Crankshaft

R2026b

Combustion engine crankshaft that connects to one or more pistons

Since R2022a

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Crankshaft block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

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

$$\tau \cdot \omega =P,$$

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

$$P={\displaystyle \sum _{i=1}^N{P}_i},$$

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

$$\frac{d}{dt}\theta =\omega .$$

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

$$\tau =\{\begin{array}{cc}\begin{array}{l}\frac{P}{\omega }\\ P\cdot \left(\frac{2}{\omega }-\frac{\omega }{{\omega }_c^2}\right)\end{array}& \begin{array}{r}\omega \ge {\omega }_c\\ \\ \omega <{\omega }_c\end{array}\end{array}$$

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

$$\begin{array}{l}{\theta }_2={\theta }_1+\left(1\cdot \frac{720}{3}\right)\\ {\theta }_3={\theta }_1+\left(2\cdot \frac{720}{3}\right)\end{array}$$

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

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, clear Input power separately.

Programmatic Use

Port: cylpwr_in

CylPwr1 — Cylinder 1 power

physical signal

Physical signal input associated with the power from cylinder 1.

Dependencies

To enable this port, select Input power separately.

Programmatic Use

Port: cylpwr_1

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 select Input power separately.

Programmatic Use

Port: cylpwr_2

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 select Input power separately.

Programmatic Use

Port: cylpwr_3

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 select Input power separately.

Programmatic Use

Port: cylpwr_4

Output

CrkPos — Crank position, deg

physical signal

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

Programmatic Use

Port: crkpos_out

Spd — Engine rotational speed, rad/s

physical signal

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

Programmatic Use

Port: w_out

AvrSpd — Cycle-average crank speed, rad/s

physical signal

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

Programmatic Use

Port: w_avr_out

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.

Programmatic Use

Port: trq_avr_out

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

physical signal

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

Programmatic Use

Port: trq_out

Conserving

F — Crankshaft

mechanical rotational

Mechanical rotational conserving port associated with the crankshaft follower.

Programmatic Use

Port: F

Parameters

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.

Programmatic Use

Parameter: ca0

Number of cylinders — Total cylinder count

Single Cylinder (default) | Two Cylinders | Three Cylinders | Four Cylinders

Number of spark ignition cylinders.

Programmatic Use

Parameter:	numCyls
Values:	"sdl.enum.engineNumCylinders.One" | "sdl.enum.engineNumCylinders.Two" | "sdl.enum.engineNumCylinders.Three" | "sdl.enum.engineNumCylinders.Four"

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.

Programmatic Use

Parameter:	SeparatePowerInputs
Values:	"true" | "false"

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.

Programmatic Use

Parameter: twoCylSADiff

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.

Programmatic Use

Parameter:	L4FiringOrder
Values:	"sdl.enum.engineFiringOrderFourCylinders.L4_1342" | "sdl.enum.engineFiringOrderFourCylinders.L4_1324"

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.

Programmatic Use

Parameter: w_thr

Output

Cycle-average speed — Option to output cycle-average speed

on (default) | off

Whether to output the cycle-average speed.

Programmatic Use

Parameter:	OutputSpeedAvr
Values:	"true" | "false"

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.

Programmatic Use

Parameter:	OutputCombTrqAvr
Values:	"true" | "false"

Instantaneous net indicated torque — Option to output instantaneous net indicated torque

on (default) | off

Whether to output the instantaneous net indicated torque.

Programmatic Use

Parameter:	OutputCombTrq
Values:	"true" | "false"

Version History

Introduced in R2022a

R2025a: Enumeration Updates

These parameters now use a checkbox.

• Input power separately

• Cycle-average speed

• Cycle-average net indicated torque

• Instantaneous net indicated torque

These parameters used drop downs in previous releases.