**2.1 Classification**

At present, the commonly used methods for measuring thrust and impulse include the deformation structure method, balance method, torsion pendulum method, and cantilever beam method. According to the different mechanical response results of the thrust platform, they can be divided into the direct transfer measurement method, pendulum force measurement method, and target transfer measurement method.

### *2.1.1 Direct transfer measurement*

The direct transfer measurement method refers to that the thruster being fixed directly on the force-measuring sensor or the thrust generated by the thruster being directly applied to the force-measuring sensor through the measuring platform. During the measurement, the thrust and impulse are identified by the sensor. This method is suitable for thrust measurement environments with large thrusts, such as chemical thrusters, electric arc thrusters, and resistance heating thrusters. The key to measurement is the measurement sensor. The commonly used sensors include a piezoelectric sensor, strain gauge sensor, and capacitance sensor [5, 13].

The direct transfer measurement method Is the preferred method for large thrust measurement. Its structure is relatively simple, and the measurement process is simple and fast. However, when the thrust magnitude is small, the mechanical signal is susceptible to be disturbed by environmental noise and mechanical vibration. This makes it difficult for the sensor to capture the weak mechanical signal.

### *2.1.2 Measurement method of swing force*

In the pendulous force measurement method, the thruster is mounted directly on the measuring platform, which can measure the thrust and impulse of the thruster with a small force. The measurement accuracy and resolution are high, which is the current mainstream scheme of the thrust and impulse measurement of the electric thruster. As shown in **Figure 1**, the swing force measurement process essentially uses the thrust of the thruster to excite the pendulum structure bench and obtains the thrust or impulse in reverse calculation by calibrating the relationship between the motion law of the pendulum structure bench to the thrust or impulse [14, 15].

The specific implementation of the swing force measurement method includes closed-loop and open-loop measurement methods. In the closed-loop measurement, the electromagnetic force is used to compensate for the effect of the thrust so that the measurement platform is in the random equilibrium and the electromagnetic force equals to the thrust [16]. The closed-loop measurement method can eliminate the interference of gravity and material rigidity on the measurement, and the

**Figure 1.** *Measurement principle of swing force.*

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

measurement results are relatively more accurate. The open-loop measurement method usually records the position change of the pendulum and then calculates the thrust and impulse through the calibration of the standard force. The commonly used sensors for measuring the change of pendulum position include a laser displacement sensor, capacitance displacement sensor, laser angle sensor, and photoelectric sensor. In addition, to control the motion of the pendulum and quickly return to the equilibrium state after the measurement, the pendulum force measurement device is usually equipped with the corresponding dampers.

According to the structural form of the pendulum, the pendulum force measurement methods can be divided into three types: suspended pendulum, inverted pendulum, and torsion pendulum, as shown in **Figure 2**. Although the three structures are slightly different, they can be considered a "spring-mass-damper" system [9].

### *2.1.3 Target transfer measurement method*

The target transfer measurement method is to impact the plume from the thruster on the target and calculate the thrust of the thruster by measuring the position change of the target under the impact force. **Figure 3** shows the schematic diagram of a typical target transfer measurement scheme, which consists of target, elastic beam, displacement sensor, and calibration device. The elastic beam with minimum rigidity is fixed with the target with maximum rigidity. When the plume from the thruster impacts the target, the elastic beam will deflect obviously, and the displacement sensor can measure the horizontal displacement of the elastic beam. Calibrate the horizontal displacement and standard force of the elastic beam through the calibration device, establish the corresponding functional relationship, and realize the accurate measurement of different thrust sizes. Most target structures are equivalent to simple pendulum structures, and their motion characteristics are similar to the pendulum force formula [17, 18].

Compared with the other two kinds of measurement methods, the target transfer measurement method is a non-contact indirect measurement, which can avoid the impact of measurement and control cable, thruster working noise, and vibration on the measurement results to a certain extent [5, 13, 16]. In addition, the target transfer measurement method has a simple structure and is easy to install and

### **Figure 2.** *Spring-mass-damper system. (a) Hanging pendulum, (b) inverted pendulum and (c) torsional pendulum.*

**Figure 3.** *Schematic diagram of a typical target transfer measurement.*

implement. However, due to the effectiveness and secondary effects of the plume, the error is relatively large. The key points are as follows:

