The Traceable Calibration of Thrust Stand by Electrostatic Force

Summary

Traceability calibration of mechanical characteristics of thrust stand is an essential prerequisite to ensure traceability measurement of thrust. Here, we describe how to calibrate the thrust stand by the electrostatic force generated by the parallel plate capacitor.

Abstract

Micro thrusters have important applications in low-frequency gravitational wave detection, satellite formation, and inter-satellite laser communication, so it is necessary to accurately measure the thrust of micro thrusters with traceability. A thrust stand is a widely used micro thrust measuring device with the advantages of high resolution and large load. Traceability calibration of mechanical characteristics of thrust stand is an essential prerequisite to ensure traceability measurement of thrust. In this study, a parallel plate capacitor was used to calibrate the thrust stand by generating a micronewton electrostatic force, which could be traced to the International System of Units (SI). The constant capacitance gradient range was obtained through simulation and theoretical calculation. Moreover, the electrostatic force could be changed by standard voltage with the advantages of simple principle, instantaneous trigger, and traceability. The device could be used for traceability calibration of micro newton thrust stand due to simple assembly and short traceability path.

Introduction

The micro thruster is indispensable for the ultra-static and ultra-stable space experimental platform to provide micro thrust to offset the non-conservative force on the spacecraft in real-time in low-frequency gravitational wave detection. Reliable measurement of the thrust of the micro thruster in the complex noise environment is the premise to achieve drag-free control. Therefore, it is essential to calibrate the thrust stand with high precision to establish the mechanical response model. The calibration methods of thrust stand mainly include two types, contact and non-contact calibration methods.

Contact calibration methods mainly include rope pulley weight system, impact hammer, and impact pendulum, which are traditional calibration methods. In 2002, Lake et al.¹ used weights and pulleys to apply calibration force in the range of mN. In 2006, Polzin et al.² also used a similar automatic system to load vertical loads into the swing arm, but it had a large error when the force was less than 10 mN. In 2004, Koizumi et al.³ obtained the generated momentum by integrating the force recorded by the force sensor in the collision process. The resolution of the force sensor was 90 mN, the effective impulse was 20-80 µNs, and the total error was 2.6 µNs at 100 µNs. The impact pendulum is only suitable for large impulse measurement because mechanical vibration seriously affects the calibration. Although the contact calibration method is easy to set up, there is zero drift error, and the calibrated force is generally larger than the non-contact methods. Therefore, it is not suitable for calibrating the micro force thrust stand.

Non-contact calibration methods mainly include gas dynamic calibration, electromagnetic calibration, and electrostatic calibration. In 2002, Jamison et al.⁴ developed a gas dynamic calibration technology, which generated a force range of 80 nN-1 µN, 86.2 nN thrust with 10.7% error, and 712 nN thrust with 2% error. Gas dynamic calibration technology can generate nN and sub-µN force reliably and is easy to implement. However, it is a kind of indirect calibration technology that cannot trace to the International System of Units (SI). What is more, gas dynamic calibration is only suitable in a vacuum.

The electromagnetic force can be as small as the order of micronewton, and there is a good linear relationship between the electromagnetic force and the current, which has good repeatability. Tang et al.⁵ developed an electromagnetic calibration technology using a permanent magnet and coil. The measurement range was 10-1000 µNs, the calibration force was less than 10 mN, and the calibration reliability of 310 µN is 95%. In 2013, He et al.⁶ used the ring electromagnet with air gap and the energized copper wire for calibration. The calibration uncertainty of 150 µN force was 4.17 µN, and the calibration force had a large range and was not sensitive to the displacement of the thrust stand arm, but there was a problem that the copper wire current would magnetize the electromagnet core. In 2019, Lam et al.⁷ used different magnets and commercial voice coils to calibrate a wide range of forces. The structure was compact and easy to install. Moreover, the force range was large, with four orders of magnitude of 30-23000 µN, and the uncertainties of static and pulse force were 18.47% and 11.38%, respectively. However, for the calibration of the thrust frame, the electromagnetic force is not traceable to SI.

Electrostatic force calibration is the most widely used direct calibration technique. Selden and Ketsdever⁸ used an electrostatic comb (ESC) as the calibration device with a measuring range of dozens of micronewton with an error of 3%. The force changed 2% as plate spacing changed 1 mm. However, the distance between the adjacent teeth should be the same, which was only applicable to the thrust stand with small displacement. In 2012, Pancotti et al.⁹ designed a symmetrical electrostatic comb whose pulse range was 0.01 mNs-20 mNs, which could generate a larger electrostatic pulse. However, the disadvantages of complex structure and easy damage of electrostatic comb need to be solved.

It is a prerequisite to provide the traceable micronewton force as a reference force to calibrate the thrust stand. The electrostatic force is widely used to trace force to SI in the metrology Institute^10,11,12. The electrostatic force has the advantages of simple principle, instantaneous trigger, and short tracing path. In this study, the parallel plate capacitor was served to generate electrostatic force as a reference force to calibrate the pendulum thrust stand, whose displacement output is proportional to the applied thrust. The ratio of the thrust and the displacement is the stiffness of the thrust stand. By calibrating the capacitance gradient of the capacitor, it was unnecessary to strictly control the pose of two parallel plates. The constant capacitance gradient range was obtained through simulation and theoretical calculation. The range of electrostatic force could be adjusted by the spacing and area of two plates, which was suitable for efficient calibration of thrust stand with different stiffness.

Protocol

1. Experimental realization

1. Gather all system components, including the circular parallel plate capacitor, the motorized linear stage, the thrust stand, the capacitance bridge, the SMU instrument, the laser interferometer, and other components, shown in Figure 1.
2. Fix Plate A on the motorized linear stage and fix Plate B on the arm of the thrust stand, making plates A and B parallel to each other.
   NOTE: The plates are processed by high precision grinding of aluminum alloy. The diameter of plate A is 6 cm, and the diameter of plate B is 4 cm so the alignment error can be ignored.
3. Control the distance D_ab between the two plates by a motorized linear stage (Resolution 0.625 µm). Completely fit the two plates and then pull a fixed distance of 1 mm through the linear stage.
4. Connect the capacitance bridge (Resolution 0.8 aF, Accuracy ±5 PPM) with the two plates to measure the capacitance C_ab variation with the change of plate spacing.
5. Apply a standard voltage to the capacitor by a high voltage source measure unit (SMU) instrument (Precision 0.012%, ±5 - ±1100 V) to generate a controllable high precision electrostatic force.
6. Adjust the laser interferometer (Resolution 10 nm) to directly face the arm of the thrust stand, and measure the displacement x in real-time.

2. Calibration of the capacitance gradient

1. Drive plate A to move to the side away from plate B with a step length of 0.02 mm by the motorized linear stage, and make the initial plate spacing equal to 1 mm.
2. Measure the capacitance value of the two parallel plates by the capacitance bridge after each step until the relative change of plate spacing is 0.12 mm.
3. Begin a reverse step with a length of 0.02 mm to return to the initial position.
4. Conduct a total of five repeatable experiments.
5. Fit the results to get the relationship between capacitance gradient and plate spacing of parallel plate capacitor, dC_ab/dD_ab.

3. Electrostatic force calibration of thrust stand

1. Disconnect the capacitor bridge from the parallel plate capacitor.
2. Connect the two plates with the SMU instrument and make the space between the two plates equal to 1 mm.
3. Increase the voltage U from zero step by step at both plates of the capacitor with a step value of 50 V until the applied voltage is 300 V. The electrostatic force F is equal to 1/2U²(dC_ab/dD_ab).
4. Use the laser interferometer to measure the displacement x of the thrust stand arm in real-time. Set the sampling frequency of the laser interferometer to 50 Hz.
5. Decrease the voltage U from 300 V step by step at both plates of the capacitor with a step value of 50 V until the applied voltage is zero.
6. Conduct a total of five repeatable experiments.
7. Fit the results to get the relationship between the electrostatic force F and the displacement x of the thrust stand arm. Calculate the stiffness k of the thrust stand according to Hooke's law, k = F/x.

Results

Following the protocol, the capacitance gradient and the stiffness of the thrust stand are calibrated. The principle of electrostatic force should be introduced. There will be relative motion D_ab between two charged plates under the action of external force F. Moreover, the work W by external force will be converted into electric energy E stored in the capacitor. The potential difference U, the charge of both plates Q and capacitance C can be obtai...

Discussion

In this protocol, a parallel plate capacitor was used to calibrate the thrust stand by generating a micro-newton electrostatic force, which could be traced to SI. It is critical for all steps to calibrate the capacitance gradient precisely. The motorized linear stage made the initial plate spacing of this parallel plate capacitor equal to 1 mm and moved the plate A at a step of 0.02 mm. The capacitance bridge was used to measure the capacitance for accurately calibrating the capacitance gradient. The electrostatic force ...

Materials

Name	Company	Catalog Number	Comments
Motorized linear stage	Zolix	TSA50-C	Resolution 0.625 μm
Capacitance bridge	Andeen-Hagerling	AH2550A	Resolution 0.8 aF, Accuracy ±5 PPM
High voltage source measure unit (SMU) instrument	Keithley	2410	Precision 0.012%, ±5 μV– ±1100 V
Laser interferometer	Renishaw	RLE10	Resolution 10 nm
Circular parallel plate capacitor	Processed by high precision grinding		The plates are processed by high precision grinding of aluminum alloy. The diameter of plate A is 6 cm, and the diameter of plate B is 4 cm.
Thrust stand	Processed by high precision grinding		Pendulum type thrust stand