## 5 Results and Discussion
### Variations in Internal Parameters  
The variations in the gas-oil emulsion properties and dynamic seal friction parameters of the considered HPS system were determined using the established model and the experimental data, in order to reveal the latent contributions of the temperature and excitation frequency during HPS operation. The gas volume fraction within the emulsion affected not only the free gas volume but also the mass and bulk modulus of the generated gas-oil emulsion, as indicated in Equations (10) and (11), respectively. The discharge coefficients of the check valve and bleed orifice in Equation (12) determines the fluid flow between the HPS chambers and the resultant hydraulic damping property. Variations in the Coulomb friction, peak friction, Stribeck coefficient, and transition velocity, as explained in Equation (3), can also be determined. The gas volume fractions at different temperatures and excitation frequencies are shown in Figure 10a. The increased temperature and/or frequency tended to increase the gas fraction within the oil, which implied more entrapped gas within the hydraulic oil (Figure 1a). More frequent operation of the HPS could thus accelerate the gas-oil mixing, which could be attributed to the faster oscillation of gas-oil interface in the piston-side chamber and the more frequent fluid flow between the two chambers. The increased temperature decreased the bulk modulus and viscosity of hydraulic oil [35], which might also facilitate the formulation of the gas-oil emulsion. As derived in Equation (9), a lower bulk modulus can lead to an increased gas volume fraction at a given pressure, while the effect of temperature is relatively less at a relatively lower frequency. An increase of 10 \({}^{\circ}\)C in temperature led to approximately a 1% increase in the gas volume fraction near the excitation frequency of 2 Hz, and it was approximately 2% from 4 Hz to 8 Hz. At the temperature of 50 \({}^{\circ}\)C, the increase in the excitation frequency from 0.5 Hz to 8 Hz led to approximately a 100% increase in the gas volume fraction within the HPS. Figure 10: Variations in fluid properties: (**a**) gas fraction within the emulsion, (**b**) discharge coefficients of bleed orifice and check valve. Figure 10b illustrates the variations in discharge coefficients of the bleed orifice and check valve. The discharge coefficient of the bleed orifice was generally higher than that of the check valve, irrespective of the temperature and excitation frequency, which was attributed to the relatively simpler structure of bleed orifices, as seen in Figure 1a. The discharge coefficients tended to decrease with the increasing excitation frequency and saturate after approximately 3 Hz, especially for the bleed orifice (approximately a 7% decrease). The discharge coefficient of the check valve was observed to be more sensitive to temperature variation. The increase in temperature resulted in negligible variation in the discharge coefficient of the bleed orifice, while the discharge coefficient of the check valve increased with the temperature, for all the considered excitation frequencies. The increase from 30 \({}^{\circ}\)C to 50 \({}^{\circ}\)C at the excitation frequency of 1 Hz led to approximately an 11% increase in the discharge coefficient of the check valve, which might be attributed to the decreased fluid viscosity and thereby less flow energy loss through the check valve. The variations in dynamic seal friction properties, namely, the Coulomb friction, peak friction, Stribeck coefficient, and transition velocity during the compression and extension strokes, are illustrated in Figure 11a-d, respectively. The Coulomb friction during compression was generally greater than that during extension stroke, especially for a relatively higher temperature. This was attributed to the asymmetric shape design of the fluid seals and dust seals, as illustrated in Figure 1c.