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

**Library:**Simscape / Fluids / Valve Actuators & Forces

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 cqrtridge valve actuator is shown below.

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`

.

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}.

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`

.

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 calculated as:

$$\widehat{F}=\frac{{F}_{A}+{F}_{B}-{F}_{Preload}-{F}_{Pilot}}{k{x}_{stroke}}.$$

The **Smoothing factor**, *s*,
is applied to the normalized force:

$${\widehat{F}}_{X,smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{F}}_{X}^{2}+{\left(\frac{s}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left({\widehat{F}}_{X}-1\right)}^{2}+{\left(\frac{s}{4}\right)}^{2}},$$

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

Cartridge Valve Insert (IL) | Pilot Valve Actuator (IL) | Pilot-Operated Check Valve (IL) | Shuttle Valve (IL) | 3-Way Directional Valve (IL)