Swash Plate

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

Since R2020a

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:

$F_{P} δ_{P} + F_{A} δ_{A} + (τ - τ_{r e s}) δ_{y} = 0,$

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:

$τ = - \frac{r_{P}}{r_{A}} x_{A} F_{P} \sin γ + τ_{r e s},$

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:

$τ_{r e s} = μ_{v i s c o u s} ω r_{P}^{2},$

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:

$x = - h_{o f f} (\sqrt{1 + \frac{x_{A}^{2}}{r_{A}^{2}}} - 1) - \frac{r_{P}}{r_{A}} x_{A} \cos γ,$

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

The piston velocity is:

$V_{P} = \frac{r_{P}}{r_{A}} x_{A} ω \sin (γ) - \frac{r_{P}}{r_{A}} V_{A} \cos γ - \frac{h_{o f f}}{r_{A}^{2}} \frac{x_{A} V_{A}}{\sqrt{1 + \frac{x_{A}^{2}}{r_{A}^{2}}}},$

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

expand all

A — Mechanical port associated with actuator
mechanical translational

Swash plate actuator velocity and force.

P — Mechanical port associated with piston
mechanical translational

Piston end velocity and force.

S — Mechanical port associated with shaft
mechanical rotational

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

Parameters

expand all

Swash plate actuator arm — Length of actuator extension
`0.065 m` (default) | positive scalar

Length of fully extended actuator arm.

Cylinder block pitch radius — Cylinder pitch radius
`0.05 m` (default) | positive scalar

Pitch radius of the rotating cylinder.

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.

Swash Plate

Description

Force Balance

Piston Dynamics

Assumptions and Limitations

Examples

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

Ports

Conserving

A — Mechanical port associated with actuator
mechanical translational

P — Mechanical port associated with piston
mechanical translational

S — Mechanical port associated with shaft
mechanical rotational

Parameters

Swash plate actuator arm — Length of actuator extension
`0.065 m` (default) | positive scalar

Cylinder block pitch radius — Cylinder pitch radius
`0.05 m` (default) | positive scalar

Piston offset from the plate — Resting piston offset
`0 m` (default) | scalar

Viscous friction coefficient — Torque viscous friction coefficient
`50 N/(m/s)` (default) | positive scalar

Extended Capabilities

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

Version History

See Also

Swash Plate

Description

Force Balance

Piston Dynamics

Assumptions and Limitations

Examples

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

Ports

Conserving

A — Mechanical port associated with actuator mechanical translational

P — Mechanical port associated with piston mechanical translational

S — Mechanical port associated with shaft mechanical rotational

Parameters

Swash plate actuator arm — Length of actuator extension 0.065 m (default) | positive scalar

Cylinder block pitch radius — Cylinder pitch radius 0.05 m (default) | positive scalar

Piston offset from the plate — Resting piston offset 0 m (default) | scalar

Viscous friction coefficient — Torque viscous friction coefficient 50 N/(m/s) (default) | positive scalar

Extended Capabilities

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

Version History

See Also

A — Mechanical port associated with actuator
mechanical translational

P — Mechanical port associated with piston
mechanical translational

S — Mechanical port associated with shaft
mechanical rotational

Swash plate actuator arm — Length of actuator extension
`0.065 m` (default) | positive scalar

Cylinder block pitch radius — Cylinder pitch radius
`0.05 m` (default) | positive scalar

Piston offset from the plate — Resting piston offset
`0 m` (default) | scalar

Viscous friction coefficient — Torque viscous friction coefficient
`50 N/(m/s)` (default) | positive scalar

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