*3.2. Variation of Main Frequency and Amplitude of Oscillation at Di*ff*erent Velocities*

It can be seen from the above section that the pressure oscillation at point 1 and point 2 of the nozzles are the most obvious. Since the flapper is in the zero position and the pressure on both sides of the flapper is the same when the velocity of investigation is affected, point 1 is chosen as the research object. The results are shown in Figures 7–10, where the figures of 20 times of l *g* "power spectrum density" are displayed, which show the "−5/3" slope of the frequency, much accorded with the k41 theory spectra distribution characteristic, which insures the simualtion results are turbulent, not numerical errors. After comparison, it can be found that the pressure fluctuation increases with the increase of velocity, and there is a positive correlation between them. However, with the increase in velocity, the relative oscillation amplitude of the pressure does not follow the positive correlation, but decreases with the increase of velocity. Thus, the higher the velocity of the nozzle, the pressure oscillation phase oscillation will occur. The lower the amplitude, it can be inferred that when the velocity is high enough, the pressure oscillation of the flapper will gradually disappear, and its oscillation will only occur in a certain velocity range. In addition, combined with the power spectrum, it can be determined that the peak frequency of the pressure decreases gradually with the increase of velocity. This is because, with the increase of velocity, the stronger the ability of the oil to maintain its original motion state before injecting the nozzle into the flapper, the smaller the tendency to develop into turbulence, and the smaller the flow field dissipation, and the smaller the oscillation frequency generated along with it. The relationship between pressure and the main frequency and velocity is shown in Figure 11.

(**c**) **Figure 7.** Pressure curves in time and frequency domains when the inlet velocity is 5 m/s. (**a**) Time domain. (**b**) Frequency domain. (**c**) 20logE frequency domain.

**Figure 8.** Pressure curves in time and frequency domains when the inlet velocity is 10 m/s. (**a**) Time domain. (**b**) Frequency domain. (**c**) 20logE frequency domain.

**Figure 9.** Pressure curves in time and frequency domains when the inlet velocity is 25 m/s. (**a**) Time domain. (**b**) Frequency domain. (**c**) 20logE frequency domain.

**Figure 10.** Pressure curves in time and frequency domains when the inlet velocity is 50 m/s. (**a**) Time domain. (**b**) Frequency domain. (**c**) 20logE frequency domain.

**Figure 11.** Pressure oscillation and main frequency of the flappers at different velocities.

*3.3. Variation of Main Frequency and Amplitude of Oscillation under Di*ff*erent Displacements*

Under different working conditions, the deflection angle of the flapper of the jet flapper servo valve is different, and the pressure on both sides of the flapper will also be different. Therefore, this section studies the pressure oscillation of the flappers under different displacements while keeping the inlet oil velocity unchanged. When the flapper is at the zero position, the distance between the flapper and the nozzles on both sides is 0.2 mm. The deflection displacement of each flapper is 0.05 mm, and it is in the right direction. Since the distance between the two sides of the flapper is different, the oil flow field on both sides is no longer the same, so in order to compare the pressure difference between the two sides, point 1 and point 2 in Figure 4 are used to observe. Since the flapper at zero point 1 is the same as point 2, only point 1 is selected, as shown in Figure 12, and its pressure oscillates near 0.57 MPa with the main pulsation frequency above 3000 Hz. In Figures 13–15, point 1 is closer to the nozzle than point 2, so its overall pressure relative to point 2 is higher, and as can be seen from the spectrum diagram, the pressure of point 1 is also higher. The frequency distribution of the force pulsation is relatively average, but there is a tendency to shift to low, while the pressure of point 2 is mainly high frequency, mainly over 2500 Hz. By analyzing the pressure oscillation curves, the relationship between the force acting on the flapper and the main frequency and the deflection distance of the flapper is obtained as shown in Figure 16. It can be seen that the smaller the distance between the nozzle and

the flapper, the stronger the pressure fluctuation, but the relative pressure fluctuation amplitude is positively correlated with the distance as a whole; the main frequency is also related to the distance: the larger the distance is, the greater the main frequency of the pressure oscillation will be. This is because as the distance between the nozzle and the baffle decreases, the fluid resistance of the variable throttle hole increases, the kinetic energy of oil converts into pressure energy increases, and the more hydraulic pressure is generated on the baffle; furthermore, as the distance increases, the greater the turbulence degree of the oil flowing through the nozzle, the greater the pressure oscillation effect of the fluid. This is why the main frequency increases.

**Figure 12.** Pressure oscillation curve of the flapper when the displacement of the flapper is *x* = 0.00 mm. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain.

**Figure 13.** Pressure oscillation curve of the flapper when the displacement of the flapper is *x* = 0.05 mm. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain. (**c**) Point 2 in the time domain. (**d**) Point 2 in the frequency domain.

**Figure 14.** Pressure oscillation curve of the flapper when the displacement of the flapper is *x* = 0.10 mm. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain. (**c**) Point 2 in the time domain. (**d**) Point 2 in the frequency domain.

**Figure 15.** Pressure oscillation curve of the flapper when the displacement of the flapper is *x* = 0.15 mm. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain. (**c**) Point 2 in the time domain. (**d**) Point 2 in the frequency domain.

**Figure 16.** Average pressure and main frequency of the flapper at different actual distances between the nozzle and flapper.
