
C
standard deviation of the particle concentrations for all the acceptable counts for all the samples is
calculated. Referring to Table 5, the total number of acceptable particle counts is ten, i.e. five counts
obtained for each of two different samples, in the example. The standard deviation, s, is calculated
using the individual particle concentration data, X , for the ten counts shown in Table 5. In this example,
i
the standard deviation, s, for the ten counts is 466,6 particle/ml. The standard uncertainty, s , for the
N
14 mV threshold setting is given by Formula (16):
sD 466,,64× 00
R
s == =590,3 (16)
N
N 10
C
Table 5 — Particle concentration data for secondary calibration samples
Sample 1 X particles Sample 2 X particles
i i
Count
ml ml
1 6 376 7 312
2 6 220 7 186
3 6 507 6 866
4 6 288 7 444
5 6 321 7 036
8 Example 5: Relating particle size to
...
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