LIBRARY

PlanarMechanics.examples.excavator.ProportionalValve

Proportional 4/3 directional valve metering flow between a supply, a tank, and the two chambers of a hydraulic cylinder.

The spool command u is expected in the range [-1, 1]. A positive command opens the paths supply -> port_a and port_b -> tank (extending a cylinder whose cap side is connected to port_a); a negative command opens supply -> port_b and port_a -> tank. Each metering path follows a turbulent orifice law with a regularized square root so the flow is smooth through zero pressure drop and admits reverse flow. All four ports share the same medium and the four port mass flows sum to zero by construction. Leakage between ports is not modeled.

Usage

MultibodyComponents.PlanarMechanics.examples.excavator.ProportionalValve(Kv=5e-7, dp_small=1e5)

Parameters:

Name	Description	Units	Default value
Kv	Valve coefficient: volumetric flow per unit command and square root of pressure drop	–	5e-7
dp_small	Pressure-drop regularization of the orifice law	–	1e5

Connectors

• port_p - (Port)

• port_t - (Port)

• port_a - (Port)

• port_b - (Port)

• u - This connector represents a real signal as an input to a component (RealInput)

Variables

Name	Description	Units
up	Positive part of the spool command	–
un	Negative part of the spool command	–
rho	Fluid density at the supply port	–
q_pa	Volumetric flow supply -> port_a	–
q_bt	Volumetric flow port_b -> tank	–
q_pb	Volumetric flow supply -> port_b	–
q_at	Volumetric flow port_a -> tank	–

Behavior

Behavior of this component cannot be rendered because it includes path variables.

Source

"""
Proportional 4/3 directional valve metering flow between a supply, a tank, and
the two chambers of a hydraulic cylinder.

The spool command `u` is expected in the range [-1, 1]. A positive command
opens the paths supply -> port_a and port_b -> tank (extending a cylinder whose
cap side is connected to port_a); a negative command opens supply -> port_b and
port_a -> tank. Each metering path follows a turbulent orifice law with a
regularized square root so the flow is smooth through zero pressure drop and
admits reverse flow. All four ports share the same medium and the four port
mass flows sum to zero by construction. Leakage between ports is not modeled.
"""
component ProportionalValve
  "Supply (pump) port"
  port_p = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": 950, "x2": 300, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  "Tank (return) port"
  port_t = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 950, "x2": 800, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  "Cylinder cap-side port"
  port_a = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -50, "x2": 300, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Cylinder rod-side port"
  port_b = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -50, "x2": 800, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Spool command in [-1, 1]"
  u = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -50, "y1": 450, "x2": 50, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Valve coefficient: volumetric flow per unit command and square root of pressure drop"
  parameter Kv::Real = 5e-7
  "Pressure-drop regularization of the orifice law"
  parameter dp_small::Real = 1e5
  "Positive part of the spool command"
  variable up::Real
  "Negative part of the spool command"
  variable un::Real
  "Fluid density at the supply port"
  variable rho::Real
  "Volumetric flow supply -> port_a"
  variable q_pa::Real
  "Volumetric flow port_b -> tank"
  variable q_bt::Real
  "Volumetric flow supply -> port_b"
  variable q_pb::Real
  "Volumetric flow port_a -> tank"
  variable q_at::Real
relations
  continuity(port_p.medium, port_t.medium, port_a.medium, port_b.medium)
  up = max(u, 0)
  un = max(-u, 0)
  rho = HydraulicComponents.density(port_p.medium, port_p.p)
  q_pa = Kv * up * (port_p.p - port_a.p) / sqrt(sqrt((port_p.p - port_a.p) ^ 2 + dp_small ^ 2))
  q_bt = Kv * up * (port_b.p - port_t.p) / sqrt(sqrt((port_b.p - port_t.p) ^ 2 + dp_small ^ 2))
  q_pb = Kv * un * (port_p.p - port_b.p) / sqrt(sqrt((port_p.p - port_b.p) ^ 2 + dp_small ^ 2))
  q_at = Kv * un * (port_a.p - port_t.p) / sqrt(sqrt((port_a.p - port_t.p) ^ 2 + dp_small ^ 2))
  port_p.m_flow = rho * (q_pa + q_pb)
  port_t.m_flow = -rho * (q_bt + q_at)
  port_a.m_flow = rho * (q_at - q_pa)
  port_b.m_flow = rho * (q_bt - q_pb)
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/ProportionalValve.svg"}}
}
end

Flattened Source

"""
Proportional 4/3 directional valve metering flow between a supply, a tank, and
the two chambers of a hydraulic cylinder.

The spool command `u` is expected in the range [-1, 1]. A positive command
opens the paths supply -> port_a and port_b -> tank (extending a cylinder whose
cap side is connected to port_a); a negative command opens supply -> port_b and
port_a -> tank. Each metering path follows a turbulent orifice law with a
regularized square root so the flow is smooth through zero pressure drop and
admits reverse flow. All four ports share the same medium and the four port
mass flows sum to zero by construction. Leakage between ports is not modeled.
"""
component ProportionalValve
  "Supply (pump) port"
  port_p = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": 950, "x2": 300, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  "Tank (return) port"
  port_t = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 950, "x2": 800, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  "Cylinder cap-side port"
  port_a = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -50, "x2": 300, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Cylinder rod-side port"
  port_b = HydraulicComponents.Interfaces.Port() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -50, "x2": 800, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Spool command in [-1, 1]"
  u = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -50, "y1": 450, "x2": 50, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Valve coefficient: volumetric flow per unit command and square root of pressure drop"
  parameter Kv::Real = 5e-7
  "Pressure-drop regularization of the orifice law"
  parameter dp_small::Real = 1e5
  "Positive part of the spool command"
  variable up::Real
  "Negative part of the spool command"
  variable un::Real
  "Fluid density at the supply port"
  variable rho::Real
  "Volumetric flow supply -> port_a"
  variable q_pa::Real
  "Volumetric flow port_b -> tank"
  variable q_bt::Real
  "Volumetric flow supply -> port_b"
  variable q_pb::Real
  "Volumetric flow port_a -> tank"
  variable q_at::Real
relations
  continuity(port_p.medium, port_t.medium, port_a.medium, port_b.medium)
  up = max(u, 0)
  un = max(-u, 0)
  rho = HydraulicComponents.density(port_p.medium, port_p.p)
  q_pa = Kv * up * (port_p.p - port_a.p) / sqrt(sqrt((port_p.p - port_a.p) ^ 2 + dp_small ^ 2))
  q_bt = Kv * up * (port_b.p - port_t.p) / sqrt(sqrt((port_b.p - port_t.p) ^ 2 + dp_small ^ 2))
  q_pb = Kv * un * (port_p.p - port_b.p) / sqrt(sqrt((port_p.p - port_b.p) ^ 2 + dp_small ^ 2))
  q_at = Kv * un * (port_a.p - port_t.p) / sqrt(sqrt((port_a.p - port_t.p) ^ 2 + dp_small ^ 2))
  port_p.m_flow = rho * (q_pa + q_pb)
  port_t.m_flow = -rho * (q_bt + q_at)
  port_a.m_flow = rho * (q_at - q_pa)
  port_b.m_flow = rho * (q_bt - q_pb)
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/ProportionalValve.svg"}}
}
end

Test Cases

No test cases defined.

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