An alternative method to using strain gauges to measure FT (please see Appendix A for a list of definitions) and TM under a static multi-component load by using a hinge flexure (also called measurement flexure or MF) is presented. Its usage in the 5 MN m torque standard machine (TSM) at the Physikalisch-Technische Bundesanstalt (PTB) to detect calibration torque moment shunts is described. The working principle consists of a displacement measurement by an interferometer and the determination of the MF stiffness in a special CSU. Essential measurement uncertainty influences, such as stiffness determination and measurement conditions, are discussed and quantified. The measurement uncertainty budget for this measurement principle is presented. A FE validation for the MF is discussed.

The growing wind energy demand led to increasing research in wind turbine optimisation. A key aspect is the wind turbine's efficiency, which was determined in a nacelle test bench. For a precise efficiency determination, a precise torque measurement is elementary. Although the Physikalisch-Technische Bundesanstalt (PTB) transfer standard already exists to calibrate the test benches' internal torque measurement, it is not possible to calibrate the transfer standard beyond 1 MN m

At PTB, a new torque standard machine (TSM) is built to calibrate such torque transducers up to 5 MN m

The measurement side and the moment shunts are depicted
in Fig.

Table

The 5 MN m TSM set-up.

Measurement side of the 5 MN m TSM.

Measurement uncertainty budget of the calibration torque moment

Usually, mechanical quantities such as force and moments can be measured easily with strain gauges. In this particular application, the objective measurands only appear with a high axial force and other similar bending and torque moments. The combined load would lead to cross-talk at the strain gauges which cannot be calibrated sufficiently at PTB. Therefore, another method is presented here to overcome these difficulties.

The alternative method uses the unique deflection line or angle of twist given to a specific load combination. A specific point on the deflection line can be observed with a high-resolution and high-accuracy length measurement system. The paper shows that the deflection in a special load scenario can be reproduced in an external calibration set-up. The result is a fixed ratio of deflection or twist compared to the corresponding FT or TM, called FT stiffness or TM stiffness. The stiffness is determined in an MF CSU providing a traceable force and torque moment. To provide a traceable calibration torque moment in TSM, the MF force and torque measurement must be characterised by a measurement uncertainty analysis, which is the main objective of this paper.

The presented method works for both types of MF (for torque moment and bending moment). The measurement uncertainty of this method is highlighted here so that it is sufficient to only focus on the bending moment MF. There are two types of bending moment MF on upper and lower level. The upper level MFs have a bigger diameter in the middle shaft than the ones on the lower level to compensate for the varying stiffness of the frame at the fixation. The varying middle shaft leads to varying stiffness that must be considered.

Measurement flexure working principle.

Figure

Measurement uncertainty influences of FT and TM measurement with MF.

A range of measurement uncertainty influences exists, which diminishes the accuracy of the described measurement principle. Figure

Working principle of LS1.

As presented in Sect.

A theoretical analysis of the measurement uncertainty of the CSU providing the calibration of FT and TM is described in

To calculate the stiffness, it is necessary to measure the MF's displacement or the angle of twist precisely during load application. The required accuracy is provided by an interferometer. A dual channel He–Ne laser interferometer (model type MI 2–5000 from SIOS Meßtechnik GmbH) is used.

To guarantee a reproducible measurement in CSU and TSM, the position at which the displacements are measured with a retro reflector need to be fixed. The MF deflection is characterised by the centre of the top flange circle area and is called RP. Both displacement measurements in CSU and TSM cannot be measured directly with the retro reflector because they are hidden beneath connection components when both are mounted in CSU and TSM. In the CSU, the retro reflector is aligned with the force vector and the RP at the outer cylinder surface near the top flange and is called measurement point 1 (MP1). A FE analysis shows that displacement deviations in LS1 at RP and MP1 are negligible. The translational movement at the RP of MF is as follows:

Working principle of LS2.

FT and TM stiffness determination.

The FT stiffness under a TSM load condition is defined as follows:

The CSU and TSM are both situated in an air-conditioned hall. At this point, the environmental condition could not be monitored due to ongoing TSM construction work. Experiences from other standard machines at varying locations show minimum changes to the environmental conditions. To cover the environmental influences on the measurement uncertainty budget (MUB) theoretically, the environmental parameters in

The measurement condition in TSM differs slightly from that in CSU. First of all, the measurement position is different. The MF is mounted vertically to the ground in the CSU. In TSM, the MF will be mounted horizontally. There are gravitational effects which may affect the measurement. A compensation construction was set up using a spring and a force transducer to compensate the gravity and avoid influences on the deflection line. Consequently, gravitational effects are not investigated any further here.

Furthermore, the MF alignment of the MF is different in the TSM and in the CSU. In both cases, a Leica Absolute Tracker laser (model AT960 LR from Hexagon Metrology) is used to align the MF. In the CSU, the MF rotation in relation to the FT direction is aligned with the laser tracker and is already covered in the CSU MU. The tilt of the MF top flange in relation the calibration force cannot be adjusted so that the tolerances of each component of the CSU are summed up. The influence is already covered in the measurement uncertainty of FT and TM. In TSM, the fixation point at the machine frame can be moved up and down and sideways. The fixations position is aligned with the MF flange of the lever using the laser tracker. The tilt deviation

The rotation of the lever is calculated according to following equation:

Equation (

Another measurement uncertainty influence arises when looking at the CSU LS1 calibration. The ratio of the FT and bending moment is fixed because of the fixed lever arm length used in CSU. The lever arm length is calculated from a FE analysis, where the FT to the bending moment ratio was found to be half the distance between the MF joints. An analysis has been performed to investigate the uncertainty effect if there is a bending moment deviation to the bending moment calculated from the fixed CSU relationship.

Expected bending moment deviation on MF.

Bending moment deviation influence on the FT measurement.

In FE, all four MFs were investigated, and the maximum bending moment deviation for all MFs to the calculated bending moment from the fixed CSU ratio is plotted at each load step. The results are depicted in Fig.

The following section sums up the results, the model equations, and the measurement uncertainty budgets. After this description, a performance of the presented measurement method is assessed in FE.

All analysed influence quantities are used to calculate the overall measurement uncertainty of FT and TM at the MF. The following model equations apply for the FT and TM calculation:

Measurement uncertainty budget of FT with a calibration torque moment of 5 MN m at the upper MF.

Measurement uncertainty budget of TM with a calibration torque moment of 5 MN m at the upper MF.

The resulting measurement uncertainty budget of FT and TM at 5 MN m is depicted in Tables

Measurement uncertainty of FT and TM at different load steps for the upper MF.

Table

The lacking experimental data for verifying a FE analysis are used to show that the measurement principle works in theory. This FE validation follows the same procedure as described in Sect.

FE validation for the FT measurement.

FE validation for the TM measurement.

Calibration torque moment measurement uncertainty reduction by the MF measurement.

An alternative method to using strain gauges is presented in this paper. The method shows how to measure calibration torque moment shunts in the 5 MN m TSM using a displacement measurement with an interferometer and the predefined stiffness. All measurement uncertainty influences were analysed and quantified. The paper shows that the measurement uncertainty of the FT measurement at the MF ranges from 0.6 % to 3 %. The measurement uncertainty of the TM measurement stays constant at 1.7 %. The dominating measurement uncertainty influence is the stiffness determination in the CSU, which must be improved if a better accuracy is needed. FE analyses were performed to show that the suggested measurement principle works in theory.

Even though the measurement uncertainty is rather high compared to uncertainties known from ordinary strain-gauge-based sensors, it is a useful measurement technique regarding the effect on the calibration torque moment uncertainty of the torque standard machine. Table

The data set for this publication can be accessed in

KG led the editing and review process and contributed to the investigation and writing of the original draft. HK created the conceptual idea. CS and RK reviewed the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Sensors and Measurement Science International SMSI 2021”. It is a result of the Sensor and Measurement Science International, 3–6 May 2021.

The authors want to thank the Projektträger Jülich (PTJ) and the Bundesministerium für Wirtschaft (BMWI) for funding this project (grant no. 0325945).

This research has been supported by the Bundesministerium für Wirtschaft und Energie (grant no. 0325945).This open-access publication was funded by the Physikalisch-Technische Bundesanstalt.

This paper was edited by Klaus-Dieter Sommer and reviewed by two anonymous referees.