# 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 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.

## 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.

• On the hydraulic side, fluid compressibility is not taken into account.

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

## Dialog Box and Parameters

Hydraulic side piston area

Effective piston area on the hydraulic side. The default value is `20e-4` m^2.

Pneumatic side piston area

Effective piston area on the pneumatic side. The default value is `10e-4` m^2.

Stroke

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

Initial position

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`.

Chamber dead volume on the pneumatic side. The default value is `0.1e-3` m^3.

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.

Initial pressure (absolute)

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

Initial temperature

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

## 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.

`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.

`E`

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