Table 1 Physical meanings and expressions of K_n

K_A

Pressure-flow coefficient of main exit port.

\(K_{{\text{A}}} = C_{{{\text{d}}1}} {\uppi }d_{1} \sin \alpha y_{{\text{x}}} \sqrt {\frac{1}{{2\rho p_{{{\text{sx}}}} }}}\)

K_B

Flow gain of main exit port.

\(K_{{\text{B}}} = C_{{{\text{d1}}}} {\uppi }d_{1} \sin \alpha \sqrt {\frac{{2p_{{{\text{sx}}}} }}{\rho }}\)

K_C

Hydraulic conductivity of orifice R₁.

\(K_{{\text{C}}} = \frac{{{\uppi }d_{{{\text{r1}}}}^{2} }}{4}C_{{{\text{r1}}}} \sqrt {\frac{1}{{2\rho \left( {p_{{{\text{sx}}}} - p_{{{\text{cx}}}} } \right)}}}\)

K_D

Equivalent stiffness of steady hydrodynamic force of the main valve.

\(K_{{\text{D}}} = C_{{{\text{d1}}}} C_{{{\text{v1}}}} {\uppi }d_{{1}} \sin \left( {2\alpha } \right)\)

K_E

Pressure-flow coefficient of pilot port.

\(K_{{\text{E}}} = C_{{{\text{d2}}}} {\uppi }d_{2} x_{{\text{x}}} \sin \beta \sqrt {\frac{1}{{2\rho p_{{{\text{cx}}}} }}}\)

K_F

Flow gain of pilot port.

\(K_{{\text{F}}} = C_{{{\text{d2}}}} {\uppi }d_{2} \sin \beta \sqrt {\frac{{2p_{{{\text{cx}}}} }}{\rho }}\)

K_G

Equivalent stiffness of Steady hydrodynamic force of the pilot valve.

\(K_{{\text{G}}} = C_{{{\text{d2}}}} C_{{{\text{v2}}}} {\uppi }d_{{2}} \sin \left( {2\beta } \right)\)

G_r

Hydraulic conductivity of orifice R₂.

\(G_{{\text{r}}} = \frac{{{\uppi }d_{{{\text{r2}}}}^{4} }}{{128\mu l_{{{\text{r}}2}} }}\)