# Pneumo-Hydraulic Actuator

Double-acting cylinder operated by hydraulic and pneumatic power

## Library

Hydraulic Cylinders

## Description

The Pneumo-Hydraulic Actuator block simulates a pneumo-hydraulic actuator, implemented as a double-acting cylinder with one side connected to a hydraulic power supply and another side operated by pneumatic power. Such devices are widely used as pneumo-hydraulic pumps, intensifiers, and converters of various types. The following illustration shows a few examples of the pneumo-hydralic actuator: a) with rigid separator; b) with flexible separator; c) pneumo-hydraulic intensifier.

The block provides two main modeling variants, accessible by right-clicking the block in your block diagram and then selecting the appropriate option from the context menu, under Simscape > Block choices:

• One mechanical port — Use this variant to model just the load on the piston. In this case, the cylinder is assumed to be grounded.

• Two mechanical ports — Use this variant to model the load on the actuator cylinder, as well as the piston. This variant also lets you include liquid compressibility on the hydraulic side of the actuator.

### Configuration with One Mechanical Port

Use this variant of the block when the load is applied only to the piston and the cylinder clamping structure is grounded. The hydraulic part of the model accounts only for fluid consumption associated with the piston velocity. The pneumatic part of the model is built with the ideal gas relationships. To simulate the limit on the piston motion, the hard stop is included in the model. The piston effective area is assumed to be constant. As a result, the model is described with the following equations:

`${q}_{H}={A}_{H}\cdot v$`
`${F}_{H}={A}_{H}\cdot p$`
`${F}_{P}={A}_{P}\cdot p$`

`${F}_{H}={F}_{P}+{F}_{HS}+{F}_{L}$`
`$v=\frac{dx}{dt}$`
`${V}_{P}={V}_{0}+{A}_{P}\cdot \left(stroke-x\right)$`
`$G=\frac{{V}_{P}}{RT}\left(\frac{dp}{dt}-\frac{p}{T}\frac{dT}{dt}\right)-\frac{{A}_{P}}{RT}p\cdot v$`
`${Q}_{P}=\frac{{c}_{v}\cdot {V}_{P}}{R}\frac{dp}{dt}-\frac{{c}_{p}\cdot {A}_{P}}{R}p\cdot v+{Q}_{HE}$`

where

 qH Hydraulic volumetric flow rate p Pressure in the actuator chambers AH Hydraulic side effective area AP Pneumatic side effective area v Piston velocity FH Force developed by piston on hydraulic side FP Force developed by piston on pneumatic side FHS Hard stop force FL Force developed by external load connected to port L K Hard stop stiffness D Hard stop damping stroke Piston stroke x Piston displacement VP Chamber volume on pneumatic side V0 Chamber dead volume on pneumatic side G Gas mass flow rate R Gas constant T Gas absolute temperature QP Heat flow through the pneumatic chamber cv Gas specific heat at constant volume cp Gas specific heat at constant pressure QHE Heat flow through the thermal port E

The model is suitable for building pneumo-hydraulic or hydro-pneumatic pumps, intensifiers, and similar devices. You can simulate piston loading (such as inertia, springs, friction) by modeling the load externally and connecting it to port L. Similarly, simulate the heat exchange with the environment through the external thermal port E, which corresponds to the gas in the chamber. Use blocks from the Simscape™ Foundation library, such as the Convective Heat Transfer, Conductive Heat Transfer, Thermal Mass, and so on, depending on the actual system configuration.

Port P is the pneumatic conserving port associated with the pneumatic side of the actuator. Port H is the hydraulic conserving port associated with the hydraulic inlet.

The block directionality assumes that pressure in the hydraulic chamber causes the piston to move in the positive direction, while pressure in the pneumatic chamber tends to move the piston in the negative direction. Flow rates are considered positive if they flow into the actuator.

### Configuration with Two Mechanical Ports

This variant of the block is suitable when the forces on both piston and cylinder are considered. This is a composite component and is built of the following blocks from the Simscape Foundation library:

• Translational Hydro-Mechanical Converter

• Pneumatic Piston Chamber

• Translational Hard Stop

Connections R and C are mechanical translational ports corresponding to the cylinder rod and cylinder clamping structure, respectively. Connection H is a hydraulic conserving port that is connected to the hydraulic Translational Hydro-Mechanical Converter. Connection P is a pneumatic conserving port that is connected to the pneumatic port of the Pneumatic Piston Chamber block. Connection E is a thermal conserving port associated with the gas in the pneumatic chamber. The fluid pressure, either on the hydraulic or pneumatic side, is transformed into mechanical energy through the converter. The piston (rod) motion is limited with the mechanical Translational Hard Stop block in such a way that the rod can travel only between cylinder caps. The fluid compressibility can also be taken into account on the hydraulic side.

You can control the block directionality using the Converter orientation parameter. If the Converter orientation is set to `Act in positive direction`, the pressure in the hydraulic chamber causes the piston to move in the positive direction, while the pressure in the pneumatic chamber tends to move the piston in the negative direction. Flow rates are considered positive if they flow into the actuator.

## Basic Assumptions and Limitations

• The effective piston area in each chamber is assumed to be constant.

• The leakage flow between chambers is assumed to be negligible because pressures in the chambers are equal.

• In One mechanical port configuration, on the hydraulic side, fluid compressibility is not taken into account. However, in Two mechanical ports configuration, you have an option to include fluid compressibility by setting the Compressibility parameter to `On`.

• On the pneumatic side, the mass flow rate and heat flow computations assume that the gas is ideal.

• In One mechanical port configuration, the cylinder is always assumed be grounded.

• In Two mechanical ports configuration, no loading on piston rod, such as inertia, friction, spring, and so on, is taken into account. If necessary, you can easily add them by connecting an appropriate building block to cylinder port R.

## Dialog Box and Parameters

### Hydraulic Side Tab

Hydraulic side piston area

Effective piston area on the hydraulic side. The default value is `2e-3` m^2.

Stroke

Piston maximum travel between caps. The default value is `0.2` m.

Piston initial distance from hydraulic port H

The distance between the piston and the cap on the hydraulic side at the beginning of simulation. This value cannot exceed the piston stroke. The default value is `0`.

Compressibility

This parameter is visible only in the Two mechanical ports configuration. Specifies whether fluid density on the hydraulic side is taken as constant or varying with pressure. The default value is `Off`, in which case the block models an ideal transducer. If you select `On`, the block dialog box displays additional parameters that let you model dynamic variations of the liquid density without adding any extra blocks.

This parameter is visible only when the Compressibility parameter is set to `On`. Fluid volume in hydraulic chamber that remains in the chamber after the rod is fully retracted. The default value is `1e-4` m^3.

Specific heat ratio

This parameter is visible only when the Compressibility parameter is set to `On`. Gas-specific heat ratio. The default value is `1.4`.

Initial liquid pressure (relative)

This parameter is visible only when the Compressibility parameter is set to `On`. The initial relative pressure of fluid in the hydraulic converter. This parameter specifies the initial condition for use in block's initial state at the beginning of a simulation run. The default value is `0`.

Converter orientation

This parameter is visible only in the Two mechanical ports configuration. Specifies hydraulic cylinder orientation with respect to the globally assigned positive direction. The cylinder can be installed in two different ways, depending upon whether it exerts force in the positive or in the negative direction when pressure is applied at its inlet. If pressure applied at port H exerts force in negative direction, set the parameter to ```Acts in negative direction```. The default value is ```Acts in positive direction```.

### Pneumatic Side Tab

Pneumatic side piston area

Effective piston area on the pneumatic side. The default value is `1e-3` m^2.

Gas volume in pneumatic chamber that remains in the chamber after the rod is fully retracted. The default value is `1e-4` m^3.

Initial gas pressure (absolute)

The initial absolute gas pressure in the pneumatic chamber. The default value is `101325` Pa.

Initial gas temperature

The initial gas temperature in the pneumatic chamber. The default value is `293.15` K.

### Hard Stop Tab

Hard stop stiffness

The hard stop model implemented in the block assumes that the stop resists penetration of the piston with force proportional to the penetration. This parameter sets the stiffness of the contact between the stop and the piston. The default value is `1e6` N/m.

Hard stop damping

The damping in the hard stop model accounts for dissipation in the piston-stop contact. The default value is `150` N*s/m.

## Ports

The block has the following ports:

`H`

Hydraulic conserving port associated with the actuator hydraulic chamber.

`P`

Pneumatic conserving port associated with the actuator pneumatic chamber.

`E`

Thermal conserving port associated with the gas in the pneumatic chamber. You can simulate the heat exchange with the environment through this port.

`L`

Mechanical translational conserving port associated with the actuator piston. You can model the load on the piston, such as external force, inertia, friction, or spring, and connect it through this port.

`R`

Mechanical translational conserving port associated with the actuator clamping structure, which is exposed by selecting the Two mechanical ports variant. You can model the load on the actuator casing through this port.