# Error Characteristic Analysis of Fluid Momentum Law Test Apparatus
## 4 Error Characteristic Analysis  
The analysis in Section 3 shows that, under the impact of the jet, the sensor vibrates in the three directions of X, Y and Z. Combined with the relevant research that has been carried out, the transverse deformation caused by the irregular vibration is the main measured error source of resistance strain sensor. Considering the measurement principle and error theory of the resistance strain sensor, the relative displacement of the characteristic point C of the sensor relative to the point E is taken as the deformation \(s\) of the strain gauge, and the jet impact force obtained by the sensor expressed as \(F=f(s)\), which is monotone increasing function [14]. The achieved studies have shown [14] that the impact force value measured by the sensor consists of a fixed value and a variable value. The displacement in the X and Y directions, respectively, affect the fixed value and the variable value measured by the sensor. The basic form of the impact force measurement value is: \(c(t)+g(t)\), where \(c(t)\) represents a fixed value, \(g(t)\) represents a variable value; \(g(t)=A_{0}+A_{1}sin(w_{1}t+\varphi_{1})+A_{2}sin(w_{2}t+\varphi_{2})+A_{3}sin(w _{3}t+\varphi_{3})\); \(A_{0}\), \(A_{1}\), \(A_{2}\), \(A_{3}\) represent the amplitude of the 0-frequency signal and three period signals, respectively. Under the impact of different momentum jets, the relative displacement or deformation of the sensor characteristic point C in the X and Y directions are shown in Figures 8 and 9, respectively. As shown in Figure 8, under the action of the jet impact load, the sensor strain gauge undergoes relative displacement and deformation in the X direction and tends to be stable after oscillation adjustment, that is, \(c(t)\) tends to be a constant value after adjustment. The deformation \(s_{x}\) of the sensor strain gage in the X direction and the jet flow are in a monotone increasing relationship, that is, the strain gauge deformation \(s_{x}\) increases with the increase of the jet flow. However, the trend of the strain gauge deformation increment \(\Delta s_{x}\) and the jet flow increment are different. The manifestation mode is that, as the jet flow increases, the influence of the jet flow increment on the increment of \(\Delta s_{x}\) gradually decreases. The reason for this phenomenon is that the greater the jet flow, the greater the impact it produces. Since the sensor and the base structure are arranged in a cantilever beam structure, the greater the deformation, the greater the displacement of point E, and the resulting increase in the relative displacement of the two points C and E decreases. The result is that the deformation of the sensor strain gauge is reduced. Above all, it can be inferred that in the jet impact direction, a linear system error is caused by the deformation of the base; the larger the jet flow, the greater the linear system error caused by the deformation of the base. The linear error can be reduced by increasing the stiffness of the base [26]. Figure 8: Relative displacement changing graph of sensor characteristic point under impacts of different momentum jets in the X direction. Figure 9: Relative displacement changing graph of sensor characteristic point under impacts of different momentum jets in the Y direction. As shown in Figures 9 and 10, the sensor strain gauge undergoes relative displacement and deformation in the Y direction under the action of the jet impact load. Within [0 ms, 5 ms], the displacement and deformation are basically 0. After 5 ms, it will continue to vibrate without stability. The vibration trend of strain gauge deformation is the same as the related analysis results in Section 3, and the amplitude of sensor strain gauge deformation \(s_{Y}\) in the Y direction is still smaller than \(s_{x}\), that is, \(s_{\rm x}>s_{\rm Y}\). The continuous periodic vibration in the Y direction causes the deformation of the sensor strain gauge in the Y direction to change periodically, and the error caused by \(s_{Y}\) is a periodic systematic error [26].