ISO/TR 4808:2021

TECHNICAL ISO/TR
REPORT 4808
First edition
2021-02
Hydraulic fluid power – Interpolation
method for particle count and filter
test data
Transmissions hydrauliques – Méthode d'interpolation pour les
données issues du comptage des particules et des essais du filtre
Reference number
©
ISO 2021
© ISO 2021
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ii © ISO 2021 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Background . 1
5 Interpolation of particle concentration and Beta Ratio data . 3
6 Example of interpolation of particle concentration data . 4
7 Example of interpolation of filter Beta Ratio and removal efficiency data .6
8 Summary .10
BIBLIOGRAPHY .12
Foreword
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This document was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee
SC 6, Contamination control.
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iv © ISO 2021 – All rights reserved

Introduction
The 2016 version of ISO 11171 provides options for reporting particle size in either units of µm(c) or
µm(b). While mathematical conversion of µm(b) sizes to µm(c) sizes is straightforward, there is no
such universal means for converting particle concentrations or filter Beta Ratios. This is problematic
when attempting to comply with contamination control and filter performance specifications given in
integral units of µm(c) when data are in integral units of µm(b) corresponding to decimal point µm(c)
sizes, or vice versa. For example, particle sizes of 4 µm(b), 6 µm(b), 14 µm(b) and 21 µm(b), correspond
to sizes of 3,6 µm(c), 5,4 µm(c), 12,6 µm(c) and 18,9 µm(c), respectively. In the absence of a common
interpolation method, otherwise acceptable fluid and filter products can be deemed unacceptable for
use because of a discrepancy in the particle sizes reported. This document describes a recommended
method for converting µm(b) data to µm(c) data and for interpolating particle concentration, Beta
Ratio, and removal efficiency data. The resultant interpolated values can be used to convert cleanliness
level or filter performance specifications and data from µm(b) to µm(c).
TECHNICAL REPORT ISO/TR 4808:2021(E)
Hydraulic fluid power – Interpolation method for particle
count and filter test data
1 Scope
This document describes a recommended method for the interpolation of particle concentration
and filter Beta Ratio data when results are not otherwise available at the desired particle sizes. It is
applicable for assessing conformance with existing fluid cleanliness and filter Beta Ratio specifications
whereby the specification and actual test results are provided in different units of particle size, for
example, the specification is in µm(c), but the particle counts or Beta Ratio data are in units of µm(b).
This document is also applicable when particle sizes in specifications and available data use the same
units of particle size, but do not correspond to exactly the same sizes, for example, when particle
counts at 20 µm(c) are specified, but data was collected at 21 µm(c). This method allows interpolation
to intermediate particle sizes within the range of existing data and does not permit extrapolation to
particle sizes outside the range of available data.
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 4406, Hydraulic fluid power — Fluids — Method for coding the level of contamination by solid particles
ISO 11171, Hydraulic fluid power — Calibration of automatic particle counters for liquids
ISO 16889, Hydraulic fluid power — Filters — Multi-pass method for evaluating filtration performance of
a filter element
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 4406, ISO 11171 and
ISO 16889 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Background
In contamination control programmes, filter purchase decisions and quality control programmes,
particle count and filter Beta Ratio data are compared to established benchmarks, such as fluid
cleanliness specifications, filter performance specifications and historical data. Meaningful assessments
can only be made if identical sizes are being compared. This became an issue with ISO 11171:2016.
Historical data and specifications prior to 2016 were reported in size units of µm(c). Beginning in 2016,
however, some chose to report size in units of µm(b) while others report in µm(c). The two units of
particle size, µm(c) and µm(b), are mathematically related, but the corresponding values for particle
concentration and Beta Ratio are not. The 10 % difference in particle size between the two units of
particle size yields differences in the corresponding particle concentrations and Beta Ratios. These, in
turn, can significantly impact critical contamination control decisions.
As an example, consider whether or not to replace the oil in a hypothetical hydraulic system. In this
example, it is assumed that the cleanliness level specification for its hydraulic fluid is an ISO 4406
code of 18/17/13. When a sample of the fluid was analyzed, particle concentrations of 5 135 particles/
mL, 1 368 particles/mL, 98,3 particles/mL and 19,5 particles/mL at 4 µm(b), 6 µm(b), 14 µm(b), and
21 µm(b) respectively, were reported. Does this fluid meet the cleanliness specification, in which case
it can continue to be used, or it is contaminated and must be replaced, and the corresponding costs of
new fluid, downtime and lost productivity incurred? An uninformed user can incorrectly convert these
µm(b) concentrations to ISO code values of 20/18/14 and conclude that the fluid was contaminated.
This would be an expensive mistake. ISO 4406 stipulates that the code applies to particle sizes of 4
µm(c), 6 µm(c) and 14 µm(c), not µm(b). Particle sizes of 4 µm(b), 6 µm(b), 14 µm(b) and 21 µm(b) sizes
correspond to 3,6 µm(c), 5,4 µm(c), 12,6 µm(c) and 18,9 µm(c), respectively. The µm(b) concentrations
appear higher than those concentrations found for µm(c) sizes of the same numerical value. Ideally,
the sample should be re-analyzed using an Automatic Particle Counter (APC) calibrated in µm(c), but
this is often impossible or impractical. A similar problem occurs whenever specifications and data (e.g.
particle concentrations, ISO codes, or filter Beta Ratios) are in different units of particle size. Thus,
there is a need for a reliable method for converting µm(b) to µm(c), and then for interpolating to obtain
data at the desired particle sizes for contamination control decisions.
The constrained cubic spline method of interpolation that is used in ISO 11171:2020 to relate particle
concentrations to threshold settings and particle sizes to create calibration curves for APCs, may
be used to interpolate particle concentration and filter Beta Ratio data. Traditional cubic spline
interpolation starts with a series of known data points, the training data set, and interpolates between
them according to the following rules:
— The cubic spline curve passes through all of the known points;
— The curve connecting consecutive points are a third-degree polynomial;
— The first derivative of the curves on each side of a known point are equal;
— The second derivative of the curves on each side of a known point are equal; and
— Boundary conditions are established for the minimum and maximum values of x.
While traditional cubic spline interpolation produces a smooth curve, its usefulness for purposes of
interpolating particle concentration and Beta Ratio data is compromised by a tendency to overshoot
between node points. In contrast, the constrained cubic spline method prevents overshooting and
improves accuracy by sacrificing a little in terms of smoothness. This is accomplished by eliminating
the requirement for second derivatives to be equal. Instead, the first order derivatives on each side of a
point are specified. Since accuracy is paramount in particle counter calibration, the constrained cubic
spline method has been adopted in ISO 11171:2020. The same rationale applies to other fluid power
cleanliness and filter performance applications.
Contamination control decisions should be made using data obtained at the actual sizes defined in
specifications or standards, but this is not always possible or practical. For example, a standard can
specify particle size in units of µm(c), but the available particle count or Beta Ratio data can be from
an APC calibrated to ISO 11171:2016 and reported size in units of µm(b). Similarly, a specification can
use µm(b) sizes from the obsolete ISO 11171:2016, but the available data can be from an APC calibrated
to ISO 11171:2020 which reports size only in units of µm(c). In such cases, the constrained cubic spline
method of interpolation is recommended for estimating particle concentrations and Beta Ratios as a
function of particle size, when data is not available at the specific sizes of interest. It should be noted
that the accuracy of the resultant interpolation is dependent upon the quality of the original data.
Accuracy is sacrificed when the input data contains errors, when there is too little data available for
accurate interpolation, or when the available sizes skew the interpolation.
2 © ISO 2021 – All rights reserved

5 Interpolation of particle concentration and Beta Ratio data
Meaningful comparisons of particle concentrations and Beta Ratios can only be made if all data is
reported in the same units of particle size. ISO 11171:2020 standardized on µm(c) as the only acceptable
unit for reporting particle size; hence it is recommended that specifications and historical data utilizing
µm(b) sizes be converted to their corresponding µm(c) sizes. The interpolation of µm(b) to µm(c) data
involves the following steps:
1) Mathematical convers
...