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Counterbalance Valve

Check valve and relief valve connected in parallel

Description

The Counterbalance 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
	One of two approaches can be selected for modeling the flow in the device. When the boolean parameter $Use constant Cd$ is true, a constant coefficient of discharge ( $C_{d}$ ) is used, otherwise a variable coefficient of discharge with maximum value ( $C_{d (\max)}$ ) and a critical flow number ( ${Crit}_{no}$ ) 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

$q = q_{A} - q_{V_{A}}$

$Orifice Fluid Equations$

${\begin{array}{c} p = \frac{π}{4} \frac{ρ ν q}{C_{d}^{2} A_{cs} \sqrt{π A_{cs}}} {(\frac{16 q^{4}}{π^{2} A_{cs}^{2} ν^{4}} + {Re}_{Cr}^{4})}^{\frac{1}{4}} & Use constant Cd = true \\ q = C_{d (\max)} \tanh (4 \frac{\sqrt{\frac{A_{cs}}{π} \frac{2 |p|}{ρ}}}{ν {Crit}_{no}}) A_{cs} \sqrt{\frac{2 |p|}{ρ}} sign (p) & otherwise \end{array}$

$p_{tot} = {\begin{array}{c} - k_{back} p_{A} + p_{B} & mode = Internal \\ k_{pilot} p_{C} - k_{back} p_{A} & mode = External \\ k_{pilot} p_{C} - k_{back} p_{A} + p_{B} & otherwise \end{array}$

${\begin{array}{c} q_{C} = 0 & mode \neq Internal \\ p_{C} = 0 & otherwise \end{array}$

${\begin{array}{c} A_{cs} = A_{i} = A_{t} & Exact \\ \{A_{cs} = \min (A_{open}, \max (A_{close}, A_{i})), t_{c} \frac{d A_{i}}{d t} + A_{i} = A_{t}\} & otherwise \end{array}$

$A_{t} = {\begin{array}{c} {\begin{array}{c} A_{close} & p_{tot} < p_{close1} \\ A_{close} + (A_{open1} - A_{close}) SmoothTrans (S, \frac{p_{tot} - p_{close1}}{p_{open1} - p_{close1}}) & p_{tot} < p_{open1} \\ A_{open1} & otherwise \end{array} & p < 0 \\ {\begin{array}{c} A_{close} & p \leq p_{close2} \\ A_{close} + (A_{open2} - A_{close}) SmoothTrans (S, \frac{p - p_{close2}}{p_{open2} - p_{close2}}) & p < p_{open2} \\ A_{open2} & otherwise \end{array} & otherwise \end{array}$

$S = {\begin{array}{c} smoothness & smoothTransition \\ 0 & otherwise \end{array}$

$Optional Volume Equations$

$V_{f_{A}} = {\begin{array}{c} Va (1 + \frac{p_{A}}{El}) & Use volume A = true \\ 0 & otherwise \end{array} V_{f_{B}} = {\begin{array}{c} Vb (1 + \frac{p_{B}}{El}) & Use volume B = true \\ 0 & otherwise \end{array}$

$q = q_{A} - q_{V_{A}} = - (q_{B} - q_{V_{B}})$

$q_{V_{A}} = {\begin{array}{c} \frac{d V_{f_{A}}}{d t} & Use volume A = true \\ 0 & otherwise \end{array} q_{V_{B}} = {\begin{array}{c} \frac{d V_{f_{B}}}{d t} & Use volume B = true \\ 0 & otherwise \end{array}$

Variables

Name	Units	Description	Modelica ID
$p$	$Pa$	Pressure drop from A to B	p
$q$	$\frac{m^{3}}{s}$	Flow rate from port A to port B	q
$q_{V_{X}}$	$\frac{m^{3}}{s}$	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
$portA$	Upstream hydraulic port	portA
$portB$	Downstream hydraulic port	portB
$portC$	Hydraulic port for external pilot	portC

Parameters

General

Name	Default	Units	Description	Modelica ID
$Smooth Transition$	$false$		True (checked) means enable the smoothness factor	smoothTransition
$smoothness$	$0.5$		Smoothness factor (0: sharpest, 1: smoothest); used when $Smooth Transition$ is enabled	smoothness

Orifice

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

Check Valve Settings

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

Leakage

Name	Default	Units	Description	Modelica ID
$A_{close}$	$1 \cdot 10^{−12}$	$m^{2}$	Valve area when closed (leakage)	Aclose

Pilot

Name	Default	Units	Description	Modelica ID
$mode$	Internal		Pilot type	mode

Pressure Ratios

Name	Default	Units	Description	Modelica ID
$k_{pilot}$	$3$		Pilot ratio	kp1
$k_{back}$	$0$		Backpressure ratio	kp2

Relief Settings

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

Valve Dynamics

Name	Default	Units	Description	Modelica ID
$Exact$	$false$		True (checked) means first-order dynamics are used for the valve area	Exact
$t_{c}$	$0.1$	$s$	Time constant	tc

Optional Volumes

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

For more information see Port Volumes.

Fluid Parameters

The following parameters, used in the equations, are properties of the Hydraulic System Properties component used in the model.

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

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