# Fixed-Displacement Motor (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Pumps & Motors

## Description

The Fixed-Displacement Motor (IL) block models a motor with constant-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.

Shaft rotation corresponds to the sign of the fluid volume moving through the motor. Positive fluid displacement at corresponds to positive shaft rotation in forward mode. Negative fluid displacement corresponds to negative shaft angular velocity in forward mode.

**Operation Modes**

**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 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.

In the tabulated data and the input signal parameterization options, the threshold
parameters **Pressure drop threshold for motor-pump transition** and
**Angular velocity threshold for motor-pump transition** identify
regions where numerically smoothed flow transition between the motor operational modes
can occur. Choose a transition region that provides some margin for the transition term,
but which is small enough relative to the pressure and angular velocity that it will not
impact calculation results.

### 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**Displacement**.*ω*_{nom}is the**Nominal shaft angular velocity**.*η*_{v, nom}is the**Volumetric efficiency at nominal conditions**.

*Δp*_{nom}is the**Nominal pressure drop**.

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

$${\tau}_{fr}=\left({\tau}_{0}+k\left|\Delta p\right|\right)\mathrm{tanh}\left(\frac{4\omega}{5\times {10}^{-5}{\omega}_{nom}}\right),$$

where:

*τ*_{0}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}$$k=\frac{{\tau}_{fr,nom}-{\tau}_{0}}{\Delta {p}_{nom}}.$$

*τ*is the friction torque at nominal conditions:_{fric}$${\tau}_{fr,nom}=\left(1-{\eta}_{m,nom}\right)D\Delta {p}_{nom}.$$

*Δp*is the pressure drop between ports**A**and**B**.*ω*is the relative shaft angular velocity, or $${\omega}_{R}-{\omega}_{C}$$.

### Tabulated 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 four operational modes, the block calculates the complementing data for the other mode(s) by extending the given data into the remaining quadrants.

**The**

```
Tabulated data - volumetric and mechanical
efficiencies
```

parameterizationThe 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

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

where:

*Δp*is*p*_{A}–*p*_{B}.*p*_{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 friction 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
```

parameterizationThe leakage flow rate is calculated as:

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

where *q*_{loss} is interpolated from the
**Volumetric loss table, q_loss(dp,w)** 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:

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

where *τ*_{loss} is interpolated from the
**Mechanical loss table, torque_loss(dp,w)** parameter,
which is based on user-supplied data for pressure drop and shaft angular
velocity.

### Input Signal Parameterization

When **Leakage and friction parameterization** is set
to```
Input 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
to`Input 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:

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

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:

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

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.

### Pump 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:

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

If you would like to know if the block is operating beyond the
supplied tabulated data, you can set **Check if operating beyond the
quadrants of supplied tabulated data** to
`Warning`

to receive a warning if this occurs, or
`Error`

to stop the simulation when this occurs. For
parameterization by input signal for volumetric or mechanical losses, you can be
notified if the simulation surpasses operating modes with the **Check if
operating outside of 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.

### Predefined Parameterization

Pre-parameterized manufacturer data is available for this block. This data allows you to model a specific supplier component.

To load a predefined parameterization,

Click the "Select a predefined parameterization" hyperlink in the block dialog description.

Select a part from the drop-down menu and click

**Update block with selected part**.If you change any parameter settings after loading a parameterization, you can check your changes by clicking

**Compare block settings with selected part**. Any difference in settings between the block and pre-defined parameterization will display in the MATLAB command window.

**Note**

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

## Ports

### Conserving

### Input

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**