Cartridge Valve Actuator (IL)

Actuator that maintains equilibrium between valve and pilot pressures in an isothermal liquid system

Since R2020a

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Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Valve Actuators & Forces

Description

The Cartridge Valve Actuator (IL) block models an actuator that maintains equilibrium between the valve and pilot-line pressures. The valve between ports A and B remains closed until the pilot spring Spring preload force is surpassed, at which point the piston begins to move. The piston position is output as a physical signal at port S. A schematic of a 4-port cartridge valve actuator is shown below.

Actuator Force Balance

The actuator piston moves to adjust the pressure in the actuator chamber, which maintains equilibrium between the actuator port pressures and pilot line pressures:

$$p_A{A}_A+p_B{A}_B=F_{preload}+F_{pilot},$$

where:

• p_A and p_B are the pressures at ports A and B.

• A_X is calculated from the Port A to port X area ratio.

• A_B is the port B area, $$A_X-A_A$$, when the Number of pressure ports is set to 3. When the Number of pressure ports is set to 4, A_B is $$A_X-A_A+A_Y$$.

• F_preload is the initial spring force in the system.

• F_pilot is $$p_X{A}_X$$ if Number of pressure ports is set to 3 and $$p_X{A}_X+p_Y{A}_Y$$ if Number of pressure ports is set to 4.

Piston Position

The steady piston displacement is calculated as:

$$x_{steady}=\frac{F\epsilon }{k}=\frac{F_A+F_B-F_{pilot}-F_{preload}}{k}\epsilon ,$$

where ε is the Opening orientation, which assigns movement in a positive direction (extension) or negative direction (retraction). The dynamic change in piston displacement is:

$${\dot{x}}_{dyn}=\frac{x_{steady}-x_{dyn}}{\tau },$$

where τ is the Actuator time constant. When $${\dot{x}}_{dyn}=\frac{x_{dyn}}{\tau }.$$ is less than the Spring preload force, x_steady = 0.

If $${\dot{x}}_{dyn}=\frac{x_{dyn}}{\tau }.$$ is greater than the sum of the preload force and kx_stroke, x_steady = x_stroke.

Opening Dynamics

If opening dynamics are modeled, a lag is introduced to the flow response to the modeled control pressure. p_control becomes the dynamic control pressure, p_dyn; otherwise, p_control is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:

$${\dot{p}}_{dyn}=\frac{p_{control}-p_{dyn}}{\tau }.$$

By default, Opening dynamics is set to Off.

Numerically-Smoothed Force

When the actuator is close to full extension or full retraction, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. A smoothing function is applied to all calculated forces, but primarily influences the simulation at the extremes of the piston motion.

The normalized force is

$$\widehat{F}=\frac{F_A+F_B-F_{Preload}-F_{Pilot}}{k{x}_{stroke}}.$$

where:

• F_A is the force at port A.

• F_B is the force at port B.

• F_Preload is the Spring preload force.

• F_Pilot is the force at port X.

If the Smoothing factor parameter is nonzero, the block smoothly saturates the normalized force between 0 and 1.

For more information, see Numerical Smoothing.

Assumptions and Limitations

Internal fluid volumes are not modeled in this block. There is no mass flow rate through ports A, B, X, and Y.

Ports

Conserving

A — Pressure port

isothermal liquid

Pressure port associated with the valve inlet.

B — Pressure port

isothermal liquid

Pressure port associated with the valve outlet.

X — Pressure port

isothermal liquid

Pressure port at poppet end.

Y — Pressure port

isothermal liquid

Pilot pressure port. To enable this port, set Number of pressure ports to 4.

Output

S — Poppet position, m

physical signal

Poppet position in m, specified as a physical signal.

Parameters

Number of pressure ports — Number of pilot pressure ports

3 (default) | 4

Number of pilot pressure ports. Port X measures the pressure at the end of the poppet. Setting this parameter to 4 enables the additional pilot-side port Y.

Port A poppet area — Cross-sectional area of port A

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

Cross-sectional area of port A.

Port A poppet to port X pilot area ratio — Ratio of inlet to pilot port area

0.5 (default) | positive scalar

Ratio of the inlet port, A, to the pilot pressure port, X. This value is used to calculate the force at port X.

Port Y pilot area — Cross-sectional area of port Y

1.5e-4 m^2 (default) | positive scalar

Cross-sectional area of port Y.

Dependencies

To enable this parameter, set Number of pressure ports to 4.

Spring preload force — Initial spring force

25 N (default) | positive scalar

Spring force in the valve due to spring preloading. This parameter is a threshold value which, when added to the pilot pressures at ports X and Y, counterbalances the valve opening due to the pressures at ports A and B.

Spring stiffness — Stiffness constant

15e3 N/m (default) | positive scalar

Spring stiffness constant.

Poppet stroke — Maximum poppet extension

5e-3 m (default) | positive scalar

Maximum poppet extension.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the piston position when it is near full extension or full retraction. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Connected valve opening orientation — Direction of poppet displacement

Positive displacement opens valve (default) | Negative displacement opens valve

Direction of the poppet displacement that opens a connected valve. Setting this parameter to Positive displacement opens valve indicates poppet extension. Setting the parameter to Negative displacement opens valve indicates poppet retraction.

Actuator dynamics — Whether to account for transients during actuation

Off (default) | On

Whether to account for transient effects in the spool position due to actuation. Setting Actuator dynamics to On approximates actuator motion by introducing a first-order lag in the spool position. The Actuator time constant also impacts the modeled dynamics.

Actuator time constant — Piston displacement time constant

0.1 s (default) | positive scalar

Constant that captures the time required for the piston to reach steady-state when moving from one position to another. This parameter impacts the modeled actuator dynamics.

Dependencies

To enable this parameter, set Actuator dynamics to On.

Extended Capabilities

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

Version History

Introduced in R2020a