# Piston Engine

Reciprocating combustion engine with variable number of pistons

**Libraries:**

Simscape /
Driveline /
Engines & Motors

## Description

The Piston Engine block represents a reciprocating combustion engine with multiple cylinders. The piston model accounts for the instantaneous torque transmitted to the engine drive shaft. The instantaneous torque enables you to model vibrations in the drivetrain due to piston revolution. To model just the piston mechanism of a combustion engine, use the Piston block.

Port **B** represents the translating piston and port
**F** the rotating crankshaft. The piston force follows from the
cylinder pressure and cross-sectional area. The block obtains the combustion pressure
from a lookup table parameterized in terms of the crank angle and, optionally, the crank
angular velocity and engine throttle level.

The crank torque follows from the piston force and crank angle as well as the crank and connecting rod lengths. In terms of these inputs, the ratio of the piston force and crank torque is

$$\frac{{T}_{\text{F}}}{{F}_{\text{B}}}=-\text{c}\left(sin(\theta )+\frac{sin(2\theta )}{2\sqrt{{\left(\frac{\text{r}}{\text{c}}\right)}^{2}-{\mathrm{sin}}^{2}(\theta )}}\right),$$

where:

*F*is the instantaneous piston force associated with the base port._{B}*T*is the instantaneous crank torque associated with the follower port._{F}*c*is the crank length.*θ*is the instantaneous crank angle.*r*is the connecting rod length.

**Piston Dimensions**

Physical signal port T lets you specify the engine throttle level as a fraction between 0 and 1. This fraction corresponds to the percentage of full power generated. The block uses the physical signal input whenever the pressure lookup table in the block property inspector is parameterized only in terms of the crank angle.

## Ports

### Input

**T** — Normalized engine throttle level, unitless

nonnegative scalar

Engine torque demand as a fraction of maximum possible torque.

### Output

**FC** — Fuel consumption rate, kg/s

physical signal

Fuel consumed by engine.

### Conserving

**B** — Base port associated with piston

mechanical translational

Translational mechanical conserving port that connects to the engine block.

**F** — Engine crankshaft

mechanical rotational

Follower port of engine. The crankshaft transmits the power generated from the combustion process. Typically, this is where you would attach a clutch and transmission.

## Parameters

### Pistons

**Number of pistons** — Total displacement calculation

`4`

(default) | positive scalar

Number of pistons in the combustion engine.

**Offset angle vector** — Top dead center offset for each piston

`[0, 180, 360, -180]`

(default) | vector

Vector of piston offset angles. The offset angle specifies the point
in the engine cycle when the piston reaches top dead center. The engine
cycle spans in angle from -*S**180 to +*S**180 degrees, where *S* is the number of
strokes per cycle.

The vector size must be the same as the number of pistons. The default vector corresponds to a four-stroke, four-piston engine.

**Cylinder bore** — Inside diameter of piston cylinder wall

`.10`

`m`

(default) | positive scalar

Inside diameter of the piston cylinder wall. The block uses this measurement to compute the torque table. You must specify a value greater than zero.

**Piston stroke** — Length of translational piston travel

`.06`

`m`

(default) | positive scalar

Distance from the fully retracted position to the fully extended position of the piston. The block uses this measurement to convert pressure on the piston into torque values. You must specify a value greater than zero.

**Piston rod length** — Length of piston-to-crankshaft connecting rod

`.1`

`m`

(default) | positive scalar

Distance from the center of the piston pin hole to the center of the crankshaft hole in the piston rod. The block uses this measurement to convert pressure on the piston into torque. You must specify a value greater than zero.

**Number of strokes per cycle** — Number of piston strokes to complete one combustion cycle

`4`

(default) | positive even scalar

Number of piston phases required to intake, compress, combust, and exhaust the combustion gases. Typically, engines are two-stroke or four-stroke. You must use a multiple of two.

**Pressure parameterization** — Determine pressure applied to piston

`By crank angle`

(default) | `By crank angle and throttle`

| ```
By crank angle, throttle, and crank
velocity
```

Parameter group that you want the block to use to parameterize the pressure data.

**Crank angle vector** — Different piston crank angles

```
[-360, -90, -30, 10, 30, 90, 160,
360]
```

`deg`

(default) | vector

Angle of the piston crank starting at or above the minimum angle and ending at or below the maximum angle. You can calculate the minimum or maximum angle by multiplying the number of strokes by -90 degrees or 90 degrees, respectively. You must specify at least two values.

Each element in **Crank angle vector** corresponds to
an element in **Pressure vector (gauge)** or the
*M*-row of **Pressure matrix
(gauge)** or each **Pressure 3D matrix
(gauge)** matrix.

**Throttle vector** — Different throttle positions

`[0, .3, .8, 1]`

(default) | vector

Different throttle positions that correspond to the pressures in the
**Pressure matrix (gauge)** or **Pressure
3D matrix (gauge)** parameters. The throttle position must
remain in the range [0,1] with 0 representing no throttle and 1
representing full throttle.

Each element in **Throttle vector** corresponds to
the *N*-column of **Pressure matrix
(gauge)** or each **Pressure 3D matrix
(gauge)** matrix.

#### Dependencies

To enable this parameter, set **Pressure
parameterization** to ```
By crank angle and
throttle
```

or ```
By crank angle, throttle,
and crank velocity
```

.

**Crank velocity vector** — Different angular velocities

`[0, 1000, 6000]`

`rpm`

(default) | vector

Different crank velocities that correspond to pressures in
**Pressure 3D matrix (gauge)**.

Each element in **Crank velocity vector** corresponds
to one of the *O*-matrices of **Pressure 3D
matrix (gauge)**.

#### Dependencies

To enable this parameter, set **Pressure
parameterization** to ```
By crank angle,
throttle, and crank velocity
```

.

**Pressure vector (gauge)** — Crank angle parameterized pressures

`[0, 3, 20, 50, 20, 10, 8, 0]`

`bar`

(default) | vector

Vector of pressure values that correspond to different crank angle positions.

#### Dependencies

To enable this parameter, set **Pressure
parameterization** to ```
By crank
angle
```

.

**Pressure matrix (gauge)** — Crank angle and throttle parametrized pressures

*M*-by-*N*
matrix (default) | matrix

Matrix of pressure values that correspond to different crank angle and
throttle combinations. The default value is ```
[0, 0, 0, 0; 0, .9,
2.4, 3; 0, 6, 16, 20; 0, 15, 40, 50; 0, 6, 16, 20; 0, 3, 8, 10; 0,
2.4, 6.4, 8; 0, 0, 0, 0]
```

`bar`

.

The elements of **Crank angle vector** correspond to
the *M*-rows in **Pressure matrix
(gauge)**. The elements of **Throttle
vector** correspond to the *N*-columns in
**Pressure matrix (gauge)**.

#### Dependencies

To enable this parameter, set **Pressure
parameterization** to ```
By crank angle and
throttle
```

.

**Pressure 3D matrix (gauge)** — Crank angle, throttle, and crank velocity parameterized pressures

*M*-by-*N*-by-*O*
matrix (default) | 3-D matrix

Concatenated matrix of pressure values that correspond to the various
crank angle, throttle, and crank velocity combinations. The default
value is ```
cat(3, [0, 0, 0, 0; 0, .9, 2.4, 3; 0, 6, 16, 20; 0,
15, 40, 50; 0, 6, 16, 20; 0, 3, 8, 10; 0, 2.4, 6.4, 8; 0, 0, 0, 0],
[0, 0, 0, 0; 0, .9, 2.4, 3; 0, 6, 16, 20; 0, 15, 40, 50; 0, 6, 16,
20; 0, 3, 8, 10; 0, 2.4, 6.4, 8; 0, 0, 0, 0], [0, 0, 0, 0; 0, .9,
2.4, 3; 0, 6, 16, 20; 0, 15, 40, 50; 0, 6, 16, 20; 0, 3, 8, 10; 0,
2.4, 6.4, 8; 0, 0, 0, 0])
```

`bar`

.

The elements of **Crank angle vector** correspond to
the *M*-rows. The elements of **Throttle
vector** correspond to the *N*-columns.
The elements of **Crank velocity vector** correspond to
the matrices you concatenate along dimension
*O*.

By default, *M* = 8, *N* =
4, and *O* = 3.

#### Dependencies

To enable this parameter, set **Pressure
parameterization** to ```
By crank angle,
throttle, and crank velocity
```

.

### Crankshaft

**Shaft dynamics** — Enable shaft dynamics modeling parameters

```
No shaft dynamics - Suitable for HIL
simulation
```

(default) | ```
Specify shaft stiffness, damping, and
inertia
```

Option to parameterize the shaft dynamics.

**Base and follower bearing viscous friction coefficients** — Characterize system friction

`[0, 0]`

`deg`

(default) | vector

Viscous friction coefficients for the base bearing and follower bearing, in that order.

**Initial crank angle** — Starting crank position

`90`

`deg`

(default) | scalar

Crank angle at time zero relative to a top dead center position. The
engine cycle spans in angle from -*S**180 to +*S**180 degrees, where *S* is the number of
strokes per cycle.

**Stiffness** — Resistance to deformation

`1e6`

`N*m/rad`

(default) | positive scalar

Translational spring stiffness of engine crankshaft. The spring stiffness accounts for elastic energy storage in the crankshaft due to material compliance.

Stiffness coefficient of the engine crankshaft. This parameter accounts for resistance to shaft deformation.

#### Dependencies

To enable this parameter, set **Shaft dynamics**
to ```
Specify shaft stiffness, damping, and
inertia
```

.

**Damping** — Tendency to drain energy from the system

`1000`

`N*m/(rad/s)`

(default) | positive scalar

Translational damping of engine crankshaft. The damping accounts for energy dissipation in the crankshaft due to material compliance.

#### Dependencies

To enable this parameter, set **Shaft dynamics**
to ```
Specify shaft stiffness, damping, and
inertia
```

.

**Inertia** — Tendency to resist change in motion

`.02`

`kg*m^2`

(default) | positive scalar

Moment of inertia of crankshaft about its rotational axis. This parameter accounts for resistance to sudden changes in motion.

#### Dependencies

To enable this parameter, set **Shaft dynamics**
to ```
Specify shaft stiffness, damping, and
inertia
```

.

**Initial angular deflection** — Angular deflection initializing parameter

`0`

`deg`

(default)

Deflection angle between the base and follower ends of the crankshaft at time zero. The deflection angle measures the angular deformation of the crankshaft due to torsion.

#### Dependencies

To enable this parameter, set **Shaft dynamics**
to ```
Specify shaft stiffness, damping, and
inertia
```

.

**Initial angular velocity** — Angular velocity initializing parameter

`0`

(default) | scalar

Angular velocity of the crankshaft at time zero.

#### Dependencies

To enable this parameter, set **Shaft dynamics**
to ```
Specify shaft stiffness, damping, and
inertia
```

.

### Fuel Consumption

The table shows how the specified options for the **Fuel consumption
model** parameter affects the availability of dependent parameters. To
learn how to read the dependencies tables, see Parameter Dependencies.

**Fuel Consumption Parameter Dependencies**

Fuel
Consumption | ||||
---|---|---|---|---|

Fuel consumption model — Choose
`No fuel consumption` ,
`Constant per revolution` ,
```
Fuel consumption by speed and
torque
``` , ```
Brake specific fuel
consumption by speed and torque
``` , or
```
Brake specific fuel consumption by speed and
brake mean effective pressure
``` | ||||

No fuel
consumption | Constant per
revolution | Fuel consumption by speed
and torque | Brake specific fuel
consumption by speed and torque | Brake specific fuel
consumption by speed and brake mean effective
pressure |

Fuel consumption per revolution | ||||

Speed vector | ||||

Torque vector | Brake mean effective pressure vector | |||

Fuel consumption table | Brake specific fuel consumption table | |||

Interpolation method —
Choose |

**Fuel consumption model** — Enable fuel consumption modeling parameters

`No fuel consumption`

(default) | `Constant per revolution`

| `Fuel consumption by speed and torque`

| ...

Fuel consumption model based on available data. Select a model for calculating engine-fuel consumption. Model parameterizations are compatible with typical industrial data. Choose from the following options:

`No fuel consumption`

— The default option`Constant per revolution`

`Fuel consumption by speed and torque`

`Brake specific fuel consumption by speed and torque`

`Brake specific fuel consumption by speed and brake mean effective pressure`

If you leave **Fuel consumption model** set to
`No fuel consumption`

, the block does not
calculate fuel consumption even when the **FC** port is
connected to another block. Selecting this option increases simulation
speed.

**Fuel consumption per piston revolution** — Constant

`25`

`mg/rev`

(default) | positive scalar

Constant rate of fuel consumption as a function of crankshaft revolutions. Enter the volume of fuel consumed in one crankshaft revolution.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Constant per
revolution
```

.

**Speed vector** — Engine speed data

```
[1000, 2000, 3000, 4000, 5000,
6000]
```

(default) | vector

Vector of engine torques that corresponds to the *M*
rows of the fuel consumption lookup table.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Fuel consumption by speed
and torque
```

, ```
Brake specific fuel
consumption by speed and torque
```

, or
```
Brake specific fuel consumption by speed and brake
mean effective pressure
```

.

**Torque vector** — Engine torque data

```
[0, 80, 160, 200, 240, 320, 360,
400]
```

(default) | vector

Vector of engine torques that corresponds to the *N*
columns of the fuel consumption lookup table.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Fuel consumption by speed
and torque
```

or ```
Brake specific fuel
consumption by speed and torque
```

.

**Fuel consumption table** — Engine fuel consumption data

*M*-by-*N*
matrix (default) | matrix

Matrix of fuel consumption values that correspond Enter matrix with
fuel consumption rates corresponding to engine speed and torque vectors.
The number of rows must equal the number of elements in the
**Speed vector**. The number of columns must equal
the number of elements in the **Torque vector**. The
default is ```
[.5, .9, 1.4, 1.6, 1.9, 2.7, 3.4, 4.4; 1, 1.7, 2.7,
3.1, 3.6, 5, 6, 7.4; 1.4, 2.7, 4, 4.8, 5.6, 7.5, 8.5, 10.5; 2, 3.6,
5.8, 6.7, 8, 10.4, 11.7, 13.3; 2.5, 4.8, 7.9, 9.4, 10.8, 14, 16.2,
18.6; 3.1, 6, 10.3, 11.9, 13.8, 18.4, 22, 26.5]
```

`g/s`

.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Fuel consumption by speed
and torque
```

.

**Brake mean effective pressure vector** — Piston pressure data

```
[0, 250, 500, 625, 750, 1000, 1150,
1250]
```

(default) | vector

Vector of brake mean effective pressure (BMEP) values. The BMEP satisfies the expression:

$$BMEP=T\cdot \left(\frac{2\pi \cdot {n}_{c}}{{V}_{d}}\right),$$

where:

*T*is the output torque.*n*is the number of cycles per revolution._{c}*V*is the cylinder displaced volume._{d}

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Brake specific fuel
consumption by speed and brake mean effective
pressure
```

.

**Brake specific fuel consumption table** — Brake specific fuel consumption data

*M*-by-*N*
matrix (default) | matrix

For the ```
Brake specific fuel consumption by speed and
torque
```

fuel model, enter the matrix with brake
specific fuel consumption (BSFC) rates corresponding to engine speed and
torque vectors. BSFC is the ratio of the fuel consumption rate to the
output power. The number of rows must equal the number of elements in
the **Speed vector**. The number of columns must equal
the number of elements in the **Torque vector**.

For the ```
Brake specific fuel consumption by speed and
brake mean effective pressure
```

fuel model, enter the
matrix with brake specific fuel consumption (BSFC) rates corresponding
to engine speed and brake mean effective pressure (BMEP) vectors. BSFC
is the ratio of the fuel consumption rate to the output power. The
number of rows must equal the number of elements in the **Speed
vector**. The number of columns must equal the number of
elements in the **Brake mean effective pressure
vector**.

For both fuel-consumption models, the default is ```
[410, 380,
300, 280, 270, 290, 320, 380; 410, 370, 290, 270, 260, 270, 285,
320; 415, 380, 290, 275, 265, 270, 270, 300; 420, 390, 310, 290,
285, 280, 280, 285; 430, 410, 340, 320, 310, 300, 310, 320; 450,
430, 370, 340, 330, 330, 350, 380]
```

`g/hr/kW`

.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Brake specific fuel
consumption by speed and torque
```

or
```
Brake specific fuel consumption by speed and brake
mean effective pressure
```

.

**Interpolation method** — Intermediate step behavior

`Linear`

(default) | `Smooth`

Interpolation method to calculate fuel consumption at intermediate speed and torque values. Outside the data range, fuel consumption remains constant at the last value given in the lookup table for both methods.

#### Dependencies

To enable this parameter, set **Fuel
consumption** to ```
Fuel consumption by speed
and torque
```

, ```
Brake specific fuel
consumption by speed and torque
```

, or
```
Brake specific fuel consumption by speed and brake
mean effective pressure
```

.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced in R2016a**

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