**3. Impulse measurement stand in NUDT**

Since 1960s, researchers across the countries both domestically and internationally have successively developed various micro-thrust/micro-impulse measurement devices, including balance, single pendulum, double pendulum, torsion pendulum, and cantilever beam. The measuring range of these devices is mostly in the millinewton scale, and some attempts have also been conducted for the lower scale. Based on the inverted pendulum structure, NASA uses capacitive displacement sensors and gravity accelerometers to detect the position change of the swing arm and then measure the thrust, which can achieve 0–700 μ N measurement range, and the noise is less than 1 μ N/Hz [26]. Researchers at the University of the Witwatersrand improved the torsion pendulum, which can achieve micro-newton thrust and 0.27–600 μN, the error of impulse measurement in the range of Ns is less than 4% [27]. NASA also developed a single-end fixed torsion wire suspension torsion pendulum, with a resolution of 25nN and a force measuring range of 100 nN 500 μN. The error is less than 25% [28]. Researchers at the University of Tokyo in Japan has developed an elastic pivot type non-equal arm torsion pendulum with a resolution of 0.7 μNs impulse measurement [29]. Researchers at Huazhong University of Science and Technology have achieved a resolution of 0.09 μN with a maximum range of 264 μN micro-thrust measurement and a resolution of 0.47 μNs with a maximum range of 1350 μNs through a special suspension and torsional balance design for the torsional pendulum [30]. Although the measurement of thrust and impulse at the level of millinewton has reached a high level, there are still many difficulties in the measurement of thrust and impulse at the level of micro-nano or even nanonano. For example, there is noise in the measuring instrument itself and the environment, which often submerges the measured signal and greatly affects the measurement accuracy. At the same time, when the micro-thruster works, the measuring platform will vibrate under the force, which will also affect the measuring accuracy. In addition, the vacuum pumping process will also have adverse effects on the vacuum chamber and internal measuring system. These difficulties lead to less thrust and impulse measurement methods of micro-newton magnitude and low accuracy. At the same time, it is extremely difficult for the existing international measurement technology to meet the requirements of integrated thrust/impulse measurement with a large range, high resolution, and high accuracy at the same time.

In order to realize the integrated measurement of micro-impulse, the National University of Defense Technology (NUDT) has built a C-tube torsion micro-impulse measurement method and a direct calibration method based on ampere force, which has solved the problems of weak signal sensing, anti-interference and antirandomness, and online calibration, and developed a C-tube torsion micro-impulse measurement device and online calibration system as shown in **Figure 4**. The theoretically achievable micro-impulse measurement range is 100 nNs–100 mNs, The micro-thrust measurement range is 100 nN–100 mN, providing a necessary device for the development and engineering application of micro-nano satellite propulsion systems.

**Figure 4.** *C-tube torsion micro-impulse measurement device.*

### **3.1 Fundamental theory**

The C-tube torsion pendulum micro-impulse measurement system can be divided into the following subsystems: (1) displacement signal optical measurement subsystem, including He-Ne laser, planar mirror array, and photoelectric displacement sensor (PDS); (2) torsion pendulum structural parts, including torsion bar, swing arm, bracket, connecting parts, etc.; (3) damping and electromagnetic calibration subsystem, including several electromagnetic coils, permanent magnets, control circuits, etc. [21].

As shown in **Figure 4**, when the thruster works, its impulse will act on the torsion pendulum system. When the thruster works, its impulse will act on the swing arm and drive the torsion bar to rotate. The reflector installed on the swing arm reflects the laser beam emitted by the He-Ne laser to the remote PDS photosensitive surface. With the action of the impulse, the light spot produces a small displacement on the PDS photosensitive surface, which makes the PDS produce a small voltage signal output. Therefore, by calibrating the relationship between the impulse and the micro voltage signal, the corresponding micro-impulse can be calculated using the voltage signal.

The elastic element of the torsion pendulum is the key component of the torsion pendulum measurement system, which determines the mechanical response characteristics of the torsion pendulum, and is also an important component that affects the measurement performance of the torsion pendulum. According to the knowledge of engineering mechanics, it can be proved that within the elastic range of the material, the torsional deformation of the metal C-tube is strictly linear with the magnitude of the axial torque it is subjected to. The C-tube torsion pendulum measurement system uses this linear relationship to measure the impulse.

Assume that the wall thickness of the C-shaped tube is *t*, the length is *l*, the length of the cross-section centerline is *m*, the material shear modulus of elasticity is *G*, the rotational inertia of the torsion pendulum relative to the axis of the C-shaped tube is *I*, the impulse generated by the propulsion system is micro *Is*, and the instantaneous rotational angular velocity of the torsion pendulum beam is *w*. When the torque *T* is loaded on the C-shaped tube, the torsional deformation generated is [31]:

$$T = \frac{2Gmt^3}{3l}a \tag{1}$$

where *α* is the torsion angle of the C-shaped pipe under the action of torque. By integrating formula (1), the rotation angle of the C-tube torsion beam can be obtained *α0*, and its stored energy is [31]:

*Impulse Measurement Methods for Space Micro-Propulsion Systems DOI: http://dx.doi.org/10.5772/intechopen.110865*

$$E = \int\_0^{a\_0} Tda = \int\_0^{a\_0} \frac{2Gmt^3}{3l} a da = \frac{Gmt^3a\_0^2}{3l} \tag{2}$$

The motion of the torsion pendulum is fixed axis rotation, and its instantaneous kinetic energy is *Iw2 /2*. When the impulse Is acts on the torsion pendulum, the torsion pendulum starts to move. In the first quarter period of its movement, it can be considered that the energy is converted between the rotational kinetic energy of the torsion pendulum and the elastic potential energy stored in the C-tube, that is, the energy consumed by the C-tube is ignored. Let the initial angular velocity of the torsion pendulum beam be *w0*, which can be obtained from the conservation of energy:

$$\frac{Iw\_0^2}{2} = \frac{Gmt^3a\_{\text{max}}^2}{3l} \tag{3}$$

where *αMax* is the maximum swing angle of the torsion pendulum in the first quarter period of motion.

Let the distance between the impulse action point and the axis of the C-shaped tube be *Ls*, which can be obtained from the conservation of the moment of momentum:

$$I\_s L\_t = I w\_0 \tag{4}$$

By combining Eqs. (3) and (4):

$$I\_s = \frac{a\_{\text{max}}}{L\_s \sqrt{\frac{2Gmt^3I}{3l}}} \tag{5}$$

Combining Eqs. (1) and (5), it can be seen that when the C-tube torsion pendulum is under the action of static force or impulse, its static force and impulse values are linear with the mechanical response of the system.

When the pendulum is stationary, the total length of the optical path from the circular mirror to the PDS is *L*, and the displacement of the light spot on the PDS is *s* when the pendulum is stationary to moving. The PDS can convert the displacement signal to the voltage signal *V* for output. Set the gain coefficient of PDS signal conversion as μ, then there are:

$$s = L 
tau \tag{6}$$

$$\mathcal{V} = \mu \text{s} \tag{7}$$

The relationship between voltage signal and impulse can be obtained from simultaneous formula (5)-(7) as follows:

$$I\_t = \frac{V\_{\text{max}}}{L\_s \frac{1}{L\_f} \sqrt{\frac{2Gmt^3I}{3l}} \frac{\alpha\_{\text{max}}}{\tan \alpha\_{\text{max}}}} \tag{8}$$

The impulse generated by the micro-nano satellite propulsion system is very small, corresponding to the maximum swing angle generated α Max is smaller, at this time *αmax/tanαmax* ≈ 1. Therefore, formula (8) can be simplified as:

$$I\_s = \frac{V\_{\text{max}}}{L\_s \frac{1}{L\mu} \sqrt{\frac{2Gmt^3I}{\mathfrak{J}l}}} \tag{9}$$

If *K*= <sup>1</sup> *LLsμ* ffiffiffiffiffiffiffiffiffiffiffi 2*Gmt*3*I* 3*l* q , the *K* value can be determined by calibrating the torsion pendulum system, and then, the measurement impulse can be calculated by recording the maximum voltage Vmax displayed on the PDS.

### **3.2 Calibration**

The establishment of a highly sensitive micro-impulse measurement platform enables accurate measurement of the thrust and impulse of the micro-thruster. In order to accurately measure thrust and impulse and ensure that the system operates properly and performs well, the measuring system must be calibrated as accurately as possible. Calibration is a necessary step prior to all accurate measurements, and the accuracy of calibration directly affects the accuracy of the measurements system. There are many kinds of calibration methods, and more than one method of calibration for the same measurement system. The measurement system should use the calibration method as accuracy as possible. The high-precision electromagnetic calibration technology based on pulsed ampere force uses the energized copper wire to pass through the magnetic field orthogonal to it to generate ampere force and uses this ampere force to act on the measuring bench as the calibration force, effectively solving the high-precision calibration problem of the C-tube torsion pendulum measuring device.

For a ring electromagnet, as shown in **Figure 5**, when the cross-sectional area and permeability of the electromagnet are the same everywhere, a magnetic circuit will be generated in the electromagnet and the magnetic lines of force will be basically concentrated in the magnetic core. When the air gap height is small, most of the magnetic force lines pass through the air gap, and only a few of the magnetic force lines are outside the air gap. In most areas of the air gap, the magnetic induction intensity is uniform, and at the edge of the air gap, the magnetic induction intensity drops rapidly. The software Ansoft is used to carry out a numerical simulation on the magnetic induction intensity of the air gap and its periphery, and the magnetic induction intensity distribution on the middle cross-section of the annular magnetic gap is obtained, as shown in **Figure 6**. In the simulation, the electromagnet material is silicon steel, the electromagnet coil is 200 turns, the energizing current is 0.5 A, the gap section area is, and the gap spacing is 2 mm. It can be seen from **Figure 6** that

**Figure 5.** *Ampere force in annular magnet and gap.*

*Impulse Measurement Methods for Space Micro-Propulsion Systems DOI: http://dx.doi.org/10.5772/intechopen.110865*

**Figure 6.** *Distribution of magnetic induction intensity.*

when the volume is 2 � <sup>15</sup> � 15 mm<sup>3</sup> , the uniformity of magnetic induction intensity is satisfied.

In magnetic field *B*, the force on the current-carrying conductor can be expressed as

$$df = I\_C \cdot dl \times B \tag{10}$$

Therefore, when the electrified straight wire is in the gap, it will be affected by the magnetic field. The force is called ampere force, that is, *L* is the effective length of the straight wire with current *IC* in the uniform magnetic field with strength *B*.

$$F = BI\_{\mathbb{C}}L \tag{11}$$

Due to the edge effect of the magnetic field, it is difficult to calculate the ampere force through Eq. (11). However, when the magnetic field remains constant and *L* remains constant, the ampere force will be proportional to the coil current. In addition, when the current in the copper coil remains constant, the ampere force will be constant. As shown in **Figure 7**, the ampere force can be obtained by the physical analysis balance weighing method, and then it can be used as the calibration force. Different coil currents will correspond to different ampere forces for calibration. If there is a pulsed current in the coil, a pulsed ampere force will be generated between the coil and the magnetic field. By integrating the pulse ampere force with time, the impulse received by the copper coil can be obtained and then used as the impulse required for calibration.

Another advantage of this electromagnetic calibration method is that the ampere force is not sensitive to the angular displacement of the force arm. This is because the magnetic field is uniform in a large range of the electromagnet gap. Therefore, as long as the energized wire is not close to the edge of the gap, the generated ampere force will not be affected by the position of the copper wire. No matter how the position of

**Figure 7.**

*Measuring ampere force with physical analytical balance. (a) Physical measurement diagram (b) schematic diagram.*

the copper wire changes, as long as the copper wire enters and exits from one side of the air gap, the ampere force will remain unchanged, thus ensuring the accuracy of the calibration process.
