The Traceable Calibration of Thrust Stand by Electrostatic Force

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.