# Error Characteristic Analysis of Fluid Momentum Law Test Apparatus
## 3 Analysis of Sensor Displacement Response Characteristics
Under the impact of different momentum jets, there is a certain difference in the displacement response trend of the sensor characteristic point C. There is no basic law that the greater the jet momentum, the greater the displacement of the characteristic point C in Y direction. In order to further explore its response law, frequency spectrum analysis is performed on the displacement response of the characteristic point C in Y direction, as shown in Figure 6. Under the impact of different momentum jets, the vibration frequencies of the sensor in the Y direction is similar, and the amplitude is different. The displacement vibration signal in the Y direction is a periodic signal, according to the Fourier transform theory, the periodic signal can be decomposed into a signal group, which is mainly composed of a 0-frequency signal and a set of periodic signals with different frequencies. In this article, the numerical sampling frequency is equal to 6666.7 Hz, the displacement vibration signal in the Y direction could be composed of four signals, including a 0-frequency signal and three sinusoidal periodic signals. The frequency of the periodic signal is distributed in the range of [33,66] Hz, [560,590] Hz and [1430,1460] Hz on the conditions of different flow rates. Taking into account the numerical calculation error and the relatively small range of the frequency distribution interval comparing to sampling frequency, to simplify analysis and calculation, it can be assumed considering that these three periodic signals are the fixed frequency. Take the middle of the frequency range and round up. Then, the frequencies of the three signals are 50 Hz, 580 Hz and 1450 Hz,  
Figure 7: Displacement changing graph of sensor characteristic point C in the Z direction under the impacts of different momentum jets. respectively. As the frequency increases, their amplitudes decrease in turn. The vibration amplitude is the largest when the jet flow rate is 2.4 m\({}^{3}\)/h. Comparing Figures 4 and 5, it can be shown that the displacement of the sensor in the X direction is significantly greater than the displacement in the Y direction, which indicates that the force \(F_{\rm{sx}}\) of the sensor in the X direction is greater than \(F_{\rm{sy}}\). As Figure 7 shows, under the action of the jet impact force, the characteristic point C of the sensor is displaced in the Z direction, and the displacement curve continues to oscillate. Under the same jet effect, the displacement amplitude in the Z direction is much smaller than the X and Y directions. Under the impact of different momentum jets, the displacements changing trend of the sensor characteristic point C are similar in time [0,5] ms; after more than 5 ms, the displacement changing trends are slightly different. The main reason for this situation is that the displacements and deformation of the sensor in the X and Y directions cause the change of displacement in the Z direction. From the above analysis of the displacement response characteristics of the sensor characteristic point C under the impact of different momentum jets, it can be shown that under the action of the jet impact force, the sensor first moves in the jet direction (X direction), and tends to be stable. The greater the jet momentum, the greater the displacement in the X direction, and the longer the oscillation adjustment time. The sensor is subjected by non-constant external force in the Y direction to produce continuous vibration, and the vibration in the Y direction is greatly enhanced after the vibration in X direction enters the stable period. The vibration in the Y direction can be decomposed into a 0-frequency signal and three fixed-frequency periodic vibration signals. Under the impact of different momentum jets, the vibration frequency is equal and the vibration amplitude has a certain difference.