Fixed-Displacement Motor (TL)

Hydraulic-mechanical power conversion device

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

Description

The Fixed-Displacement Motor (TL) block represents a device that extracts power from a thermal liquid network and delivers it to a mechanical rotational network. The motor displacement is fixed at a constant value that you specify through the Displacement parameter.

Ports A and B represent the motor inlets. Ports R and C represent the motor drive shaft and case. During normal operation, a pressure drop from port A to port B causes a positive flow rate from port A to port B and a positive rotation of the motor shaft relative to the motor case. This operation mode is referred to here as forward motor.

Operation Modes

The block has four modes of operation. The working mode depends on the pressure drop from port A to port B, Δp = p_A – p_B and the angular velocity, ω = ω_R – ω_C:

• 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.

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

Energy Balance

Mechanical work done by the pump is associated with an energy exchange. The governing energy balance equation is:

$${\varphi }_A+{\varphi }_B-P_{hydro}=0,$$

where:

• Φ_A and Φ_B are energy flow rates at ports A and B, respectively.

• P_hydro is the motor hydraulic power. It is a function of the pressure difference between the motor ports: $$P_{hydro}=\Delta p\frac{\dot{m}}{\rho }$$

The motor mechanical power is generated from the motor torque, τ and angular velocity, ω:

$$P_{mech}=T\omega .$$

Flow Rate and Driving Torque

The mass flow rate generated at the motor is

$$\dot{m}={\dot{m}}_{\text{Ideal}}+{\dot{m}}_{\text{Leak}},$$

where:

• $$\dot{m}$$ is the actual mass flow rate.

• $${\dot{m}}_{\text{Ideal}}$$ is the ideal mass flow rate.

• $${\dot{m}}_{\text{Leak}}$$ is the internal leakage mas flow rate.

The torque generated at the motor is

$$\tau ={\tau }_{\text{Ideal}}-{\tau }_{\text{Friction}},$$

where:

• τ is the actual torque.

• τ_Ideal is the ideal torque.

• τ_Friction is the friction torque.

Ideal Flow Rate and Ideal Torque

The ideal mass flow rate is

$${\dot{m}}_{\text{Ideal}}=\rho D\omega ,$$

and the ideal generated torque is

$${\tau }_{\text{Ideal}}=D\Delta p,$$

where:

• ρ is the average of the fluid densities at thermal liquid ports A and B.

• D is the Displacement parameter.

• ω is the shaft angular velocity.

• Δp is the pressure drop from inlet to outlet.

Analytical Leakage and Friction Parameterization

If you set Leakage and friction parameterization to Analytical, the block calculates leakage and friction from constant values of shaft velocity, pressure drop, and friction 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,

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

  where:

  • D is the value of the Displacement parameter.

  • ω_nom is the value of the Nominal shaft angular velocity parameter.

  • η_{v, nom} is the value of the Volumetric efficiency at nominal conditions parameter.

• Δp_nom is the value of the Nominal pressure drop parameter.

The friction torque, which is correlated with shaft angular velocity, is calculated as:

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

where:

• τ₀ is the value of the No-load torque parameter.

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

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

  τ_fric is the friction torque at nominal conditions:

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

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

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

Tabulated Leakage and Friction 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 four operational modes, the block calculates the complementing data for the other mode or modes by extending the given data into the remaining quadrants.

Tabulated Data - Volumetric and Mechanical Efficiencies

When you set Leakage and friction parameterization to Tabulated data - volumetric and mechanical efficiencies, the leakage flow rate is

$${\dot{m}}_{\text{Leak}}={\dot{m}}_{\text{Leak,Motor}}\frac{\left(1+\alpha \right)}{2}+{\dot{m}}_{\text{Leak,Pump}}\frac{\left(1-\alpha \right)}{2},$$

and the friction torque is

$${\tau }_{\text{Friction}}={\tau }_{\text{Friction,Motor}}\frac{1+\alpha }{2}+{\tau }_{\text{Friction,Pump}}\frac{1-\alpha }{2},$$

where:

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

• $${\dot{m}}_{\text{Leak,Motor}}$$ is the leakage flow rate in motor mode.

• $${\dot{m}}_{\text{Leak,Pump}}$$ is the leakage flow rate in pump mode.

• τ_{Friction,Motor} is the friction torque in motor mode.

• τ_{Friction,Pump} is the friction torque in pump mode.

The smoothing parameter α is given by the hyperbolic function

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

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 Angular velocity threshold for motor-pump transition block parameter.

The leakage flow rate is calculated from the volumetric efficiency, a quantity that is specified in tabulated form over the Δp–ɷ–D domain via the Volumetric efficiency table block parameter. When operating in motor mode (quadrants 1 and 3 of the Δp–ɷ–D chart shown in the Operation Modes figure), the leakage flow rate is:

$${\dot{m}}_{\text{Leak,Motor}}=\left(1-{\eta }_{\text{v}}\right)\dot{m},$$

where η_v is the volumetric efficiency, obtained either by interpolation or extrapolation of the tabulated data. Similarly, when operating in pump mode (quadrants 2 and 4 of the Δp–ɷ–D chart), the leakage flow rate is:

$${\dot{m}}_{\text{Leak,Pump}}=-\left(1-{\eta }_{\text{v}}\right){\dot{m}}_{\text{Ideal}}.$$

The friction torque is similarly calculated from the mechanical efficiency, a quantity that is specified in tabulated form over the Δp–ɷ–D domain via the Mechanical efficiency table block parameter. When operating in motor mode (quadrants 1 and 3 of the Δp–ɷ–D chart):

$${\tau }_{\text{Friction,Motor}}=\left(1-{\eta }_{\text{m}}\right){\tau }_{\text{Ideal}},$$

where η_m is the mechanical efficiency, obtained either by interpolation or extrapolation of the tabulated data. Similarly, when operating in pump mode (quadrants 2 and 4 of the Δp–ɷ–D chart):

$${\tau }_{\text{Friction,Pump}}=-\left(1-{\eta }_{\text{m}}\right)\tau .$$

Tabulated Data - Volumetric and Mechanical Losses

When you set Leakage and friction parameterization to Tabulated data - volumetric and mechanical losses, the leakage (volumetric) flow rate is specified directly in tabulated form over the Δp–ɷ domain:

$$q_{\text{Leak}}=q_{\text{Leak}}\left(\Delta p,\omega \right).$$

The mass flow rate due to leakage is calculated from the volumetric flow rate:

$${\dot{m}}_{\text{Leak}}=\rho q_{\text{Leak}}.$$

The friction torque is

$${\tau }_{\text{Friction}}={\tau }_{\text{Loss}}\left(\Delta p,\omega \right)\tanh \left(\frac{4\omega }{{\omega }_{threshold}}\right),$$

where q_Leak(Δp,ω) and τ_Loss(Δp,ω) are the volumetric and mechanical losses, obtained through interpolation or extrapolation of the tabulated data specified via the Volumetric loss table and Mechanical loss table block parameters.

Tabulated Data - Torque and Speed Parameterization

When you set Leakage and friction parameterization to Tabulated data - torque and speed, the block calculates the volumetric loss table, q_loss,TLU and the mechanical loss table, τ_loss,TLU, as

$$\begin{array}{l}{\text{q}}_{loss,TLU}=q_{TLU}-D{\omega }_{TLU}\\ {\tau }_{loss,TLU}=D\Delta p_{TLU}-T_{TLU}\end{array}$$

where:

• q_TLU is the value of the Flow rate vector, q parameter.

• ω_TLU is the value of the Shaft speed table, w(q,dp) parameter.

• Δp_TLU is the value of the Pressure drop vector, dp parameter.

• T_TLU is the value of the Torque table, T(q,dp) parameter.

If the supplied values for the Shaft speed table, w(q,dp) and Torque table, T(q,dp) parameters do not cover all four quadrants, the block extends the data by

• Symmetrically mirroring the values of the Pressure drop vector, dp and Flow rate vector, q parameters to contain negative values.

• Symmetrically extending the values of the volumetric loss table, q_loss,TLU, to additional quadrants. The signs of these extended values match the sign Δp_TLU in each quadrant.

• Calculating the extended values of the shaft speed vector, ω_TLU, from the extended values of the flow rate vector and volumetric loss table, $${\omega }_{TLU}=\frac{q_{TLU}-q_{loss,TLU}}{D}.$$

• Symmetrically extending the values of the mechanical loss table, τ_loss,TLU, to additional quadrants. The signs of these extended values match the sign ω_TLU in each quadrant.

If your data tables have unknown data points in any of the four corners or the Shaft speed table, w(q,dp) or Torque table, T(q,dp) parameters, use NaN in place of these values. The block fills in the NaN elements in the resulting volumetric loss table and mechanical loss table with nearest extrapolation with respect to pressure drop. The block adjusts the signs in the extrapolated mechanical loss table to match the sign of the corresponding elements in the shaft speed vector, ω_TLU, where $${\omega }_{TLU}=\frac{q_{TLU}-q_{loss,TLU}}{D}.$$

After extending or filling in the unknown data, the block uses linear interpolation and nearest extrapolation to calculate the volumetric and mechanical loss tables during simulation

$$\begin{array}{l}{q}_{loss}=tablelookup\left(q_{TLU},\Delta p_{TLU},q_{loss,TLU},Q,\Delta p,interpolation=linear,extrapolation=nearest\right)\\ {\tau }_{loss}=tablelookup\left(q_{TLU},\Delta p_{TLU},{\tau }_{loss,TLU},Q,\Delta p,interpolation=linear,extrapolation=nearest\right)\end{array}$$

where $$Q=\frac{{\dot{m}}_A}{{\rho }_{avg}}.$$

Input Signal Parameterizations

When you set Leakage and friction parameterization to Input signal - volumetric and mechanical efficiencies, the leakage flow rate and friction torque calculations are identical to the Tabulated data - volumetric and mechanical efficiencies setting. The volumetric and mechanical efficiency lookup tables are replaced with physical signal inputs that you specify through ports EV and EM.

The efficiencies are positive quantities with value between 0 and 1. Input values outside of these bounds are set equal to the nearest bound (0 for inputs smaller than 0, 1 for inputs greater than 1). The efficiency signals are saturated at the Minimum volumetric efficiency or Minimum mechanical efficiency and Maximum volumetric efficiency or Maximum mechanical efficiency .

When you set Leakage and friction parameterization to Input signal - volumetric and mechanical losses, the leakage flow rate and friction torque calculations are identical to the Tabulated data - volumetric and mechanical losses setting. The volumetric and mechanical loss lookup tables are replaced with physical signal inputs that you specify through ports LV and LM.

The block expects the inputs to be positive. It sets the signs automatically from the operating conditions established during simulation—more precisely, from the Δp–ɷ quadrant in which the component happens to be operating.

Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. Use the fault parameters to specify the fault properties. For more information about fault modeling, see Introduction to Simscape Faults.

You can model a displacement fault, leakage, or a shaft friction torque fault.

When you enable the Displacement fault parameter, the block scales the displacement by the value of the Faulted displacement factor parameter when the fault triggers,

$${\text{D}}_{Fault}=f_{D}D,$$

where f_D is the value of the Faulted displacement factor parameter. When the Leakage and friction parameterization parameter is Analytical, the block does not use the faulted displacement value to calculate the Hagen-Poiseuille coefficient or the friction torque.

When you enable the Leakage fault parameter and Leakage and friction parameterization is Analytical, Tabulated data - volumetric and mechanical efficiencies, or Input signal - volumetric and mechanical efficiencies, the faulted volumetric efficiency is

$${\eta }_{v,Fault}=\frac{{\eta }_v}{f_{Leak}},$$

where f_Leak is the value of the Faulted leakage factor parameter and η_v is the volumetric efficiency. When Leakage and friction parameterization is Analytical, the block uses the faulted volumetric efficiency to calculate the Hagen-Poiseuille coefficient.

When Leakage and friction parameterization is Tabulated data - volumetric and mechanical losses, Input signal - volumetric and mechanical losses, or Tabulated data - torque and speed, the faulted leakage volumetric flow rate is

$$q_{Leak,Fault}=f_{Leak}{q}_{Leak}.$$

When Leakage and friction parameterization is Tabulated data - torque and speed, the block calculates q_Leak from the shaft speed and torque parameters.

When you enable the Shaft friction torque fault parameter and Leakage and friction parameterization is Analytical, Tabulated data - volumetric and mechanical efficiencies, or Input signal - volumetric and mechanical efficiencies, the faulted mechanical efficiency is

$${\eta }_{m,Fault}=\frac{{\eta }_m}{f_{Friction}},$$

where f_Friction is the value of the Shaft friction torque fault parameter and η_m is the mechanical efficiency. When Leakage and friction parameterization is Analytical, the block uses the faulted mechanical efficiency to calculate the friction torque.

When Leakage and friction parameterization is Tabulated data - volumetric and mechanical losses, Input signal - volumetric and mechanical losses, or Tabulated data - torque and speed, the faulted friction torque is

$${\tau }_{Friction,Fault}=f_{Friction}{\tau }_{Friction}.$$

When Leakage and friction parameterization is Tabulated data - torque and speed, the block calculates τ_Leak from the shaft speed and torque parameters.

Assumptions and Limitations

• The motor is treated as a quasi-steady component.

• The effects of fluid inertia and elevation are ignored.

• The motor wall is rigid.

• External leakage is ignored.

Ports

Input

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

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

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

Dependencies

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

LM — Mechanical loss, N*m

physical signal

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

Dependencies

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

Conserving

A — Motor inlet

thermal liquid

Thermal liquid conserving port associated with the motor inlet.

B — Motor outlet

thermal liquid

Thermal liquid conserving port associated with the motor outlet.

C — Motor Case

mechanical rotational

Mechanical rotational conserving port associated with the motor case.

R — Motor Shaft

mechanical rotational

Mechanical rotational conserving port associated with the rotational motor shaft.

Parameters

Parameters

Leakage and friction parameterization — Parameterization of leakage flow rate and friction torque

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

Method to compute flow-rate and torque losses due to internal leaks and friction. When you select Analytical, the block parameters are generally available from component data sheets. When you select Tabulated data - volumetric and mechanical efficiencies or Tabulated data - volumetric and mechanical losses, the block uses lookup tables to map pressure drop, angular velocity, and displacement to component efficiencies or losses. When you select Tabulated data - torque and speed, you can enter the torque and shaft speed as functions of flow rate and pressure drop by using the Torque table T(q,dp) and Shaft speed table w(q,dp) parameters.

When you select Input signal - volumetric and mechanical efficiencies or Input signal - volumetric and mechanical losses, the block performs the leakage flow rate and friction torque calculations the same as the Tabulated data - volumetric and mechanical efficiencies or Tabulated data - volumetric and mechanical losses settings, respectively. When you select Input signal - volumetric and mechanical efficiencies the block enables the physical signal ports, EV and EM. You use these ports to specify the volumetric and mechanical efficiency. When you select Input signal - volumetric and mechanical losses the block enables the physical signal ports, LV and LM. You use these ports to specify the volumetric and mechanical losses.

Displacement — Fluid volume displaced per shaft rotation

30 cm^3/rev (default) | positive scalar

Fluid volume displaced per shaft rotation. The block maintains this value throughout the simulation.

Nominal shaft angular velocity — Shaft angular velocity for given volumetric efficiency

1800 rpm (default) | scalar

Angular velocity of the rotary shaft that corresponds to the given volumetric efficiency. These values are typically available at standard operating conditions in the manufacturer data sheet. The block uses this parameter to calculate the leakage flow rate and friction torque.

Dependencies

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

Nominal pressure drop — Pressure drop for corresponding volumetric efficiency

10 MPa (default) | scalar

Pressure drop that corresponds to the given volumetric efficiency. These values are typically available at standard operating conditions in manufacturer data sheet. The block uses this parameter to calculate the internal leakage flow rate.

Dependencies

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

Nominal dynamic viscosity — Dynamic viscosity at which to specify the volumetric efficiency

0.9 cP (default) | scalar

Dynamic viscosity of the hydraulic fluid for the given volumetric efficiency. These values are typically available at standard operating conditions in manufacturer data sheet. The block uses this parameter to calculate the internal leakage flow rate.

Dependencies

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

Volumetric efficiency at nominal conditions — Volumetric efficiency at the specified nominal conditions

0.92 (default) | positive scalar

Volumetric efficiency for the given conditions. The block defines the volumetric efficiency as the ratio of actual to ideal volumetric flow rates. These values are typically available at standard operating conditions in manufacturer data sheet. The block uses this parameter to calculate the internal leakage flow rate.

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.

No-load torque — Minimum torque required to induce shaft rotation

0 N*m (default) | scalar

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

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 parameter or the Flow rate vector, q parameter for the 3-D dependent Volumetric efficiency table, e_v(dp,w), Mechanical efficiency table, e_m(dp,w), Torque table, T(q,dp), and Shaft speed table, w(q,dp) 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

• Tabulated data - torque and speed

Shaft angular velocity vector, w — Angular velocities at which to specify the volumetric and mechanical efficiencies

[250, 500, 1000, 2000, 3000, 4000] rpm | vector

Shaft angular velocities for the corresponding tabular efficiency data. The vector must be at least two elements in strictly increasing order.

You can specify the data for a single quadrant, (ɷ, Δp). Refer to the block description for the operation modes corresponding to the various quadrants.

Dependencies

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

Flow rate vector, q — Vector of flow rate data

[.125, .25, .5, 1, 1.5, 2] * 1e-3 m^3/s (default) | 1-by-n vector

Vector of flow rate data for the tabular parameterization of torque and speed. This vector forms an independent axis with the Pressure drop vector, dp parameter for the 3-D dependent Torque table, T(q,dp) and Shaft speed table, w(q,dp) parameters. The vector elements must be listed in ascending order.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - torque and speed.

Volumetric efficiency table, e_v(dp,w) — Volumetric efficiencies for given pressure drops and angular velocities

[.816, .908, .954, .977, .981, .984; .325, .663, .831, .916, .925, .946; .137, .568, .78, .892, .893, .91] | matrix

Volumetric efficiencies for the given fluid pressure drops and shaft angular velocities.. The efficiencies must be in the range (0,1]. M and N are the sizes of the specified lookup-table 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.

You can specify the data for a single quadrant, (ɷ, Δp). Refer to the block description for the operation modes corresponding to the various quadrants.

Dependencies

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

Mechanical efficiency table, e_m(dp,w) — Mechanical efficiencies for given pressure drops and angular velocities

[.996, .996, .996, .996, .996, .996; .988, .989, .989, .989, .989, .99; .981, .981, .982, .982, .983, .984] | matrix

Mechanical efficiencies for the given fluid pressure drops and shaft angular velocities. The efficiencies must be in the range (0,1]. M and N are the sizes of the specified lookup-table 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.

You can specify the data for a single quadrant, (ɷ, Δp). Refer to the block description for the operation modes corresponding to the various quadrants.

Dependencies

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

Volumetric loss table, q_loss(dp,w) — Internal leakage flow rates for corresponding pressure drops and angular velocities

[.023, .023, .023, .023, .0285, .032; .0844, .0842, .0845, .084, .1125, .108; .1079, .108, .11, .108, .1605, .18] * 1e-3 m^3/s

Volumetric losses at the specified fluid pressure drops and shaft angular velocities. Volumetric loss is defined here as the internal leakage volumetric flow rate between port A and port B. M and N are the sizes of the specified lookup-table 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.

You can specify the data for a single quadrant, (ɷ, Δp). Refer to the block description for the operation modes corresponding to the various quadrants.

Dependencies

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

Mechanical loss table, torque_loss(dp,w) — Friction torques for the corresponding pressure drops and angular velocities

[.002, .002, .002, .002, .002, .002; .0607, .0556, .0556, .0556, .0556, .0505; .1937, .1937, .1833, .1833, .1729, .1626] N*m

Mechanical losses for the given pressure drops and shaft angular velocities. The block defines mechanical loss as the friction torque due to seals and internal components. M and N are the sizes of the specified lookup-table 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.

You can specify the data for a single quadrant, (ɷ, Δp). Refer to the block description for the operation modes corresponding to the various quadrants. The tabulated data for the mechanical losses must obey the convention in the figure, with positive values at positive angular velocities and negative values at negative angular velocities.

Dependencies

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

Torque table, T(q,dp) — Torque values for tabulated data parameterization

[.47, 4.72, 9.35; .47, 4.7, 9.36; .47, 4.7, 9.4; .47, 4.7, 9.41; .47, 4.7, 9.46; .47, 4.68, 9.5] N*m (default) | M-by-N matrix

M-by-N matrix of torque values at the specified fluid pressure drop and flow rate. The block employs linear interpolation between table elements. M and N are the sizes of the correlated vectors:

• M is the number of elements in the Flow rate vector, q parameter.

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

If your table has unknown data points in any of the four corners, use NaN in place of these values.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - torque and speed.

Shaft speed table, w(q,dp) — Shaft speed for tabulated data parameterization

[205, 80, 35; 455, 330, 285; 955, 831, 780; 1950, 1830, 1780; 2940, 2775, 2680; 3940, 3780, 3640] rpm (default) | M-by-N matrix

M-by-N matrix of shaft speed values at the specified fluid pressure drop and flow rate. The block employs linear interpolation between table elements. M and N are the sizes of the correlated vectors:

• M is the number of elements in the Flow rate vector, q parameter.

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

If your table has unknown data points in any of the four corners, use NaN in place of these values.

Dependencies

To enable this parameter, set Leakage and friction parameterization to Tabulated data - torque and speed.

Minimum volumetric efficiency — Lower saturation bound on the volumetric efficiency input signal

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

Smallest allowed value of the volumetric efficiency. The input from the physical signal port EV saturates inputs below this value.

Dependencies

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

Maximum volumetric efficiency — Upper saturation bound on the volumetric efficiency input signal

1 (default) | positive scalar

Largest allowed value of the volumetric efficiency. The input from the physical signal port EV saturates inputs above this value.

Dependencies

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

Minimum mechanical efficiency — Lower saturation bound on the volumetric efficiency input signal

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

Smallest allowed value of the mechanical efficiency. The input from the physical signal port EM saturates inputs below this value.

Dependencies

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

Maximum mechanical efficiency — Upper saturation bound on the volumetric efficiency input signal

1 (default) | scalar in the range (0,1)

Largest allowed value of the mechanical efficiency. The input from the physical signal port EM saturates inputs above this value.

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 drop at which to initiate a smooth transition between motor and pump modes

1e-3 MPa (default) | scalar

Pressure drop from inlet to outlet below which the block begins to transition between motoring and pumping modes. The block uses a hyperbolic tangent function to smooth the leakage flow rate and friction torque.

Dependencies

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

Angular velocity threshold for motor-pump transition — Angular velocity at which to initiate a smooth transition between pump and motor modes

100 rpm (default) | scalar

Shaft angular velocity below which the block begins to transition between motoring and pumping modes. The block uses the hyperbolic tangent function to smooth the leakage flow rate and friction torque.

Dependencies

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

Cross-sectional area at ports A and B — Flow area at the component inlet and outlet

0.01 m^2 (default) | positive scalar

Flow area at the component inlet and outlet. The areas are assumed equal.

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.

When Leakage and friction parameterization to Tabulated data - torque and speed, this parameter also checks if the block is operating in a region of supplied NaN values.

Dependencies

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

• Tabulated data - volumetric and mechanical efficiencies

• Tabulated data - volumetric and mechanical losses

• Tabulated data - torque and speed

Check if operating outside of motor mode — Simulation warning mode for operating conditions outside motoring mode

None (default) | Warning

Simulation warning mode for operating conditions outside the motoring mode. The block generates a warning if the motor transitions to pumping mode. Select Warning to be notified when this transition occurs. The warning does not cause simulation to stop.

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 outlet pressure falls below a minimum specified value. Select Error to stop the simulation when the outlet 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 to 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

Faults

Displacement fault — Option to model displacement fault

Add fault

Option to model a displacement fault in the block. When a fault occurs, the displacement scales by the value of the Faulted displacement factor parameter. To add a fault, click the Add fault hyperlink.

Faulted displacement factor — Factor by which to scale faulted displacement

0.5 (default) | positive scalar

Factor that the block uses to scale the displacement when a fault occurs.

Dependencies

To enable this parameter, click the Add fault hyperlink for the Displacement fault parameter.

Leakage fault — Option to model leakage fault

Add fault

Option to model a leakage fault in the block. When a fault occurs, the volumetric efficiencies or losses scale by the value of the Faulted leakage factor parameter. To add a fault, click the Add fault hyperlink.

Faulted leakage factor — Factor by which to scale leakage fault

2.0 (default) | positive scalar

Factor that the block uses to scale the volumetric efficiencies or losses when a fault occurs.

Dependencies

To enable this parameter, click the Add fault hyperlink for the Leakage fault parameter.

Shaft friction torque fault — Option to model shaft friction torque fault

Add fault

Option to model a shaft friction torque fault in the block. When a fault occurs, the mechanical efficiencies or losses scale by the value of the Faulted shaft friction torque factor parameter. To add a fault, click the Add fault hyperlink.

Faulted shaft friction torque factor — Factor by which to scale shaft friction torque fault

2.0 (default) | positive scalar

Factor that the block uses to scale the mechanical efficiencies or losses when a fault occurs.

Dependencies

To enable this parameter, click the Add fault hyperlink for the Shaft friction torque fault parameter.

Extended Capabilities

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

Version History

Introduced in R2016a

R2024b: Model faults with the Simscape faults interface

The Fixed-Displacement Motor (TL) block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.

R2024b: Parameterize block using torque and shaft speed

You can now parameterize the block by specifying the torque and shaft speed by setting the Leakage and friction parameterization parameter to Tabulated data - torque and speed. Manufacturers often provide motor datasheets in this format.

R2024b: Check if port pressures are less than pump minimum pressure

Use the Check if pressures are less than pump minimum pressure parameter to determine what happens if the fluid at port A or B falls below the value of the Pump pressure minimum parameter.

R2024a: Check if block operates outside range of calculated data

The Check if operating beyond the quadrants 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.