IEC 60172:2015

IEC 60172 ®
Edition 4.0 2015-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Test procedure for the determination of the temperature index of enamelled and
tape wrapped winding wires
Méthode d’essai pour la détermination de l’indice de température des fils de
bobinage émaillés et enveloppés de ruban

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IEC 60172 ®
Edition 4.0 2015-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Test procedure for the determination of the temperature index of enamelled and

tape wrapped winding wires
Méthode d’essai pour la détermination de l’indice de température des fils de

bobinage émaillés et enveloppés de ruban

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.060.10 ISBN 978-2-8322-2676-6

– 2 – IEC 60172:2015 © IEC 2015
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 Summary of procedure . 7
5 Test specimens . 7
5.1 Preparation . 7
5.1.1 Enamelled round wire with a nominal conductor diameter of 0,224 mm
up to and including 2,65 mm . 7
5.1.2 Tape wrapped round wire and enamelled or tape wrapped rectangular
wire . 10
5.2 Varnish impregnation . 12
5.3 Notes on number of test specimens . 13
5.4 Specimen holder . 13
5.4.1 For specimens according to 5.1.1 . 13
5.4.2 For specimens according to 5.1.2 . 14
6 Temperature exposure. 14
7 Test voltage and its application . 16
8 Calculations . 16
8.1 Specimen failure time . 16
8.2 Time to failure . 17
8.3 Linearity of data . 17
8.4 Calculating and plotting thermal endurance and temperature index . 17
9 Report . 18
Annex A (normative) Method for calculation of the regression line . 19
Annex B (normative) Correlation coefficient . 24
Bibliography . 26

Figure 1 – Device used to form enamelled round wire test specimen . 8
Figure 2 – Spacer . 8
Figure 3 – Twist forming jig . 9
Figure 4 – Test specimen set up in forming jig . 9
Figure 5 – Test specimen formed with loop cut . 10
Figure 6 – Jig for bending large magnet wire, dielectric test specimen . 11
Figure 7 – Forming jig and test specimen . 12
Figure 8 – Specimen holder . 13
Figure 9 – Specimen holder and electrical connection fixture . 14
Figure 10 – Thermal endurance graph – Temperature index . 18
Figure A.1 – Plot of regression line based on sample calculation (Table A.2) . 23

Table 1 – Force and number of twists for specimens . 8
Table 2 – Proof voltage for round enamelled wire . 10
Table 3 – Recommended exposure times in days per cycle. 15

Table 4 – Proof voltage for tape-wrapped round and for enamelled or tape-wrapped
rectangular wire . 16
Table A.1 – Commonly used test temperatures in degrees Celsius and the
corresponding kelvins with its reciprocal and reciprocal squared values . 21
Table A.2 – Sample calculation . 22

– 4 – IEC 60172:2015 © IEC 2015
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
TEST PROCEDURE FOR THE DETERMINATION OF THE TEMPERATURE
INDEX OF ENAMELLED AND TAPE WRAPPED WINDING WIRES

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
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with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
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6) All users should ensure that they have the latest edition of this publication.
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60172 has been prepared by IEC Technical Committee 55:
Winding wires.
This fourth edition cancels and replaces the third edition published in 1987,
Amendment 1:1997 and Amendment 2:2010. This edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
– Revision of Clause 1, Scope, to incorporate appropriate text from former Clause 2, Object;
– Deletion of Clause 2, Object, by placement of its text into existing clauses;
– New Clause 2, Normative references;
– Revision of 5.1.1, 5.3 and 5.4 with corrections to Amendment 2 to the third edition;
– Revision of Clause 7 as to clarify which specimens comply with Table 3 and Table 4;
– Revision of figures with high-resolution photos and graphs.

The text of this standard is based on the following documents:
FDIS Report on voting
55/1518/FDIS 55/1524/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – IEC 60172:2015 © IEC 2015
TEST PROCEDURE FOR THE DETERMINATION OF THE TEMPERATURE
INDEX OF ENAMELLED AND TAPE WRAPPED WINDING WIRES

1 Scope
This International Standard specifies, in accordance with the provisions of IEC 60216-1, a
method for evaluating the temperature index of enamelled wire, varnished or unvarnished with
an impregnating agent, and of tape wrapped round and rectangular wire, in air at atmospheric
pressure by periodically monitoring changes in response to AC proof voltage tests. This
procedure does not apply to fibre-insulated wire or wire covered with tapes containing
inorganic fibres.
NOTE The data obtained according to this test procedure provide the designer and development engineer with
information for the selection of winding wire for further evaluation of insulation systems and equipment tests.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60216-1, Electrical insulating materials – Thermal endurance properties – Part 1: Ageing
procedures and evaluation of test results
IEC 60216-3, Electrical insulating materials – Thermal endurance properties – Part 3:
Instructions for calculating thermal endurance characteristics
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
temperature index
TI
numerical value of the Celsius temperature expressed in degrees Celsius characterizing the
thermal capability of an insulating material or an insulation system
Note 1 to entry: In case of insulating materials, the temperature index is derived from the thermal endurance
relationship at a given time, normally 20 000 hours. It may be used as basis for determination of the material’s
temperature class.
Note 2 to entry: In case of insulation systems, the temperature index may be derived from known service
experience or from a known comparative functional evaluation of an evaluated and established reference insulation
system as basis.
[SOURCE: IEC 60050-212:2010, 212-12-11]
3.2
specimen failure time
number of hours at the exposure temperature that have elapsed at the time a specimen
fails the proof test
3.3
time to failure
L
number of hours to failure calculated from the specimen failure times for a set of
specimens at one exposure temperature
4 Summary of procedure
A set of specimens in accordance with Clause 5 is subjected to a testing cycle. This cycle
consists of a heat-storing period at a temperature given in Clause 6, followed by a proof
voltage test at room temperature in accordance with Clause 7.
This cycle is repeated until a sufficient number of specimens has failed. The time to failure is
calculated in accordance with Clause 8. The test is carried out at three or more
temperatures. A regression line is calculated in accordance with 8.4 and the time to failure
values plotted on thermal endurance graph paper as a function of the exposure
temperature.
The temperature in degrees Celsius, corresponding to the point of intersection of the
regression line with the ordinate of 20 000 h endurance represents the temperature index of
the winding wire under test.
5 Test specimens
5.1 Preparation
5.1.1 Enamelled round wire with a nominal conductor diameter of 0,224 mm up to and
including 2,65 mm
The grade of insulation used for determining the thermal index shall be grade 2 or grade 2B
for self-bonding winding wires.
Wire sizes 0,315 mm and 0,28 mm are permitted for use when the specification size range is
limited to 0,50 mm and finer.
NOTE For round enamelled winding wires, in order to avoid undue fragility of the test specimen, experience has
shown that nominal conductor diameters of 0,800 mm up to and including 2,65 mm are generally found convenient
to handle and test.
Specimens shall be prepared as follows:
a) A wire specimen approximately 400 mm in length shall be twisted together over a distance
of 125 mm with a device as shown in Figure 1. The force (weight) applied to the wire pair
while being twisted and the number of twists are specified in Table 1.

– 8 – IEC 60172:2015 © IEC 2015

IEC
Figure 1 – Device used to form enamelled round wire test specimen
Table 1 – Force and number of twists for specimens
Nominal diameter Force applied to wire pair Number of twists per
125 mm
mm N
Over Up to and including
0,224 0,25 0,85 33
0,25 0,35 1,7 23
0,35 0,50 3,4 16
0,50 0,75 7,0 12
0,75 1,05 13,5 8
1,05 1,50 27,0 6
1,50 2,15 54,0 4
2,15 3,50 108,0 3
b) Spacers may be prepared as shown in Figure 2. Such thermally stable insulating
materials as ceramic or silicone glass fibre laminate may be used. The spacers are
marked with a suitable identifying letter or number.
3 19
Drill two holes to match wire diameter
IEC
Material: Silicone glass laminate
Dimensions in millimetres
Figure 2 – Spacer
c) The test specimens may be shaped in a jig, an engineering drawing of which is shown
in Figure 3. A specimen is placed in the jig and a spacer, placed on the parallel leads
of the twisted pair, is brought up to the face of the jig as shown in Figure 4. The leads
are then bent parallel to hold the spacer in position. The forming jig provides more
uniform test specimens. If a specimen holder is used, the spacers are unnecessary.
R3,2
R1,2
R3,2
6,5 ∅ pin, press fit
IEC
R = Radius of bend
Dimensions in millimetres
Figure 3 – Twist forming jig
Forming jig
Push spacer to top
Enamelled wire twist
Bend ends parallel to hold spacer
IEC
Figure 4 – Test specimen set up in forming jig
d) The loop at the end of the twisted section shall be cut at two places (not one) to
provide the maximum spacing between the cut ends as shown in Figure 5. Any bending
of the wires, at this end or the other untwisted end, to ensure adequate separation
insulation.
between the wires shall avoid sharp bends or damage to the

– 10 – IEC 60172:2015 © IEC 2015
Cut loop in two places
IEC
Figure 5 – Test specimen formed with loop cut
e) In order to ensure homogeneity of the batch of test specimens, it is recommended that
test specimens be subjected to a test voltage three times the value given in
Table 2 for 1 s.
Table 2 – Proof voltage for round enamelled wire
Voltage
Increase in diameter due to the insulation
(rms)
(mm)
Over Up to and including
– 0,015 300
0,015 0,024 300
0,024 0,035 400
0,035 0,050 500
0,050 0,070 700
0,070 0,090 1 000
0,090 0,130 1 200
5.1.2 Tape wrapped round wire and enamelled or tape wrapped rectangular wire
NOTE This procedure applies to any convenient dimension of round or rectangular wire. However, selecting wires
having dimensions that minimize the bending force needed to shape the test specimen will make the procedure
easier to perform. Wire with high stiffness will yield specimens with poor wire-to-wire contact areas.
Specimens shall be prepared as follows:
a) Two straight specimens of wire each of 250 mm length shall be cut from the supply spool.
b) 10 mm to 15 mm of the insulation shall be removed from one end of each piece of wire to
provide for electrical connection.
c) Each specimen shall be formed in a jig, as shown in Figure 6. This produces a straight
centre section of about 150 mm with bent ends, which provide the necessary flare at both
ends of the final specimen.
IEC
All parts 12,5 mm thick
a) Fixed template
compound plate stock
Phenolic impregnated fabric
IEC
b) Movable template (same dimensions as a))
IEC
IEC
a mounting screws for fixed template
b mounting screws for movable template (template shall be free to slide)
c mounting screw for clamping lever (lever shall be free to rotate)
c) Platine
d) Clamping lever
Dimensions in millimetres
Figure 6 – Jig for bending large magnet wire, dielectric test specimen
d) The two formed specimens shall be placed together back-to-back and tightly wrapped with
glass yarn over the straight centre section of the specimen, as shown in Figure 7.

– 12 – IEC 60172:2015 © IEC 2015
Forming jig
Test specimen
IEC
Figure 7 – Forming jig and test specimen
Care shall be taken that the centre section shows a close contact between the two pieces.
After tying, further bending of the ends shall be avoided. Pre-annealing of the specimen prior
to testing or impregnating will remove stress and craze marks and therefore may be desirable
with certain material.
e) Prior to testing the specimen shall be proof-tested at 1 000 V a.c.
5.2 Varnish impregnation
Experience has shown that insulated wire according to IEC 60317 and impregnating agents
according to IEC 60455-3-5 or IEC 60464-3-2 can affect one another during the thermal
ageing process.
NOTE 1 Testing varnished specimens will allow for evaluation of the compatibility of the wire insulation with an
impregnating agent. Thus the temperature indices of different combinations can be compared.
Interaction between wire insulation and such agent may increase or decrease the relative
thermal life of this combination compared with the life of the wire tested without impregnation.
Therefore, with impregnated specimens, this test procedure may give an indication of the
thermal endurance of a combination of wire insulation and impregnating agent.
If such impregnation is required, the following procedure shall be applied:
With the specimen in the vertical position, it shall be immersed in the impregnating agent for
(60 ± 10) s (see note). It shall be removed slowly and uniformly at a rate of about 1 mm/s. It
shall be drained horizontally for 10 min to 15 min and cured horizontally according to the
manufacturer's recommendation or to an agreed schedule. If more than one treatment is to be
given, immerse, drain and cure the specimen vertically reversing the specimen for each
subsequent treatment.
NOTE 2 Some impregnating agents, such as high viscosity or thixotropic products require alternative processing
methods.
5.3 Notes on number of test specimens
The accuracy of the test results depends largely upon the number of test specimens aged at
each temperature. A greater number of test specimens is required to achieve an acceptable
degree of accuracy if there is a wide spread in results among the specimens exposed at each
temperature.
Experience has shown that twenty specimens without impregnation and ten specimens with
impregnation give results with an acceptable tolerance. A minimum of ten specimens shall be
used.
5.4 Specimen holder
5.4.1 For specimens according to 5.1.1
Since individual handling of the twisted specimens may result in premature failures, it is
recommended that the specimens be placed in a suitable holder, as shown in Figure 8. The
holder should be designed in a manner that will protect the twisted specimens from external
mechanical damage and warping. The holder will be so constructed as to allow the ends of
the twist to protrude from the holder to make electrical connection for the proof testing as
shown in Figure 9. The holder shall be designed for at least ten specimens to decrease
handling time.
IEC
Figure 8 – Specimen holder
– 14 – IEC 60172:2015 © IEC 2015

IEC
Figure 9 – Specimen holder and electrical connection fixture
5.4.2 For specimens according to 5.1.2
The specimen shall be hung in the oven. No special holder is required.
6 Temperature exposure
Recommended temperatures to which the test specimens are subjected are given in this
Clause 6.
In Table 3, the recommended temperature and time of exposure in each cycle are given. A
test cycle is defined as one exposure to a high temperature followed by one proof-voltage test
at room temperature (20°C – 30°C). The test specimens shall be placed directly into and
removed from the ageing ovens without controlling the heating or cooling rate.
The ovens should be heated to the proper temperature before the specimens are subjected to
the exposure temperature.
The specimens should be aged in a forced air circulation oven which is capable of maintaining
the temperature of the specimens under test within 2°C of the selected exposure temperature.
The exposure times are selected to subject the test specimens to approximately 10 cycles at
each temperature before the time to failure is reached.

Table 3 – Recommended exposure times in days per cycle
Exposure or Estimated temperature index
ageing
105-109 120-130 150-159 180-189 200-209 220-239 240-249
temperature
(ºC)
320 – – – – – – 1
310 – – – – – – 2
300 – – – – – 1 4
290 – – – – – 2 7
280 – – – – 1 4 14
270 – – – – 2 7 28
260 – – – 1 4 14 49
250 – – – 2 7 28 –
240 – – – 4 14 49 –
230 – – – 7 28 – –
220 – – 1 14 49 – –
210 – 1 2 28 – – –
200 – 2 4 49 – – –
190 1 4 7 – – – –
180 2 7 14 – – – –
170 4 14 28 – – – –
160 7 28 49 – – – –
150 14 49 – – – – –
140 28 – – – – – –
130 49 – – – – – –
120 – – – – – – –
NOTE The recommendations in Table 3 differ from those in IEC 60216-3 but have been found to be more
suitable for enamelled wires.
Thermal endurance values obtained from test specimens subjected to an average of less than
eight or more than twenty cycles at the exposed temperature may not be reliable and should
not be used to predict the temperature rating of the enamelled wire. Therefore, a shorter or
longer cycle time than those given in Table 3 may be chosen for certain exposure
temperatures, to ensure that the average number of cycles to failure falls within this range.
After the specimens have been subjected to a particular cycle, the time may be appropriately
increased or decreased to control the number of cycles required to reach the time to failure.
Test specimens should be exposed to a minimum of three and preferably four exposure
temperatures. The lowest temperature, recommended at 20 °C above the desired thermal
class, should be one which results in a time frame to failure of more than 5 000 h. The
highest exposure temperature shall have a value of at least 100 h to be considered a valid
data point. Exposure temperatures should not be more than 20 °C apart. The accuracy of the
temperature index predicted from the results will improve as the exposure temperature
approaches the temperature to which the insulation is exposed in service.

– 16 – IEC 60172:2015 © IEC 2015
7 Test voltage and its application
The voltage to be applied shall be an a.c. voltage and shall have a nominal frequency of
50 Hz or 60 Hz of an approximately sine-wave form, the peak factor being within the limits of
√2 ± 5% (1,34 to 1,48). The test transformer shall have a rated power of at least 500 VA and
shall provide a current of essentially undistorted waveform under test conditions.
To detect failure, the overcurrent indication device shall operate when a current of 5 mA or
more flows through the high-voltage circuit. The test voltage source shall have a capacity to
supply the detection current (5 mA or more) with a maximum voltage drop of 10 %.
The test specimens are removed from the ovens and cooled to room temperature. Each
specimen shall be subjected to a proof voltage according to the increase in diameter due to
insulation as specified in Table 3 for specimens according to 5.1.1 and in Table 4 for
specimens according to 5.1.2. In the case of self-bonding wires, the self-bonding layer is
included in the increase in diameter due to the insulation.
Table 4 – Proof voltage for tape-wrapped round and for enamelled
or tape-wrapped rectangular wire
Increase in dimension due to the insulation Voltage
(mm) (rms)
Over Up to and including
0,035 0,050 300
0,050 0,065 375
0,065 0,080 450
0,080 0,090 550
0,090 0,100 650
0,100 0,115 700
0,115 0,130 750
0,130 0,140 800
0,140 0,150 850
The proof voltage shall be applied to the test specimens for approximately 1 s.
NOTE A relatively short time of application of the test voltage is desirable to minimize the effects of corona and
dielectric fatigue.
Care shall be taken in all cases to avoid mechanical damage to the test specimens. The
specimens that fail the proof test shall be discarded and the remaining specimens returned to
the oven for another temperature exposure.
8 Calculations
8.1 Specimen failure time
The failure time of an individual specimen at one exposure temperature is determined by
calculating the mid-point between the total hours of exposure temperature at which the
specimen failed the proof voltage and the total hours of exposure of the previous cycles. This
assumes that the specimen would probably have failed the proof voltage at some point in the
middle of the last temperature exposure cycle. Thus, the specimen failure time is the sum of
the total hours at the time to failure, minus half the hours of the last exposure cycle.

8.2 Time to failure
The time to failure of a set of specimens at one exposure temperature shall be calculated by
using either the median value or the logarithmic mean value. For many materials, the median
value is statistically valid. In most cases, use of the median will significantly reduce testing
time, since the test ceases once the median value has been obtained.
When using the median value, the time to failure is calculated as follows:
Where there are a total number of n specimens in a set of specimens, the time to failure of the
set equals:
a) the specimen failure time of specimen number (n + 1)/2; if n is odd (see 8.1);
b) the logarithmic mean value of the specimen failure times of specimens number n/2 and (n
+ 2)/2; if n is even (see 8.1).
For instance, if n is 12, the time to failure of the set would be the mean value of the specimen
failure times of the sixth and the seventh specimen. For convenience, it is suggested that
when the median value is used for calculating the time to failure of the set, the total number of
specimens of a set be odd, thus simplifying calculation.
When using the logarithmic mean value, the time to failure is calculated by dividing the sum of
the logarithms of the specimen failure times of the set (see 8.1) by the total number n of
specimens in the set. The antilogarithm of this mean value is the time to failure of the set.
8.3 Linearity of data
To avoid misleading extrapolations (see 8.4), the correlation coefficient should be calculated
as shown in Annex B, to provide a measure of linearity.
If the correlation coefficient r is equal to or greater than 0,95, the data are said to be linear
and the data points will be reasonably close to a straight line. In the event that the correlation
coefficient is less than 0,95, the data are said to be non-linear and an additional test should
be performed at a temperature below the lowest previous temperature.
The new temperature point may be 10 ºC below the previous lowest temperature point. When
re-calculating the temperature index and correlation coefficient, one temperature point may be
deleted, starting with the highest temperature, for each new temperature point obtained.
The data will be linear if the thermal deterioration of the enamelled wire or the varnished
enamelled wire appears as one chemical reaction. Non-linearity may indicate that:
a) two or more reactions which have different activation energies (slopes) are predominant at
different temperatures within the testing range; or
b) errors have been introduced through the sampling technique and/or the testing procedure.
Non-linear data should not be used for extrapolation.
8.4 Calculating and plotting thermal endurance and temperature index
Thermal endurance is graphically presented by plotting the time to failure (see 8.2) versus its
respective exposure temperature on graph paper having a logarithmic time scale as the
ordinate and the reciprocal of absolute temperature as the abscissa. The exposure
temperatures at 2 000 h and 20 000 h are estimated based on the first order regression
calculation presented in Annex A. A regression line is drawn through these two points on the
graph, which represents the thermal endurance of the enamelled winding wire
(see Figure 10).
– 18 – IEC 60172:2015 © IEC 2015
TI 164
10 Time (hours)
Logaritmic scale
2 × 10
Temperature °C
160 170 180 190 200 210 220 230 240 250 260
1 –2 –1
(10 × K )
T
0,23 0,22 0,21 0,20 0,19
IEC
Figure 10 – Thermal endurance graph – Temperature index
The Temperature Index of the enamelled wire is the number corresponding to the temperature
in degrees Celsius at which the regression line intersects the 20 000 h line. It is listed without
reference to degrees Celsius.
If further statistical analysis of the data is necessary, reference may be made to IEC 60216-3.
9 Report
The report of the results shall contain the following information as a minimum:
a) identification or description of the wire enamel, grade and the type of conductor (e.g.
copper, aluminium, etc.);
b) identification or description of the impregnating varnish and varnishing process;
c) time to failure of each set of specimens at each exposure temperature;
d) a graph of the first order regression line through the time to failure values;
e) the temperature index (TI)
Annex A
(normative)
Method for calculation of the regression line
This Annex A presents a method for quickly plotting the regression line for thermal
endurance data. This method may be used for any number of measurements at various
test temperatures. If information concerning the confidence limits is required, a more
detailed analysis shall be made in accordance with IEC 60216-3.
It has been established that many insulations deteriorate in such a manner that the following
equation applies:
B/T
L = Ae (1)
where:
L
= insulation endurance in hours;
T = absolute temperature in kelvins;
A, B
= constants for each insulation, and
e = base of natural logarithms.

Equation (1) may be expressed as a linear function by taking logarithms:
B
log L =log A+(log e) ⋅ (2)
10 10 10
T
Let:
Y = log L
a = log A
X = 1/T
b = (log e) B
Then:
Y = a + bX (3)
Thus, data from testing at higher temperatures may be plotted on log L versus 1/T graph
paper and a straight line extrapolated to lower temperatures. However, since the nature of
logarithmic plots does not allow accurate extrapolation by the method of drawing the best
apparent straight line through the data points, a more rigorous method shall be used for
greater accuracy and uniformity. By using the method of least squares, the constants a

– 20 – IEC 60172:2015 © IEC 2015
and b may be derived in terms of the experimental data obtained. These equations are
as follows:
∑Y −b ∑ X
a = (4)
N
N ∑ XY − ∑ X ∑Y
b = (5)
2 2
N ∑ X −(∑ X )
where:
X = 1/T = reciprocal of the test temperature in kelvins (θ°C + 273°C);
N = number of test temperatures used;
Y = log L = logarithm of time to failure;

Ʃ = summation of N values.
Knowing the constant a, and the slope b of the regression line, the temperature at any
required life value may be calculated as follows:
Y = a + bX
1 b
T = = (6)
X Y − a
b
Temperature at 20 000 h in degrees Celsius = − 273 (7)
4,3010 − a
(temperature index)
b
Temperature at 2 000 h in degrees Celsius = − 273 (8)
3,3010 − a
To simplify the handling of the test data used in Equations (4) to (8), it is suggested that
the steps for a sample calculation be followed as outlined below (see Table A.1 and
Table A.2):
a) In column 1, list the temperatures in ºC, as illustrated in Table A.2, at which a set of
specimens was tested.
2 2
b) In columns 2 and 3, list the reciprocals (X = 1/T) and the reciprocals squared (X 1/T ) of
the above test temperatures converted to kelvins (see also Table A.1).
c) In column 4, list the time to failure L, in hours, of each set of specimens, and in the
column 5, list the log of the values in the fourth column (Y = log L).

10 10
d) In column 6, list the products of X and Y.
e) Provide summation for columns 2, 3, 5 and 6 and enter the summation
by Ʃ) at the bottom of the respective column.
(indicated
f) Indicate the number N of times to failure on the worksheet.
g) Using the values obtained in steps e) and f), compute b (Equation 5) and a
(Equation 4) in that order. The constant a will always be negative.

h) Using constants a and b, calculate the temperature in degrees Celsius at 20 000 h
(Equation 7) and at 2 000 h (Equation 8).
i) Plot the above two temperature points from step h) on log L versus 1/T graph paper
and draw the regression line through them (see Figure A.1).
j) Plot the times to failure L at their respective temperatures on the same graph.
Table A.1 – Commonly used test temperatures in degrees Celsius and the
corresponding kelvins with its reciprocal and reciprocal squared values
2 2
θ T X = 1/T X = 1/T
-1 -2
(ºC) (K) (K ) (K )
−3 −6
105 378 2,646 × 10 6,999 × 10
−3 −6
120 393 2,545 x 10 6,475 x 10
−3 −6
125 398 2,513 × 10 6,313 × 10
−3 −6
130 403 2,481 × 10 6,157 × 10
−3 −6
140 413 2,421 × 10 5,863 × 10
−3 −6
150 423 2,364 × 10 5,589 × 10
−3 −6
155 428 2,336 x 10 5,459 x 10
−3 −6
165 438 2,283 × 10 5,212 × 10
−3 −6
175 448 2,232 × 10 4,982 × 10
−3 −6
180 453 2,208 × 10 4,873 × 10
−3 −6
185 458 2,183 × 10 4,767 × 10
−3 −6
190 463 2,160 × 10 4,665 × 10
−3 −6
200 473 2,114 × 10 4,470 × 10
−3 −6
210 483 2,070 × 10 4,287 × 10
−3 −6
220 493 2,028 × 10 4,114 × 10
−3 −6
225 498 2,008 × 10 4,032 × 10
−3 −6
230 503 1,988 × 10 3,952 × 10
−3 −6
240 513 1,949 × 10 3,800 × 10
−3 −6
250 523 1,912 × 10 3,656 × 10
−3 −6
260 533 1,876 × 10 3,520 × 10
−3 −6
270 543 1,842 × 10 3,392 × 10
−3 −6
280 553 1,808 × 10 3,270 × 10
−3 −6
300 573 1,745 × 10 3,048 × 10
-3 -6
320 593 1,686 x 10 2,844 x 10
²
NOTE Calculations for X are based on n
...