Counter Balance Valve - MapleSim Help

Counter Balance Valve

Check valve and relief valve connected in parallel

Description

The Counter Balance Valve component is a check valve and a relief valve connected in parallel, which can be piloted internally, externally, or both internally and externally.

When pressure at port A is greater than the pressure at port B, the check valve orifice area is assumed to be a piecewise linear function of the pressure difference between port A and port B.

When pressure at port B is greater than the pressure at port A, the relief valve orifice area is assumed to be a piecewise linear function and will be affected by the pilot mode selected.

Based on the orifice area, the pressure vs. flow rate relationship is calculated by the formulation used in the Orifice component.

 Formulation Approaches Two approaches were taken for formulation of the flow equation inside the device. When the boolean parameter $\mathrm{Use constant Cd}$ is true, a constant coefficient of discharge (${C}_{d}$) is used, otherwise a variable coefficient of discharge with maximum value (${C}_{d\left(\mathrm{max}\right)}$) and a critical flow number (${\mathrm{Crit}}_{\mathrm{no}}$) are used.
 Optional Volumes The boolean parameters Use volume A and Use volume B, when true, add optional volumes ${V}_{A}$  and ${V}_{B}$ to ports A and B, respectively. See Port Volumes for details. If two orifices or valves are connected, enabling a volume at the common port reduces the stiffness of the system and improves the solvability.
 Equations $q={q}_{A}-{q}_{{V}_{A}}$ $\mathbf{Orifice Fluid Equations}$ $\left\{\begin{array}{cc}p=\frac{\mathrm{\pi }}{4}\frac{\mathrm{\rho }\mathrm{\nu }q}{{C}_{d}^{2}{A}_{\mathrm{cs}}\sqrt{\mathrm{\pi }{A}_{\mathrm{cs}}}}{\left(\frac{16{q}^{4}}{{\mathrm{\pi }}^{2}{A}_{\mathrm{cs}}^{2}{\mathrm{\nu }}^{4}}+{\mathrm{\Re }}_{\mathrm{Cr}}^{4}\right)}^{\frac{1}{4}}& \mathrm{Use constant Cd}=\mathrm{true}\\ q={C}_{d\left(\mathrm{max}\right)}\mathrm{tanh}\left(4\frac{\sqrt{\frac{{A}_{\mathrm{cs}}}{\mathrm{\pi }}\frac{2\left|p\right|}{\mathrm{\rho }}}}{\mathrm{\nu }{\mathrm{Crit}}_{\mathrm{no}}}\right){A}_{\mathrm{cs}}\sqrt{\frac{2\left|p\right|}{\mathrm{\rho }}}\mathrm{sign}\left(p\right)& \mathrm{otherwise}\end{array}$ ${p}_{\mathrm{tot}}=\left\{\begin{array}{cc}-{k}_{\mathrm{back}}{p}_{A}+{p}_{B}& \mathrm{mode}=\mathrm{Internal}\\ {k}_{\mathrm{pilot}}{p}_{C}-{k}_{\mathrm{back}}{p}_{A}& \mathrm{mode}=\mathrm{External}\\ {k}_{\mathrm{pilot}}{p}_{C}-{k}_{\mathrm{back}}{p}_{A}+{p}_{B}& \mathrm{otherwise}\end{array}$ $\left\{\begin{array}{cc}{q}_{C}=0& \mathrm{mode}\ne \mathrm{Internal}\\ {p}_{C}=0& \mathrm{otherwise}\end{array}$ $\left\{\begin{array}{cc}{A}_{\mathrm{cs}}={A}_{i}={A}_{t}& \mathrm{Exact}\\ \left\{{A}_{\mathrm{cs}}=\mathrm{min}\left({A}_{\mathrm{open}},\mathrm{max}\left({A}_{\mathrm{close}},{A}_{i}\right)\right),{t}_{c}\frac{\mathrm{d}{A}_{i}}{\mathrm{d}t}+{A}_{i}={A}_{t}\right\}& \mathrm{otherwise}\end{array}$ ${A}_{t}=\left\{\begin{array}{cc}\left\{\begin{array}{cc}{A}_{\mathrm{close}}& {p}_{\mathrm{tot}}<{p}_{\mathrm{close1}}\\ \left\{\begin{array}{cc}{A}_{\mathrm{close}}+\left({p}_{\mathrm{tot}}-{p}_{\mathrm{close1}}\right)\frac{{A}_{\mathrm{open1}}-{A}_{\mathrm{close}}}{{p}_{\mathrm{open1}}-{p}_{\mathrm{close1}}}& {p}_{\mathrm{tot}}<{p}_{\mathrm{open1}}\\ {A}_{\mathrm{open1}}& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}& p<0\\ \left\{\begin{array}{cc}{A}_{\mathrm{close}}& p\le {p}_{\mathrm{close2}}\\ \left\{\begin{array}{cc}{A}_{\mathrm{close}}+\left(p-{p}_{\mathrm{close2}}\right)\frac{{A}_{\mathrm{open2}}-{A}_{\mathrm{close}}}{{p}_{\mathrm{open2}}-{p}_{\mathrm{close2}}}& p\le {p}_{\mathrm{open2}}\\ {A}_{\mathrm{open2}}& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}$ $\mathbf{Optional Volume Equations}$ ${V}_{{f}_{A}}=\left\{\begin{array}{cc}\mathrm{Va}\left(1+\frac{{p}_{A}}{\mathrm{El}}\right)& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{V}_{{f}_{B}}=\left\{\begin{array}{cc}\mathrm{Vb}\left(1+\frac{{p}_{B}}{\mathrm{El}}\right)& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$ $q={q}_{A}-{q}_{{V}_{A}}=-\left({q}_{B}-{q}_{{V}_{B}}\right)$ ${q}_{{V}_{A}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{A}}}{\mathrm{d}t}& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{4.0ex}{0.0ex}}{q}_{{V}_{B}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{B}}}{\mathrm{d}t}& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $p$ $\mathrm{Pa}$ Pressure drop from A to B p $q$ $\frac{{m}^{3}}{s}$ Flow rate from port A to port B q ${q}_{\mathrm{VX}}$ $\frac{{m}^{3}}{s}$ Flow rate into port X's optional volume qVX ${V}_{{f}_{X}}$ ${m}^{3}$ Effective volume at port X VfX

Connections

 Name Description Modelica ID $\mathrm{portA}$ Upstream hydraulic port portA $\mathrm{portB}$ Downstream hydraulic port portB $\mathrm{portC}$ Hydraulic port for external pilot portC

Parameters

General

 Name Default Units Description Modelica ID $\mathrm{Use constant Cd}$ $\mathrm{true}$ True (checked) means a constant coefficient of discharge is implemented, otherwise a variable ${C}_{d}$ is used in flow calculation UseConstantCd ${C}_{d}$ $0.7$ Flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is true Cd ${\mathrm{\Re }}_{\mathrm{Cr}}$ $12$ Reynolds number at critical flow; used when $\mathrm{Use constant Cd}$ is true ReCr ${C}_{d\left(\mathrm{max}\right)}$ $0.7$ Maximum flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is false Cd_max ${\mathrm{Crit}}_{\mathrm{no}}$ $1000$ Critical flow number; used when $\mathrm{Use constant Cd}$ is false Crit_no

Check Valve Settings

 Name Default Units Description Modelica ID ${p}_{\mathrm{close}}$ $1.9·{10}^{4}$ $\mathrm{Pa}$ Pressure at which valve is fully closed ($A={A}_{\mathrm{close}}$) pclose2 ${p}_{\mathrm{open}}$ $2.05·{10}^{4}$ $\mathrm{Pa}$ Pressure at which valve is fully open ($A={A}_{\mathrm{open}}$) popen2 ${A}_{\mathrm{open}}$ $1·{10}^{-5}$ ${m}^{2}$ Valve area when fully open Aopen2

Leakage

 Name Default Units Description Modelica ID ${A}_{\mathrm{close}}$ $1·{10}^{-12}$ ${m}^{2}$ Valve area when closed (leakage) Aclose

Pilot

 Name Default Units Description Modelica ID $\mathrm{mode}$ Internal Pilot type mode

Pressure Ratios

 Name Default Units Description Modelica ID ${k}_{\mathrm{pilot}}$ $3$ Pilot ratio kp1 ${k}_{\mathrm{back}}$ $0$ Backpressure ratio kp2

Relief Settings

 Name Default Units Description Modelica ID ${p}_{\mathrm{close}}$ $1.9·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully closed (A = Aclose) pclose1 ${p}_{\mathrm{open}}$ $2.05·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully open (A = Aopen) popen1 ${A}_{\mathrm{open}}$ $1·{10}^{-5}$ ${m}^{2}$ Valve area when fully open Aopen1

Valve Dynamics

 Name Default Units Description Modelica ID $\mathrm{Exact}$ $\mathrm{false}$ True (checked) means a first-order dynamics is used for the valve area Exact ${t}_{c}$ $0.1$ $s$ Time constant tc

Optional Volumes

 Name Default Units Description Modelica ID $\mathrm{Use volume A}$ $\mathrm{false}$ True (checked) means a hydraulic volume chamber is added to portA useVolumeA ${V}_{A}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber A Va $\mathrm{Use volume B}$ $\mathrm{false}$ True (checked) means a hydraulic volume chamber is added to portB useVolumeB ${V}_{B}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber B Vb

 Name Units Description Modelica ID $\mathrm{\nu }$ $\frac{{m}^{2}}{s}$ Kinematic viscosity of fluid nu $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density of fluid rho $\mathrm{El}$ $\mathrm{Pa}$ Bulk modulus of fluid El