Field of application
Static calibration of torque transducers, both for general and “transfer standard” applications
The procedure for classifying torque transducers is described
Not suitable for calibrating torque wrenches
The numbers below identify the paragraphs of the standard
4. Characteristics of the torque transducers
All components of the instrument, including the cable, must be identified (manufacturer name, type, 4 or 6 wires, serial number, etc.)
The measuring side must be indicated (torque application side) if important. This is the case, for example, with rotating transducers, depending on the presence of slip-rings
The torque transducer and mounting parts must not introduce cross-forces or bending-moments
5.1 Calibration of the torque transducers
Calibration = Applying known torques to the transducer and recording the data furnished by it
I can exchange the reading unit if the additional uncertainty due to the exchange is less than 1/3 of the relative uncertainty of the calibration result (SCS takes this into account in the uncertainty balance)
Components and adapters must withstand 1.5 times the maximum torque transmitted
At maximum torque the length variation of the measuring device and adapters must be less than 1 mm
Before calibration the transducer and adapters must be charged at least 4 times with an overload of 8 to 12% of the nominal torque, for 1 to 1.5 minutes (for safety and to avoid damage during calibration)
5.2 Resolution of the indicating device
The resolution r is the increment of the last active number, provided that the maximum fluctuation is 1 increment when the instrument is unloaded
If the indication changes more than 1 increment, the resolution is half the fluctuation + 1 digit
The minimum value of the measuring range is defined according to the class in the further table (classification criteria)
5.3 Preparation of the calibration
All adjustments, if any, must be recorded
Measurements shall be made after temperature stabilization
The zero signal must be recorded before and after the calibration with unloaded torque in the vertical position
Apply torque from the side defined by the manufacturer
Positive indication for clockwise torque
5.4 Calibration procedure
Clockwise or counterclockwise calibration in the specified steps (usually 5 steps in the measuring range)
We have defined a wait time of 10 seconds every step, as constant as possible
Preload to nominal torque must be performed 3 times in the first cycle of the direction of calibration and once after each change of mounting position
After each preload (short time) wait for zero stabilization (max. 3 minutes) and record the value
After the last preload in the first mounting position, record the creep after 3 minutes
Preferably the calibration should be done in 3 positions at 120°
For torque transducers with square coupling, 4 x 90° positions are used
For classes 1, 2 and 5 it possible only one rotation at 90° or 120°
The number of measurement depends on the class of the torque transducer, as shown in the following table
Number of measurement series required
The minimum number of torque stages (in addition to the zero stage) shall be as follow for each direction:
– classes 0,05 and 0,1 = 8 (suitably distributed over the measuring range)
Note: for exemple, in steps of 10, 20, 30, 40, 50, 60, 80 e 100 % ME or 2, 5, 10, 20, 40, 60, 80 e 100 % ME
– classes 0,2 and 0,5 = 5 (20, 40, 60, 80 e 100 % ME)
– classes 1 to 5 = 3 (20, 60 e 100 % di ME) (SCS procedure for class 1: 5 steps)
The minimum value of the measuring range shall be one of the calibration value
A torque transducer can be separately calibrated for several torque measuring ranges
Sequence of calibration for class 1
The ambient temperature must be between 18 and 28°C (preferably 22°C) and stable within ±1 K.
The interval between two loading steps must be the same, especially in the presence of creeping
The indication before measurement may be zeroed or taken into account in the calculation
For instruments with a defined scale (N∙m) the indication must be zeroed at the beginning of each series of measurements
5.4.7 Evaluation of the torque transducer
Case I: only increasing series
The calibration result is calculated for each calibration torque as an average over the different mounting positions of the displayed values from the increasing series, corrected for the zero point. The cubic and linear smoothing functions are calculated using the origin point and the error of interpolation is determined
Hysteresis does not participate to classification and does not contribute to standard measurement uncertainty, while error of interpolation is considered
Case II: decreasing and increasing series
The calibration result is calculated for each calibration torque as an average over the different mounting positions of the displayed values from the decreasing and increasing series, corrected for the zero point. The linear smoothing function is calculated using the origin point and the error of interpolation is determined
In the case of instruments with fixed scale (N∙m) the interpolation error is replaced by the error of indication
Reversibility error (hysteresis) and interpolation ion (or error of indication) are taken into account for classification and as a contribution to the relative uncertainty error
Calibration result
Case I: only increasing series
The calibration result Y(Mk) is calculated for each calibration torque as an average over the different mounting positions of the displayed values from the increasing series, corrected for the zero point
Case II: decreasing and increasing series
The calibration result Yh(Mk) is calculated for each calibration torque as an average over the different mounting positions of the displayed values from the decreasing and increasing series, corrected for the zero point
Note: for the 0° position in the second increasin series (classes0,05 to 0,5) are not included in the calculation of calibration result
Reproducibility b(MK) e repeatability b’(MK
The reproducibility b(MK) is calculated for each torque as the repeatability error of the displayed values of the increasing series reduced by the zero point in different mounting positions
The repeatability b’(MK) is calculated for each calibration torque as the amount of the repeatability error of the displayed values of the increasing series reduced by the zero point in the same mounting position
Relative error of the zero signal f0
The zero value shall be recorded prior to each increasing series and after each decreasing series.
The zero value shall be read approximately 30 s after complete unloading
The zero error f0 is calculated as the maximum absolute value of the difference between the two readings at all mounting positions
Reversibility (histeresis) h(MK)
The reversibility error h(MK) is determined for each calibration torque as the maximum value of the absolute values of the differences between the indications of the increasing and decreasing series for each torque step
Interpolation error fa(MK)
The interpolation error fa(MK) is determined with the aid of a smoothing function running through the point of origin in the measuring range:
Case I: 3rd degree – cubic (not applied to the classes 1 to 5, first degree is applied)
Case II: 1° degree equation – linear
The interpolation error is calculated for each calibration step as the difference between the calibration result* and the associated value of the smoothing function. The equation used must be indicated in the calibration certificate.
*Calibration result: without histeresis Yh(MK), with histeresis Y(MK)
Indication error fq(MK)
The indication deviation fq(MK) is only determined for torque instrument which display the result directly in the torque unit and for which an electronic adaptation of the indication to the interpolation function of the calibration result is not possible
It represents the difference between the calibration result and the applied reference torque
Short-time creep
Short-time creep is a good indication of the quality of the torque transducer (the higher the value, the lower the quality)
In the first mounting position, it is the difference between the zero point before the first measurement series (after 3 minutes of waiting) and the zero point immediately after the discharge of the third preload divided by the calibration result at the upper limit of the range
Principle of classification
The measuring range for which a certain class is assigned to the torque transducer comprises all calibration torques for which the corresponding classification criteria are met – from the upper limit of the measurement range to the smallest calibration torque
For the classification, the minimum value of the measurement range shall be:
- ≤ 20% of ME for classes 0.2 to 5
- ≤ 40% of ME for classes 0.05 to 0.1
Classification criteria
For the purposes of classification, the absolute quantities determined in 5.4.7 are converted into relative quantities according to the next table. The following criteria must thereby be taken into account:
– relative reproducibility;
– relative repeatability;
– relative zero variation;
– relative reversibility error (Case II only);
– relative indication or interpolation deviation;
– resolution of the display unit at the lower limit of the measuring range
Classification criteria for torque measurement devices
Calibration certificate
We will later analyse in detail the calibration certificate, which must contain the following information at least:
- identity of all elements of the torque measuring device and of the components for the introduction of the torque;
- indication on right and/or left torque;
- ambient temperature at which the calibration was carried out;
- date of calibration;
- information on the calibration laboratory and the standards used;
- reference to this standard;
- classification result with indication of the associated measuring range;
- calibration result (averages of the displayed values from the different mounting positions for Case I and Case II) stating the relative measurement uncertainty for the interpolated calibration result or the relative uncertainty interval, e.g. determined on the basis of Annex C, and, if applicable, the associated interpolation equation as well as the corresponding methods of determination;
- short-time creep.
In addition, the calibration certificate shall contain:
- a table of the measurement values and calculated parameters according to 5.4.7;
- a graphic representation of the deviations of the displayed values from a cubic (Case I) or a linear (Case II) interpolation function;
- a graphic representation of the relative measurement uncertainty for the interpolated calibration result or of the relative uncertainty interval – determined, e.g., on the basis of Annex C – as a function of the calibration torques;
- a loading diagram representing the time-dependent course of the torque changes and the time during which a torque has been applied constantly in the calibration facility with a resolution of approx. 10 seconds.
Period of validity
-The maximum period of validity of the certificate must not exceed 26 months, but annual frequency is generally recommended, especially if there are particular traceability requirements or required by quality assurance regulations
The torque transducer shall be re-calibrated:
– if it has undergone an overload which is higher than that applied during the overload test
– after corrective maintenance has taken place; or after an improper operation which can have an influence on the metrological properties or the measurement uncertainty.
Calculation of relative uncertainty (according to DIN 51309)
Case IA: classes 0,05 to 0,5 with cubic smoothing function
Case IB: with linear smoothing function
Classes 0,05 to 0,5
Classes 1 to 5
Case IIA: only with linear function – unknow scale
Classes 0,05 to 0,5
Classes 1 to 5
Case IIB: only linear function – defined scale
Classes 0,05 to 0,5
Classes 1 to 5
Reference uncertainty
This single calculation formula is considered with contributions as shown in the table:
Calibration certificate
Page 1: cover page
The first page is in conformity with the ACCREDIA model: in addition to the Accredia logo, there is also the SCS logo. These logos are shown on each page of the calibration certificate. The page contains identification of the customer and information concerning the order, information on the instrument to be calibrated (type, model and serial number), date of receipt of the instrument and date of calibration, logistical information of the laboratory and authorized signature (the Head of the Centre or the Substitute)
Page 2: informations
In the second page, in accordance with the Accredia model, further informations are provided:
– the reference standard
– the identification details of the Laboratory reference and its traceability (calibration certificate and uncertainties)
– identification and characteristics of the amplifier connected to the reference
– cable and adapters characteristics
Page 3: informations
The following informations are detailed:
characteristics of the instrument to be calibrated, its amplifier, cables, adapters, sensitivity, calibration installation, environmental conditions, calibration location (in case of external calibrations) and zero signal value, before and after calibration, and any other information related to calibration
Pagina 4: calibration and classification results
In this page are indicated the uncertainty values in function of the interpolation curves:
– case I cubic and linear
– case II linear only.
If appropriate, it is indicated the uncertainty for instruments with defined scale.
The second table provides the classification according to DIN 51309 according to the parameters contained in table 10 on the next page.
Short-term creep is also indicated.
Page 5: interpolation equations and classification criteria
In this page are indicated:
9. Interpolation equations, which will be used for the classification of the torque transducer and to obtain the values of the following tab. 13 on page 7 (cubic interpolation)
10. Values for the classification criteria of the torque transducer.
The class is determined automatically, verifying that all the parameters meet the requirements of the standard
Page 6: measuring data
– In this page there is a table where are indicated the measured values as a function of the applied torque, according to the defined measuring cycles.
– In this table the values are in N∙m but could also be expressed in mV/V.
Page 7: results in diagram and cubic interpolation
– The first graph shows the relative error in the individual calibration steps
– The second graph shows the trend of the interpolation error
– The cubic interpolation table shows the values calculated using the formulas in paragraph 9.1 of page 5 for the intermediate values of the various measurement steps