Variable-Displacement Motor (IL)

Variable-displacement motor in an isothermal liquid system

Since R2020a

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Libraries:
Simscape / Fluids / Isothermal Liquid / Pumps & Motors

Description

The Variable-Displacement Motor (IL) block models a motor with variable-volume displacement. The fluid may move from port A to port B, called forward mode, or from port B to port A, called reverse mode. Motor mode operation occurs when there is a pressure drop in the direction of the flow. Pump mode operation occurs when there is a pressure gain in the direction of the flow.

The shaft rotation corresponds to the sign of the fluid volume moving through the motor, which is received as a physical signal at port D. Positive fluid displacement at D corresponds to positive shaft rotation in forward mode. Negative fluid displacement at D corresponds to negative shaft angular velocity in forward mode.

Operation Modes

The block has eight modes of operation. The working mode depends on the pressure drop from port A to port B, Δp = p_A – p_B; the angular velocity, ω = ω_R – ω_C; and the fluid volumetric displacement at port D. The figure above maps these modes to the octants of a Δp-ω-D chart:

• Mode 1, Forward Motor: Flow from port A to port B causes a pressure decrease from A to B and a positive shaft angular velocity.

• Mode 2, Reverse Pump: Negative shaft angular velocity causes a pressure increase from port B to port A and flow from B to port A.

• Mode 3, Reverse Motor: Flow from port B to port A causes a pressure decrease from B to A and a negative shaft angular velocity.

• Mode 4, Forward Pump: Positive shaft angular velocity causes a pressure increase from port A to port B and flow from A to B.

• Mode 5, Reverse Pump: Positive shaft angular velocity causes a pressure increase from port B to port A and flow from B to A.

• Mode 6, Forward Motor: Flow from port A to port B causes a pressure decrease from A to B and a positive shaft angular velocity.

• Mode 7, Forward Pump: Negative shaft angular velocity causes a pressure increase from port A to port B and flow from A to B.

• Mode 8, Reverse Motor: Flow from B to A causes a pressure decrease from B to A and positive shaft angular velocity.

The motor block has analytical, lookup table, and physical signal parameterizations. When using tabulated data or an input signal for parameterization, you can choose to characterize the motor operation based on efficiency or losses.

The threshold parameters Pressure drop threshold for motor-pump transition, Angular velocity threshold for motor-pump transition, and Displacement threshold for motor-pump transition identify regions where numerically smoothed flow transition between the motor operational modes can occur. For the pressure and angular velocity thresholds, choose a transition region that provides some margin for the transition term, but which is small enough relative to the typical motor pressure drop and angular velocity so that it will not impact calculation results. For the displacement threshold, choose a threshold value that is smaller than the typical displacement volume during normal operation.

Analytical Leakage and Friction Parameterization

If you set Leakage and friction parameterization to Analytical, the block calculates internal leakage and shaft friction from constant nominal values of shaft velocity, pressure drop, volumetric displacement, and torque. The leakage flow rate, which is correlated with the pressure differential over the motor, is calculated as:

$${\dot{m}}_{leak}=K{\rho }_{avg}\Delta p,$$

where:

• Δp is p_A – p_B.

• ρ_avg is the average fluid density.

• K is the Hagen-Poiseuille coefficient for analytical loss,

  $$K=\frac{D_{nom}{\omega }_{nom}\left(\frac{1}{{\eta }_{v,}{}_{nom}}-1\right)}{\Delta p_{nom}},$$

  where:

  • D_nom is the Nominal displacement.

  • ω_nom is the Nominal shaft angular velocity.

  • η_nom is the Volumetric efficiency at nominal conditions.

  • Δp_nom is the Nominal pressure drop.

The torque, which is related to the motor pressure differential, is calculated as:

$${\tau }_{fr}=\left({\tau }_0+k\left|\Delta p\frac{D}{D_{nom}}\right|\right)\tanh \left(\frac{4\omega }{5\times {10}^{-5}{\omega }_{nom}}\right),$$

where:

• τ₀ is the No-load torque.

• k is the friction torque vs. pressure gain coefficient at nominal displacement, which is determined from the Mechanical efficiency at nominal conditions, η_m,nom:

  $$k=\frac{{\tau }_{fr,nom}-{\tau }_0}{\Delta p_{nom}}.$$

  τ_fr,nom is the friction torque at nominal conditions:

  $${\tau }_{fr,nom}=\left(1-{\eta }_{m,nom}\right)D_{nom}\Delta p_{nom}.$$

• Δp is the pressure drop between ports A and B.

• ω is the relative shaft angular velocity, or $${\omega }_R-{\omega }_C$$.

Tabulated Data Parameterizations

When using tabulated data for motor efficiencies or losses, you can provide data for one or more of the motor operational modes. The signs of the tabulated data determine the operational regime of the block. When data is provided for less than eight operational modes, the block calculates the complementing data for the other mode(s) by extending the given data into the remaining octants.

The Tabulated data - volumetric and mechanical efficiencies parameterization

The leakage flow rate is calculated as:

$${\dot{m}}_{leak}={\dot{m}}_{leak,motor}\left(\frac{1+\alpha }{2}\right)+{\dot{m}}_{leak,pump}\left(\frac{1-\alpha }{2}\right),$$

where:

• $${\dot{m}}_{leak,pump}=\left({\eta }_{\upsilon }-1\right){\dot{m}}_{ideal}$$

• $${\dot{m}}_{leak,motor}=\left(1-{\eta }_v\right)\dot{m}$$

and η_v is the volumetric efficiency, which is interpolated from the user-provided tabulated data. The transition term, α, is

$$\alpha =\tanh \left(\frac{4\Delta p}{\Delta p_{threshold}}\right)\tanh \left(\frac{4\omega }{{\omega }_{threshold}}\right)\tanh \left(\frac{4D}{D_{threshold}}\right),$$

where:

• Δp is p_A – p_B.

• Δp_threshold is the Pressure drop threshold for motor-pump transition.

• ω is ω_R – ω_C.

• ω_threshold is the Angular velocity threshold for motor-pump transition.

The torque is calculated as:

$${\tau }_{fr}={\tau }_{fr,pump}\left(\frac{1+\alpha }{2}\right)+{\tau }_{fr,motor}\left(\frac{1-\alpha }{2}\right),$$

where:

• $${\tau }_{fr,pump}=\left({\eta }_m-1\right)\tau$$

• $${\tau }_{fr,motor}=\left(1-{\eta }_m\right){\tau }_{ideal}$$

and η_m is the mechanical efficiency, which is interpolated from the user-provided tabulated data.

The Tabulated data - volumetric and mechanical losses parameterization

The leakage flow rate is calculated as:

$${\dot{m}}_{leak}={\rho }_{avg}{q}_{loss}\left(\Delta p,\omega ,D\right),$$

where q_loss is interpolated from the Volumetric loss table, q_loss(dp,w,D) parameter, which is based on user-supplied data for pressure drop, shaft angular velocity, and fluid volumetric displacement.

The shaft friction torque is calculated as:

$${\tau }_{fr}={\tau }_{loss}\left(\Delta p,\omega ,D\right),$$

where τ_loss is interpolated from the Mechanical loss table, torque_loss(dp,w,D) parameter, which is based on user-supplied data for pressure drop, shaft angular velocity, and fluid volumetric displacement.

Input Signal Parameterization

When Leakage and friction parameterization is set toInput signal - volumetric and mechanical efficiencies, ports EV and EM are enabled. The internal leakage and shaft friction are calculated in the same way as the Tabulated data - volumetric and mechanical efficiencies parameterization, except that η_v and η_m are received directly at ports EV and EM, respectively.

When Leakage and friction parameterization is set toInput signal - volumetric and mechanical losses, ports LV and LM are enabled. These ports receive leakage flow and friction torque as positive physical signals. The leakage flow rate is calculated as:

$${\dot{m}}_{leak}={\rho }_{avg}{q}_{LV}\tanh \left(\frac{4\Delta p}{p_{thresh}}\right),$$

where:

• q_LV is the leakage flow received at port LV.

• p_thresh is the Pressure drop threshold for motor-pump transition parameter.

The friction torque is calculated as:

$${\tau }_{fr}={\tau }_{LM}\tanh \left(\frac{4\omega }{{\omega }_{thresh}}\right),$$

where

• τ_LM is the friction torque received at port LM.

• ω_thresh is the Angular velocity threshold for motor-pump transition parameter.

The volumetric and mechanical efficiencies range between the user-defined specified minimum and maximum values. Any values lower or higher than this range will take on the minimum and maximum specified values, respectively.

Motor Operation

The motor flow rate is:

$$\dot{m}={\dot{m}}_{ideal}+{\dot{m}}_{leak},$$

where $${\dot{m}}_{ideal}={\rho }_{avg}D\cdot \omega .$$

The motor torque is:

$$\tau ={\tau }_{ideal}-{\tau }_{fr},$$

where $${\tau }_{ideal}=D\cdot \Delta p.$$

The mechanical power extracted by the motor shaft is:

$${\phi }_{mech}=\tau \omega ,$$

and the motor hydraulic power is:

$${\phi }_{hyd}=\frac{\Delta p\dot{m}}{{\rho }_{avg}}.$$

To be notified if the block is operating beyond the supplied tabulated data, you can set Check if operating beyond the range of supplied tabulated data to Warning to receive a warning if this occurs, or Error to stop the simulation when this occurs. When using input signal for volumetric or mechanical losses, you can be notified if the simulation surpasses operating modes with the Check if operating beyond motor mode parameter.

You can also monitor motor functionality. Set Check if pressures are less than motor minimum pressure to Warning to receive a warning if this occurs, or Error to stop the simulation when this occurs.

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit port to the motor.

B — Liquid port

isothermal liquid

Liquid entry or exit port to the motor.

R — Mechanical port

mechanical rotational

Rotating shaft angular velocity and torque.

C — Mechanical port

mechanical rotational

Motor casing reference angular velocity and torque.

Input

D — Volumetric displacement, m^3/rad

physical signal

Volumetric displacement of the motor, in m^3/rad, specified as a physical signal.

EV — Volumetric efficiency

physical signal

Motor efficiency for fluid displacement, specified as a physical signal. The value must be between 0 and 1.

Dependencies

To enable this port, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

EM — Mechanical efficiency

physical signal

Motor efficiency for the mechanical extraction of energy, specified as a physical signal. The value must be between 0 and 1.

Dependencies

To enable this port, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

LV — Leakage flow rate, m^3/s

physical signal

Motor volumetric losses, in m^3/s, specified as a physical signal.

Dependencies

To enable this port, set Leakage and friction parameterization to Input signal - volumetric and mechanical losses.

LM — Friction torque, N*m

physical signal

Motor mechanical losses in N*m, specified as a physical signal.

Dependencies

To enable this port, set Leakage and friction parameterization to Input signal - volumetric and mechanical losses.

Parameters

Leakage and friction parameterization — Method of calculating leakage flow rate and friction torque

Analytical (default) | Tabulated data - volumetric and mechanical efficiencies | Tabulated data - volumetric and mechanical losses | Input signal - volumetric and mechanical efficiencies | Input signal - volumetric and mechanical losses

Parameterization of the leakage and friction characteristics of the motor.

• In the Analytical parameterization, the leakage flow rate and the friction torque are calculated by analytical equations.

• In the Tabulated data - volumetric and mechanical efficiencies parameterization, the leakage flow rate and torque friction are calculated from the user-supplied Pressure drop vector, dp, Shaft angular velocity vector, w, and Displacement vector, D parameters and interpolated from the 3-D dependent Volumetric efficiency table, e_v(dp,w,D) and Mechanical efficiency table, e_m(dp,w,D) tables.

• In the Tabulated data - volumetric and mechanical loss parameterization, the leakage flow rate and torque friction are calculated from the user-supplied Pressure drop vector, dp; Shaft angular velocity vector, w; and Displacement vector, D parameters and interpolated from the 3-D dependent Volumetric loss table, q_loss(dp,w,D) and Mechanical loss table, torque_loss(dp,w,D) tables.

• In the Input signal - volumetric and mechanical efficiencies parameterization, the volumetric and mechanical efficiencies are received as physical signals at ports EV and EM, respectively.

• In the Input signal - volumetric and mechanical loss parameterization, the leakage flow rate and friction torque are received as physical signals at ports LV and LM, respectively.

Nominal displacement — Fixed-volume fluid displacement

30 cm^3/rev (default) | scalar

Amount of fluid displaced by shaft rotating under nominal operating conditions.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

Nominal shaft angular velocity — Shaft angular velocity

1800 rpm (default) | scalar

Angular velocity of the shaft under nominal operating conditions.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

Nominal pressure drop — Pressure drop between fluid entry and exit

10 MPa (default) | scalar

Motor pressure drop between the fluid entry and exit under nominal operating conditions.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

Volumetric efficiency at nominal conditions — Ratio of actual flow rate to ideal flow rate at nominal conditions

0.92 (default) | positive scalar in the range of (0,1]

Ratio of actual flow rate to ideal flow rate at nominal conditions.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

No-load torque — Baseline torque

0 N*m (default) | scalar

Minimum value of torque to overcome seal friction and induce shaft motion.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

Mechanical efficiency at nominal conditions — Ratio of actual to ideal mechanical power

0.88 (default) | positive scalar

Ratio of actual mechanical power to ideal mechanical power at nominal conditions.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Analytical.

Pressure drop vector, dp — Vector of pressure data for tabulated data parameterization

[.1, 1, 2] MPa (default) | 1-by-n vector

Vector of pressure differential values for the tabular parameterization of leakage and torque friction. This vector forms an independent axis with the Shaft angular velocity vector, w and the Displacement vector, D parameters for the 3-D dependent Volumetric efficiency table, e_v(dp,w,D) and Mechanical efficiency table, e_m(dp,w,D) parameters. The vector elements must be listed in ascending order.

Dependencies

To enable this parameter, set Leakage and friction parameterization to either:

• Tabulated data - volumetric and mechanical efficiencies

• Tabulated data - volumetric and mechanical losses

Shaft angular velocity vector, w — Vector of angular velocity data for tabulated data parameterization

[250, 500, 1000, 2000, 3000, 4000] rpm (default) | 1-by-n vector

Vector of angular velocity data for the tabular parameterization of leakage and torque friction. This vector forms an independent axis with the Shaft angular velocity vector, w and the Displacement vector, D parameters for the 3-D dependent Volumetric efficiency table, e_v(dp,w,D) and Mechanical efficiency table, e_m(dp,w,D) parameters. The vector elements must be listed in ascending order.

Dependencies

To enable this parameter, set Leakage and friction parameterization to either:

• Tabulated data - volumetric and mechanical efficiencies

• Tabulated data - volumetric and mechanical losses

Displacement vector, D — Vector of displacement volumes for tabulated data parameterization

[-30, -19, 19, 30] cm^3/s (default) | 1-by-n vector

Vector of volumetric displacement data for the tabular parameterization of leakage and torque friction. This vector forms an independent axis with the Shaft angular velocity vector, w and the Pressure drop vector, dp parameters for the 3-D dependent Volumetric efficiency table, e_v(dp,w,D) and Mechanical efficiency table, e_m(dp,w,D) parameters. The vector elements must be listed in ascending order.

Dependencies

To enable this parameter, set Leakage and friction parameterization to either:

• Tabulated data - volumetric and mechanical efficiencies

• Tabulated data - volumetric and mechanical losses

Volumetric efficiency table, e_v(dp,w,D) — Volumetric efficiency for tabulated data parameterization

repmat([.816, .908, .954, .977, .981, .984; .325, .663, .831, .916, .925, .946; .137, .568, .78, .892, .893, .91], 1, 1, 4) (default) | M-by-N-by-P matrix

M-by-N-by-P matrix of volumetric efficiencies at the specified fluid pressure drop, shaft angular velocity, and volumetric displacement. Linear interpolation is employed between table elements. M, N, and P are the sizes of the corresponding vectors:

• M is the number of vector elements in the Pressure drop vector, dp parameter.

• N is the number of vector elements in the Shaft angular velocity vector, w parameter.

• P is the number of vector elements in the Displacement vector, D parameter.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - volumetric and mechanical efficiencies.

Mechanical efficiency table, e_m(dp,w,D) — Mechanical efficiency for tabulated data parameterization

repmat([.996, .996, .996, .996, .996, .996; .988, .989, .989, .989, .989, .99; .981, .981, .982, .982, .983, .984], 1, 1, 4) (default) | M-by-N-by-P matrix

M-by-N-by-P matrix of mechanical efficiencies at the specified fluid pressure drop, shaft angular velocity, and displacement. Linear interpolation is employed between table elements. M, N, and P are the sizes of the corresponding vectors:

• M is the number of vector elements in the Pressure drop vector, dp parameter.

• N is the number of vector elements in the Shaft angular velocity vector, w parameter.

• P is the number of vector elements in the Displacement vector, D parameter.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - volumetric and mechanical efficiencies.

Volumetric loss table, q_loss(dp,w,D) — Volumetric losses for tabulated data parameterization

repmat([.023, .023, .023, .023, .0285, .032; .0844, .0842, .0845, .084, .1125, .108; .1079, .108, .11, .108, .1605, .18] * 1e-3, 1, 1, 4) (default) | M-by-N-by-P matrix

M-by-N-by-P matrix of volumetric leakage at the specified fluid pressure drop, shaft angular velocity, and displacement. Linear interpolation is employed between table elements. M, N, and P are the sizes of the corresponding vectors:

• M is the number of vector elements in the Pressure drop vector, dp parameter.

• N is the number of vector elements in the Shaft angular velocity vector, w parameter.

• P is the number of vector elements in the Displacement vector, D parameter.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - volumetric and mechanical losses.

Mechanical loss table, torque_loss(dp,w,D) — Mechanical losses for tabulated data parameterization

repmat([.002, .002, .002, .002, .002, .002; .0607, .0556, .0556, .0556, .0556, .0505; .1937, .1937, .1833, .1833, .1729, .1626], 1, 1, 4) N*m (default) | M-by-N-by-P matrix

M-by-N-by-P matrix of mechanical losses at the specified fluid pressure drop and shaft angular velocity. Linear interpolation is employed between table elements. M, N, and P are the sizes of the correlated vectors:

• M is the number of vector elements in the Pressure drop vector, dp parameter.

• N is the number of vector elements in the Shaft angular velocity vector, w parameter.

• P is the number of vector elements in the Displacement vector, D parameter.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - volumetric and mechanical losses.

Minimum volumetric efficiency — Minimum value of volumetric efficiency

1e-3 (default) | positive scalar in the range of (0,1]

Minimum value of volumetric efficiency. If the input signal is below this value, the volumetric efficiency is set to the minimum volumetric efficiency.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

Maximum volumetric efficiency — Maximum value of volumetric efficiency

1 (default) | positive scalar in the range of (0,1]

Maximum value of volumetric efficiency. If the input signal is above this value, the volumetric efficiency is set to the maximum volumetric efficiency.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

Minimum mechanical efficiency — Minimum value of mechanical efficiency

1e-3 (default) | positive scalar in the range of (0,1]

Minimum value of mechanical efficiency. If the input signal is below this value, the mechanical efficiency is set to the minimum mechanical efficiency.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

Maximum mechanical efficiency — Maximum value of mechanical efficiency

1 (default) | positive scalar in the range of (0,1]

Maximum value of mechanical efficiency. If the input signal is above this value, the mechanical efficiency is set to the maximum mechanical efficiency.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies.

Pressure drop threshold for motor-pump transition — Pressure threshold for mode transition

1e-3 MPa (default) | positive scalar

Motor pressure drop that indicates the transition threshold between motor and pump functionality. A transition region is defined around 0 MPa between the positive and negative values of the pressure drop threshold. Within this transition region, the computed leakage flow rate and friction torque are adjusted according to the transition term α to ensure smooth transition from one mode to the other.

Dependencies

To enable this parameter, set Leakage and friction parameterization to either:

• Tabulated data - volumetric and mechanical efficiencies

• Input signal - volumetric and mechanical efficiencies

• Input signal - volumetric and mechanical losses

Angular velocity threshold for motor-pump transition — Angular velocity threshold for mode transition

100 rpm (default) | positive scalar

Shaft angular velocity that indicates the transition threshold between motor and pump functionality. A transition region is defined around 0 rpm between the positive and negative values of the angular velocity threshold. Within this transition region, the computed leakage flow rate and friction torque are adjusted according to the transition term α to ensure smooth transition from one mode to the other.

Dependencies

To enable this parameter, set Leakage and friction parameterization to:

• Tabulated data - volumetric and mechanical efficiencies

• Input signal - volumetric and mechanical efficiencies

• Input signal - volumetric and mechanical losses

Displacement threshold for motor-pump transition — Displacement threshold for mode transition

0.1 cm^3/s (default) | positive scalar

Volumetric displacement that indicates the transition threshold between motor and pump functionality. A transition region is defined around 0 cm^3/s between the positive and negative values of the displacement threshold. Within this transition region, the computed leakage flow rate and friction torque are adjusted according to the transition term α to ensure smooth transition from one mode to the other. It is also used to transition the ideal mass flow rate when the sign of D changes.

Check if operating beyond the range of supplied tabulated data — Whether to notify if extents of supplied data are surpassed

None (default) | Warning | Error

Whether to notify if the extents of the supplied data are surpassed. Select Warning to be notified when the block uses values beyond the supplied data range. Select Error to stop the simulation when the block uses values beyond the supplied data range.

Dependencies

To enable this parameter, set Leakage and friction parameterization to:

• Tabulated data - volumetric and mechanical efficiencies

• Tabulated data - volumetric and mechanical losses

Check if operating beyond motor mode — Whether to notify if block operates outside of the motor mode functionality

None (default) | Warning | Error

Whether to notify if the block operates outside of the motor mode functionality. Select Warning to be notified when the block operates in the forward or reverse pump modes. Select Error to stop the simulation when the block operates in the forward or reverse pump modes.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Input signal - volumetric and mechanical losses.

Check if pressures are less than motor minimum pressure — Whether to notify if fluid exit pressure is low

None (default) | Warning | Error

Whether to notify if the fluid at port A or B experiences low pressure. Select Warning to be notified when the pressure falls below a minimum specified value. Select Error to stop the simulation when the pressure falls below a minimum specified value.

The parameter helps identify potential conditions for cavitation, when the fluid pressure falls below the fluid vapor pressure.

Motor minimum pressure — Lower threshold of acceptable pressure at the motor outlet

0.101325 MPa (default) | positive scalar

Lower threshold of acceptable pressure at the motor inlet or outlet.

Dependencies

To enable this parameter, set Check if pressures are less than motor minimum pressure to either:

• Warning

• Error

Extended Capabilities

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

Version History

Introduced in R2020a

R2024a: Check if block operates outside range of calculated data

The Check if operating beyond the octants of supplied tabulated data parameter has been renamed to Check if operating beyond the range of supplied tabulated data. You can enable the Check if operating beyond the range of supplied tabulated data parameter to check if the block is operating beyond the data specified in the block parameters, that is, operating in a region where the block has extended the data.