Fixed-Displacement Pump (TL)
A constant-volume pump in a heat-conducting fluid network.
blockType: EngeeFluids.ThermalLiquid.Turbomachinery.FixedDisplacementPump
Path in the library:
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Description
The Fixed-Displacement Pump (TL) block It is a pump that receives energy from a mechanical rotary system and transmits it to a heat-conducting fluid network. The working volume of the pump is fixed at a constant value, which is set using the Displacement parameter.
Ports A and B represent the pump inlet ports. Ports R and C represent the drive shaft and pump housing. The liquid flow can be directed from port A to port B (forward mode) or from port B to port A (reverse mode). Operation in the pump mode occurs when the pressure in the flow direction increases. The operation mode of the hydraulic motor occurs when the pressure drops in the flow direction.
_ Modes of operation_
The unit has four operating modes. The operating mode depends on the pressure drop from port A to port B and angular velocity :
-
Mode 1, Direct pump mode: the positive angular velocity of the shaft causes pressure to rise from port A to port B and flow from port A to port B.
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Mode 2, reverse hydraulic motor mode: the flow from port B to port A causes a decrease in pressure from port B to port A and a negative angular velocity of the shaft.
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Mode 3, Reverse pump mode: the negative angular velocity of the shaft causes pressure to rise from port B to port A and flow from port B to port A.
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Mode 4, direct hydraulic motor mode: the flow from port A to port B causes a decrease in pressure from port A to port B and a positive angular velocity of the shaft.
The time constant of the pump is negligible compared to the time constant of the system. The pump reaches a steady state almost instantly and is considered as a quasi-stationary component.
Energy conservation
The mechanical work performed by the pump is related to the exchange of energy. The energy conservation equation has the form:
where
-
and — energy flows in ports A and B respectively;
-
— hydraulic power of the pump. It is a function of the pressure difference between the pump ports: .
The mechanical power of the pump is determined from the torque and angular velocity :
Flow rate and torque
The mass flow rate of the pump is:
where
-
— actual mass consumption;
-
— ideal mass flow rate;
-
— mass consumption of internal leakage.
The torque required to actuate the pump is:
where
-
— actual torque;
-
— perfect torque;
-
— the moment of friction.
The ideal flow rate and ideal torque are calculated as
where:
-
— the average value of the liquid density in the ports of the heat-conducting liquid A and B;
-
— value of the Displacement parameter;
-
— angular rotation speed of the shaft;
-
— pressure increase from inlet to outlet.
Analytical parameterization of leakage and friction moment
If the Leakage and friction parameterization parameter is set to Analytical
, the unit calculates the leakage and friction moment based on the nominal values of shaft rotation speed, pressure drop, mechanical and volumetric efficiency. The leakage rate, which depends on the pressure drop across the hydraulic motor, is calculated as:
and the moment of friction is calculated as:
where
-
— the Hagen-Poiseuille coefficient for laminar flows. The unit calculates this coefficient from the specified nominal parameters;
-
— the average dynamic viscosity of the liquid in the ports;
-
— average density of liquid in ports;
-
— coefficient of dependence of the moment of friction on pressure at nominal working volume, which is determined by the value of the parameter Mechanical efficiency at nominal conditions, :
where — the moment of friction under nominal conditions:
-
— pressure increase for a given volumetric efficiency, the value of the parameter Nominal pressure gain. This value represents the pressure increase factor at which the nominal volumetric efficiency is indicated.;
-
— value of the No-load torque parameter;
-
— angular velocity for a given volumetric efficiency, the value of the parameter Nominal shaft angular velocity. This value represents the angular velocity at which the unit sets the nominal volumetric efficiency.
The unit determines the Hagen-Poiseuille coefficient based on the nominal parameters of the liquid and components
where:
-
— dynamic viscosity for a given volumetric efficiency, the value of the parameter Nominal Dynamic viscosity. This value represents the dynamic viscosity at which the unit determines the nominal volumetric efficiency.;
-
— volumetric efficiency under nominal conditions, the value of the parameter Volumetric efficiency at nominal conditions, is the volumetric efficiency corresponding to the specified nominal conditions.
Tabular data for parameterization
When using tabular data for the efficiency or losses of a hydraulic motor, data can be provided for one or more operating modes. The signs of the tabular data determine the operating mode of the block. If data is provided for less than four operating modes, the block calculates additional data for another mode(s), expanding the specified data into the remaining quadrants.
Tabular data — parameterization of volumetric and mechanical efficiency
If the Leakage and friction parameterization parameter is set to Tabulated data - volumetric and mechanical efficiencies
, the block performs parameterization based on tabular data for volumetric and mechanical efficiency.
The leakage rate is:
and the moment of friction is:
where
-
— numerical smoothing parameter for the transition process from the hydraulic motor to the pump;
-
— leakage rate in pump mode;
-
— leakage rate in hydraulic motor mode;
-
— the moment of friction in the pump mode;
-
— the moment of friction in the hydraulic motor mode.
Smoothing parameter is defined by a hyperbolic function
where
-
— the value of the parameter Pressure gain threshold for motor-pump transition;
-
— the value of the Angular velocity threshold for motor-pump transition parameter.
The volumetric flow rate is calculated based on volumetric efficiency, a value that is set in tabular form in the using the Volumetric efficiency table block parameter.
When operating in pump mode, the leakage rate is:
where — volumetric efficiency obtained by interpolation or extrapolation of tabular data.
Similarly, when operating in the hydraulic motor mode, the leakage rate is:
The moment of friction is calculated in a similar way from the mechanical efficiency, a value that is set in tabular form in the area of using the Mechanical efficiency table block parameter.
When operating in pump mode, the friction moment is:
where — mechanical efficiency, obtained either by interpolation or extrapolation of tabular data.
Similarly, when operating in the hydraulic motor mode, the friction moment is:
Tabular data — parameterization of volume and mechanical losses
If the Leakage and friction parameterization parameter is set to Tabulated data - volumetric and mechanical loss
, then the leakage volume flow rate is set directly in tabular form in the :
The mass flow rate of the leak is calculated from the volume flow rate:
The moment of friction is:
where and — volumetric and mechanical losses obtained by interpolation or extrapolation of tabular data specified in the Volumetric loss table and Mechanical loss table parameters.
Parameterization via the input signal
If the Leakage and friction parameterization parameter is set to Input signal - volumetric and mechanical efficiencies', then ports EV and EM are enabled. Internal leakage and shaft friction are calculated in the same way as with the parameterization of `Tabulated data - volumetric and mechanical efficiencies
, except that the efficiency values and They are delivered directly to the EV and EM ports, respectively.
Efficiency is a positive value with a value between 0
and 1'. The values of the input signals outside these boundaries are set equal to the nearest boundary (`0
for inputs less than 0
and 1
for inputs greater than 1
). Volumetric and mechanical efficiency vary between user-defined minimum and maximum values. Any values below or above this range will take the minimum and maximum set values, respectively.
If the Leakage and friction parameterization parameter is set to `Input signal - volumetric and mechanical losses', then ports LV and LM are enabled. These ports receive the values of the leakage current and the moment of friction in the form of positive scalars.
Ports
Conserving
#
R
—
mechanical port
`rotational mechanics
Details
Angular velocity of rotation and torque of a shaft.
Program usage name |
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#
C
—
mechanical port
`rotational mechanics
Details
Angular velocity of rotation and torque of the body.
Program usage name |
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#
A
—
thermal liquid port
thermal liquid
Details
The fluid inlet or outlet port of a pump.
Program usage name |
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#
B
—
thermal liquid port
thermal liquid
Details
The fluid inlet or outlet port of a pump.
Program usage name |
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Input
#
EV
—
volumetric efficiency
scalar
Details
Volumetric efficiency specified as a scalar. The value must be in the range from 0
to 1
.
Dependencies
To use this port, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Data types |
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Complex numbers support |
No |
#
EM
—
mechanical efficiency
scalar
Details
The mechanical efficiency of the pump, given as a scalar. The value must be in the range from 0
to 1
.
Dependencies
To use this port, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Data types |
|
Complex numbers support |
No |
#
LV
—
leakage volume flow rate
scalar
Details
Pump losses, in m3/s, given as a scalar.
Dependencies
To use this port, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Data types |
|
Complex numbers support |
No |
#
LM
—
friction moment
scalar
Details
The mechanical losses of the pump, in N⋅m, given as a scalar.
Dependencies
To use this port, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Data types |
|
Complex numbers support |
No |
Parameters
Parameters
#
Leakage and friction parameterization —
method for calculating leakage flow rate and friction torque
Analytical
| Tabulated data - volumetric and mechanical efficiencies
| Tabulated data - volumetric and mechanical losses
| Input signal - volumetric and mechanical efficiencies
| Input signal - volumetric and mechanical losses
Details
Parametrization of pump leakage and friction characteristics:
-
`Analytical' - leakage flow and friction torque are calculated using analytical equations.
-
Tabulated data - volumetric and mechanical efficiencies
- volumetric and mechanical efficiencies are calculated from the user defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated from the corresponding two-dimensional tables Volumetric efficiency table, e_v(dp,w) and Mechanical efficiency table, e_m(dp,w). -
`Tabulated data - volumetric and mechanical loss' - leakage flow rate and friction torque are calculated from the user defined parameters Pressure gain vector, dp and Shaft angular velocity vector, w and interpolated from the corresponding two-dimensional tables Volumetric loss table, q_loss(dp,w) and Mechanical loss table, torque_loss(dp,w).
-
`Input signal - volumetric and mechanical efficiencies' - volumetric and mechanical efficiencies are input as signals to the EV and EM ports respectively.
-
Input signal - volumetric and mechanical loss
- leakage flow rate and friction torque are input as signals to ports LV and LM respectively.
Values |
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Default value |
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Program usage name |
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Evaluatable |
No |
#
Displacement —
working volume
l/rad
| l/rev
| gal/rad
| gal/rev
| igal/rad
| m^3/deg
| m^3/rad
| m^3/rev
| cm^3/rad
| cm^3/rev
| mm^3/rad
| km^3/rad
| ft^3/rad
| in^3/deg
| in^3/rad
| in^3/rev
| N*m/Pa/rad
| N*m/bar/rad
| lbf*ft/psi/rad
Details
The volume of fluid displaced when the shaft is rotated by a certain angle. The unit stores this value throughout the simulation.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Nominal shaft angular velocity —
nominal angular speed of the shaft
rpm
| deg/s
| rad/s
Details
The angular speed of the rotating shaft corresponding to a given volumetric efficiency. This value under standard operating conditions is usually given in the manufacturer’s specification. The unit uses this parameters to calculate leakage flow and friction torque.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Nominal pressure gain —
nominal pressure increase between inlet and outlet
Pa
| GPa
| MPa
| atm
| bar
| kPa
| ksi
| psi
| uPa
| kbar
Details
The pressure increase corresponding to the specified volumetric efficiency. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Nominal dynamic viscosity —
nominal dynamic viscosity for a given volumetric efficiency
P
| cP
| reyn
| s*uPa
Details
The nominal dynamic viscosity of the fluid corresponding to a given volumetric efficiency. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
# Volumetric efficiency at nominal conditions — volumetric efficiency at nominal conditions
Details
The ratio of the actual flow rate to the ideal flow rate under nominal conditions. This value under standard operating conditions can usually be found in the manufacturer’s specification. The unit uses this parameters to calculate the internal leakage flow rate.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Default value |
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Program usage name |
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Evaluatable |
Yes |
# Mechanical efficiency at nominal conditions — mechanical efficiency at rated conditions
Details
The ratio of the actual torque to the ideal torque produced under nominal conditions.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Analytical'.
Default value |
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Program usage name |
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Evaluatable |
Yes |
#
No-load torque —
rest friction torque
N*m
| mN*m
| lbf*ft
Details
The minimum torque value to overcome seal friction. This torque is the load-independent component of the total friction torque.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameter to `Analytical'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Pressure gain vector, dp —
vector of pressure increase values for tabular parameterization
Pa
| GPa
| MPa
| atm
| bar
| kPa
| ksi
| psi
| uPa
| kbar
Details
Vector of differential pressure values for the tabular parameterization of leakage and torque friction. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Shaft angular velocity vector, w —
vector of angular velocity values for tabular parameterization
rpm
| deg/s
| rad/s
Details
Vector of angular velocity data for tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Units |
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Default value |
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Program usage name |
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Evaluatable |
Yes |
# Volumetric efficiency table, e_v(dp,w) — table of volumetric efficiency values
Details
Matrix at of volumetric efficiencies at a given fluid pressure drop and angular speed of shaft rotation. The block uses linear interpolation between the elements of the table.
The values and are the dimensions of the corresponding vectors:
-
- number of vector elements in the Pressure gain vector parameters, dp.
-
- number of vector elements in the Shaft angular velocity vector parameters, w.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Default value |
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Program usage name |
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Evaluatable |
Yes |
# Mechanical efficiency table, e_m(dp,w) — table of mechanical efficiency values
Details
Matrix at mechanical efficiencies at a given fluid pressure drop and angular speed of shaft rotation. The block uses linear interpolation between the elements of the table. The values and are the dimensions of the corresponding vectors:
-
- number of elements in the pressure drop vector Pressure gain vector, dp.
-
- number of elements in the angular velocity vector Shaft angular velocity vector, w.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical efficiencies'.
Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Pressure gain vector, dp —
vector of pressure increase values for tabular parameterization
Pa
| GPa
| MPa
| atm
| bar
| kPa
| ksi
| psi
| uPa
| kbar
Details
Vector of pressure increase values for the tabular parameterization of leakage and torque friction. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Units |
|
Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Shaft angular velocity vector, w —
vector of angular velocity values for tabular parameterization
rpm
| deg/s
| rad/s
Details
Vector of angular velocity data for tabular parameterization of leakage and friction torque. The elements of the vector must be listed in ascending order.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Units |
|
Default value |
|
Program usage name |
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Evaluatable |
Yes |
#
Volumetric loss table, q_loss(dp,w) —
table of volume loss values
m^3/s
| m^3/h
| cm^3/s
| mm^3/s
| ft^3/s
| lpm
| l/s
| gpm
| gal/s
| gal/h
Details
Matrix at volume losses at a given fluid pressure drop and angular speed of shaft rotation. The block uses linear interpolation between the elements of the table.
The values and are the dimensions of the corresponding vectors:
-
- number of elements in the pressure gain vector Pressure gain vector, dp.
-
- number of elements in the angular velocity vector Shaft angular velocity vector, w.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Units |
|
Default value |
|
Program usage name |
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Evaluatable |
Yes |
#
Mechanical loss table, torque_loss(dp,w) —
table of mechanical loss values
N*m
| mN*m
| lbf*ft
Details
Matrix at of mechanical losses at a given fluid pressure drop and angular speed of shaft rotation.
The block uses linear interpolation between the elements of the table. The values and are the dimensions of the corresponding vectors:
-
- number of elements in the pressure gain vector Pressure gain vector, dp.
-
- number of elements in the angular velocity vector Shaft angular velocity vector, w.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Tabulated data - volumetric and mechanical losses'.
Units |
|
Default value |
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Program usage name |
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Evaluatable |
Yes |
# Minimum volumetric efficiency — minimum volumetric efficiency
Details
The minimum value of the volumetric efficiency. If the input signal is below this value, the volumetric efficiency is set to the minimum volumetric efficiency value.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
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Evaluatable |
Yes |
# Maximum volumetric efficiency — maximum volumetric efficiency
Details
The maximum value of the volumetric efficiency. If the input signal exceeds this value, the volumetric efficiency is set to the maximum volumetric efficiency value.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
# Minimum mechanical efficiency — minimum mechanical efficiency
Details
The minimum value of the mechanical efficiency. If the input signal is below this value, the mechanical efficiency is set to the minimum mechanical efficiency value.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
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Evaluatable |
Yes |
# Maximum mechanical efficiency — maximum mechanical efficiency
Details
The maximum value of the mechanical efficiency. If the input signal is higher than this value, the mechanical efficiency is set to the maximum mechanical efficiency value.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical efficiencies'.
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Pressure gain threshold for pump-motor transition —
threshold pressure for transient operation
Pa
| GPa
| MPa
| atm
| bar
| kPa
| ksi
| psi
| uPa
| kbar
Details
The differential pressure threshold for the transition between pump and motor operation. The transition region is defined in the region of 0 MPa between the positive and negative values of the threshold differential pressure. Within this region, the calculated leakage rate and friction torque are corrected according to the transition term , to ensure a smooth transition from one mode to the other.
Dependencies
To use this parameter, set Leakage and friction parameterization to one of the values:
-
`Tabulated data - volumetric and mechanical efficiencies';
-
`Input signal - volumetric and mechanical efficiencies';
-
Input signal - volumetric and mechanical losses
.
Units |
|
Default value |
|
Program usage name |
|
Evaluatable |
Yes |
#
Angular velocity threshold for pump-motor transition —
threshold angular velocity for transient mode
rpm
| deg/s
| rad/s
Details
The angular velocity threshold for the transition between pump and hydraulic motor operation. The transition region is defined around 0 rpm between the positive and negative values of the angular velocity threshold. Within this region, the calculated leakage rate and friction torque are corrected according to the transition term , to ensure a smooth transition from one mode to the other.
Dependencies
To use this parameter, set Leakage and friction parameterization to one of the values:
-
`Tabulated data - volumetric and mechanical efficiencies';
-
`Input signal - volumetric and mechanical efficiencies';
-
Input signal - volumetric and mechanical losses
.
Units |
|
Default value |
|
Program usage name |
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Evaluatable |
Yes |
#
Cross-sectional area at ports A and B —
cross-sectional area of ports A and B
m^2
| cm^2
| ft^2
| in^2
| km^2
| mi^2
| mm^2
| um^2
| yd^2
Details
Cross-sectional area of ports A and B. It is assumed that the areas are equal.
Units |
|
Default value |
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Program usage name |
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Evaluatable |
Yes |
#
Check if operating beyond the range of supplied tabulated data —
reporting of data overruns
None
| Error
Details
Select Error
to stop the simulation when the block uses values outside the provided data range.
If the Leakage and friction parameterization parameter is set to Tabulated data - torque and speed
, this parameter also checks if the block is running in the NaN
value range.
Dependencies
To use this parameter, set the Leakage and friction parameterization to one of the values:
-
Tabulated data - volumetric and mechanical efficiencies
; -
`Tabulated data - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
No |
#
Check if operating beyond pump mode —
message about unit operation outside pump mode
None
| Error
Details
Select Error
to stop the simulation when the unit is operating in forward or reverse hydraulic motor modes.
Dependencies
To use this parameter, set the Leakage and friction parameterization parameters to `Input signal - volumetric and mechanical losses'.
Values |
|
Default value |
|
Program usage name |
|
Evaluatable |
No |