Swash Plate

R2026b

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

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Swash Plate block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simscape / Fluids / Isothermal Liquid / Pumps & Motors / Auxiliary Components

Description

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

Force Balance

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_Pδ_P is the work done due to piston displacement.

• F_Aδ_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:

$$\tau =-\frac{r_P}{r_A}{x}_A{F}_P\sin \gamma +{\tau }_{res},$$

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.

Piston Dynamics

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

$$x=-h_{off}\left(\sqrt{1+\frac{x_A^2}{r_A^2}}-1\right)-\frac{r_P}{r_A}{x}_A\cos \gamma ,$$

where h_off is the Piston offset from the plate. Displacement is positive if it moves toward the cylinder block.

The piston velocity is:

$$V_P=\frac{r_P}{r_A}{x}_A\omega \sin \left(\gamma \right)-\frac{r_P}{r_A}{V}_A\cos \gamma -\frac{h_{off}}{r_A^2}\frac{x_A{V}_A}{\sqrt{1+\frac{x_A^2}{r_A^2}}},$$

where V_A is the actuator velocity.

Assumptions and Limitations

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

Examples

Hydraulic Axial-Piston Pump with Load-Sensing and Pressure-Limiting Control

A test rig designed to investigate the interaction between an axial-piston pump and a typical control unit simultaneously performing the load-sensing and pressure-limiting functions. To increase the fidelity of the simulation, this example uses a detailed model of the pump that accounts for the interaction between the pistons, swash plate, and valve plate.

• Open Model

Ports

Conserving

A — Mechanical port associated with actuator

mechanical translational

Swash plate actuator velocity and force.

Programmatic Use

Port: A

P — Mechanical port associated with piston

mechanical translational

Piston end velocity and force.

Programmatic Use

Port: P

S — Mechanical port associated with shaft

mechanical rotational

Drive shaft angular velocity and torque. Rotation is relative to the environment.

Programmatic Use

Port: S

Parameters

Swash plate actuator arm — Length of actuator extension

0.065 m (default) | positive scalar

Length of fully extended actuator arm.

Programmatic Use

Parameter: actuator_arm

Cylinder block pitch radius — Cylinder pitch radius

0.05 m (default) | positive scalar

Pitch radius of the rotating cylinder.

Programmatic Use

Parameter: pitch_radius

Piston offset from the plate — Resting piston offset

0 m (default) | scalar

Piston offset when the actuator is in neutral position. A positive, nonzero value indicates a partially retracted piston. A negative, nonzero value indicates an extended piston that remains within the cylinder block during an initial actuator displacement away from the cylinder.

Programmatic Use

Parameter: h_offset

Viscous friction coefficient — Torque viscous friction coefficient

50 N/(m/s) (default) | positive scalar

Coefficient used in the equation for torque due to viscous friction.

Programmatic Use

Parameter: mu_visc

Programmatic Use: Add Block

To add the block programmatically, use the add_block function with one of these library block paths as the source.

"SimscapeFluids_lib/Isothermal Liquid/Pumps & Motors/Auxiliary Components/Swash Plate"

Example: add_block("SimscapeFluids_lib/Isothermal Liquid/Pumps & Motors/Auxiliary Components/Swash Plate","myModel/myBlock",MakeNameUnique="on")

For information about programmatic access to individual block parameters, see the Programmatic Use section of parameter descriptions on this page.

Extended Capabilities

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

Version History

Introduced in R2020a