Crankshaft

Combustion engine crankshaft that connects to one or more pistons

Since R2022a

Libraries:
Simscape / Driveline / Engines & Motors / Engine Subcomponents

Description

The Crankshaft block represents the crankshaft component of an abstracted internal combustion engine. Connect this block to one or more SI Combustion Cylinder blocks to compute the crank-angle-resolved instantaneous torque.

Equations

The generic torque-speed-power relationship governs the block, such that

$τ \cdot ω = P,$

where

τ is the torque.
ω is the rotational speed, which the block assumes is nonnegative.
P is the power.

The block calculates the power as

$P = \sum_{i = 1}^{N} P_{i},$

where N is the value of the Number of cylinders parameter. The block calculates ω as the time derivative of the crank position, θ, such that

$\frac{d}{d t} θ = ω .$

The constant ω_c is the Threshold to avoid divide-by-zero parameter. When ω < ω_c, the block applies 1/ω linearization.

$τ = {\begin{matrix} \begin{array}{l} \frac{P}{ω} \\ P \cdot (\frac{2}{ω} - \frac{ω}{ω_{c}^{2}}) \end{array} & \begin{array}{r} ω \geq ω_{c} \\ ω < ω_{c} \end{array} \end{matrix}$

Crank Position

The block calculates the crank position with respect to the top dead center position for each combustion cylinder, where 0 ≤ θ_i ≤ 720 degrees. How the block performs this calculation depends on N. For all values of N, θ₁ = θ. For N = 2, θ₂ = θ₁+Δ, where Δ is the Spark angle difference parameter. This parameter value is specific to the engine you want to model. It may be a value such as 270° or 360°. When N = 3, the block assumes that the cylinders are evenly phased such that

$\begin{array}{l} θ_{2} = θ_{1} + (1 \cdot \frac{720}{3}) \\ θ_{3} = θ_{1} + (2 \cdot \frac{720}{3}) \end{array}$

When N = 4, the block assumes that the cylinders are evenly phased at 180° and enables the Firing order parameter.

Examples

Single Cylinder Spark Ignition Engine

A crank-angle-resolved, naturally aspirated spark ignition engine. Control inputs such as throttle, intake VVT, air-to-fuel ratio, and spark advance vary during the simulation. You can simulate results from either an Otto cycle engine or an Atkinson cycle engine.

Open Model

Ports

Input

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CylPwr — Cylinder power array
physical signal

Physical signal input associated with the cylinder power when the block acts as a subcomponent.

Dependencies

To enable this port, set Input power separately to Off.

CylPwr1 — Cylinder 1 power
physical signal

Physical signal input associated with the power from cylinder 1.

Dependencies

To enable this port, set Input power separately to On.

CylPwr2 — Cylinder 2 power
physical signal

Physical signal input associated with the power from cylinder 2.

Dependencies

To enable this port, set Number of cylinders to Two Cylinders, Three Cylinders, or Four Cylinders and Input power separately to On.

CylPwr3 — Cylinder 3 power
physical signal

Physical signal input associated with the power from cylinder 3.

Dependencies

To enable this port, set Number of cylinders to Three Cylinders or Four Cylinders and Input power separately to On.

CylPwr4 — Cylinder 4 power
physical signal

Physical signal input associated with the power from cylinder 4.

Dependencies

To enable this port, set Number of cylinders to Four Cylinders and Input power separately to On.

Output

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CrkPos — Crank position, deg
physical signal

Physical signal output associated with the crank position, in degrees.

Spd — Engine rotational speed, rad/s
physical signal

Physical signal output associated with the engine rotational speed, in rad/s.

AvrSpd — Cycle-average crank speed, rad/s
physical signal

Physical signal output associated with the cycle-average crank speed, in rad/s.

AvrTrq — Cycle-average net-indicated crank torque, N*m
physical signal

Physical signal output associated with the cycle-average net-indicated crank torque, in Nm.

Trq — Instantaneous net-indicated crank torque, N*m
physical signal

Physical signal output associated with the instantaneous net-indicated crank torque, in Nm.

Conserving

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F — Crankshaft
mechanical rotational

Mechanical rotational conserving port associated with the crankshaft follower.

Parameters

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Mechanical

Initial crank position, ca0 (0-720 CAdeg) — Crank position when simulation begins
`0` `deg` (default) | nonnegative scalar in the range [0,720)

Initial crank position.

Number of cylinders — Total cylinder count
`Single Cylinder` (default) | `Two Cylinders` | `Three Cylinders` | `Four Cylinders`

Number of spark ignition cylinders.

Input power separately — Option to input power
`On` (default) | `Off`

Whether to input power as an array or to assign each combustion cylinder to its own port.

Spark angle difference — Two cylinder engine spark angle phase
`270` `deg` (default) | positive scalar

Spark angle difference for two cylinder engines. This value can vary from engine to engine.

Dependencies

To enable this parameter, set Number of cylinders to Two Cylinders.

Firing order — Ignition order for four cylinder engines
`1-3-4-2` (default) | `1-3-2-4`

Firing order for four-cylinder engines. Firing order is engine-specific, but your selection for this parameter will not affect the block performance. You can use the firing order information for controller development.

Dependencies

To enable this parameter, set Number of cylinders to Four Cylinders.

Simulation

Threshold to avoid divide-by-zero — Threshold engine speed
`0.1` `rad/s` (default)

Engine rotational speed at which the block applies linearization to avoid discontinuities at ω = 0.

Output

Cycle-average speed — Option to output cycle-average speed
`On` (default) | `Off`

Whether to output the cycle-average speed.

Cycle-average net indicated torque — Option to output cycle-average net indicated torque
`On` (default) | `Off`

Whether to output the cycle-average net indicated torque.

Instantaneous net indicated torque — Option to output instantaneous net indicated torque
`On` (default) | `Off`

Whether to output the instantaneous net indicated torque.

Version History

Introduced in R2022a

Crankshaft

Description

Equations

Examples

Single Cylinder Spark Ignition Engine

Ports

Input

CylPwr — Cylinder power array physical signal

Dependencies

CylPwr1 — Cylinder 1 power physical signal

Dependencies

CylPwr2 — Cylinder 2 power physical signal

Dependencies

CylPwr3 — Cylinder 3 power physical signal

Dependencies

CylPwr4 — Cylinder 4 power physical signal

Dependencies

Output

CrkPos — Crank position, deg physical signal

Spd — Engine rotational speed, rad/s physical signal

AvrSpd — Cycle-average crank speed, rad/s physical signal

AvrTrq — Cycle-average net-indicated crank torque, N*m physical signal

Trq — Instantaneous net-indicated crank torque, N*m physical signal

Conserving

F — Crankshaft mechanical rotational

Parameters

Mechanical

Initial crank position, ca0 (0-720 CAdeg) — Crank position when simulation begins 0 deg (default) | nonnegative scalar in the range [0,720)

Number of cylinders — Total cylinder count Single Cylinder (default) | Two Cylinders | Three Cylinders | Four Cylinders

Input power separately — Option to input power On (default) | Off

Spark angle difference — Two cylinder engine spark angle phase 270 deg (default) | positive scalar

Dependencies

Firing order — Ignition order for four cylinder engines 1-3-4-2 (default) | 1-3-2-4

Dependencies

Simulation

Threshold to avoid divide-by-zero — Threshold engine speed 0.1 rad/s (default)

Output

Cycle-average speed — Option to output cycle-average speed On (default) | Off

Cycle-average net indicated torque — Option to output cycle-average net indicated torque On (default) | Off

Instantaneous net indicated torque — Option to output instantaneous net indicated torque On (default) | Off

Version History

See Also

CylPwr — Cylinder power array
physical signal

CylPwr1 — Cylinder 1 power
physical signal

CylPwr2 — Cylinder 2 power
physical signal

CylPwr3 — Cylinder 3 power
physical signal

CylPwr4 — Cylinder 4 power
physical signal

CrkPos — Crank position, deg
physical signal

Spd — Engine rotational speed, rad/s
physical signal

AvrSpd — Cycle-average crank speed, rad/s
physical signal

AvrTrq — Cycle-average net-indicated crank torque, N*m
physical signal

Trq — Instantaneous net-indicated crank torque, N*m
physical signal

F — Crankshaft
mechanical rotational

Initial crank position, ca0 (0-720 CAdeg) — Crank position when simulation begins
`0` `deg` (default) | nonnegative scalar in the range [0,720)

Number of cylinders — Total cylinder count
`Single Cylinder` (default) | `Two Cylinders` | `Three Cylinders` | `Four Cylinders`

Input power separately — Option to input power
`On` (default) | `Off`

Spark angle difference — Two cylinder engine spark angle phase
`270` `deg` (default) | positive scalar

Firing order — Ignition order for four cylinder engines
`1-3-4-2` (default) | `1-3-2-4`

Threshold to avoid divide-by-zero — Threshold engine speed
`0.1` `rad/s` (default)

Cycle-average speed — Option to output cycle-average speed
`On` (default) | `Off`

Cycle-average net indicated torque — Option to output cycle-average net indicated torque
`On` (default) | `Off`

Instantaneous net indicated torque — Option to output instantaneous net indicated torque
`On` (default) | `Off`