Single-Acting Actuator (IL)

Single-acting linear actuator in an isothermal liquid system

Since R2020a

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Libraries:
Simscape / Fluids / Isothermal Liquid / Actuators

Description

The Single-Acting Actuator (IL) block represents an actuator that converts the liquid pressure at port A into a mechanical force at port R via an extending-retracting piston. The piston motion is limited by a hard stop model. When the piston position is calculated internally, it is reported at port p, and when the position is set by a connection to a Simscape™ Multibody™ joint, it is received as a physical signal at port p.

The Initial piston displacement, Fluid dynamic compressibility, and reference environmental pressure can be modified. Fluid and mechanical inertia are not modeled.

Displacement

The piston displacement is measured as the position at port R relative to port C. The Mechanical orientation identifies the direction of piston displacement. The piston displacement is neutral, or 0, when the chamber volume is equal to the Dead volume. When displacement is received as an input, ensure that the derivative of the position is equal to the piston velocity. This is automatically the case when the input is received from a Translational Multibody Interface block connection to a Simscape Multibody joint.

Hard Stop Model

Four models are available to model the extension limit of the actuator piston. This block uses a similar formulation as the Translational Hard Stop block and models uniform damping and stiffness coefficients at both ends of the piston stroke. For more information on the hard stop model options, see the Translational Hard Stop block.

The hard stop force is modeled when the piston is at its upper or lower bound. The boundary region is within the Transition region of the Piston stroke or Piston initial displacement. Outside of this region, $$F_{HardStop}=0.$$

Cushion

The block can model cushioning toward the extremes of the piston stroke. Select Cylinder end cushioning to slow the piston motion as it approaches the maximum extension, defined by the Piston stroke parameter. For more information on the functionality of a cylinder cushion, see the Cylinder Cushion (IL) block.

Friction

The block can model friction against piston motion. When you select Cylinder friction, the resulting friction is a combination of the Stribeck, Coulomb, and viscous effects. The block measures the pressure difference between the chamber pressure and the environment pressure. For more information on the friction model and its limitations, see the Cylinder Friction (IL) block.

Leakage

You can optionally model leakage between the liquid chamber and the piston reservoir. When you select Leakage, Poiseuille flow is modeled between the piston and cylinder. This block uses the Simscape Foundation Library Laminar Leakage (IL) block. The flow rate is calculated as:

$$\dot{m}=\frac{\frac{\pi }{128}\left(d_0^4-d_i^4-\frac{{\left(d_0^2-d_i^2\right)}^2}{\log (d_0/d_i)}\right)}{\upsilon L}\left(p_A-p_{env}\right),$$

where:

• ν is the fluid kinematic viscosity.

• L is the piston length, p – P₀.

• p_A is the pressure at port A.

• p_env is the environmental pressure, which is selected in the Environment pressure specification parameter.

The cylinder diameter, d₀, is $$d_0=d_i+2c,$$ where c is the Piston-cylinder clearance, and the piston diameter, d_i, is $$d_i=\sqrt{\frac{4A_P}{\pi }},$$ where A_P is the Piston cross-sectional area.

Numerically-Smoothed Area and Pressure

You can maintain numerical robustness in your simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smooths the cushion orifice area and the check valve pressure range. The orifice area is smoothly saturated between the Leakage area between plunger and cushion sleeve and Cushion plunger cross-sectional area parameters while the valve pressure is saturated between the Check valve cracking pressure differential and Check valve maximum pressure differential parameters. For more information, see Numerical Smoothing.

Block Sub-Components

The Single-Acting Actuator (IL) block comprises four Simscape Foundation and two Fluids Library blocks:

• Translational Hard Stop

• Laminar Leakage (IL)

• Translational Mechanical Converter (IL)

• Ideal Translational Motion Sensor

• Cylinder Cushion (IL)

• Cylinder Friction (IL)

Actuator Structural Diagram

Examples

Closed-Circuit Hydraulic Actuator

A closed-circuit hydraulic actuator driven by a variable-speed pump. The actuator is arranged as a closed fluid system with two replenishment valves (check valves) and a spring-loaded accumulator serving as a replenishment reservoir. The pump speed is controlled by the difference between the commanded and measured piston position. The actuator acts against a spring, a damper, and a time-varying load.

• Open Model

Drill-Ream Actuator

An actuator that drives a machine tool working unit performing a sequence of three technological operations: coarse drilling, fine drilling, and reaming. The actuator speed is controlled by one of three pressure-compensated flow control valves metering out return flow from the cylinder. The selection of an appropriate flow control is performed by directional valves that are activated by a control unit.

• Open Model

Front-Loader Actuation System

A simplified version of an actuation system consisting of the lift and tilt cylinders. Each cylinder is controlled by an open center, 6-way, 3-position directional valve. The valves are connected in series through their unloading branch such that the system pump is unloaded when both command levers are in neutral position. If either tilt or lift command is applied, the unloading path is closed.

• Open Model

Ports

Input

p — Multibody piston position input, m

physical signal

Physical signal input port associated with the piston position, in m. Connect this port to a Simscape Multibody block.

Dependencies

To enable this port, set Piston displacement to Provide input signal from Multibody joint.

Output

p — Piston position, m

physical signal

Piston position in m, returned as a physical signal.

Dependencies

To expose this port, set Piston displacement to Calculate from velocity of port R relative to port C.

Conserving

A — Liquid port

isothermal liquid

Thermal liquid conserving port associated with chamber A.

C — Actuator casing

translational mechanical

Translational mechanical conserving port associated with the actuator casing.

R — Actuator piston

translational mechanical

Translational mechanical conserving port associated with the actuator piston.

Parameters

Actuator

Mechanical orientation — Piston displacement direction

Pressure at A causes positive displacement of R relative to C (default) | Pressure at A causes negative displacement of R relative to C

Sets the piston displacement direction. When you set this parameter to:

• Pressure at A causes positive displacement of R relative to C the piston displacement is positive when the volume of liquid at port A is expanding. This corresponds to rod extension.

• Pressure at A causes negative displacement of R relative to C the piston displacement is negative when the volume of liquid at port A is expanding. This corresponds to rod contraction.

Piston cross-sectional area — Cross-sectional area of piston rod

0.01 m^2 (default) | positive scalar

Cross-sectional area of the piston rod.

Piston stroke — Maximum piston travel distance

0.1m (default) | positive scalar

Maximum piston travel distance.

Dead volume — Fluid volume at full piston retraction

1e-5 m^3 (default) | positive scalar

Volume of liquid when the piston displacement is 0. This is the liquid volume when the piston is up against the actuator end cap.

Environment pressure specification — Reference environment pressure

Atmospheric pressure (default) | Specified pressure

Environment reference pressure. The Atmospheric pressure option sets the environmental pressure to 0.101325 MPa.

Environment pressure — User-defined environmental pressure

0.101325 MPa (default) | positive scalar

User-defined environmental pressure.

Dependencies

To enable this parameter, set Environment pressure specification to Specified pressure.

Hard Stop

Hard stop model — Select the hard stop model

Stiffness and damping applied smoothly through transition region, damped rebound (default) | Full stiffness and damping applied at bounds, undamped rebound | Full stiffness and damping applied at bounds, damped rebound | Based on coefficient of restitution

Model choice for the force on the piston at full extension or full retraction. See the Translational Hard Stop block for more information.

Hard-stop stiffness coefficient — Stiffness coefficient

1e10 N/m (default) | positive scalar

Piston stiffness coefficient.

Dependencies

To enable this parameter, set Hard stop model to

• Stiffness and damping applied smoothly through transition region, damped rebound

• Full stiffness and damping applied at bounds, undamped rebound

• Full stiffness and damping applied at bounds, damped rebound

Hard-stop damping coefficient — Damping coefficient

150 N*s/m (default) | positive scalar

Piston damping coefficient.

Dependencies

To enable this parameter, set Hard stop model to

• Stiffness and damping applied smoothly through transition region, damped rebound

• Full stiffness and damping applied at bounds, undamped rebound

• Full stiffness and damping applied at bounds, damped rebound

Transition region — Application range of hard stop force model

0.1 mm (default) | positive scalar

Application range of the hard stop force model. Outside of this range of the piston maximum extension and piston maximum retraction, the Hard stop model is not applied and there is no additional force on the piston.

Dependencies

To enable this parameter, set Hard stop model to Stiffness and damping applied smoothly through transition region, damped rebound.

Coefficient of restitution — Ratio of final-to-initial relative speed between slider and stop after collision

0.7 (default) | unitless value between 0 and 1

Ratio of the final to the initial relative speed between the slider and the stop after the slider bounces.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Static contact speed threshold — Threshold relative speed between slider and stop before collision

0.001 m/s (default) | nonnegative scalar

Threshold relative speed between slider and stop before collision. When the slider hits the case with speed less than the value of the Static contact speed threshold parameter, they stay in contact. Otherwise, the slider bounces. To avoid modeling static contact between the slider and the case, set this parameter to 0.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Static contact release force threshold — Threshold force needed to transition from contact mode to free mode

0.001 N (default) | positive scalar

Minimum force needed to release the slider from a static contact mode.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Cushion

Cylinder end cushioning — Whether to model piston slow-down at maximum extension

off (default) | on

Whether to model piston slow-down at the maximum extension. See the Cylinder Cushion (IL) block for more information.

Cushion plunger cross-sectional area — Cylinder cushion plunger area

1e-4 m^2 (default) | positive scalar

Area of the plunger inside the actuator cushion element.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Cushion plunger length — Length of cushion plunger

1e-3 m (default) | positive scalar

Length of the cushion plunger.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Cushion orifice area — Area of orifice between cushion chambers

1e-6 m^2 (default) | positive scalar

Area of the orifice between the cushion chambers.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Leakage area between plunger and cushion sleeve — Gap between cushion plunger and sleeve

1e-7 m^2 (default) | positive scalar

Gap area between the cushion plunger and sleeve. This value contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Check valve cracking pressure differential — Cushion threshold pressure

0.01 MPa (default) | positive scalar

Pressure beyond which the valve operation triggers. When the pressure difference between port A and P_env meets or exceeds the value of this parameter, the cushion valve begins to open.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Check valve maximum pressure differential — Cushion differential pressure maximum

0.1 MPa (default) | positive scalar

Maximum cushion valve differential pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Check valve maximum area — Area of fully opened cushion valve

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the cushion valve in the fully open position.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Check valve leakage area — Cushion valve gap area in fully closed position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the cushion check valve is in the fully closed position. Any area smaller than this value saturates to the specified leakage area. This value contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the variable orifice and check valve are in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Dependencies

To enable this parameter, select Cylinder end cushioning.

Friction

Cylinder friction — Whether to model friction against piston motion

off (default) | on

Whether to model friction against piston motion. The block accounts for Coulomb, Stribeck, and viscous friction. See the Cylinder Friction block for more information.

Breakaway to Coulomb friction force ratio — Ratio of breakaway force to Coulomb friction force

1.2 (default) | positive scalar

Ratio of the breakaway force to the Coulomb friction force.

Dependencies

To enable this parameter, select Cylinder friction.

Breakaway friction velocity — Threshold for motion

0.1 m/s (default) | positive scalar

Threshold velocity for the motion against the friction force to begin.

Dependencies

To enable this parameter, select Cylinder friction.

Preload force — Initial force in cylinder due to seal assembly

20 N (default) | scalar

Initial force in the cylinder due to the seal assembly.

Dependencies

To enable this parameter, select Cylinder friction.

Coulomb friction force coefficient — Coulomb friction force coefficient

1e-6 N/Pa (default) | positive scalar

Coulomb force coefficient of friction.

Dependencies

To enable this parameter, select Cylinder friction.

Viscous friction coefficient — Viscous friction coefficient

100 N*s/m (default) | positive scalar

Viscous friction coefficient.

Dependencies

To enable this parameter, select Cylinder friction.

Leakage

Leakage — Whether to model annular leakage

off (default) | on

Whether to model annular leakage between the fluid chamber and the piston reservoir at reference environment conditions. The leakage is considered laminar. See the Laminar Leakage (IL) block for more information.

Piston-cylinder clearance — Radial clearance

1e-4 m (default) | positive scalar

Radial distance between the piston rod and cylinder casing.

Dependencies

To enable this parameter, select Leakage.

Piston head length — Annular length of piston mounting

0.01 m (default) | positive scalar

Length of the piston head.

Dependencies

To enable this parameter, select Leakage.

Initial conditions

Piston displacement — Method for determining piston position

Calculate from velocity of port R relative to port C (default) | Provide input signal from Multibody joint

Method for determining the piston position. The block can receive the position from a Multibody block when set to Provide input signal from Multibody joint, or calculates the position internally and reports the position at port p. The position is between 0 and the Piston stroke when the mechanical orientation is positive and 0 and –Piston stroke when the mechanical orientation is negative.

Initial piston displacement — Piston position at start of simulation

0 m (default) | scalar

Piston position at the start of the simulation.

Dependencies

To enable this parameter, set Piston displacement to Calculate from velocity of port R relative to port C.

Fluid dynamic compressibility — Whether to model fluid compressibility

on (default) | off

Whether to model any change in fluid density due to fluid compressibility. When you select Fluid dynamic compressibility, changes due to the mass flow rate into the block are calculated in addition to density changes due to changes in pressure. In the Isothermal Liquid Library, all blocks calculate density as a function of pressure.

Initial liquid pressure — Starting liquid pressure for compressible fluids

0.101325 MPa (default) | positive scalar

Starting liquid pressure for compressible fluids.

Dependencies

To enable this parameter, select Fluid dynamic compressibility.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

R2023a: New hard stop parameterization option

The block has a new option for the Hard stop model parameter. This option, called Based on coefficient of restitution, models the hard stop by using a mode chart.