Piston Engine

R2026b

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 engine block, and port F represents 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

$\frac{T_{F}}{F_{B}} = - c (s i n (θ) + \frac{s i n (2 θ)}{2 \sqrt{{(\frac{r}{c})}^{2} - \sin^{2} (θ)}}),$

where:

F_B is the instantaneous piston force associated with the base port.
T_F is the instantaneous crank torque associated with the follower port.
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

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T — Normalized engine throttle level, unitless
nonnegative scalar

Engine torque demand as a fraction of maximum possible torque.

Programmatic Use

Port: T

Output

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FC — Fuel consumption rate, kg/s
physical signal

Fuel consumed by engine.

Programmatic Use

Port: FC

Conserving

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B — Base port associated with engine block
mechanical rotational

Rotational mechanical conserving port associated with the engine block.

Programmatic Use

Port: B

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.

Programmatic Use

Port: F

Parameters

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Pistons

Number of pistons — Total displacement calculation
`4` (default) | positive scalar

Number of pistons in the combustion engine.

Programmatic Use

Parameter: piston_num

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.

Programmatic Use

Parameter: theta_offset_vector

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.

Programmatic Use

Parameter: bore

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.

Programmatic Use

Parameter: stroke

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.

Programmatic Use

Parameter: rod

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.

Programmatic Use

Parameter: stroke_num

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.

Programmatic Use

Parameter:	`parameterization`
Values:	`"sdl.enum.piston_parameterization.Angle"` \| `"sdl.enum.piston_parameterization.AngleThrottle"` \| `"sdl.enum.piston_parameterization.AngleThrottleVelocity"`

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.

Programmatic Use

Parameter: angle_vector

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.

Programmatic Use

Parameter: throttle_vector

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.

Programmatic Use

Parameter: velocity_vector

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.

Programmatic Use

Parameter: pressure_vector

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.

Programmatic Use

Parameter: pressure_matrix

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.

Programmatic Use

Parameter:	`shaft_dynamics`
Values:	`"sdl.enum.shaft_dynamics.Off"` \| `"sdl.enum.shaft_dynamics.On"`

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.

Programmatic Use

Parameter: mu_visc

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.

Programmatic Use

Parameter: theta_init

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.