The Design and Performance of an Electronic Torque Standard Directly Traceable to the Revised SI

The United States National Institute of Standards and Technology (NIST) has been developing a new device for primary standard realization of torque utilizing established traceability to quantum-electrical standards following the 2019 revision of the International system of units (SIs). This device, the Electronic NIST Torque Realizer (ENTR) is a device directly traceable to the quantum-electrical standards of the revised SI with the goal of outperforming current commercial torque transducer uncertainty levels, improving torque tool calibration at low torque ranges, and shortening the torque standards dissemination chain. This project’s goal is to create a device for torque calibrations with an operational range of $7\,\, {}\times {}10^{-4}$ Nm to 1 Nm with uncertainty at or below 0.1%. We intend ENTR to be a possible replacement for present transfer standards used in the torque standards dissemination chain, easing the financial and logistical burdens of current torque standards dissemination systems.

, [4]. Progress on table-top sized Kibble balances at national metrology institutes such as the National Institute of Standards and Technology (NIST) of the U.S. [5] and Physikalisch-Technische Bundesanstalt of Germany [6], has inspired a similar device capable of realizing torque with SI traceability to quantum-electrical standards.
For torque lower than 1 × 10 −2 N m, balancing small mass artifacts required to calibrate fragile transducers is difficult, burdensome, and often irreproducible. A collaborative effort between NIST and the U.S. Air Force to design, construct, and characterize a Kibble-style electromechanical system for directly calibrating torque tools is currently under development.
This effort's goal is to create a tabletop-sized electromagnetic torque calibration device capable of generating 7 × 10 −4 N m to 1 N m with 0.1% uncertainty.
We note that this value of accuracy is significantly larger than uncertainty levels achieved by previous work from other national metrology institutes [2], [3]. This device, the Electronic NIST Torque Realizer (ENTR) is designed for robustness, commercial utilization, simplicity, and affordability. A primary goal of the project is to insert a quantum-electrical standard traceable device as far downstream in the traceability chain as possible, removing the necessity for calibrated masses and length standards in torque calibrations. ENTR is intended to re-route the SI standards dissemination chain from mechanical to quantum-electrical standards, empowering calibration facilities ranging from military to research and industry to directly realize torque for themselves.
This publication is an extended version of a proceedings article from the 2022 Conference on Precision Electromagnetic Measurements [7]. In the following text, we describe the theory, the apparatus, and show the first result.
II. THEORY Forces and torques are related phenomena. Forces change linear momentum while torques change rotational momentum. Hence, it is not surprising that applying the Kibble principle to a rotational system can be used to realize torque just as a linear Kibble balance realizes force. In previously designed Kibble balances such as the NIST-4 Kibble balance, a coil is translated vertically through a fixed magnet system [8]. For the rotational version, a magnet system spins with respect to a fixed coil. Theoretically, the system could be constructed from a rotating coil with a stationary magnet system, but this was not chosen for this project due to foreseen complications with wiring and electrical connections.
Still, the measurement requires two modes of operation: spin mode and torque mode where V is the induced voltage in the coil from the spinning magnet, B is the magnetic flux density of the magnetic circuit, L is the total length of the radial wire segments of the coil, and r is the distance between the axis of rotation and the center of each wire segment. We define φ as the angular position of the magnet system, and ω =φ as the angular velocity. The torque τ a is applied externally from a device that is to be calibrated and the servo system adjusts the current I in the coil to maintain it at a fixed angle φ o . The magnetic coupling factor, B Lr , which we abbreviate in the following with β is a function of angular position φ, i.e., the relative position between coil and magnet. The induced voltage is not only a function of φ, but also time since the velocity of the rotating magnet is slowly decreasing due to friction From a fitting procedure, outlined below, to the quotient of pairs of measurements V (t, φ)/ω(t, φ), taken at the same time and angle, the value of β(φ o ) at the angle φ o can be obtained. In the division of the voltage by the angular velocity, the time dependence cancels and β only depends on the angle. Hence, the measured torque is given by The remainder of this article explains the mentioned steps in detail and discusses the measured agreement between τ a and τ m .

A. Mechanical Design
The ENTR mechanical components consist of a central rotor, two ceramic ball bearings, a base plate, and an upper cantilever structure. One bearing sits in the base plate, while the other rests in the cantilever structure, and both constrain the motion of the central rotor. The base plate and cantilever are fabricated from an acetal plastic to maintain structural rigidity without influencing the magnetic field generated by the NdFeB magnets of the central rotor. A rendering of ENTR is shown in Fig. 1.
For the NdFeB magnets, two ring-shaped magnets were cut along a diameter. One-half of each magnet was flipped upside down, and the magnets were placed on the steel yokes and affixed to the central rotor, oriented in attraction. A detailed rendering of the rotor is visible in Fig. 2. We chose to rotate the magnet instead of the coil to avoid electrical connections to the rotor, which may have produced unwanted torques and friction.
Radial alignment of the bearings is ensured by tight machining tolerances between the cantilever with the base plate. Both parts have an arc cut out of equal radius concentric to the bearing locations. Ceramic ball bearings were chosen as they had the lowest friction out of a sample of bearings tested, including stainless steel, hybrid, and angular contact ceramic bearings. Air bearings were determined not to be appropriate for this initial prototype due to practical reasons such as requiring an active air hose and higher cost.

B. Electromagnetic Design
For ease of construction, the electromagnetic coil is constructed from a stack of identical printed circuit boards (PCBs).
A drawing of the top side of one PCB is shown in Fig. 3. Current flows from the conductive pad at the top of one board along the traces in the top layer, then through a via to the bottom layer of the PCB. The current then follows a path in the same direction along the trace on the bottom side of the board until it reaches a conductive pad at the same location as the top conductive pad on the opposite side of the board. Because of the identical pad locations, these PCBs can be stacked and soldered with the current moving from one PCB to the next. Eight boards are connected by soldering at the pad locations and securing the assembly with polyimide tape. The stack of PCBs is then placed in an oven to re-melt the solder and ensure the electrical connections.

C. Data Acquisition
The primary data acquisition device (DAQ) is a National Instruments universal serial bus (USB)-6351 Multifunction I/O Device 1 (Hereafter referred to as "the DAQ"). Voltage measurements are made with a Keysight 34465A digital voltmeter (DVM), and angular position measurements are made with a dual-readhead Renishaw VIONiC encoder system. The encoder scale has a 20 µm graduation and the encoders utilize 500× interpolation to give a resolution of 40 nm. The encoder output signal is 20 MHz. Two readheads are used to minimize systematic effects caused by the runout of the encoder disk. The signals of both encoders are combined at hardware using a component provided by the manufacturer to a quadrature signal that is digitized by the DAQ. Voltage and position measurements are synchronized by a 400 Hz clock generated by the DAQ. Position data from the optical encoder is received through the DAQ, while voltage data is recorded in the internal buffer of the DVM and read via USB.

IV. MEASUREMENT PROCEDURE AND OPERATION A. Spin Mode
In spin mode, the value of β is determined by driving the rotor to a target angular velocity, ω max = 6.1 rad s by driving a current through the electromagnetic coil, where the current is modulated with a simple angular position feedback loop. After reaching ω max , the rotor is allowed to freely spin while measurements of voltage and angular position are taken. After reaching a set minimum angular velocity, ω min = 3 rad s −1 , data collection is paused. These values of ω max and ω min are chosen as to ensure the speed limit of the angular encoder is not exceeded, and an adequate number of data points are taken per revolution. The voltage and position data taken within ω max to ω min are recorded for a profile fit as discussed below. The rotor is then driven in the opposite direction to −ω max and data is collected until −ω min . The process is automatically repeated giving as many values of β as desired until stopped by the operator. When the operator chooses to end the calibration, ENTR stops taking data and a Python script calculates the value of β for a chosen angle φ o . From experience, a typical spin mode session includes about 240 magnet revolutions in both clockwise and counterclockwise directions spanning about 15 minutes. Each individual rotation's β profile is fit with a 6 • polynomial (Fig. 4) in the region of interest about φ o . These values are then averaged to give one β(φ o ) value per "spin-down" from ±ω max to ±ω min . ENTR then switches into torque mode.

B. Torque Mode
Upon entering torque mode, the electrical circuit of the system is changed such that the voltmeter measures the current through the electromagnetic coil via the voltage drop across a known resistor connected in series with the electromagnetic coil and the current source.
Closed-loop angular position control is used to rotate the magnet assembly to the angle φ o at which β has been calculated. As the rotor of the magnet assembly is held at the desired position by the control loop, any torque applied to the rotor is counteracted by a torque generated by the current through the coil.
The electromagnetic torque produced by the current can be calculated using (4), where β(φ o ) is determined from the average of the preceding and following spin mode values.

C. Comparison to Present Standard
A key design feature of ENTR is its ability to operate horizontally. This allows for a direct comparison between the electromagnetically produced torque of ENTR and the torque produced by known masses on known lever arms. Utilizing this feature, we perform an experiment comparing ENTR to a "dead-weight" torque standard; presently the standard process for calibrating torque transducers at the national metrology institute level.
A truncated wheel of 2r w = 508 mm diameter is mounted to the shaft of ENTR, while care is taken to align the shaft horizontally in the lab.
A 50 g mass hanger is suspended from a fiber with a diameter (2r f = 0.30 mm) off each end of the truncated wheel. Three wire masses m x , (x ∈ {1, 2, 3}) can be placed on either hanger to produce a known torque, τ a , applied to ENTR's rotary shaft. By placing the wire mass on the hanger the change in torque is τ a = m x g(r f + r w ).
Here g is the local gravitational acceleration in the laboratory. The value of g = 9.80101 m/s 2 was taken from an NOAA website with a relative uncertainty of 2 × 10 −6 .
The value of torque generated by the mass on the lever arm is compared to the torque reported by ENTR, τ m . A photograph of the torque verification assembly is shown in Fig. 5.
Measurements are conducted in an A-B-A-B-A. . . style of data collection. Measurements of torque on the rotor having no mass (A) on the hanger are alternated with measurements of torque with the wire mass on the hanger (B). A total of 31 measurements per mass per side are taken, each lasting 20 s and containing approximately 2200 voltage data points. We choose these measurement parameters to achieve a statistically significant torque value for each A or B measurement. Placement and removal of the wire test masses are automated using a linear stage and stepper motor system, removing irreproducible human effects in placing and removing the masses.
A friction hysteresis erasing procedure is also performed before each measurement. We borrow a technique for hysteresis erasing used in Kibble balances for decades. Robinson [9] in 2012 describes a hysteresis erasing procedure for a Kibble balance utilizing a knife edge, and we adapt the technique for a ball-bearing-constrained rotor. After an excursion occurs in a mechanical pivot due to a load change, the pivot is exercised consistently regardless of the load change. In this case, the rotor is driven in a decaying sinusoidal fashion with an initial amplitude of 2 • , while typical excursions of the rotor during mass placement and removal are approximately 0.1 • . This erasing procedure reduces a possible systematic error due to inelastic forces and torque on the pivot.
Three masses are used in the comparison experiment with nominal values of m 1 = 500 mg, m 2 = 3 g, and m 3 = 8 g.
The mass values are determined with a series of measurements on mass comparators. These masses are chosen to cover the lower range of the operational goals as we foresee the greatest difficulty in achieving the desired uncertainty at the lowest operational ranges of ENTR.

V. UNCERTAINTY ANALYSIS A. Repeatability of Measurement
To determine uncertainty due to the repeatability of torque measurements, an experiment is conducted in which a wire mass is repeatedly placed on and removed from one hanger to measure applied torques and null measurements. 913 pairs of applied torque and null measurements are taken over the course of approximately 40 h. The Allan deviation of the repeatability measurement study is shown in Fig. 6. From this Allan deviation plot, we believe 80 measurements in the present verification experiment set up to be acceptable in order to achieve reasonable levels of type A uncertainty.

B. Encoder Uncertainty
Uncertainty in the angular encoder measurement creates uncertainty in the value of β(φ) determined in spin mode and is found to contribute approximately 1 × 10 −7 N m of uncertainty in the measured torque. This uncertainty value is obtained by the value given in the manufacturer's specifications for installed encoder accuracy with proper alignment of the encoder confirmed by an alignment device provided by the manufacturer.

C. Voltage Measurement and Resistance
Voltage measurement uncertainty for the spin mode and the torque mode contribute a combined uncertainty of 3 × 10 −7 N m. These values of voltage measurement uncertainty are calculated with consideration of the measurement range and integration time settings of the voltmeter using values provided by the manufacturer. The value of the resistor used in the torque measurement is well-known and contributes only 1 × 10 −8 N m of uncertainty.

D. Data Acquisition Hardware Timing
In order to characterize the veracity of the measurement timing system, a virtual quadrature encoder signal is generated using a waveform generator and fed into the DAQ to mimic an encoder with constant velocity. The theoretical velocity of the reference signal is compared to the velocity values calculated by position data taken from the DAQ. The discrepancy between these values gives an uncertainty due to measurement timing of approximately 91 parts in 10 6 . This corresponds to a torque measurement uncertainty of 1 × 10 −7 N m. A second systematic associated with timing occurs when the voltage and velocity measurements are not perfectly aligned in time. The geometric factor is obtained correctly Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
using β = V (t V )/ω(t ω ) when the two measurement times are identical, t V = t ω . In reality, however, there is sampling jitter on the voltage measurement, t V = t ω + δt, where δt is a random number from a normal distribution with mean zero and standard deviation σ δ . We estimate that effect to contribute a relative uncertainty of 5 × 10 −6 .

E. Data Analysis and Curve Fitting
During the data analysis process, each individual rotation has a calculated β value determined at the chosen angle φ o by fitting a sixth-order polynomial within the region of interest to the values of β(φ). Various fitting algorithms were tested with no significant difference in the calculated β(φ o ) value. The fitting process was determined to contribute approximately 1 × 10 −7 N m of uncertainty to the torque measurement.

F. Applied Torque Uncertainty for Verification
Uncertainty in the value of torque applied to the rotor during the verification must also be included in the uncertainty analysis.
The length standard used for verification is measured on a coordinate-measuring machine to a nominal diameter of 508 mm with an uncertainty of 3 µm.
While the diameter of the length standard wheel (2r w ) is well known, there is uncertainty in the actual lever arm applying the torque, δr w , as the true location of the center mounting hole of the length standard is not known exactly. The noncentered hole creates an effect where the torque applied on one side of the length standard wheel is higher than expected from an expected 254 mm lever arm, and the other side will have a lower torque than expected. Thus (5) becomes τ a = m x g r f + r w ± δr w (6) where ± evaluates to + for clockwise and − for counterclockwise torques. By taking the difference in the values of torque measured on each side of the bar for the same applied mass, we approximate an additional uncertainty in the lever of 1.9 × 10 −5 m due to the δr w factor. Furthermore, the uncertainty in the measurement of the radius of the fiber suspending the mass hangers contributes an additional 3×10 −8 N m of uncertainty in torque applied. Mass measurement remains the greatest source of type B uncertainty in the comparison measurement.
The total absolute uncertainty in torque applied for the lowest value under test is 480 × 10 −9 N m of torque. Table I presents the total relative uncertainties for the lowest torque value tested in the verification experiment.

VI. RESULTS AND DISCUSSION
Results of the comparison experiment are shown in Fig. 7 and Table II. We perform a first-degree least squares fit taking into account uncertainties in both the measured torques and the applied torques, see [10]. The fit line with uncertainties applied gives an overall agreement between measured and applied torques of 0.051%.
While the lowest torque applied in this comparison (1.18 × 10 −3 N m) does not reach the minimum of the operational range goal (7 × 10 −4 N m), it offers significant insight into the largest contributing factors of uncertainty in the measurement, namely the repeatability of the measurement and the uncertainty in the voltage measurement. In the future   development of ENTR, focus will be placed on reducing these uncertainties to reach the desired goal of 0.1% relative uncertainty for a coverage factor of k = 2.
VII. CONCLUSION The goal of this project is to build a device that can calibrate torques of order 1 mN m with relative uncertainties below 1 × 10 −3 . Fig. 7 clearly indicates this goal has been met for the torque values tested as the mean value of all measurements falls within the required range, and total measurement uncertainty is well below 0.1%. While the uncertainty values for τ m are higher than that of τ a (see Table II), the τ m values have significantly less uncertainty than presently used torque transfer standards such as commercial torque transducers, indicating ENTR demonstrates significantly greater performance while offering a shorter path in standards dissemination.
In addition, as a computer-controlled device, ENTR is easy to use and keeps a digital data log of the calibrated torque values. Further developments of the project will result in an expanded operational range, as it is easier to reach the uncertainty and accuracy goals for torques larger than 1.8 × 10 −2 N m, the largest torque value tested in this experiment.