## 3 Torsional Thrust Balance Assembly and Calibration
### Steady-State Characteristic  
The intrinsic drift of the torsional balance has an important effect on long duration thrust measurement. To accurately calibrate the steady-state performance, the primary goal is to estimate the intrinsic drift rate of the torsional balance. Figure 11 shows three repeated measurements for arm displacement over a period of 1000 s at a sample rate of 0.02 s. Both the electrostatic comb and the wire were not applied with voltage excitation. From the figure we can find that the torsional balance drifts towards the FODS probe. The recorded data of each measurement was divided into 50 s segments to estimate the intrinsic drift rate. Each data segment was fitted by a linear function, then we averaged all the slopes, resulting in an average drift rate of 0.0023 \(\upmu\)m/s. Figure 11: The intrinsic drift of the balance during 1000 s.  
Figure 10: Dynamic response to a step force. The torsional thrust balance was calibrated by applying a sequence of known forces producing and the corresponding arm deflection displacement was recorded. The force was generated by electrostatic combs and the value was determined by the electrostatic comb calibration Equation (9), according to the applied voltage. Figure 12 shows the voltage profile applied to the electrostatic comb. Each step lasts 24 s long which can ensure the arm reaches a stable position. The blue values in the figure are the actual electrostatic force calculated in each voltage step. The arm response to the sequence voltage profile applied to electrostatic comb is shown in Figure 13. The displacements shown in the figure are the average displacements during the last 10 s in each step. It can be found in the figure that due to intrinsic drift, the arm displacement is distinct in the loading and unloading condition. For clarifying and quantifying the distinctions, the calibration procedure was repeated three times to exclude the influence of random error. Figure 14a shows the electrostatic force-displacement relationship in the loading and unloading process; the standard deviation of three displacement measurements under the same excitation voltage is so small that it is not shown in the figure in the form of error bars. It was found that the arm displacement is only in good agreement at high voltage, while it has a large deviation at low voltage. The main reason for this phenomenon is that the high voltage is in the middle of the calibration history, the time interval between loading and unloading at the same voltage is short, and the intrinsic drift of the arm during this period is small. However, the low voltage is at the beginning and the end of the calibration history, and the time interval is longer, resulting in a larger displacement deviation. We compensated the arm displacement according to the obtained intrinsic drift rate. Figure 14b shows the resulting electrostatic force-displacement; it can be seen that the two curves in the loading and unloading process are in good agreement after compensation. We averaged the data in Figure 14b and  
Figure 12: Voltage profile applied to the electrostatic comb. Figure 13: The dynamic response to the sequence voltage profile applied to the electrostatic comb. the resulting steady-state calibration result is shown in Figure 15. The function of arm displacement and thrust can be determined by linear fitting the data as:  
\[F_{t}=0.47968\cdot\Delta x-0.2445, \tag{13}\]  
To obtain the thrust resolution of the torsional thrust balance, two step voltage sequences of 200-240 V (voltage increment of 4 V) and 740-750 V (voltage increment of 2 V) were applied to the electrostatic comb, respectively. The arm displacement response to these two voltage sequences was recorded and substituted into Equation (13) to calculate the corresponding thrust. Figure 16 shows the voltage profiles and the thrust calculation results; the error bars are the standard deviation of the average force in each step loading.