Development of a torque transducer applying a new elastic structure, and a vibration damping device based on the principle of eddy current brake

In recent years, demand for precise torque measurement less than 1 N·m has increased in various fields as equipment becomes smaller and improves performance. To ensure the proper traceability in the small torque capacity region, high-resolution torque transducers with small capacity as well as quite stable and precise torque standard machines (torque calibration equipment), are necessary. Torque transducers with small capacities have had worse resolution than transducers with medium or large capacities, and few have been capable of precise torque measurement. Therefore, the authors developed a small torque transducer that can measure torque with good resolution by using a new torque detection mechanism. The torque transducer designed in this study improved the resolution by about 16.8% compared to the conventional torque transducer with the same capacity. In addition, we introduced a new moment-arm damping control device based on the eddy current brake principle into our torque standard machine for more precise calibration.


Introduction
Torque measurement plays a significant role in the evaluation of energy conversion processes.For example, when rotational motion occurs in an energy conversion process, such as wind power generation, torque measurement provides accurate information about the generator and optimizes power generation efficiency.In addition, a proper understanding of the operating state of the generator through torque measurement leads to early detection of malfunctions and failures, which contributes to reduced maintenance costs and increased availability.Torque measurement plays a crucial role in motor development as it is essential to evaluate the output and efficiency of the motor accurately.In recent years, with the proliferation of IoT (Internet of Things) devices and smart home products, there has been a growing demand for high-performance, lightweight, and energy-efficient small motors.Accurate and reliable torque measurement is indispensable for evaluating such high-performance motors.
Torque measurement also plays a crucial role in the product assembly process.For example, torque measurement is essential in the automotive assembly process when tightening bolts on engines and tires.Accurate torque measurement when tightening bolts, nuts, and other fasteners affects product quality and safety.If screws are not tightened with the proper torque, parts may loosen or fall off, defective products may be produced, and security may be compromised.In addition, exact torque measurement is required for products where higher quality and safety are essential, such as medical equipment and aircraft.
In general, hand torque tools such as torque wrenches and torque screwdrivers are used to tighten screws properly.To correctly manage the tightening torque of screws with hand torque tools, one must accurately use hand torque tools that ensure the reliability of torque values.For the latter, hand torque tools need to be calibrated or tested by a higher reference standard, such as a torque wrench tester or torque screwdriver tester.The international standards ISO 6789-1:2017 [1] and ISO 6789-2:2017 [2] specify the calibration or testing of hand torque tools.In recent years, demand for torque screwdrivers and torque wrenches with a rated capacity of around 1 N•m has grown, especially as the need for precise tightening torque control of small screws used in the assembly of information and telecommunications equipment has increased.To meet such demands, several National Metrology Institutes (NMIs), such as the Physikalisch-Technische Bundesanstalt (PTB) and the Korea Research Institute of Standards and Science (KRISS), are actively conducting research and development on low-torque generation technology, including the development of torque generators capable of achieving precise torque of around 1 N•m [3][4][5].The National Metrology Institute of Japan (NMIJ), part of the National Institute of Advanced Industrial Science and Technology (AIST), has developed a deadweight torque standard machine with a nominal capacity of 10 N•m (10-N•m-DWTSM), which can realize precise torque by applying gravity to the tip of a moment-arm and has been used to disseminate torque standards in the range from 0.1 N•m to 10 N•m [6].
On the other hand, a high-precision torque transducer is needed as a transfer standard to transfer the precise torque realized by the torque standard machine to the torque wrench tester (TWT) or torque screwdriver tester (TST) according to the traceability system of torque in Japan [7].Currently, extremely highprecision pure torque transducers have been developed and are generally available in the medium to large capacity torque range of 100 N•m to 20 kN•m [8][9][10].In addition, NMIJ has succeeded in developing a torquewrench-type torque transducer with an extremely high precision rated capacity of 5 kN•m, achieving more precise calibration for the large capacity torque range [11].However, in the torque range smaller than 10 N•m, few torque transducers can precisely measure torque due to lower resolution than torque transducers in the medium and large capacity torque ranges.Therefore, a backbone comparison to ensure the equivalence of the torque realized by each NMI has not been proven in the small capacity torque range due to the difficulty of obtaining good intermediaries.This study aims to develop a high-resolution torque transducer applying an utterly new torque detection mechanism we have invented to realize precise torque measurement in the range of 0.1-1 N•m [12].
The machine uses an aerostatic bearing to reduce the effects of friction at the fulcrum.The machine is also subject to airflow from air conditioning, vibration from the floor, and other influences.The machine is enclosed in a windshield and installed on a high-mass stone surface plate to prevent the arm from vibrating under the above influences.However, to calibrate a low-nominalcapacity torque transducer with the high-resolution, it was necessary to reduce the vibration effect of the moment-arm more strictly.Then, we developed a new moment-arm damping control device, the eddy current damper (ECD), based on the eddy current brake principle [13] to reduce the moment-arm sway during calibration.After that, the new low-nominal-capacity torque transducer to be developed in this study was evaluated using the 10-N•m-DWTSM with developed ECD at NMIJ.   mounted on the moment-arm of the 10-N•m-DWTSM and sandwiched between ring-shaped permanent magnets.The ring-shaped permanent magnets are cut into eight equal parts and placed on a circular base plate to arrange the N and S poles alternately.They are then mounted on an L-shaped bracket so that the N and S poles face each other.The distance between the poles of the magnetic circuit arranged in this way is 3 mm.When the moment-arm vibrates under the influence of disturbance, the brass plate also vibrates in the magnetic field, generating an eddy current.Then, according to Fleming's law, Lorentz force is generated in the opposite direction of the vibration, which is expected to suppress the vibration of the moment-arm.

Low-nominal-capacity torque transducer with a new elastic structure
Figure 3 shows a picture of the torque transducers used in this study.Also, Table 1 shows the specifics of each torque transducer.TP-1N-1801 was developed by applying an elastic body of a new structure invented by us.TP-1N-0302 uses an elastic body of an existing  structure [14].DmTN/1Nm was commercially manufactured by GTM GmbH, Germany.DmTN/1Nm has been used as a transfer standard in the bilateral comparison between NMIJ and PTB and is recognized as one of the proven and accurate torque transducers [15].Figure 4 shows a schematic diagram of the internal structure of TP-1N-1801.TP-1N-1801 was entirely made of super duralmin, including the base flange, shaft, and case in order to obtain good characteristics.The shaft diameter is 8 mm, and the base flange and cover are 60 mm in diameter.The torque sensing part consists of three beams, which is a completely new structure in the newly developed TP-1N-1801, whereas the existing TP-1N-0302 had a four-beam structure [12].In general, thinner elastic materials can achieve higher resolution in torque transducers, but thinner materials are more difficult to process and more breakage-prone.In our new structure of torque detection mechanism, we reduced the number of beams and further devised its shape to achieve high resolution while maintaining strength.In addition, we aimed to reduce misalignment by manufacturing everything from the shaft on the measurement side to the detection part and the shaft on the fixed side in one piece.

Effectiveness of the ECD
The effectiveness of the ECD developed for the 10-N•m-DWTSM was investigated.A torque transducer with a rated capacity of 1 N•m was used to see how the measurement result were different before and after the installation of the ECD.The torque transducer was DmTN/1Nm.The indicator/amplifier was DMP40S2, manufactured by HBM GmbH, Germany.Figure 5 shows the loading cycle based on the JMIF015:2004 technical guideline [16].The torque transducer installation was changed to three directions: 0°, 120°, and 240°; two calibration cycles of increasing-decreasing in the 0°direction and one calibration cycle of increasingdecreasing in the other installation directions.Measurements were taken separately in the clockwise (CW) and counterclockwise (CCW) orientations.The measurement value x and expanded uncertainties U were evaluated according to JCG209S11-05 [17], which is the guideline for the uncertainty evaluation of calibration for torque measuring devices and reference torque wrenches.Furthermore, the measurement value before and after the installation of the ECD were evaluated in terms of the E n number.
Next, another experiment was conducted to evaluate the performance of the ECD, also using DmTN/1Nm and DMP40S2.Figure 6 shows the apparatus of the moment-arm vibration measurement experiment.In this experiment, one 200 g weight is first loaded on the weight loading mechanism at the end of the momentarm.Then, the inclined moment-arm is horizontally controlled by a counter drive via DmTN/1Nm.A torque of 1 N•m was applied to DmTN/1Nm.The momentarm is once fixed using clamping devices that motors can control.The clamping devices are then released faster than during regular calibration, intentionally causing the moment-arm to vibrate.The displacement near the tip of the vibrating moment-arm was then measured with a laser displacement metre at 0.01second intervals for approximately 10 min.How the vibration was damped with and without the ECD was compared.

Performance evaluation of the new torque transducer
At first, to evaluate the performance of the developed TP-1N-1801, creep characteristic evaluation tests were conducted using the 10-N•m-DWTSM with the ECD installed.Figure 7 shows the loading cycle of the creep test based on the JMIF015:2004 technical guideline [16].In this study, a no-load condition and a torque load up to 100% of rated capacity were repeated three times.Each measurement lasts 20 min, during which time the output of the torque transducer is evaluated for change.For comparison, the same creep test was performed for TP-1N-0302 and DmTN/1Nm.

Effectiveness of the ECD
Figure 8 shows the evaluation results using the E n number for the calibrations performed before and after the installation of the ECD on the 10-N•m-DWTSM.The E n number is defined by the following equation [18].
where x pre and U pre are the measurement value and uncertainties before the installation of the ECD, and x post and U post are the measurement value and expanded uncertainties after the installation.The longterm stability of DmTN/1Nm was also taken into account for U post .|E n | < 1 was satisfied for all torque steps, indicating that both results were satisfactory within the uncertainty.This meant that the installation of the ECD did not affect the measurement value.
Figure 9 shows the vibration (vertical displacement) at the tip of the moment-arm with and without the ECD.The moment-arm vibrated significantly in the range of −30 μm to +50 μm when the clamping device was quickly released in both case of with and without the device.The vibration gradually decreased, and after more than 400 s, the moment-arm vibration was within ±10 μm, the threshold value at which the moment-arm can be judged to have reached a horizontal position in the case without installation.On the other hand, the vibration was immediately damped, and the momentarm vibration was within ±10 μm after about 20 s when the device was used.The vibration of the moment-arm remained extremely small, within a few μm, until the end of the measurement and remained stable.These results indicate that the ECD can effectively dampen moment-arm vibration and maintain this state for a long period.

Performance evaluation of the new torque transducers
The creep test results of TP-1N-1801, TP-1N-0302, and DmTN/1Nm are shown in Figure 10(a)-(c).The vertical axis is the relative variation from the stable zero value after a holding time of 20 min.These results were calculated based on the analysis method of the creep test [19].For each sensor, the creep characteristics were   almost identical for CW and CCW orientation.The creep characteristics of TP-1N-1801 were about twice as large as those of TP-1N-0302 and DmTN/1Nm.However, both the maximum relative creep variation and the maximum relative creep recovery for about 20 min could be obtained less than 2.0 × 10 −5 .This result is a much better value since the creep characteristic of commercially available torque transducers is about 2.0 × 10 −3 [11].
Table 2 shows the measurement value for each torque transducer and Figure 11 shows the relative deviation of the output of each torque transducer.The measurement values are the average of the values measured by changing the installation of the torque transducers in three different directions (0°, 120°, and 240°).A larger output signal of torque transducer, higher resolution if the capacity of torque is same.As shown in Figure 11, the relative deviation of the output for TP-1N-1801 is larger than that of TP-1N-0302 and DmTN/1Nm for all torque steps, indicating that the output signal is larger and the resolution is improved.The specific measurement values are shown in Table 2, the output signal (mV/V) of TP-1N-1801 was about 8.2% larger than that of TP-1N-0302 and about 16.8% larger than that of DmTN/1Nm.Therefore, high resolution was achieved by employing a torque detection mechanism with a new elastic structure.
The relative expanded uncertainty W was evaluated using the following equation in the JCG209S11-05 uncertainty estimation guideline [17].
where w c_cal , w c_TSM , and w c_tra are the relative combined uncertainties of the measurement value at each torque step, due to the torque standard machine, and due to the torque measurement device, respectively.k is a coverage factor, and i is the index of the calibration step.In this study, w c_tra is expressed as follows since the method used is to evaluate the decreasing torque separately from the increased torque.where w rot , w rep , w int , and w res are the relative standard uncertainties ascribable to the repeatability when changing the mounting position, the repeatability without changing the mounting position, the deviation from the value calculated using the interpolation equation, and the resolution.Figures 12(a), (b),and (c) show the results for each torque transducer at each uncertainty contribution.w res is so small compared to other uncertainties that the graph is omitted.TP-1N-1801 and DmTN/1Nm had almost the same order of magnitude for both uncertainty factors.TP-1N-1801 showed to have a similar performance with DmTN/1Nm.However, the results of TP-1N-0302 expressed a slightly larger w rep .Since TP-1N-0302 is a prototype, its temperature and humidity dependencies and short-and long-term stabilities have not been evaluated, so the detailed cause is unknown; there are several possible reasons for the poor repeatability.For example, since this torque transducer has greater temperature and atmospheric pressure dependence than other torque transducers, the measured values might have been affected by ambient temperature or atmospheric pressure fluctuations, resulting in deviations.In addition, since TP-1N-0302 has been in development for nearly 15 years, some age-related changes to the torque detection mechanism might have affected the measurement result.
In this study, the newly developed TP-1N-1801 has the same level of uncertainty as DmTN/1Nm, and a 16.8% improvement in resolution.It is necessary to evaluate its temperature and humidity dependencies and short-and long-term stabilities to verify whether TP-1N-1801 can be used in the international comparisons.To contribute to the enhancement of torque traceability systems in the small-capacity region, we plan to perform calibration and clarify these characteristics continuously.

Summary
Demand for precise measurement of small torques increases as equipment becomes smaller and more sophisticated.On the other hand, torque transducers with small capacities have lower resolution than ones with medium or large capacities, and few of them are capable of precise torque measurement.Therefore, in this study, we developed a torque transducer that can measure torque with good resolution by using a new structure of torque detection mechanism.In addition, ECD was developed to reduce the effect of slight vibration of the moment-arm in 10-N•m-DWTSM used to evaluate the developed torque transducer.As a result, it was confirmed that the developed ECD was effective in damping the vibration of the moment-arm.The device itself did not affect the measurement value as well.The torque transducer developed in this study succeeded in improving the resolution by about 16.8% compared to the conventional torque transducer with the same capacity.

Figures 1
Figures 1 and 2 show a photograph and schematic diagram of ECD attached to the 10-N•m-DWTSM, respectively.The device consists of a one mm-thick brass plate

Figure 1 .
Figure 1.Photograph of a 10 N•m dead weight torque standard machine with eddy current damper (ECD).

Figure 2 .
Figure 2. Schematic of an eddy current damper (ECD) for the 10 N•m dead weight torque standard machine.

Figure 4 .
Figure 4. Schematic of the internal structure of a new torque transducer.

Figure 6 .
Figure 6.Vibration measurement at the end of the momentarm using a laser displacement metre.

Figure 8 .
Figure 8.Comparison of calibration results before and after the ECD installation by E n number.

Figure 7 .
Figure 7. Schematic of the loading cycle of creep test according to the JMIF015:2004 technical guideline [16].

Figure 9 .
Figure 9. Evaluation of vibration damping performance of the ECD.

Figure 11 .
Figure 11.The relative deviation of the output of each torque transducer.(a) Relative standard uncertainty due to reproducibility when changing the mounting position, w rot .(b) Relative standard uncertainty due to repeatability without changing the mounting position, w rep .(c)Relative standard uncertainty due to the deviation from the value calculated using the interpolation equation, w int .

Table 2 .
Measurement value and relative expanded uncertainties of calibration for each torque transducer.