Microsoft Word - 4-prima pagina


ACTA IMEKO 
ISSN: 2221‐870X 
June 2015, Volume 4, Number 2, 23‐31 

 

ACTA IMEKO | www.imeko.org  June 2015 | Volume 4 | Number 2 | 23 

Uncertainty restrictions of transfer click‐torque wrenches 

Andreas Brüge 

Physikalisch‐Technische Bundesanstalt (PTB), Bundesallee 100 , 38116 Braunschweig, Germany 

 

 

Section: RESEARCH PAPER  

Keywords: Torque; click‐torque wrench; ISO 6789; transfer 

Citation: Andreas Brüge, Uncertainty restrictions of transfer click‐torque wrenches, Acta IMEKO, vol. 4, no. 2, article 5, June 2015, identifier: IMEKO‐ACTA‐04 
(2015)‐02‐05 

Editor: Paolo Carbone, University of Perugia, Italy 

Received April 21, 2015; In final form June 8, 2015; Published June 2015 

Copyright: © 2015 IMEKO. This is an open‐access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits 
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 

Corresponding author: Andreas Brüge, e‐mail: Andreas.Bruege@ptb.de 

 

1. INTRODUCTION 

Click-torque wrenches (CTWs) are setting torque tools of 
the type II according to ISO 6789 [1], which are wrenches with 
a release mechanism to limit the transferable torque. In 
particular this definition excludes screwdrivers or wrenches 
with flexion bars. They are to be calibrated according to ISO 
6789, where conformity limits are required which amount to ±4 
% and ±6 % respectively, for the relative deviation of the 
releasing value. Nevertheless, CTWs intended as transfer 
standards for the traceability of the calibration facilities 
concerned should comply with much stricter requirements.  

They should correspond to the best measurement 
capabilities (bmcs) of laboratories accredited for CTW 
calibration in the German accreditation body (DAkkS). These 
bmcs cover the range from 0.2 % to 1 % (Figure 1). 

A key comparison of the Deutscher Kalibrierdienst (DKD) 
based on procedures according to the ISO 6789 using CTWs 
demonstrated the insufficiency of the combination of the 
CTWs with these procedures for transfer purposes. Therefore, 
nowadays only indicating transfer torque wrenches can deliver 
the traceability of the static torque calibration in the concerning 
facilities according to the bmc values of calibration laboratories. 
But specific dynamic requests to the facilities destined for CTW 
calibration cannot be verified by indicating torque wrenches.  

 
 
 

Therefore the use of transfer CTWs is necessary particularly 
during assessments to complement the traceability of 
laboratories working in the field of ISO 6789. 

In order to submit proposals for the selection of suitable 
types of CTWs and for measurement procedures which help 
overcome known restrictions of the available types, this work 
surveys important sources of measurement uncertainty of 
different types of CTWs. 

Figure 1. Distribution of  listed bmcs  in the DAkkS for click‐torque wrench 
calibration according to ISO 6789.

ABSTRACT 
For  different  types  of  click‐torque  wrenches,  measurement  uncertainty  contributions  of  typical  calibration  conditions  were 
investigated. Procedures which differ from those given in ISO 6789 were suggested for transfer measurements at calibration facilities 
for click‐torque wrenches in order to improve their reproducibility. Examinations were carried out for influences like lever length, rise 
time, temperature and humidity. 



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 24 

2. CHARACTERISATION OF CTWS 

2.1. Calibration facility 

The measurements for this paper were performed at the 2-
kN·m calibration facility of the Physikalisch-Technische 
Bundesanstalt (PTB) in Braunschweig.  

This facility generates torque loads continuously using an 
electric motor and a gearbox. The detection of the load was 
conducted with Raute reference torque transducers of type 
TT1 and an HBM DMCplus transient recorder.  
Fitted with a DV55 carrier frequency amplifier module, this 
recorder is able to detect releasing signals (Figure 2) under the 
following conditions: 

 carrier frequency               4.8 kHz  
resolution         (24 ... 15) bit  
sampling rate  (150 ... 9600) Hz. 

Altogether, the expanded relative contribution of the 
reference measuring chain results in approximately 8·10-4. 

2.2. Measurements 

Calibrations of CTWs according to ISO 6789 are mainly 
meant to achieve the deviation of the actual release torque A 
from the value which is set at the CTW. For this purpose, 
repeated releases are to be performed five times each at 20 %, 
60 % and 100 % of the nominal torque. Hence inherent 
properties of the CTW, like running-in and repeatability, 
should be part of the result. 

In contrast the intention of the measurements in this work 
is to figure out the CTW’s coefficients of disturbing quantities 
and other contributions to their measurement uncertainty. 

Furthermore, procedures are questioned in order to 
minimize the impact of disturbing quantities and to maximize 
the reproducibility during a transfer measurement in a 
calibration laboratory. These procedures are discussed later in 
this paper. 

In the following, brief descriptions of the measurement 
procedures used for determining considerable influences on the 
calibration of CTWs are given. 

2.3. Release torque A   

The calibration facility performs a constantly increasing load 
until the CTW releases and the measured torque falls sharply. 
The peak value A of the recorded signal of the reference 
measuring chain is calculated, taking into account the relative 
noises of the release curve by detecting the span bA (Figure 3), 
which is a specific value of the CTWs between 2·10-5 and 
2·10-4 and of the reference measurement chain’s zero signal 
(typically 3.5·10-5). 

Together with the relative uncertainties of the signal 
recording and of the sensitivity of the reference transducer, 
plus the influences of the reference transducer creeping and of 
the zero signal drift, the combined relative uncertainty of the 
determination of the release torque A amounts to about 4·10-4.  

2.4. Relative repeatability srpt 

As a mechanical mechanism, a CTW is affected by the 
history of the load, temperature and humidity. Every CTW in 
this investigation was stored under laboratory conditions for 
one day at least before use. Furthermore, preliminary series of 
releases were executed. 

With this preliminary series of up to 120 releases, several 
purposes are to be served. First, the CTWs’ lubrication after 
long idleness should be recovered and, second, the maximum 
release rate should be achieved. If releases succeed too fast, 
thermal effects in the release mechanism provoke a drift of the 
release torque value. Furthermore, the relative standard 
deviation of the values of A provides the relative repeatability 
srpt of the mean value ̅	of the release torque (Figure 4). 

rpt

∑ ̅

1
  (1)

Achieving the mean value of the release torque is a specific task 
of a transfer measurement. Usually measurements with a CTW 
according to ISO 6789 are never given as an average, because 
every single release in the calibration has to fulfil the demands 
of the standard. 

Figure 3. Determination of the release torque A from the torque signal of a 
releasing click‐torque wrench over time considering the contribution bA of 
the signal noise to the measurement uncertainty.  

 

Figure  4. Devolution of the release torque A of a CTW during consecutive 
releases.  The  running‐in  reaches  to  value  No.  14  (shaded  area)  and  the 
relative  standard  deviation  of  the  rest  of  the  data  delivers  a  relative
repeatability srpt of 7.6∙10

‐4
. Figure 2. Torque signal of a releasing click‐torque wrench over time.  



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 25 

Due to friction and resolution effects within the release 
mechanism, even without thermal effects the relative short-
term repeatability of consecutive releases can exceed 10-3. Series 
of 30 repeated release events at least were performed and 
averaged for the determination of each value of ̅ in order to 
overcome this instability of the CTWs. This is important, as a 
high value of the repeatability relative to the other coefficients 
is to be taken into account at the uncertainty estimations of 
them. 

2.5. Relative reproducibility srpr 

The relative reproducibility srpr is defined as the relative 
difference between two independent measurements of ̅ with 
one CTW. 

Manufacturers of CTWs recommend readjusting them to a 
minimum value after each use to avoid mechanical drifting 
during long-term storage due to the spring tension inside the 
release mechanism. Nevertheless, keeping up the tension of the 
CTW over the days of investigation turned out to be 
advantageous. The drift that manufacturers warn against could 
not be detected during extensive tests of the specimens. 
Therefore, avoiding the readjustment of the CTWs between 
measurements yields the benefit of a smaller value of srpr by 
eliminating the resolution uncertainty (Figure 5). The relative 
resolution of the CTW, which amounts from 2·10-4 to 3·10-3 
for the specimens used in this work, is one of the main 
uncertainty contributions for calibrations according to ISO 
6789. It originates from the uncertainty of the adjusting scale 
due to the width of lines and due to mechanical clearance in the 
adjusting mechanism, even if these are latching. 

As usual, calibrations at the beginning and at the end of a 
transfer can deliver a reliable value of srpr. In this work, these 
calibrations were simulated by repeated remounting of the 
CTW while the adjustment was kept. 

2.6. Relative coefficient of lever length cl 

The distance between the pivot of the square drive and the 
support at the handhold of a CTW affects the amount of A 
supposedly by a cross force effect in the pivot. Furthermore, 
deviations of A correlative to the lever length could be caused 
by an eccentric female square drive in the calibration facility [2]. 
This has been avoided by careful alignment of the facility axis 
with an eccentricity of less than 0.05 mm. So it is possible to 
detect just such an eccentricity in the calibration facility under 
test during a transfer calibration using the CTW, by gaining 
increased values of c l there.  

To find the value of c l, two additional series of 30 releases 
each are performed at a lever length 10 mm shorter respectively 
longer than the normal length. The relative coefficient of lever 
length thus can be found with 

 

̅
  (2)

 
where ̅ is the average of peak signals of the calibration facility 
gained at the preliminary series mentioned above, and S is the 
averaged peak signal with the longer or the shorter lever 
respectively, which length is given by l.  

Though the determination of c l usually has to be performed 
at minimum level of torque adjustment, for the purposes of 
transfer measurements this should be done preferably at 
nominal torque adjustment in this context. In this way, no 
readjustment of the CTW takes place and the uncertainty 
contribution of adjustment reproducibility can be avoided. 

2.7. Relative coefficient of temperature cT 

The peak value of a CTW can be influenced by its 
temperature by way of altering the lubrication viscosity, by way 
of dimensional changes in the release mechanism or, if a strain 
gauge is integrated, by temperature dependence of the gauge 
sensitivity [3].  

One possibility to get an estimation of cT is to track the 
relaxation of a heated CTW from 40 °C by repeated series of 
30 release events each to the normal laboratory temperature of 
21 °C. The CTW can be heated inside a climate cabinet 
overnight and then it will have to be moved quickly into the 
calibration facility, which is assisted by the quick and easy 
mounting of the CTW with a square drive. At the beginning of 
the experiment, the repetition rate of the series should be high. 
Because of the downtime of measurements during the 
transport of the CTW from the climate cabinet into the 
calibration facility, the initial status of the CTW is only available 
by an extrapolation. The relaxated state, in contrast, is to be 
measured simply by waiting some hours until the stability of 
occasional measurements is equal to the repeatability of the 
CTW obtained at the preliminary measurement. This method is 
equivalent to the method which was proposed for simplified 
measurements of the relative humidity coefficient [4]. 

With this set-up, cT can be obtained by  
 

̅  
 (3)

 
where ̅ and S are defined analogical to (2), but in the case of a 
temperature step Cab Lab between a climate cabinet and the 
laboratory.  

In contrast to CTW calibration according to ISO 6789, 
transfer measurements can be reduced to very close limits of 
temperature, because these measurements are only reasonable 
in laboratories with low uncertainty budget and thereby with an 
efficient temperature control. Thus, the contribution of cT in a 
transfer measurement usually remains small. 

2.8. Relative coefficient of humidity cF 

Like temperature, humidity can affect the lubrication of the 
mechanism or the sensitivity of a gauge within a CTW [5]. In a 
similar way as described above, the humidity of a CTW can be 
changed in a climate cabinet and its relaxation to the laboratory 
level can be observed. Then c F is given by 

Figure  5.  Amount  of  CTWs’  relative  resolution,  given  mainly  by  adjusting 
uncertainty.  



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 26 

̅	
  (4)

 
with ̅ and S defined analogical to (2), but in the case of a 
humidity step  between a climate cabinet and the 
laboratory. 

Strict humidity control is challenging and expensive even 
for ambitious laboratories. Therefore, humidity deviation 
between PTB and a laboratory under test is usually greater than 
5 %rh, often greater than 10 %rh. Consequently, the impact of 
c F on the uncertainty budget potentially could be higher than 
that of other coefficients discussed in this paper. 

2.9. Relative coefficient of rise time ctB 

The rise time tB of a CTW release event is defined as the 
time between 80 % load and the release load which defines the 
100 % load. The dedicated relative coefficient ctB can be 
obtained by  

 

̅	 , ,
  (5)

 
with ̅ and S defined analogical to (2), but in the case of a step 
in the rise time , , . 

Measurement of the rise time needs correction if the CTW 
under test exhibits a high reading error. Then the release torque 
is far away from the expected nominal value and the starting 
point of the rise time has to be shifted to 80 % of the actual 
release torque. In the most cases, shifting to an earlier time is 
necessary, which is possible if the loading curve was recorded 
completely as given in this work. If a calibration facility delivers 
only the peak value of the curve, correction of the rise time 
value is impossible. 

2.10. Relative coefficient of square drive influence cV 

The quality of the square drive can influence the result of a 
CTW calibration by reactive forces and moments which are 
possible if angularity, planarity and dimensional accuracy are 
inadequate. The usual procedure to determine cV is to perform 
five series of 10 measurements with orientation alterations of 
the square drive by 90° between them. 

During this investigation only a short version of this 
procedure was performed with 30 release events at 0° and 90° 
position of the square drive each, because of the great time 
need of such measurements. Then, a coefficient could be 
obtained using  

 
° °

̅	
  (6)

with ̅ and S defined analogical to (2), but in the case of the 
alteration of the square drive position from 0° to 90°. 

Of course, transfer measurements should be performed 
with a fixed position of the square drive in both calibration 
facilities involved, but the determination of cV does not become 
dispensable. Assuming the female square drive of the PTB 
facility to be well aligned, an increased value of cV in the facility 
under test would indicate some of the mechanical problems 
described above at the female square drive of the latter. In this 
sense, cV is due to the properties of the calibration facility in the 
first order. Therefore, the contribution of cV to the 
measurement uncertainty of the CTW should be taken into 
account if cV is increased in the laboratory under test.  

2.11. Relative coefficient of the ratchet influence crch 

If the CTW comes with a ratchet, eccentricity of the 
rotating part of it is an important source of deviation, as in the 
case of eccentricity of the machine’s axis, mentioned in section 
2.6. about c l.  

Because the ratchet is not a part of the calibration facility 
under test, in a transfer measurement this influence should be 
eliminated by using a fixed or labelled position of the ratchet in 
both facilities. Since ratchets often come with high angular 
resolution and are not usually fixable, an alteration of the 
ratchet position could take place unnoticed during each 
handling. Thus, the effect of the ratchet position alteration was 
determined by 

 

̅  
 (7)

with ̅ and S defined analogical to (2), but in the case of the 
alteration in the ratchet position by ± 1 cog. Because of the 
sinusoidal character of the eccentricity this measurement was 
undertaken at a ratchet position of 0° and of 90°. The 
maximum value of crch was used. 

2.12. Uncertainty of coefficients 

The uncertainties of the coefficient determinations 
described in this paragraph are dominated by that of S, which is 
given mainly by the repeatability srpt of the CTW. Therefore, 
the contribution of the coefficients to the uncertainty is at least 
in the range of srpt multiplied by a sensitivity coefficient given 
by the amount of alteration of the influence quantity in 
question (see section 4.4). This underlines the importance of 
small repeatabilities for the value of a CTW for transfer 
measurements. The use of at least 30 release events for the 
determination of each value of ̅ reduces the influence of the 
release instability by more than a factor of 5. 

3. SPECIMENS 

In order to obtain an overview of possible properties of 
CTWs, some different types of them were investigated in the 
manner described in the chapter above (Table 1). 

Most of them are of the common mechanical release type. 
These wrenches are equipped with a release mechanism 
consisting of an instable crank, which can be pre-stressed by a 
spring and thereby be adjusted for a certain release torque. 
When the torque load exceeds the adjusted value, the instable 
crank turns over and the torque load at the square drive falls 
abruptly.  

While this mechanism is integrated into the body of the 
mechanical CTW, a buckling CTW is constructed to fold 

Table 1. CTWs used in this investigation.  

No.  Type 
Nom. 
torque  in 
N∙m 

Release type 

1 M210 210  mechanical
2 S.305 DA 350  mechanical
3 No 18 700  buckling 
4 714/10 100  electromechanical
5 5122 CT 180  mechanical
6 1800 QL 180  mechanical
7 721Nf/80 800  mechanical
8 Typ D 760  mechanical



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 27 

entirely at the half-way point of the lever. This design is 
outdated and nowadays in use merely for screwing in 
workshops. One exponent of this type is used in the survey to 
have a look at the lower end of the state-of-the-art. 

An electromechanical CTW includes a strain gauge to 
measure the torque load. When this measure exceeds a digitally 
preset limit, an electromagnetic force unlocks the square drive 
for release. This design is quite new, but nevertheless it raises 
expectations for solving some of the problems which are 
known about mechanical CTWs. 

4. RESULTS 

4.1. Sampling rate 

To obtain a CTW with a well-defined and repeatable release 
value, the act of releasing has to be as short as possible.  

The signal in time therefore tends to be discontinuous, 
which implies high requirements for the sampling rate of the 
amplifier which detects the release event. Comparisons of 
release measurements with different sampling rates exhibit 
relative deviations of the peak value up to 1.3·10-3 (Figure 6). 

Using a signal of a release event measured with a sampling 
rate of 9.6 kHz, a simulation of signal integrations with time 
periods corresponding to lower sampling rates was calculated. 
This simulation curve shows a qualitative shape similar to that 
of the measurements. According to that, the curve should 
change from a high inclination at lower sampling rates to an 
approximately constant part for rates higher than 2 kHz. 
Therefore it is advisable for a comparison of two calibration 
facilities either to use a sampling rate of more than 2 kHz or to 
agree on a certain value of the sampling rate, if only lower rates 
are available. 

4.2. Rise time 

In daily workshop use a CTW is loaded with torque by 
hand and as quickly as the worker is able to. Thus, the typical 
rise time of torque is shorter than one second. To 
accommodate this fact, in ISO 6789 values of tB are required to 
be within 0.5 s and 4 s. The higher value is far beyond the 
practical value for manual loading and is to be seen as a 
concession to the deficient speed of calibration machines. 

The mechanical parts of CTWs are subject to inertia effects 
and to friction. Both depend on the velocity of the moving 
parts. In this way, rise time can affect the release torque value 
in CTWs. Electromechanical CTWs additionally have to face 
the runtime error of the release bolt and the influences of the 
sensing element resolution and of the internal sampling rate. In 

this spirit, a rise time of 0.5 s is unreasonably short for transfer 
measurements. 

In this connection, the limits of ISO 6789 are too broad for 
practical application and too close for the requirements of 
transfer measurements. The situation becomes worse if the 
calibration facility under test lacks a precise rise time gauging. 
Then the transfer measurement not only has to test the release 
torque measurement capability of the calibration machine 
under test. Besides this, the procedure should provide 
information about the rise time of the calibration machine in 
question.  

Measurements with different rise times show a relative 
deviation of the release torque of some 10-3 per second at rise 
times shorter than 4 s, in agreement with the consideration 
above (Figure 7). 

In the range between 4 s and 5 s the dependence of the 
release torque on the rise time is minimal. Thus, for the 
purpose of transfer, measurements should be performed slowly 
with a rise time of 5 s.  

As manufacturers are obliged to design their calibration 
machines according to ISO 6789, the machines are often 
unable to run so slowly. In this case, the two comparing 
laboratories should agree upon rise time, which poses the 
problem of measuring the rise time exactly. 

4.3. Selection of a transfer CTW 

In order to rate the ability of the CTWs for transfer 
purposes, a table of the coefficients of the CTWs in the survey 
is given (Table 2). 

  

Figure 6. Relative deviation of peak value, depending on the sampling rate 
of  the  amplifier.  The  dashed  curve  is  the  result  of  a  simulation  which
performs signal integrations with corresponding time periods at a measured
release signal gained at a sampling rate of 9.6 kHz.  

Table 2. Absolute values of relative coefficients in 10
‐6
 of CTWs listed in Table 1. Some data were not measured due to time constraints; the referring 

coefficients were treated as equalling zero. The deviation of specimen No. 3 is due to friction‐induced drift and was treated as a systematic contribution. 

rel. coefficient 
in 10

‐6 1  2  3  4  5  6  7  8 

c l in mm
‐1 

2548  92  no data 326  394  636  330  37 

c  T in K
‐1  1041  351  no data 507 903  510  1008  181 

c  F in (%rh)
‐1 

1154  560  no data 20  268  77  no data  229 

c tB in s
‐1 

8153  6029  no data 2293  5749  1259  4537  3084 

c V   no data  4071  no data 220  7453  586  151  8041 
crch (one cog)

 
6787  1249  no data 305  5783  2316  2635  no ratchet 

srpr  2748  217  no data 143  3419  674  989  5184 
srpt  580  234  27842  96  139  524  646  334 



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 28 

This survey is neither representative of the CTWs available 
on the market nor could a conclusion be drawn about the 
properties of a CTW type, this would require tests at a higher 
number of CTWs of a certain type. The survey shall give 
examples of which parameters are important. Better than a 
competition of coefficients, an analysis of their uncertainty 
impacts give evidence of the suitability of a CTW for transfer 
calibrations (Table 3, Figure 8).  

The contributions in Table 3 indicate the priority for 

compensating the uncertainty sources of a CTW or for its 
improvement in order to qualify it for transfer measurements. 
The most influential contribution to the measurement 
uncertainty to be considered at the selection of a transfer CTW 
is the repeatability srpt.  

Further parameters not included in Table 2 are the object 
of a qualitative appraisal. The shape of a release curve should 
feature a well-defined peak value with a monotone rising and a 
fast break off, kickback-free for at least one second. The 
specific running-in of the release value from the initial increase 
to stable amounts has to be observed at preliminary tests and is 
to be considered at the calibrations by omitting the referring 
data points. Moreover, it has to be ensured by tests that 
keeping the CTW in tension during a transfer calibration would 
not increase repeatability uncertainty due to mechanical drift as 
mentioned in section 2.5.  

4.4. Uncertainty budgets 

The combined relative uncertainty of the reference torque 
measurement with a CTW wRef consists of the contributions of 
the reproducibility wrpr (9), of the release torque detection wA 
(10) and of the influence of the coefficients wx (11): 
 

Ref rpr A x   (8)

 

rpr
rpr

12
2 rpt  (9)

 

A 2 zero NN NN
A

12
  (10)

 
The contribution of the reproducibility is given by the 

measured amount of srpr and twice the uncertainty of this 
measurement which is dominated by the repeatability srpt.  

The contribution wA consists - in addition to the span bA - 
of the relative uncertainty of the national standard facility wNN, 
the relative long-term stability of the facility sNN and twice the 
relative stability of the zero signal of the standard facility. 

Table 3. Relative standard measurement uncertainties w in % of CTWs listed in Table 1 due to examined quantities introduced in the text for a transfer 
measurement  between  a  national  standard  machine  and  a  calibration  laboratory.  The  contributions  of  the  specific  coefficients  listed  in  Table 2  are 
calculated  using  the  calibration  conditions  listed  in  Table 4  both  for  a  standard  machine  and  for  a  calibration  laboratory.  The  resulting  combined 
expanded relative uncertainty WRef is given both under the assumptions given in Table 4 and neglecting the influence of a ratchet. The contributions, 
except for wrch, are graded in reference to their amount by colour. The highest contributions are printed in red, the second highest in orange. 

uncertainty in %  1  2  3  4  5  6  7  8 

wA  0.042  0.041  0.044  0.041  0.044  0.043  0.042  0.041 
wrpr  0.161  0.048  0.557  0.020  0.142  0.108  0.135  0.222 
w l 

 

0.026  0.001  0.007  0.003  0.004  0.007  0.004  0.001 
wT   0.063  0.021  0.041  0.030  0.054  0.031  0.061  0.012 
wF   0.180  0.087  0.053  0.004  0.042  0.016  0.012  0.036 
wtB   0.122  0.089  0.100  0.034  0.085  0.026  0.071  0.047 
wrch 

 

0.041  0.119  0.197  0.009  0.215  0.041  0.046  no ratchet 
         

WRef , k=2  0.57  0.37  1.29  0.13  0.57  0.26  0.35  0.47 
WRef, k=2  
(no ratchet)  0.56  0.28  1.12  0.13  0.37  0.25  0.34  0.47 

 

Figure 8. Relative standard uncertainties of the  investigated contributions
calculated according to (9), (10) and (11).  

Figure 7.  Peak value of a CTW depending on the torque load rise time. 



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 29 

The coefficients cx (x stands for one of the indices l, T, F, 
tB and rch introduced in chapter 2), stability contributions srpr 
and srpt, uncertainty of calibration conditions ux (Table 4), and 
distribution functions were processed to relative standard 
uncertainty contributions wx under the condition that the 
sampling rate is chosen adequately and cv is equal in both 
laboratories. Because the complete analysis according to the 
Guide to the Expression of Uncertainty in Measurement [6] is 
disproportionately extensive, a simplified approximation was 
used: 

 

NN x Lab 12
2

rpt

∆
  (11)

 
While the uncertainty of the coefficient’s detection - given 

mainly by the repeatability srpt - cannot be neglected, the 
contribution of a specific coefficient cx has to be extended by 
the xth fraction of srpt. Here, x is the step of the calibration 
condition quantity, in units of this quantity, performed during 
the detection of the coefficient. The contribution of the 
coefficient cx is derived from a span, thus a rectangular 
distribution is to be taken into account. In contrast, the 
repeatability srpt originates from an averaging, thus a normal 
distribution is to be assumed. Because cx is achieved by a 
difference, the extension due to the repeatability is to be taken 
into account twice. 

To obtain the actual contribution of the coefficients, the 
expanded specific coefficients have to be multiplied by the 
uncertainty of the corresponding calibration conditions x, 
which are given in Table 4 for the reference calibration with the 
national standard machine (NN) and for a typical accredited 
calibration laboratory (Lab). Thus the relative standard 
uncertainty x includes the impact of the CTW properties at 
both calibration facilities involved. 
The uncertainty contribution of the stability wrpr is calculated 
equivalent to the second part of (11) from the reproducibility 
srpr with a rectangular distribution and twice the repeatability srpt 
with a normal distribution. 

As an overall result, the expanded relative combined 
uncertainty WRef (k=2) is given for each CTW in Figure 9. This 
uncertainty implies the contributions due to CTW properties in 
combination both with the calibration conditions in the 
national standard machine (TN-NN) and with those in a 
calibration machine of a laboratory under test (TN-Lab) as well 
as a contribution from the national standard machine (NN). If 
a transfer calibration should confirm the bmc of a calibration 
machine under test, the En value (12) must not exceed 1: 

 

| |
̅ ̅

Ref Lab	
	 1  (12)

The En value compares the difference between two 
measurements of the release torque	 ̅	with the quadratic sum 
of uncertainties referring to these calibrations. In this work, the 
transfer CTW is to be understood as a part of the reference 
calibration, thus the referring expanded uncertainty URef 
corresponds to the relative expanded uncertainty WRef given in 
Figure 9: 
 

Ref NN TN-NN TN-Lab   (13)

 
The examination of URef is important since (12) implies that 

even at equality of the two comparison measurements 
 ( ̅ ̅ ,	 the smallest bmc the comparison could verify 
is Lab Ref. Therefore, a CTW for transfer application 
without restriction in accredited laboratories according to 
Figure 1 should feature a value of WRef smaller than 0.2 %. 
Only specimen No. 4 meets this requirement and is able to be 
used in transfer measurements for all laboratories. The majority 
of bmc values in Figure 1 is greater than or equal to 0.5 %. 
Transfer to these laboratories should be possible also with 
CTW No. 6 with a sufficient uncertainty buffer. 

The best results were achieved with CTW No. 4 which is of 
the electromechanical type. Apparently the higher effort in 
engineering is reflected in a very low dependency of the release 
torque on calibration conditions.  

In Table 3, the contributions are graded in reference to 
their amount by colour. The highest contributions are printed 
in red, the second highest in orange. Excluded is wrch, because 
this contribution could be avoided by using no ratchet but 
rather a fixed square drive.  

For CTW No. 4, the contribution of wA, which is mainly 
the uncertainty of the standard calibration facility, is the 
highest, the contribution of wtB is the second highest. A further 
improvement of this CTW should start with an enhancement 
of the internal sampling rate, which should reduce the influence 
of the rise time. For the other CTWs, an improvement of this 
aspect is only to be expected by re-designing the releasing parts 
– quite a large effort which does not meet the actual goals of 
the manufacturers. But many of the CTWs could be improved 
fundamentally in this field.  

Most of the CTWs would benefit also from an 
improvement of the relative repeatability srpt. This is indicated 
in Table 2 by the amount of the repeatability of a CTW in 
comparison to the other influences. srpt should be in the range 

Figure 9. Combined expanded relative uncertainty WRef for the investigated 
specimens  in  comparison  to  the  smallest  bmc  of  the  DAkkS‐accredited 
laboratories (yellow bar). 

Table  4.  Uncertainty  of  calibration  conditions  ux  expressed  as  a  half‐span 
value  used  for  the  calculation  of  an  uncertainty  budget  in  a  transfer 
measurement  (Table 3).  Given  are  measured  values  of  the  PTB  standard 
calibration  machine  (NN)  and  assumed  values  for  typical  accredited 
calibration laboratories (Lab). 

Condition  Index x  ux (NN)  ux (Lab)

Lever length  l  0.25 mm  0.25 mm
Temperature  T  0.5 K  2 K 
Humidity  F  2 %rh  5 %rh
Rise time  tB  0.1 s  0.5  s
Ratchet position  rch  0 cog  1 cog



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 30 

of the smallest contribution in this compilation. Many of the 
tested CTWs cannot fulfil this requirement. 

CTW No. 3 exhibits friction-induced drift during the 
preliminary measurements. This drift is to be understood as a 
systematic contribution and therefore has to be taken into 
account by absolute value. Thus, this contribution on its own 
exceeds the requirements of transfer application and hence no 
more measurements were performed with this CTW. 
Coefficients which were not measured are marked in Table 2 
with “no data”. These are counted as zero in order to get a 
lower estimation of Wref at the end. Nevertheless, the 
uncertainty contributions wx of these conditions are greater 
than zero in this analysis because of the contribution of srpt in 
(11). 

4.5. Procedure for transfer measurements  

The measurements of the survey show that the procedure 
of ISO 6789 (Figure 10) is not adequate for transfer 
measurements with CTWs. 

Readjusting uncertainty of the CTWs can be avoided when 
the adjustment of the CTW is not changed during the 
measurements. This adjustment should be made at the nominal 
value of the CTW in order to use the best possible signal-to-
noise ratio. Extensive tests with CTWs stored several days 
under the tension of this adjustment did not show a drift of the 
release torque. Furthermore, the CTW with the best overall 
uncertainty is of the electromechanical type and hence is free of 
mechanical tension due to adjustment. 

The transfer measurement should consist of series of at 
least 30 release events to reduce the repeatability uncertainty 
(Figure 11). The load rise time should be fixed to a certain 
value, preferably at 5 s. Furthermore, the laboratories should 
agree on a fixed value of the sampling rate, at best more than 
2 kHz. The position of the square drive and of the ratchet 
should be the same in both laboratories. Additional series after 
alteration of the square drive position by 90° should be 
performed at least for two positions. The length of the lever, 
the temperature and the humidity should be controlled and 
documented. 

5. CONCLUSIONS 

The capability of CTWs for use as transfer transducers 
depends not only on their technical specifications. Restricted 
specifications could be compensated if adapted procedures are 
employed which can largely differ from those according to 
ISO 6789. The objective of these procedures should be an 

optimization of the reproducibility of the CTWs’ response. A 
suggested procedure designates the measurements required in 
ISO 6789 at 20 % and 60 % of the nominal value, but calls for 
at least 30 repeated measurements instead of 5. Parameters like 
rise time, positions of square drive and ratchet, sample rate, 
temperature, humidity and lever length are to be agreed upon 
and reproduced in the laboratories within narrow limits.  
The survey delivers the following results:  

1. The use of transfer CTWs for DAkkS assessments is 
possible under special conditions and with adequate 
types of CTWs for the laboratories accredited by the 
DAkkS. Therefore, the development both of specific 
measurement procedures and of selection criteria for 
CTWs, which was carried out to complement the 
traceability of the laboratories working in the field 
of ISO 6789, should be supplemented by further 
improvement of the CTWs, especially of their 
repeatability and rise time sensitivity.  

2. The detected coefficients of the used specimens vary 
over a wide range of amounts. The selection of a CTW 
for transfer application therefore requires the analysis of 
the combined measurement uncertainty budget in the 
setup of the intended transfer measurement. 

3. A new design of CTW with an electromechanical 
release mechanism yields the best results among the 
tested specimens. Here further improvements could be 
possible with higher internal sampling rates.  

ACKNOWLEDGMENT 

Thanks go to Sebastian Kaletka, who carefully performed 
hundreds of measurements for this investigation. 

REFERENCES 

[1] ISO 6789:2003-10, “Assembly tools for screws and nuts - Hand 
torque tools - Requirements and test methods for design 
conformance testing, quality conformance testing and 
recalibration procedure”, International Organization for 
Standardization, Geneva, Switzerland. 

[2] Brüge A., “Influence of eccentric mounting on the calibration of 
torque measuring devices”, Proceedings of the 15th IMEKO 
TC3 Conference, October 7-11, 1996, Madrid, Spain, pp. 255-
259. 

[3] Sanponpute, T.; Arksonnarong N., “Temperature and humidity 
dependence on stability of torque measuring devices”, IMEKO 
22nd TC3, 15th TC5 and 3rd TC22 International Conferences, 
February 3-5, 2014, Cape Town, Republic of South Africa 

Figure 10. Loading schedule according to ISO 6789.   Figure 11. Proposed loading schedule for transfer measurement with CTW. 



 

ACTA IMEKO | www.imeko.org   June 2015| Volume 4 | Number 2| 31 

URL: http://www.imeko.org/publications/tc3-2014/IMEKO-
TC3-2014-006.pdf 

[4] Brüge A., “Influence of humidity on torque transducers – 
Estimation methods for calibration laboratories”, XX IMEKO 
World Congress, Metrology for Green Growth, 9 – 14 Sept. 
2012, Busan, Republic of Korea.  
URL:http://www.imeko.org/publications/wc-012/IMEKO-
WC-2012-TC3-O30.pdf 

[5] Röske, D.; Mauersberger, D., ”On the stability of measuring 
devices for torque key comparisons”, IMEKO XVIII World 
Congress and IV Brazilian Congress of Metrology, "Metrology 
for a Sustainable Development", Rio de Janeiro, 17-22, 
September, 2006, Brazil, on CD-ROM, file name: 00181.pdf 

[6] BIPM, “Evaluation of measurement data – Guide to the 
expression of uncertainty in measurement”, JCGM 100:2008 
URL:http://www.bipm.org/utils/common/documents/jcgm/J
CGM_100_2008_E.pdf