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The VCCM equation is a good test.
[TEX]
v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }
[/TEX]
[LaTex]
v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }
[/LaTex]
\[
v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }
\]
v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }
\begin{equation}
v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }
\end{equation}
I couldn't find an option that would allow me to paste the VCCM equation into my post. On our forum there is a button like those in the advanced editor that allows adding LaTex or Mathml equations. They are like the code, html and php buttons in the advance editor.
I tried many options and none work.
The VCCM equation is handy for computing the maximum steady state speed of a hydraulic servo system. In reality the value calculated for the maximum steady state velocity must be reduced some what because the supply pressure usually drops during motion.
[latex]v_{ ss }=K_{ vpl }\sqrt { \frac { P_{ s }\cdot A_{ pe }-F_{ l } }{ A_{ pe }^{ 3 }\cdot (1+\frac { { \rho }_{ v }^{ 2 } }{ { \rho }_{ c }^{ 3 } } ) } }[/latex]
Where:
[latex]v_{ ss }[/latex] is the maximum steady state velocity
[latex]K_{ vpl }[/latex] is the valve flow constant computed from the valve specifications.
[latex]P_{ s }[/latex] is the supply pressure
[latex]A_{ pe }[/latex] is the area of the powered or pushing side of the piston.
[latex]F_{ l }[/latex] is the load force. Subtract if opposing motion, add if aiding motion.
[latex]{ \rho }_{ v }[/latex] is the ratio of the flow constant of the power land to the exhausting land. Normally valves are symmetrical so [latex]{ \rho }_{ v }=1[/latex]
[latex]{ \rho }_{ c }[/latex] is the ratio of the piston's pushing area to the side that is exhausting.
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