# Counterbalance Valve

Hydraulic counterbalance valve

## Library

Flow Control Valves

## Description

Counterbalance valves are used in hydraulic systems working with overriding (running-away) or suspended load. They are designed to create backpressure at the return line of the actuator to prevent losing control over the load. The following illustration shows a counterbalance valve schematic.

If a directional valve (not shown in the picture) is shifted into position that lowers the load, then the fluid from the rod chamber of the cylinder can exit only if pressure at port P (pilot pressure) and port L (load pressure) create enough force to overcome the spring force and open the valve. In statics, the valve is described with the equation

 ${F}_{0}+c\cdot x={p}_{pilot}\cdot {A}_{pilot}+{p}_{load}\cdot {A}_{load}-{p}_{back}\cdot {A}_{back}$ (1-5)

where

 F0 Spring setting c Spring rate x Valve opening ppilot Pilot pressure (pressure at port P) pload Load pressure (pressure at port L) pback Backpressure (pressure at return port B) Apilot Valve effective area at pilot port P Aload Valve effective area at load port L Aback Valve effective area at return port B

Counterbalance valve, classified by type, is an internally-externally piloted valve because both the pilot pressure and the load pressure tend to open the valve. After minor rearrangements, Equation 1-5 takes the form

 ${p}_{set}+{c}_{p}\cdot x={p}_{pilot}\cdot {k}_{pilot}+{p}_{load}-{p}_{back}\cdot {k}_{back}$ (1-6)
`$\begin{array}{l}{p}_{set}={F}_{0}/{A}_{load}\\ {c}_{p}=c/{A}_{load}\\ {k}_{pilot}={A}_{pilot}/{A}_{load}\\ {k}_{back}={A}_{back}/{A}_{load}\end{array}$`

where

 pset Valve pressure setting cp Spring pressure stiffness (Pa/m) x Valve opening kpilot Pilot ratio kback Backpressure ratio

The valve displacement is determined from Equation 1-6

 $x=\frac{{p}_{pilot}\cdot {k}_{pilot}+{p}_{load}-{p}_{back}\cdot {k}_{back}-{p}_{set}}{{c}_{p}}$ (1-7)
`$0\le x\le {x}_{max}$`

where xmax is the maximum valve displacement.

The Counterbalance Valve block can be represented as the following structural model.

The pressure sensors measure pressure at respective ports and convey their values to the Fcn block, which, together with the PS Saturation block, performs calculations in accordance with Equation 1-7. The valve displacement is passed through the first order lag block, built of the PS Subtract, PS Gain, and PS Integrator blocks, to account for valve dynamics. The gain of the PS Gain block is set to 1/T, where T is the time constant. The Variable Orifice and Check Valve blocks simulate the counterbalance valve orifice and check valve. In the actual Counterbalance Valve block model, the operations performed by the sensors and the Fcn block are executed in the block equation section.

The Counterbalance Valve block is essentially a data-sheet-based model. Depending on data listed in the manufacturer's catalogs or data sheets for your particular valve, you can choose one of the following model parameterization options:

• `By maximum area and opening` — Use this option if the data sheet provides only the orifice maximum area and the control member maximum stroke.

• `By area vs. opening table` — Use this option if the catalog or data sheet provides a table of the orifice passage area based on the control member displacement.

In the latter case, the PS Saturation block in the structural model is replaced with the PS Lookup Table (1D) block, and you can choose from three interpolation and two extrapolation methods.

Connections L and B are hydraulic conserving ports associated with the load and backpressure ports of the valve. The hydraulic conserving port P is associated with the pilot port. The block positive direction is from port L to port B. Positive pressure at port P opens the valve.

## Assumptions and Limitations

• Valve dynamics are approximated by introducing the first order lag between the pressure sensors and the variable orifice control member displacement.

• Inertia, friction, or hydraulic forces acting on the valve control member are not taken into account.

## Parameters

### Basic Parameters Tab

Valve pressure setting

The parameter specifies the pressure at port L necessary to start opening the valve. The setting is controlled with the valve spring. The default value is `50e5` Pa.

Valve spring stiffness

The valve spring pressure stiffness cp. The default value is `1e8` Pa/m.

Pilot ratio

The ratio between the effective areas of the control member face in the pilot chamber and in the load chamber. This is one of the fundamental valve characteristics in a catalog or data sheet. The default value is `3`.

Backpressure ratio

The ratio between the effective area of the control member, onto which the backpressure acts, and the load chamber valve area. There is a wide variety of counterbalance valves with compensated or partially-compensated backpressure. The parameter can take zero value if the valve is completely compensated. The default value is `4`.

Time constant

The valve dynamics are approximated with the first order lag. This parameter is the time constant of the lag. The default value is `0.06` s.

Leakage area

The total area of possible leaks in the completely closed orifice and check valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the orifice or check valve is completely closed. The parameter value must be greater than 0. The default value is `1e-9` m^2.

### Variable Orifice Tab

Variable orifice parameterization

Select one of the following methods for specifying the orifice:

• `By maximum area and opening` — Provide values for the maximum orifice area and the maximum orifice opening. The passage area is linearly dependent on the control member displacement, that is, the orifice is closed at the initial position of the control member (zero displacement), and the maximum opening takes place at the maximum displacement. This is the default method.

• `By area vs. opening table` — Provide tabulated data of orifice openings and corresponding orifice areas. The passage area is determined by one-dimensional table lookup. You have a choice of two interpolation methods and two extrapolation methods.

Orifice maximum area

Specify the area of a fully opened orifice. The parameter value must be greater than zero. The default value is `8e-5` m^2. This parameter is used if Variable orifice parameterization is set to `By maximum area and opening`.

Orifice maximum opening

Specify the maximum displacement of the control member. The parameter value must be greater than zero. The default value is `5e-4` m. This parameter is used if Variable orifice parameterization is set to `By maximum area and opening`.

Orifice flow discharge coefficient

Semi-empirical parameter for orifice capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is `0.7`.

Orifice laminar transition specification

Select how the block transitions between the laminar and turbulent regimes:

• `Pressure ratio` — The transition from laminar to turbulent regime is smooth and depends on the value of the Orifice laminar flow pressure ratio parameter. This method provides better simulation robustness.

• `Reynolds number` — The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the Orifice critical Reynolds number parameter.

Orifice laminar flow pressure ratio

Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is `0.999`. This parameter is visible only if the Orifice laminar transition specification parameter is set to ```Pressure ratio```.

Orifice critical Reynolds number

The maximum Reynolds number for laminar flow. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is `12`. This parameter is visible only if the Orifice laminar transition specification parameter is set to `Reynolds number`.

Tabulated orifice openings

Specify the vector of input values for orifice openings as a one-dimensional array. The input values vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for smooth interpolation. The default values, in meters, are `[-2e-3,0,5e-3,15e-3]`. This parameter is used if Variable orifice parameterization is set to `By area vs. opening table`. Tabulated orifice openings values will be used together with Tabulated orifice area values for one-dimensional table lookup.

Tabulated orifice area

Specify the vector of orifice areas as a one-dimensional array. The vector must be of the same size as the orifice openings vector. All the values must be positive. The default values, in m^2, are `[1e-12,4e-12,1.e-5,1.02e-5]`. This parameter is used if Variable orifice parameterization is set to `By area vs. opening table`.

Interpolation method

This parameter is used if Variable orifice parameterization is set to `By area vs. opening table`. Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

• `Linear` — Select this option to get the best performance.

• `Smooth` — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

Extrapolation method

This parameter is used if Variable orifice parameterization is set to `By area vs. opening table`. Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

• `Linear` — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

### Check Valve Tab

Check valve maximum passage area

Valve passage maximum cross-sectional area. The default value is `1e-4` m^2.

Check valve cracking pressure

Pressure level at which the orifice of the valve starts to open. The default value is `3e4` Pa.

Check valve maximum opening pressure

Pressure differential across the valve needed to fully open the valve. Its value must be higher than the cracking pressure. The default value is `1.2e5` Pa.

Check valve flow discharge coefficient

Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is `0.7`.

Check valve laminar transition specification

Select how the block transitions between the laminar and turbulent regimes:

• `Pressure ratio` — The transition from laminar to turbulent regime is smooth and depends on the value of the Check valve laminar flow pressure ratio parameter. This method provides better simulation robustness.

• `Reynolds number` — The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the Check valve critical Reynolds number parameter.

Check valve laminar flow pressure ratio

Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is `0.999`. This parameter is visible only if the Check valve laminar transition specification parameter is set to ```Pressure ratio```.

Check valve critical Reynolds number

The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is `12`. This parameter is visible only if the Check valve laminar transition specification parameter is set to ```Reynolds number```.

## Global Parameters

Parameters determined by the type of working fluid:

• Fluid density

• Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

## Ports

The block has the following ports:

`P`

Hydraulic conserving port associated with the valve pilot port.

`L`

Hydraulic conserving port associated with the valve load port.

`B`

Hydraulic conserving port associated with the valve backpressure port.

## Examples

The Hydraulic Actuator with Counterbalance Valve example illustrates the use of counterbalance valve to balance the load of a double-acting cylinder controlled by an open-center 4-way directional valve.