Variable-Displacement Pump

(To be removed) Variable-displacement bidirectional hydraulic pump

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

Libraries:
Simscape / Fluids / Hydraulics (Isothermal) / Pumps and Motors

Description

The Variable-Displacement Pump block represents a device that extracts power from a mechanical rotational network and delivers it to a hydraulic (isothermal liquid) network. The pump displacement varies in proportion to the physical signal specified at port C or D. The exact port used depends on the block variant selected. See Ports.

Ports T and P represent the pump inlets. Port S represents the pump drive shaft. During normal operation, the pressure gain from port T to port P is positive if the angular velocity at port S is positive also. This operation mode is referred to here as forward pump.

Operation Modes

A total of four operation modes are possible. The working mode depends on the pressure gain from port T to port P (Δp), the angular velocity at port S (ω), and on the instantaneous displacement of the component (D). The Operation Modes figure maps the modes to the octants of a Δp-ω-D chart. The modes are labeled 1–4:

Mode 1: forward pump — A positive shaft angular velocity generates a positive pressure gain.
Mode 2: reverse motor — A negative pressure drop (shown in the figure as a positive pressure gain) generates a negative shaft angular velocity.
Mode 3: reverse pump — A negative shaft angular velocity generates a negative pressure gain.
Mode 4: forward motor — A positive pressure drop (shown in the figure as a negative pressure gain) generates a positive shaft angular velocity.

The response time of the pump is considered negligible in comparison with the system response time. The pump is assumed to reach steady state nearly instantaneously and is treated as a quasi-steady component.

Block Variants and Loss Parameterizations

The pump model accounts for power losses due to leakage and friction. Leakage is internal and occurs between the pump inlet and outlet only. The block computes the leakage flow rate and friction torque using your choice of five loss parameterizations. You select a parameterization using block variants and, in the Analytical or tabulated data case, the Leakage and friction parameterization parameter.

Loss Parameterizations

The block provides three Simscape™ variants to select from. To change the active block variant, use the Modeling option parameter. The available variants are:

Analytical or tabulated data — Obtain the mechanical and volumetric efficiencies or losses from analytical models based on nominal parameters or from tabulated data. Use the Leakage and friction parameterization parameter to select the exact input type.
Input efficiencies — Provide the mechanical and volumetric efficiencies directly through physical signal input ports.
Input losses — Provide the mechanical and volumetric losses directly through physical signal input ports. The mechanical loss is defined as the internal friction torque. The volumetric loss is defined as the internal leakage flow rate.

Displacement Parameterizations

The displacement volume input depends on the block variant selected. If the active block variant is Input efficiencies or Input losses, the block obtains the instantaneous displacement volume directly from the physical signal input at port D.

If the active block variant is Analytical or tabulated data, the block computes the instantaneous displacement volume from the control member position specified at port C. This computation depends on the Displacement parameterization parameter setting:

Maximum displacement and control member stroke — Compute the displacement volume per unit rotation as a linear function of the control member position specified at port C.
Displacement vs. control member position table — Compute the displacement volume per unit volume using interpolation or extrapolation of displacement tabular data specified at discrete control member positions.

Flow Rate and Driving Torque

The volumetric flow rate generated at the pump is

$q = q_{Ideal} + q_{Leak},$

where:

q is the net volumetric flow rate.
q_Ideal is the ideal volumetric flow rate.
q_Leak is the internal leakage volumetric flow rate.

The driving torque required to power the pump is

$τ = τ_{Ideal} + τ_{Friction},$

where:

τ is the net driving torque.
τ_Ideal is the ideal driving torque.
τ_Friction is the friction torque.

Ideal Flow Rate and Ideal Torque

The ideal volumetric flow rate is

$q_{Ideal} = D_{Sat} \cdot ω,$

and the ideal driving torque is

$τ_{Ideal} = D_{Sat} \cdot Δ p,$

where:

D_Sat is a smoothed displacement computed so as to remove numerical discontinuities between negative and positive displacements.
ω is the instantaneous angular velocity of the rotary shaft.
Δp is the instantaneous pressure gain from inlet to outlet.

Saturation Displacement

The saturation displacement depends on the block variant selected. If the active variant is Analytical or tabulated data,

$D_{Sat} = {\begin{array}{l} sign (D) \cdot D_{Max}, & | D | \geq D_{Max} \\ \sqrt{D^{2} + D_{Threshold}^{2}}, & D \geq 0 \\ - \sqrt{D^{2} + D_{Threshold}^{2}}, & D < 0 \end{array},$

where:

D is the instantaneous fluid displacement determined from the physical signal input specified at port C or port D.
D_Max is the specified value of the Maximum displacement block parameter.
D_Threshold is the specified value of the Displacement threshold for pump-motor transition block parameter.

If the active variant is Input efficiencies or Input losses, there is no upper bound on the displacement input and the saturation displacement reduces to:

$D_{S a t} = {\begin{array}{l} \sqrt{D^{2} + D_{T h r e s h}^{2}}, & D \geq 0 \\ - \sqrt{D^{2} + D_{T h r e s h}^{2}}, & D < 0 \end{array} .$

Leakage Flow Rate and Friction Torque

The internal leakage flow rate and friction torque calculations depend on the block variant selected. If the block variant is Analytical or tabulated data, the calculations depend also on the Leakage and friction parameterization parameter setting. There are five possible permutations of block variant and parameterization settings.

Case 1: Analytical Efficiency Calculation

If the active block variant is Analytical or tabulated data and the Leakage and friction parameterization parameter is set to Analytical, the leakage flow rate is

$q_{Leak} = K_{HP} Δ p,$

and the friction torque is

$τ_{Friction} = (τ_{0} + K _{TP} | \frac{D_{Sat}}{D_{Max}} | | Δ p |) \tanh (\frac{4 ω}{ω_{Thresh}}),$

where:

K_HP is the Hagen-Poiseuille coefficient for laminar pipe flows. This coefficient is computed from the specified nominal parameters.
K_TP is the specified value of the Friction torque vs pressure gain coefficient block parameter.
τ₀ is the specified value of the No-load torque block parameter.
ω_Threshold is the threshold angular velocity for the motor-pump transition. The threshold angular velocity is an internally set fraction of the specified value of the Nominal shaft angular velocity block parameter.

The Hagen-Poiseuille coefficient is determined from nominal fluid and component parameters through the equation

$K_{HP} = \frac{ν_{Nom}}{ρ v} \frac{ρ_{Nom} ω_{Nom} D_{Max}}{Δ p_{Nom}} (1 - η_{v,Nom}),$

where:

ν_Nom is the specified value of the Nominal kinematic viscosity block parameter. This is the kinematic viscosity at which the nominal volumetric efficiency is specified.
ρ_Nom is the specified value of the Nominal fluid density block parameter. This is the density at which the nominal volumetric efficiency is specified.
ω_Nom is the specified value of the Nominal shaft angular velocity block parameter. This is the angular velocity at which the nominal volumetric efficiency is specified.
ρ is the actual fluid density in the attached hydraulic (isothermal liquid) network. This density can differ from the specified value of the Nominal fluid density block parameter.
v is the kinematic viscosity of the fluid associated with the fluid network.
Δp_Nom is the specified value of the Nominal pressure gain block parameter. This is the pressure drop at which the nominal volumetric efficiency is specified.
η_v,Nom is the specified value of the Volumetric efficiency at nominal conditions block parameter. This is the volumetric efficiency corresponding to the specified nominal conditions.

Case 2: Efficiency Tabulated Data

If the active block variant is Analytical or tabulated data and the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies, the leakage flow rate is

$q_{Leak} = q_{Leak,Pump} \frac{(1 + α)}{2} + q_{Leak,Motor} \frac{(1 - α)}{2},$

and the friction torque is

$τ_{Friction} = τ_{Friction,Pump} \frac{1 + α}{2} + τ_{Friction,Motor} \frac{1 - α}{2},$

where:

α is a numerical smoothing parameter for the motor-pump transition.
q_Leak,Pump is the leakage flow rate in pump mode.
q_Leak,Motor is the leakage flow rate in motor mode.
τ_{Friction,Pump} is the friction torque in pump mode.
τ_{Friction,Motor} is the friction torque in motor mode.

The smoothing parameter α is given by the hyperbolic function

$α = tanh (\frac{4 Δ p}{Δ p_{Threshold}}) \cdot tanh (\frac{4 ω}{ω_{Threshold}}) \cdot \tanh (\frac{4 D}{D_{Threshold}}),$

where:

Δp_Threshold is the specified value of the Pressure drop threshold for motor-pump transition block parameter.
ω_Threshold is the specified value of the Angular velocity threshold for motor-pump transition block parameter.
D_Threshold is the specified value of the Displacement threshold for motor-pump transition block parameter.

The leakage flow rate is computed from efficiency tabulated data through the equation

$q_{Leak,Pump} = (1 - η_{v}) q_{Ideal},$

in pump mode and through the equation

$q_{Leak,Motor} = - (1 - η_{v}) q,$

in motor mode, where:

η_v is the volumetric efficiency obtained through interpolation or extrapolation of the Volumetric efficiency table, e_v(dp,w,D) parameter data.

Similarly, the friction torque is computed from efficiency tabulated data through the equation

$τ_{Friction,Pump} = (1 - η_{m}) τ,$

in pump mode and through the equation

$τ_{Friction,Motor} = - (1 - η_{m}) τ_{Ideal},$

in motor mode, where:

η_m is the mechanical efficiency obtained through interpolation or extrapolation of the Mechanical efficiency table, e_m(dp,w,D) parameter data.

Case 3: Loss Tabulated Data

$q_{Leak} = q_{Leak} (Δ p, ω, D_{Sat}) .$

and the friction torque equation is

$τ_{Friction} = τ_{Friction} (Δ p, ω, D_{Sat}),$

where q_Leak(Δp,ω,D_Sat) and τ_Friction(Δp,ω,D_Sat) are the volumetric and mechanical losses, obtained through interpolation or extrapolation of the Volumetric loss table, q_loss(dp,w,D) and Mechanical loss table, torque_loss (dp,w,D) parameter data.

Case 4: Efficiency Physical Signal Inputs

If the active block variant is Input efficiencies, the leakage flow rate and friction torque calculations are as described for efficiency tabulated data (case 2). The volumetric and mechanical efficiency lookup tables are replaced with physical signal inputs that you specify through ports EV and EM.

Case 5: Loss Physical Signal Inputs

If the block variant is Input losses, the leakage flow rate and friction torque calculations are as described for loss tabulated data (case 3). The volumetric and mechanical loss lookup tables are replaced with physical signal inputs that you specify through ports LV and LM.

Assumptions

Fluid compressibility is negligible.
Loading on the pump shaft due to inertia, friction, and spring forces is negligible.

Ports

Input

expand all

C — Control member offset, `m`
physical signal

Physical signal input port for the control member position. The block maps the control member offset to the corresponding displacement volume using the tabulated data specified in the block dialog box.

Dependencies

This port is exposed only when the block variant is set to Analytical or tabulated data.

D — Displacement volume, `cm^3/rev`
physical signal

Physical signal input port for the volume of fluid displaced per unit rotation. A smoothing function eases the transition between positive and negative input values.

Dependencies

This port is exposed only when the block variant is set to Input efficiencies or Input losses.

EV — Volumetric efficiency, unitless
physical signal

Physical signal input port for the volumetric efficiency coefficient. The input signal has an upper bound at the Maximum volumetric efficiency parameter value and a lower bound at the Minimum volumetric efficiency parameter value.

Dependencies

This port is exposed only when the block variant is set to Input efficiencies.

EM — Mechanical efficiency, unitless
physical signal

Physical signal input port for the mechanical efficiency coefficient. The input signal has an upper bound at the Maximum mechanical efficiency parameter value and a lower bound at the Minimum mechanical efficiency parameter value.

Dependencies

This port is exposed only when the block variant is set to Input efficiencies.

LV — Volumetric loss, `m^3/s`
physical signal

Physical signal input port for the volumetric loss, defined as the internal leakage flow rate between the pump inlets.

Dependencies

This port is exposed only when the block variant is set to Input losses.

LM — Mechanical loss, `N*m`
physical signal

Physical signal input port for the mechanical loss, defined as the friction torque on the rotating pump shaft.

Dependencies

This port is exposed only when the block variant is set to Input losses.

Conserving

expand all

T — Pump inlet
hydraulic (isothermal liquid)

Hydraulic (isothermal liquid) conserving port representing the pump inlet.

P — Pump outlet
hydraulic (isothermal liquid)

Hydraulic (isothermal liquid) conserving port representing the pump outlet.

S — Pump shaft
mechanical rotational

Mechanical rotational conserving port representing the pump shaft.

Parameters

expand all

The exposed block parameters depend on the active block variant. See Block Variants and Loss Parameterizations.

Modeling option — Loss parameterizations
`Analytical or tabulated data` | `Input efficiencies` | `Input losses`

Set the variant for mechanical and volumetric efficiencies or losses for the block.

Variant 1: Analytical or tabulated data

Displacement parameterization — Parameterization used to map control positions to displacements
`Maximum displacement and control member stroke` (default)

Parameterization used to convert the physical signal at input port C to an instantaneous displacement:

Maximum displacement and control member stroke — Compute the displacement as a linear function of the control position specified at port C.
Displacement vs. control member position table — Obtain the displacement through interpolation or extrapolation of tabulated data specified over a range of control positions.

Restricted Parameter

This parameter is locked for editing when using the Simscape Restricted mode.

Maximum stroke — Control position corresponding to maximum displacement
`0.005 m` (default) | scalar with units of length

Control position corresponding to a maximum displacement. The physical signal input at port C saturates at this value. If the input rises higher, the block sets the control position to the maximum stroke.

Maximum displacement — Maximum fluid volume swept per unit shaft rotation
`30 cm^3/rev` (default) | scalar with units of volume/angle

Maximum fluid volume swept per unit shaft rotation. The displacement reaches this value when the control position hits the maximum stroke.

Dependencies

This parameter is enabled when the Displacement parameterization parameter is set to Maximum displacement and control member stroke.

Control member position vector — Control positions at which to specify displacement tabular data
`[-0.0075, -0.0025, 0.0, 0.0025, 0.0075] m` (default) | M-element vector with units of length

M-element vector of control positions at which to specify the instantaneous displacement. The vector size, M, must be two or greater. The vector elements need not be uniformly spaced. However, they must be monotonically increasing or decreasing.

Dependencies

This parameter is enabled when the Displacement parameterization parameter is set to Displacement vs. control member position table.

Displacement vector — Displacement tabular data for the specified control positions
`[-30.0, -19.0, 0.0, 19.0, 30.0] cm^3/rev` (default) | M-element vector with units of volume/angle

M-element vector with the displacement tabular data for the specified control positions. The vector size, M, must match that of the Control member position vector parameter.

Dependencies

This parameter is enabled when the Displacement parameterization parameter is set to Displacement vs. control member position table.

Interpolation method — Numerical technique used to determine displacements within the tabular data range
`Linear` (default) | `Smooth`

Numerical technique used to map control position signals to displacements within the tabular date range. The interpolation method joins tabular data points using straight or curved line segments. Displacements within the range of the tabular data are assumed to lie on these segments.

Linear — Join neighboring data points using straight line segments. Line slopes are generally discontinuous at the line segment end points.
Smooth — Join neighboring data points using curved line segments generated with a modified Akima algorithm. Line slopes are continuous at the line segment end points.

Dependencies

This parameter is enabled when the Displacement parameterization parameter is set to Displacement vs. control member position table.

Restricted Parameter

This parameter is locked for editing when using the Simscape Restricted mode.

Extrapolation method — Numerical technique used to determine displacements outside the tabular data range
`Linear` (default) | `Nearest`

Numerical technique used to map control position signals to displacements outside the tabular date range. The extrapolation method extends the first and last tabular data points outward using horizontal or sloped straight line segments. Displacements outside the range of the tabular data are assumed to lie on these segments.

Linear — Extend the tabular data using sloped straight line segments. The line slopes are computed from the first and last two tabular data points.
Nearest — Extend the tabular data using horizontal straight line segments. The lines correspond to the displacements specified in the first and last tabular data points.

Dependencies

This parameter is enabled when the Displacement parameterization parameter is set to Displacement vs. control member position table.

Restricted Parameter

This parameter is locked for editing when using the Simscape Restricted mode.

Leakage and friction parameterization — Parameterization used to compute leakage flow rate and friction torque
`Analytical` (default) | `Tabulated data — volumetric and mechanical efficiencies` | `Tabulated data — volumetric and mechanical losses`

Parameterization used to compute flow-rate and torque losses due to internal leaks and friction. The Analytical parameterization relies on nominal parameters generally available from component data sheets. The remaining, tabular, options rely on lookup tables to map pressure drop, angular velocity, and displacement to component efficiencies or losses. The tabular options include:

Tabulated data — volumetric and mechanical efficiencies
Tabulated data — volumetric and mechanical losses

Nominal shaft angular velocity — Shaft angular velocity at which to specify the volumetric efficiency
`188 rad/s` (default) | scalar with units of angle/time

Angular velocity of the rotating shaft at which the component’s nominal volumetric efficiency is known. Nominal parameters are typically published for standard operating conditions in manufacturer’s data sheets. The block uses this parameter to calculate, using simple linear functions, the leakage flow rate and friction torque.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

Nominal pressure gain — Pressure gain at which to specify the volumetric efficiency
`100e5 Pa` (default)

Pressure gain from inlet to outlet at which the component’s nominal volumetric efficiency is known. Nominal parameters are typically published for standard operating conditions in manufacturer’s data sheets. The block uses this parameter to calculate, using a simple linear function, the internal leakage flow rate.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

Nominal kinematic viscosity — Kinematic viscosity at which to specify the volumetric efficiency
`18 cSt` (default) | scalar with units of area/time

Kinematic viscosity of the hydraulic fluid at which the component’s nominal volumetric efficiency is known. Nominal parameters are typically published for standard operating conditions in manufacturer’s data sheets. The block uses this parameter to calculate, using a simple linear function, the internal leakage flow rate.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

Nominal fluid density — Fluid density at which to specify the volumetric efficiency
`900 kg/m^3` (default) | scalar with units of mass/volume

Mass density of the hydraulic fluid at which the component’s nominal volumetric efficiency is known. Nominal parameters are typically published for standard operating conditions in manufacturer’s data sheets. The block uses this parameter to calculate, using a simple linear function, the internal leakage flow rate.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

Volumetric efficiency at nominal conditions — Volumetric efficiency at the specified nominal conditions
`0.92` (default) | unitless scalar between `0` and `1`

Volumetric efficiency, defined as the ratio of actual to ideal volumetric flow rates, at the specified nominal conditions. Nominal parameters are typically published for standard operating conditions in manufacturer’s data sheets. The block uses this parameter to calculate, using a simple linear function, the internal leakage flow rate.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

No-load torque — Minimum torque required to induce shaft rotation
`0.05 N*m` (default) | scalar with units of torque

Torque required to overcome seal friction and induce rotation of the mechanical shaft. This torque is the load-independent component of the total friction torque.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Analytical.

Friction torque vs. pressure gain coefficient at maximum displacement — Proportionality constant at maximum displacement between friction torque and pressure gain
`0.6e-6 N*m/Pa` (default) | scalar with units of torque/pressure

Proportionality constant at maximum displacement between the friction torque on the mechanical shaft and the pressure gain from inlet to outlet.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Displacement threshold for pump—motor transition — Displacement at which to initiate the transition between pumping and motoring modes
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Absolute value of the instantaneous displacement below which the component transitions between pumping and motoring modes. A hyperbolic Tanh function transforms the leakage flow rate and friction torque such that the transition is continuous and smooth.

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Simulation warning mode for invalid pressures at the component ports. Select Warning to be notified when pressure falls below a minimum specified value. The warning can be useful in models where pressure can fall below the saturated vapor pressure of the hydraulic fluid, causing cavitation to occur.

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

Lower bound of the pressure validity range. A warning is issued if pressure falls below the specified value.

Dependencies

This parameter is enabled when the Check if lower side pressure violating minimum valid condition parameter is set to Warning.

Pressure gain vector for efficiencies, dp — Pressure gains at which to specify the volumetric and mechanical efficiencies
M-element vector with units of pressure (default)

M-element vector of pressure gains at which to specify the efficiency tabular data. The vector size, M, must be two or greater. The vector elements need not be uniformly spaced. However, they must monotonically increase in value from left to right.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Shaft angular velocity vector for efficiencies, w — Angular velocities at which to specify the volumetric and mechanical efficiencies
N-element vector with units of angular velocity (default)

N-element vector of shaft angular velocities at which to specify the efficiency tabular data. The vector size, N, must be two or greater. The vector elements need not be uniformly spaced. However, they must monotonically increase in value from left to right.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Displacement vector for efficiencies, D — Displacements at which to specify the volumetric and mechanical efficiencies
L-element vector with units of volume/angle (default)

L-element vector of displacements at which to specify the efficiency tabular data. The vector size, N, must be two or greater. The vector elements need not be uniformly spaced. However, they must be monotonically increasing or decreasing.

Volumetric efficiency table, e_v(dp,w,D) — Volumetric efficiencies at the specified pressure gains, angular velocities, and displacements
unitless M-by-N-byL matrix

M-by-N-by-L matrix with the volumetric efficiencies at the specified fluid pressure gains, shaft angular velocities, and displacements. The efficiencies must fall in the range of 0–1. M, N, and L are the sizes of the specified lookup-table vectors:

M is the number of vector elements in the Pressure gain vector for efficiencies, dp parameter.
N is the number of vector elements in the Shaft angular velocity vector for efficiencies, w parameter.
L is the number of vector elements in the Displacement vector for efficiencies, D parameter.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Mechanical efficiency table, e_m(dp,w,D) — Mechanical efficiencies at the specified pressure drops, angular velocities, and displacements
unitless M-by-N matrix

M-by-N-by-L matrix with the mechanical efficiencies corresponding to the specified fluid pressure gains, shaft angular velocities, and displacements. The efficiencies must fall in the range of 0–1. M, N, and L are the sizes of the specified lookup-table vectors:

M is the number of vector elements in the Pressure gain vector for efficiencies, dp parameter.
N is the number of vector elements in the Shaft angular velocity vector for efficiencies, w parameter.
L is the number of vector elements in the Displacement vector for efficiencies, D parameter.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Pressure gain from inlet to outlet below which the component begins to transition between motoring and pumping modes. A hyperbolic Tanh function transforms the leakage flow rate and friction torque such that the transition is continuous and smooth.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Angular velocity threshold for pump—motor transition — Shaft angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Shaft angular velocity below which the component begins to transition between motoring and pumping modes. A hyperbolic Tanh function transforms the leakage flow rate and friction torque such that the transition is continuous and smooth.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies.

Check if operating beyond the octants of supplied tabulated data — Simulation warning mode for operating conditions outside the range of tabulated data
`None` (default) | `Warning`

Simulation warning mode for operating conditions outside the range of tabulated data. Select Warning to be notified when the fluid pressure gain, shaft angular velocity, or instantaneous displacement cross outside the specified tabular data. The warning does not cause simulation to stop.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical efficiencies or Tabulated data — volumetric and mechanical losses.

Pressure gain vector for losses, dp — Pressure gains at which to specify the volumetric and mechanical losses
M-element vector with units of pressure (default)

M-element vector of pressure gains at which to specify the loss tabular data. The vector size, M, must be two or greater. The vector elements need not be uniformly spaced. However, they must monotonically increase in value from left to right.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical losses.

Shaft angular velocity vector for losses, w — Angular velocities at which to specify the volumetric and mechanical losses
N-element vector with units of angle/time (default)

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical losses.

Displacement vector for losses, D — Displacements at which to specify the volumetric and mechanical losses
L-element vector with units of volume/angle (default)

L-element vector of displacements at which to specify the loss tabular data. The vector size, N, must be two or greater. The vector elements need not be uniformly spaced. However, they must be monotonically increasing or decreasing.

Volumetric loss table, q_loss(dp,w,D) — Internal leakage flow rates at the specified pressure gains, angular velocities, and displacements
M-by-N-by-L matrix with units of volume/time

M-by-N-by-L matrix with the volumetric gains at the specified fluid pressure drops, shaft angular velocities, and displacements. Volumetric loss is defined here as the internal leakage volumetric flow rate between port A and port B. M, N, and L are the sizes of the specified lookup-table vectors:

M is the number of vector elements in the Pressure gain vector for losses, dp parameter.
N is the number of vector elements in the Shaft angular velocity vector for losses, w parameter.
L is the number of vector elements in the Displacement vector for losses, D parameter.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical losses.

Mechanical loss table, torque_loss(dp,w,D) — Friction torques at the specified pressure gains, angular velocities, and displacements
M-by-N-by-L matrix with units of torque

M-by-N-by-L matrix with the mechanical losses at the specified fluid pressure gains, shaft angular velocities, and displacements. Mechanical loss is defined here as the friction torque due to seals and internal components. M, N, and L are the sizes of the specified lookup-table vectors:

M is the number of vector elements in the Pressure gain vector for losses, dp parameter.
N is the number of vector elements in the Shaft angular velocity vector for losses, w parameter.
L is the number of vector elements in the Displacement vector for losses, D parameter.

Dependencies

This parameter is enabled when the Leakage and friction parameterization parameter is set to Tabulated data — volumetric and mechanical losses.

Variant 2: Input efficiencies

Minimum volumetric efficiency — Lower saturation bound on the volumetric efficiency input signal
`1e-3` (default) | unitless scalar between `0` and `1`

Smallest allowed value of the volumetric efficiency. The input from physical signal port EV saturates at the specified value. If the input signal falls below the minimum volumetric efficiency, the volumetric efficiency is set to the minimum volumetric efficiency.

Maximum volumetric efficiency — Upper saturation bound on the volumetric efficiency input signal
`1` (default) | unitless scalar between `0` and `1`

Largest allowed value of the volumetric efficiency. The input from physical signal port EV saturates at the specified value. If the input signal rises above the maximum volumetric efficiency, the volumetric efficiency is set to the maximum volumetric efficiency.

Minimum mechanical efficiency — Lower saturation bound on the volumetric efficiency input signal
`1e-3` (default) | unitless scalar between `0` and `1`

Smallest allowed value of the mechanical efficiency. The input from physical signal port EM saturates at the specified value. If the input signal falls below the minimum mechanical efficiency, the mechanical efficiency is set to the minimum mechanical efficiency.

Maximum mechanical efficiency — Upper saturation bound on the volumetric efficiency input signal
`1` (default) | unitless scalar between `0` and `1`

Largest allowed value of the mechanical efficiency. The input from physical signal port EM saturates at the specified value. If the input signal rises above the maximum mechanical efficiency, the mechanical efficiency is set to the maximum mechanical efficiency.

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Angular velocity threshold for pump—motor transition — Angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Displacement threshold for motor-pump transition — Displacement at which to initiate a smooth transition between pump and motor modes
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Absolute value of the instantaneous displacement below which the component transitions between motoring and pumping modes. A hyperbolic Tanh function transforms the leakage flow rate and friction torque such that the transition is continuous and smooth.

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

Lower bound of the pressure validity range. A warning is issued if pressure falls below the specified value.

Dependencies

This parameter is enabled when the Check if lower side pressure violating minimum valid condition parameter is set to Warning.

Variant 3: Input losses

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Angular velocity threshold for pump—motor transition — Angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Displacement threshold for pump—motor transition — Displacement below which the transition between pumping and motoring modes begins
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Check if operating beyond the pump mode — Simulation warning mode for operating conditions outside pumping mode
`None` (default) | `Warning`

Simulation warning mode for operating conditions outside the pumping mode. A warning is issued if the pump transitions to motoring mode. Select Warning to be notified when this transition occurs. The warning does not cause simulation to stop.

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

Lower bound of the pressure validity range. A warning is issued if pressure falls below the specified value.

Dependencies

This parameter is enabled when the Check if lower side pressure violating minimum valid condition parameter is set to Warning.

Extended Capabilities

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

Version History

collapse all

R2023a: To be removed

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead.

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

Variable-Displacement Pump

Description

Block Variants and Loss Parameterizations

Displacement Parameterizations

Flow Rate and Driving Torque

Assumptions

Ports

Input

C — Control member offset, m physical signal

Dependencies

D — Displacement volume, cm^3/rev physical signal

Dependencies

EV — Volumetric efficiency, unitless physical signal

Dependencies

EM — Mechanical efficiency, unitless physical signal

Dependencies

LV — Volumetric loss, m^3/s physical signal

Dependencies

LM — Mechanical loss, N*m physical signal

Dependencies

Conserving

T — Pump inlet hydraulic (isothermal liquid)

P — Pump outlet hydraulic (isothermal liquid)

S — Pump shaft mechanical rotational

Parameters

Modeling option — Loss parameterizations Analytical or tabulated data | Input efficiencies | Input losses

Displacement parameterization — Parameterization used to map control positions to displacements Maximum displacement and control member stroke (default)

Restricted Parameter

Maximum stroke — Control position corresponding to maximum displacement 0.005 m (default) | scalar with units of length

Maximum displacement — Maximum fluid volume swept per unit shaft rotation 30 cm^3/rev (default) | scalar with units of volume/angle

Dependencies

Control member position vector — Control positions at which to specify displacement tabular data [-0.0075, -0.0025, 0.0, 0.0025, 0.0075] m (default) | M-element vector with units of length

Dependencies

Displacement vector — Displacement tabular data for the specified control positions [-30.0, -19.0, 0.0, 19.0, 30.0] cm^3/rev (default) | M-element vector with units of volume/angle

Dependencies

Interpolation method — Numerical technique used to determine displacements within the tabular data range Linear (default) | Smooth

Dependencies

Restricted Parameter

Extrapolation method — Numerical technique used to determine displacements outside the tabular data range Linear (default) | Nearest

Dependencies

Restricted Parameter

Leakage and friction parameterization — Parameterization used to compute leakage flow rate and friction torque Analytical (default) | Tabulated data — volumetric and mechanical efficiencies | Tabulated data — volumetric and mechanical losses

Nominal shaft angular velocity — Shaft angular velocity at which to specify the volumetric efficiency 188 rad/s (default) | scalar with units of angle/time

Dependencies

Nominal pressure gain — Pressure gain at which to specify the volumetric efficiency 100e5 Pa (default)

Dependencies

Nominal kinematic viscosity — Kinematic viscosity at which to specify the volumetric efficiency 18 cSt (default) | scalar with units of area/time

Dependencies

Nominal fluid density — Fluid density at which to specify the volumetric efficiency 900 kg/m^3 (default) | scalar with units of mass/volume

Dependencies

Volumetric efficiency at nominal conditions — Volumetric efficiency at the specified nominal conditions 0.92 (default) | unitless scalar between 0 and 1

Dependencies

No-load torque — Minimum torque required to induce shaft rotation 0.05 N*m (default) | scalar with units of torque

Dependencies

Friction torque vs. pressure gain coefficient at maximum displacement — Proportionality constant at maximum displacement between friction torque and pressure gain 0.6e-6 N*m/Pa (default) | scalar with units of torque/pressure

Dependencies

Displacement threshold for pump—motor transition — Displacement at which to initiate the transition between pumping and motoring modes 0.5 cm^3/rev (default) | scalar with units of volume/angle

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure None (default) | Warning

Minimum valid pressure — Pressure required to trigger simulation warning 0 (default) | scalar with units of pressure

Dependencies

Pressure gain vector for efficiencies, dp — Pressure gains at which to specify the volumetric and mechanical efficiencies M-element vector with units of pressure (default)

Dependencies

Shaft angular velocity vector for efficiencies, w — Angular velocities at which to specify the volumetric and mechanical efficiencies N-element vector with units of angular velocity (default)

Dependencies

Displacement vector for efficiencies, D — Displacements at which to specify the volumetric and mechanical efficiencies L-element vector with units of volume/angle (default)

Volumetric efficiency table, e_v(dp,w,D) — Volumetric efficiencies at the specified pressure gains, angular velocities, and displacements unitless M-by-N-byL matrix

Dependencies

Mechanical efficiency table, e_m(dp,w,D) — Mechanical efficiencies at the specified pressure drops, angular velocities, and displacements unitless M-by-N matrix

Dependencies

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes 1e5 Pa (default) | scalar with units of pressure

Dependencies

Angular velocity threshold for pump—motor transition — Shaft angular velocity at which to initiate a smooth transition between pump and motor modes 10 rad/s (default) | scalar with units of angle/time

Dependencies

Check if operating beyond the octants of supplied tabulated data — Simulation warning mode for operating conditions outside the range of tabulated data None (default) | Warning

Dependencies

Pressure gain vector for losses, dp — Pressure gains at which to specify the volumetric and mechanical losses M-element vector with units of pressure (default)

Dependencies

Shaft angular velocity vector for losses, w — Angular velocities at which to specify the volumetric and mechanical losses N-element vector with units of angle/time (default)

Dependencies

Displacement vector for losses, D — Displacements at which to specify the volumetric and mechanical losses L-element vector with units of volume/angle (default)

C — Control member offset, `m`
physical signal

D — Displacement volume, `cm^3/rev`
physical signal

EV — Volumetric efficiency, unitless
physical signal

EM — Mechanical efficiency, unitless
physical signal

LV — Volumetric loss, `m^3/s`
physical signal

LM — Mechanical loss, `N*m`
physical signal

T — Pump inlet
hydraulic (isothermal liquid)

P — Pump outlet
hydraulic (isothermal liquid)

S — Pump shaft
mechanical rotational

Modeling option — Loss parameterizations
`Analytical or tabulated data` | `Input efficiencies` | `Input losses`

Displacement parameterization — Parameterization used to map control positions to displacements
`Maximum displacement and control member stroke` (default)

Maximum stroke — Control position corresponding to maximum displacement
`0.005 m` (default) | scalar with units of length

Maximum displacement — Maximum fluid volume swept per unit shaft rotation
`30 cm^3/rev` (default) | scalar with units of volume/angle

Control member position vector — Control positions at which to specify displacement tabular data
`[-0.0075, -0.0025, 0.0, 0.0025, 0.0075] m` (default) | M-element vector with units of length

Displacement vector — Displacement tabular data for the specified control positions
`[-30.0, -19.0, 0.0, 19.0, 30.0] cm^3/rev` (default) | M-element vector with units of volume/angle

Interpolation method — Numerical technique used to determine displacements within the tabular data range
`Linear` (default) | `Smooth`

Extrapolation method — Numerical technique used to determine displacements outside the tabular data range
`Linear` (default) | `Nearest`

Leakage and friction parameterization — Parameterization used to compute leakage flow rate and friction torque
`Analytical` (default) | `Tabulated data — volumetric and mechanical efficiencies` | `Tabulated data — volumetric and mechanical losses`

Nominal shaft angular velocity — Shaft angular velocity at which to specify the volumetric efficiency
`188 rad/s` (default) | scalar with units of angle/time

Nominal pressure gain — Pressure gain at which to specify the volumetric efficiency
`100e5 Pa` (default)

Nominal kinematic viscosity — Kinematic viscosity at which to specify the volumetric efficiency
`18 cSt` (default) | scalar with units of area/time

Nominal fluid density — Fluid density at which to specify the volumetric efficiency
`900 kg/m^3` (default) | scalar with units of mass/volume

Volumetric efficiency at nominal conditions — Volumetric efficiency at the specified nominal conditions
`0.92` (default) | unitless scalar between `0` and `1`

No-load torque — Minimum torque required to induce shaft rotation
`0.05 N*m` (default) | scalar with units of torque

Friction torque vs. pressure gain coefficient at maximum displacement — Proportionality constant at maximum displacement between friction torque and pressure gain
`0.6e-6 N*m/Pa` (default) | scalar with units of torque/pressure

Displacement threshold for pump—motor transition — Displacement at which to initiate the transition between pumping and motoring modes
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

Pressure gain vector for efficiencies, dp — Pressure gains at which to specify the volumetric and mechanical efficiencies
M-element vector with units of pressure (default)

Shaft angular velocity vector for efficiencies, w — Angular velocities at which to specify the volumetric and mechanical efficiencies
N-element vector with units of angular velocity (default)

Displacement vector for efficiencies, D — Displacements at which to specify the volumetric and mechanical efficiencies
L-element vector with units of volume/angle (default)

Volumetric efficiency table, e_v(dp,w,D) — Volumetric efficiencies at the specified pressure gains, angular velocities, and displacements
unitless M-by-N-byL matrix

Mechanical efficiency table, e_m(dp,w,D) — Mechanical efficiencies at the specified pressure drops, angular velocities, and displacements
unitless M-by-N matrix

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Angular velocity threshold for pump—motor transition — Shaft angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Check if operating beyond the octants of supplied tabulated data — Simulation warning mode for operating conditions outside the range of tabulated data
`None` (default) | `Warning`

Pressure gain vector for losses, dp — Pressure gains at which to specify the volumetric and mechanical losses
M-element vector with units of pressure (default)

Shaft angular velocity vector for losses, w — Angular velocities at which to specify the volumetric and mechanical losses
N-element vector with units of angle/time (default)

Displacement vector for losses, D — Displacements at which to specify the volumetric and mechanical losses
L-element vector with units of volume/angle (default)

Volumetric loss table, q_loss(dp,w,D) — Internal leakage flow rates at the specified pressure gains, angular velocities, and displacements
M-by-N-by-L matrix with units of volume/time

Mechanical loss table, torque_loss(dp,w,D) — Friction torques at the specified pressure gains, angular velocities, and displacements
M-by-N-by-L matrix with units of torque

Minimum volumetric efficiency — Lower saturation bound on the volumetric efficiency input signal
`1e-3` (default) | unitless scalar between `0` and `1`

Maximum volumetric efficiency — Upper saturation bound on the volumetric efficiency input signal
`1` (default) | unitless scalar between `0` and `1`

Minimum mechanical efficiency — Lower saturation bound on the volumetric efficiency input signal
`1e-3` (default) | unitless scalar between `0` and `1`

Maximum mechanical efficiency — Upper saturation bound on the volumetric efficiency input signal
`1` (default) | unitless scalar between `0` and `1`

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Angular velocity threshold for pump—motor transition — Angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Displacement threshold for motor-pump transition — Displacement at which to initiate a smooth transition between pump and motor modes
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

Pressure gain threshold for pump—motor transition — Pressure gain at which to initiate a smooth transition between motor and pump modes
`1e5 Pa` (default) | scalar with units of pressure

Angular velocity threshold for pump—motor transition — Angular velocity at which to initiate a smooth transition between pump and motor modes
`10 rad/s` (default) | scalar with units of angle/time

Displacement threshold for pump—motor transition — Displacement below which the transition between pumping and motoring modes begins
`0.5 cm^3/rev` (default) | scalar with units of volume/angle

Check if operating beyond the pump mode — Simulation warning mode for operating conditions outside pumping mode
`None` (default) | `Warning`

Check if lower side pressure violating minimum valid condition — Simulation warning mode for minimum valid pressure
`None` (default) | `Warning`

Minimum valid pressure — Pressure required to trigger simulation warning
`0` (default) | scalar with units of pressure

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