Main Content

Swash plate in a single-piston, isothermal axial piston pump

**Library:**Simscape / Fluids / Isothermal Liquid / Actuators / Auxiliary Components

The Swash Plate block models a single, piston-actuated swash plate within an axial-piston pump. It translates linear actuation into rotational motion that, when connected to the Valve Plate Orifice (IL) block, periodically connects the piston with the pump intake and discharge. You can connect multiple swash plate blocks to multiple pistons.

**Schematic of a Swash Plate Within an Axial-Piston Pump Unit**

The plate is in dynamic equilibrium if the net work by the piston, actuator, and plate is zero:

$${F}_{P}{\delta}_{P}+{F}_{A}{\delta}_{A}+\left(\tau -{\tau}_{res}\right){\delta}_{y}=0,$$

where:

*F*_{P}*δ*_{P}is the work done due to piston displacement.*F*_{A}*δ*_{A}is the work done due to actuator displacement.*(τ-τ*_{res}*)δ*_{y}is the work done due to the net plate torque tangent to plate motion.

The plate torque is:

$$\tau =-\frac{{r}_{P}}{{r}_{A}}{x}_{A}{F}_{P}\mathrm{sin}\gamma +{\tau}_{res},$$

where:

*r*_{P}is the**Cylinder block pitch radius**.*r*_{A}is the**Swash plate actuator arm**.*X*_{A}is the actuator displacement.*F*_{P}is the piston force.*γ*is the plate angular displacement.

The viscous friction torque, or the resistance to motion due to plate-piston contact, is:

$${\tau}_{res}={\mu}_{viscous}\omega {r}_{P}^{2},$$

where:

*μ*_{viscous}is the**Viscous friction coefficient**.*ω*is the rotor angular velocity.

The piston displacement, *x*, is proportional to the actuator
displacement:

$$x=-{h}_{off}\left(\sqrt{1+\frac{{x}_{A}^{2}}{{r}_{A}^{2}}}-1\right)-\frac{{r}_{P}}{{r}_{A}}{x}_{A}\mathrm{cos}\gamma ,$$

where *h*_{off} is the **Piston
offset from the plate**. Displacement is positive if it moves toward
the cylinder block.

The piston velocity is:

$${V}_{P}=\frac{{r}_{P}}{{r}_{A}}{x}_{A}\omega \mathrm{sin}\left(\gamma \right)-\frac{{r}_{P}}{{r}_{A}}{V}_{A}\mathrm{cos}\gamma -\frac{{h}_{off}}{{r}_{A}^{2}}\frac{{x}_{A}{V}_{A}}{\sqrt{1+\frac{{x}_{A}^{2}}{{r}_{A}^{2}}}},$$

where *V*_{A} is the
actuator velocity.

This block accounts for the effect of viscous friction between the piston and plate, but neglects plate and fluid inertia.

**Note**

This reference page is for the Isothermal Liquid library block. For the Hydraulics (Isothermal) Liquid library block, see Swash Plate.