Configuration K of hydraulic continuous 4-way directional valve

Directional Valves

The 4-Way Directional Valve K block simulates a configuration of hydraulic continuous 4-way directional valve. Ports A and B are connected to port P in the right valve position. In the left position, port P is connected to port B, while port A is connected to port T. In neutral position, port P is connected to port T to unload the pump. The fluid is pumped in the valve through the inlet line P and is distributed between two outside hydraulic lines A and B (usually connected to a double-acting actuator) and the return line T. The block has four hydraulic connections, corresponding to inlet port (P), actuator ports (A and B), and return port (T), and one physical signal port connection (S), which controls the spool position. The block is built of six Variable Orifice blocks, connected as shown in the following diagram.

All Variable Orifice blocks are controlled by the same position
signal, provided through the physical signal port S, but the **Orifice
orientation** parameter in the block instances is set in
such a way that positive signal at port `S`

opens
the orifices colored blue in the block diagram (orifices P-A1, P-T1,
and B-T) and closes the orifices colored yellow (orifices P-A2, P-B,
and T1-T). As a result, the openings of the orifices are computed
as follows:

$${h}_{PA1}={h}_{PA10}+x$$

$${h}_{PA2}={h}_{PA20}-x$$

$${h}_{PT1}={h}_{PT10}+x$$

$${h}_{T1T}={h}_{T1T0}-x$$

$${h}_{PB}={h}_{PB0}-x$$

$${h}_{BT}={h}_{BT0}+x$$

where

`h` | Orifice opening for the `Variable Orifice P-A1` block |

`h` | Orifice opening for the `Variable Orifice P-A2` block |

`h` | Orifice opening for the `Variable Orifice P-T1` block |

`h` | Orifice opening for the `Variable Orifice T1-T` block |

`h` | Orifice opening for the `Variable Orifice P-B` block |

`h` | Orifice opening for the `Variable Orifice B-T` block |

`h` | Initial opening for the `Variable Orifice P-A1` block |

`h` | Initial opening for the `Variable Orifice P-A2` block |

`h` | Initial opening for the `Variable Orifice P-T1` block |

`h` | Initial opening for the `Variable Orifice T1-T` block |

`h` | Initial opening for the `Variable Orifice P-B` block |

`h` | Initial opening for the `Variable Orifice B-T` block |

`x` | Control member displacement from initial position |

For information on the block parameterization options, basic parameter descriptions, assumptions and limitations, global and restricted parameters, see the 4-Way Directional Valve block reference page.

**Model parameterization**Select one of the following methods for specifying the valve:

`By maximum area and opening`

— Provide values for the maximum valve passage area and the maximum valve opening. The passage area is linearly dependent on the control member displacement, that is, the valve is closed at the initial position of the control member (zero displacement), and the maximum opening takes place at the maximum displacement. This is the default method.`By area vs. opening table`

— Provide tabulated data of valve openings and corresponding valve passage areas. The passage area is determined by one-dimensional table lookup. You have a choice of three interpolation methods and two extrapolation methods.`By pressure-flow characteristic`

— Provide tabulated data of valve openings, pressure differentials, and corresponding flow rates. The flow rate is determined by two-dimensional table lookup. You have a choice of three interpolation methods and two extrapolation methods.

**Valve passage maximum area**Specify the area of a fully opened valve. The parameter value must be greater than zero. The default value is

`5e-5`

m^2. This parameter is used if**Model parameterization**is set to`By maximum area and opening`

.**Valve maximum opening**Specify the maximum displacement of the control member. The parameter value must be greater than zero. The default value is

`5e-3`

m. This parameter is used if**Model parameterization**is set to`By maximum area and opening`

.**Tabulated valve openings**Specify the vector of input values for valve openings as a one-dimensional array. The input values vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for cubic or spline interpolation. The default values, in meters, are

`[-0.002 0 0.002 0.005 0.015]`

. If**Model parameterization**is set to`By area vs. opening table`

, the**Tabulated valve openings**values will be used together with**Tabulated valve passage area**values for one-dimensional table lookup. If**Model parameterization**is set to`By pressure-flow characteristic`

, the**Tabulated valve openings**values will be used together with**Tabulated pressure differentials**and**Tabulated flow rates**for two-dimensional table lookup.**Tabulated valve passage area**Specify the vector of output values for valve passage area as a one-dimensional array. The valve passage area vector must be of the same size as the valve openings vector. All the values must be positive. The default values, in m^2, are

`[1e-09 2.0352e-07 4.0736e-05 0.00011438 0.00034356]`

. This parameter is used if**Model parameterization**is set to`By area vs. opening table`

.**Tabulated pressure differentials**Specify the vector of input values for pressure differentials as a one-dimensional array. The vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for cubic or spline interpolation. The default values, in Pa, are

`[-1e+07 -5e+06 -2e+06 2e+06 5e+06 1e+07]`

. This parameter is used if**Model parameterization**is set to`By pressure-flow characteristic`

.**Tabulated flow rates**Specify the flow rates as an

`m`

-by-`n`

matrix, where`m`

is the number of valve openings and`n`

is the number of pressure differentials. Each value in the matrix specifies flow rate taking place at a specific combination of valve opening and pressure differential. The matrix size must match the dimensions defined by the input vectors. The default values, in m^3/s, are:This parameter is used if[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07; -2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05; -0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736; -0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438; -0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]

**Model parameterization**is set to`By pressure-flow characteristic`

.**Interpolation method**Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

`Linear`

— For one-dimensional table lookup (`By area vs. opening table`

), uses a linear interpolation function. For two-dimensional table lookup (`By pressure-flow characteristic`

), uses a bilinear interpolation algorithm, which is an extension of linear interpolation for functions in two variables.`Cubic`

— For one-dimensional table lookup (`By area vs. opening table`

), uses the Piecewise Cubic Hermite Interpolation Polynomial (PCHIP). For two-dimensional table lookup (`By pressure-flow characteristic`

), uses the bicubic interpolation algorithm.`Spline`

— For one-dimensional table lookup (`By area vs. opening table`

), uses the cubic spline interpolation algorithm. For two-dimensional table lookup (`By pressure-flow characteristic`

), uses the bicubic spline interpolation algorithm.

For more information on interpolation algorithms, see the PS Lookup Table (1D) and PS Lookup Table (2D) block reference pages.

**Extrapolation method**Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

`From last 2 points`

— Extrapolates using the linear method (regardless of the interpolation method specified), based on the last two output values at the appropriate end of the range. That is, the block uses the first and second specified output values if the input value is below the specified range, and the two last specified output values if the input value is above the specified range.`From last point`

— Uses the last specified output value at the appropriate end of the range. That is, the block uses the last specified output value for all input values greater than the last specified input argument, and the first specified output value for all input values less than the first specified input argument.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) and PS Lookup Table (2D) block reference pages.

**Flow discharge coefficient**Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the valve, and usually is provided in textbooks or manufacturer data sheets. The default value is

`0.7`

.**Critical Reynolds number**The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is

`12`

.**Leakage area**The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is

`1e-12`

m^2.

**Orifice P-A1 initial opening**Initial opening for the

`Variable Orifice P-A1`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`-0.0025`

m.**Orifice P-A2 initial opening**Initial opening for the

`Variable Orifice P-A2`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`-0.0025`

m.**Orifice P-T1 initial opening**Initial opening for the

`Variable Orifice P-T1`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`0.0025`

m.**Orifice T1-T initial opening**Initial opening for the

`Variable Orifice T1-T`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`0.0025`

m.**Orifice P-B initial opening**Initial opening for the

`Variable Orifice P-B`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`-0.0025`

m.**Orifice B-T initial opening**Initial opening for the

`Variable Orifice B-T`

block. The parameter can be positive (underlapped orifice), negative (overlapped orifice), or equal to zero for zero lap configuration. The default value is`-0.0025`

m.

The block has the following ports:

`P`

Hydraulic conserving port associated with the pressure supply line inlet.

`T`

Hydraulic conserving port associated with the return line connection.

`A`

Hydraulic conserving port associated with the actuator connection port.

`B`

Hydraulic conserving port associated with the actuator connection port.

`S`

Physical signal port to control spool displacement.

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