# Variable-Displacement Pump

Variable-displacement bidirectional hydraulic pump

• Library:
• Hydraulics (Isothermal) / Pumps & 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 Friction and leakage parameterization parameter.

Loss Parameterizations

The block provides three Simulink® variants to select from. To change the active block variant, right-click the block and select Simscape > Block choices. 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 Friction and leakage 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

`$q={q}_{\text{Ideal}}+{q}_{\text{Leak}},$`
where:

• q is the net volumetric flow rate.

• qIdeal is the ideal volumetric flow rate.

• qLeak is the internal leakage volumetric flow rate.

The driving torque required to power the pump is

`$\tau ={\tau }_{\text{Ideal}}+{\tau }_{\text{Friction}},$`
where:

• τ is the net driving torque.

• τIdeal is the ideal driving torque.

• τFriction is the friction torque.

#### Ideal Flow Rate and Ideal Torque

The ideal volumetric flow rate is

`${q}_{\text{Ideal}}={D}_{\text{Sat}}·\omega ,$`
and the ideal driving torque is
`${\tau }_{\text{Ideal}}={D}_{\text{Sat}}·\Delta p,$`
where:

• DSat 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`,

`${D}_{\text{Sat}}=\left\{\begin{array}{ll}\text{sign}\left(D\right)·{D}_{\text{Max}},\hfill & |D|\ge {D}_{\text{Max}}\hfill \\ \sqrt{{D}^{2}+{D}_{\text{Threshold}}^{2}},\hfill & D\ge 0\hfill \\ -\sqrt{{D}^{2}+{D}_{\text{Threshold}}^{2}},\hfill & D<0\hfill \end{array},$`
where:

• D is the instantaneous fluid displacement determined from the physical signal input specified at port C or port D.

• DMax is the specified value of the Maximum displacement block parameter.

• DThreshold 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:

`${D}_{Sat}=\left\{\begin{array}{ll}\sqrt{{D}^{2}+{D}_{Thresh}^{2}},\hfill & D\ge 0\hfill \\ -\sqrt{{D}^{2}+{D}_{Thresh}^{2}},\hfill & D<0\hfill \end{array}.$`

#### 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

`${q}_{\text{Leak}}={K}_{\text{HP}}\Delta p,$`
and the friction torque is
`${\tau }_{\text{Friction}}=\left({\tau }_{0}+K{\text{​}}_{\text{TP}}|\frac{{D}_{\text{Sat}}}{{D}_{\text{Max}}}||\Delta p|\right)\mathrm{tanh}\left(\frac{4\omega }{{\omega }_{\text{Thresh}}}\right),$`
where:

• KHP is the Hagen-Poiseuille coefficient for laminar pipe flows. This coefficient is computed from the specified nominal parameters.

• KTP 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.

• ωThreshold 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

`${K}_{\text{HP}}=\frac{{\nu }_{\text{Nom}}}{\rho v}\frac{\text{\hspace{0.17em}}{\rho }_{\text{Nom}}{\omega }_{\text{Nom}}D}{\Delta {p}_{\text{Nom}}}\left(1-{\eta }_{\text{v,Nom}}\right),$`
where:

• νNom is the specified value of the Nominal kinematic viscosity block parameter. This is the kinematic viscosity at which the nominal volumetric efficiency is specified.

• ρNom is the specified value of the Nominal fluid density block parameter. This is the density at which the nominal volumetric efficiency is specified.

• ωNom 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.

• ΔpNom is the specified value of the Nominal pressure gain block parameter. This is the pressure drop at which the nominal volumetric efficiency is specified.

• ηv,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

`${q}_{\text{Leak}}={q}_{\text{Leak,Pump}}\frac{\left(1+\alpha \right)}{2}+{q}_{\text{Leak,Motor}}\frac{\left(1-\alpha \right)}{2},$`
and the friction torque is
`${\tau }_{\text{Friction}}={\tau }_{\text{Friction,Pump}}\frac{1+\alpha }{2}+{\tau }_{\text{Friction,Motor}}\frac{1-\alpha }{2},$`
where:

• α is a numerical smoothing parameter for the motor-pump transition.

• qLeak,Pump is the leakage flow rate in pump mode.

• qLeak,Motor is the leakage flow rate in motor mode.

• τFriction,Pump is the friction torque in pump mode.

• τFriction,Motor is the friction torque in motor mode.

The smoothing parameter α is given by the hyperbolic function

`$\alpha =\text{tanh}\left(\frac{4\Delta p}{\Delta {p}_{\text{Threshold}}}\right)·\text{tanh}\left(\frac{4\omega }{{\omega }_{\text{Threshold}}}\right)·\mathrm{tanh}\left(\frac{4D}{{D}_{\text{Threshold}}}\right),$`
where:

• ΔpThreshold is the specified value of the Pressure drop threshold for motor-pump transition block parameter.

• ωThreshold is the specified value of the Angular velocity threshold for motor-pump transition block parameter.

• DThreshold 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

`${q}_{\text{Leak,Pump}}=\left(1-{\eta }_{\text{v}}\right){q}_{\text{Ideal}},$`
in pump mode and through the equation
`${q}_{\text{Leak,Motor}}=-\left(1-{\eta }_{\text{v}}\right)q,$`
in motor mode, where:

• ηv 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

`${\tau }_{\text{Friction,Pump}}=\left(1-{\eta }_{\text{m}}\right)\tau ,$`
in pump mode and through the equation
`${\tau }_{\text{Friction,Motor}}=-\left(1-{\eta }_{\text{m}}\right){\tau }_{\text{Ideal}},$`
in motor mode, where:

• ηm 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

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 losses`, the leakage flow rate equation is
`${q}_{\text{Leak}}={q}_{\text{Leak}}\left(\Delta p,\omega ,{D}_{\text{Sat}}\right).$`
and the friction torque equation is
`${\tau }_{\text{Friction}}={\tau }_{\text{Friction}}\left(\Delta p,\omega ,{D}_{\text{Sat}}\right),$`
where qLeak(Δp,ω,DSat) and τFriction(Δp,ω,DSat) 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

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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```.

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`.

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```.

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```.

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```.

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

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

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

Mechanical rotational conserving port representing the pump shaft.

## Parameters

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

#### Variant 1: `Analytical or tabulated data`

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data```.

#### Restricted Parameter

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

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data```.

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 block variant is set to ```Analytical or tabulated data``` and the Displacement parameterization parameter is set to ```Maximum displacement and control member stroke```.

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 block variant is set to ```Analytical or tabulated data``` and the Displacement parameterization parameter is set to ```Displacement vs. control member position table```.

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 block variant is set to ```Analytical or tabulated data``` and the Displacement parameterization parameter is set to ```Displacement vs. control member position table```.

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 block variant is set to ```Analytical or tabulated data``` and 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.

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 block variant is set to ```Analytical or tabulated data``` and 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.

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```

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data```.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to `Analytical`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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.

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.

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 parameter is set to `Warning`.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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.

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 parameter.

• L is the number of vector elements in the Displacement vector for efficiencies, D parameter.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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 parameter.

• L is the number of vector elements in the Displacement vector for efficiencies, D parameter.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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 block variant is set to ```Input efficiencies``` or when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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 block variant is set to ```Input efficiencies``` or when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies```.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical efficiencies``` or ```Tabulated data — volumetric and mechanical losses```.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical losses```.

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 block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical losses```.

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.

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 parameter.

• L is the number of vector elements in the Displacement vector for losses, D parameter.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical losses```.

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 parameter.

• L is the number of vector elements in the Displacement vector for losses, D parameter.

#### Dependencies

This parameter is enabled when the block variant is set to ```Analytical or tabulated data``` and the Leakage and friction parameterization parameter is set to ```Tabulated data — volumetric and mechanical losses```.

#### Variant 2: `Input efficiencies`

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 block variant is set to ```Input efficiencies```.

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 block variant is set to ```Input efficiencies```.

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.

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Input efficiencies```.

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Input efficiencies```.

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Input efficiencies```.

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Input efficiencies```.

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.

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 parameter is set to `Warning`.

#### Variant 3: `Input losses`

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.

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.

#### Dependencies

This parameter is enabled when the block variant is set to ```Input losses```.

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.

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 parameter is set to `Warning`.