Engee documentation

Independent Suspension - Double Wishbone

Independent suspension on double wishbones.

blockType: SubSystem

independent suspension double wishbone

Path in the library:

/Automotive/Suspension/Independent Suspension - Double Wishbone

Description

Block Independent Suspension - Double Wishbone Implements independent suspension on double wishbones for multiple axles with multiple wheels on each axle.

The block simulates the elasticity, damping, and geometric effects of the suspension as functions of the relative positions and speeds of the vehicle and the wheel hub, taking into account the compliance and damping parameters specific to each axle. Using data on suspension compliance and damping, the unit calculates the force exerted on the vehicle and wheel. The block uses a coordinate system with a downward pointing axis (defined in the SAE J670 standard). The following parameters can be configured for each suspension element:

  • For the axle — the number of wheels, the presence of a stabilizer bar for axles with two wheels, suspension parameters;

  • For the wheel, the angles of rotation.

The block contains spring elements that store energy and damping elements that dissipate energy. It does not contain mass elements that store energy. The block assumes that the vehicle blocks (sprung mass) and wheels (unsprung mass) connected to the block accumulate suspension energy related to the mass.

To simulate a vehicle with the following characteristics: two axles, two wheels on each axle, the angle of rotation for both wheels on the front axle and the stabilizer bar on the front axle, set the parameters:

  • Number of axles NumAxl meaning 2;

  • Number of wheels per axle [NumWhlsByAxl] meaning [2 2];

  • Steered axle enable by axle [StrgEnByAxl] meaning [1 0];

  • Anti-sway axle enable by axle [AntiSwayEnByAxl] meaning [1 0].

The block uses the wheel number for indexing input and output signals. The table below provides information about the wheel, axle and the corresponding wheel number for a vehicle with the following characteristics: two axles and two wheels on each axle.

Wheel The axis Wheel number

Front left

The front

1

Front right

The front

2

Rear left

The back

1

Rear right

The back

2

Suspension ductility and damping

The unit uses a linear spring and a damper to simulate the vertical dynamic effects of the suspension system. Using the relative positions and speeds of the vehicle and the wheel hub, the unit calculates the vertical suspension forces on the wheel and the vehicle. The unit uses a linear equation that relates vertical damping and ductility to the height of the suspension, the rate of change in suspension height, and the absolute value of the turning angles.

The block implements the following equation:

where

  • — suspension force applied to the numbered wheel on the axis along the axis , mounted on the wheel;

  • — the preload force of the vertical suspension spring applied to the wheels on the axle ;

  • — the stiffness coefficient of the vertical spring for the axes;

  • — movement and speed of the vehicle for the axis And the wheels along the inertial axis ;

  • — movement and speed of the wheel at the axis attachment point along the axis the inertial coordinate system;

  • — the angle of rotation of the wheel relative to the vector of force applied to the wheel hub;

  • — the input angle of rotation of the wheels for the axle And the wheels ;

  • — damping coefficient;

  • — the vertical force of the rigid stop on the axis and the wheel along the inertial axis ;

  • — vertical force from the stabilizer bar on the axis and the wheel along the axis the inertial coordinate system.

Damping coefficient depends on the parameter value Enable active damping. If this option is unchecked, the damping coefficient remains constant. , where — the coefficient of vertical damping of the wheel suspension on the axle . If this option is selected, an interpolation table is used, which is a function of the fill factor of the active damper and the drive speed.:

Within the framework of this block, it is assumed that the suspension elements have no mass. Therefore, the suspension forces and torques acting on the vehicle are equal to the suspension forces and torques acting on the wheel.









where

  • — the force and moment of suspension applied to the vehicle on the axle and the wheel along the axis , mounted on the wheel;

  • — the force and moment of suspension applied to the vehicle on the axle and the wheel along the axis , mounted on the wheel;

  • — the force and moment of suspension applied to the vehicle on the axle and the wheel along the axis , mounted on the wheel;

  • — the force and moment of suspension applied to the wheel under the number on the axis along the axis , mounted on the wheel;

  • — the force and moment of suspension applied to the wheel under the number on the axis along the axis , mounted on the wheel;

  • — the force and moment of suspension applied to the wheel under the number on the axis along the axis , mounted on the wheel;

  • and — effective wheel radius for the axle And the wheels along the axes and accordingly;

  • — suspension height for the axle And the wheels .

The unit sets the wheel positions and speeds equal to the transverse and longitudinal positions and speeds of the vehicle.



where

  • — movement and speed of the wheel on the axis along the inertial axis ;

  • — movement and speed of the vehicle on the axle and the wheel along the inertial axis ;

  • — wheel movement and speed on the axis along the inertial axis ;

  • — movement and speed of the vehicle on the axle and the wheel along the inertial axis .

The forces of the stops

Thrust feedback force which is applied in the block depends on whether the suspension is compressed or stretched. The force arises:

  • during compression, when the suspension is compressed by more than the maximum value set by the parameter Suspension maximum height Hmax, m;

  • when stretched, when the suspension is stretched by more than the maximum value set by the parameter Suspension maximum height Hmax, m.

The stiffness coefficient based on hyperbolic tangent and exponential scaling is used to calculate the force in the block.

Stabilizer bar

Optionally, you can use the parameter Anti-sway axle enable by axle [AntiSwayEnByAxl], which allows to activate the stabilizer bar for each axle with two wheels. The figure below shows how the stabilizer bar transmits torque between two wheels of an independent suspension on a common axle. Each independent suspension transmits torque to the stabilizer bar through a lever that connects the stabilizer bar to the independent suspension.

independent suspension double wishbone 1

To calculate the force acting on the stabilizer bar, the unit uses the following equations:

  • Angular deviation of the stabilizer bar for this axis And the wheels :



    where

    • — the initial angle of rotation of the stabilizer bar;

    • — the vertical distance from the mounting point of the stabilizer bar to the center line of the stabilizer;

    • — the radius of the stabilizer bar.

  • Angle of rotation of the stabilizer bar :

  • Torque of the stabilizer bar :

  • The forces of the stabilizer applied to the wheel on the axis along the axis , mounted on the wheel:



    where

    • — moving the vehicle on the axle and the wheel along the inertial axis ;

    • — movement and speed of the wheel on the axis along the inertial axis .

Angles of camber, longitudinal tilt of the axis of rotation of the wheel and convergence

The unit uses linear functions of suspension height and angle of rotation to calculate camber angles, longitudinal tilt of the wheel axis and convergence.





where

  • — the camber angle of the wheel on the axle and the wheel ;

  • — the angle of the longitudinal inclination of the axis of rotation of the wheel on the axis and the wheel ;

  • — the angle of convergence of the wheel on the axle and the wheel ;

  • , , — nominal angles of camber, tilt and convergence (respectively) of the axis suspension at zero angle of rotation;

  • , , — the dependence of the angles of camber, tilt and convergence, respectively, on the height of the suspension for the axle ;

  • , , — the dependence of the angles of collapse, tilt and convergence, respectively, on the angle of rotation for the axis ;

  • — the dependence of the rotation angle on the vertical force for the axis ;

  • — input rotation angle for the axis And the wheels ;

  • — moving the vehicle on the axle and the wheel along the inertial axis ;

  • — moving the wheel on the axis along the inertial axis .

Wheel rotation angles

Optionally, you can use the parameter Steered axle enable by axle [StrgEnByAxl], which allows you to set the rotation angles. To calculate the rotation angles, the unit shifts the set rotation angles using a linear function of the suspension height.:

where

  • — dependence of the angle of convergence of the axis from the angle of rotation;

  • — dependence of the axis rotation angle from the tilt of the vertical force;

  • — dependence of the angle of convergence of the axis from the height of the suspension;

  • — the angle of rotation of the wheel for the axle And the wheels ;

  • — input rotation angle for the axis And the wheels ;

  • — moving the vehicle on the axle and the wheel along the inertial axis ;

  • — moving the wheel on the axis along the inertial axis .

Power and energy

The unit calculates these suspension characteristics for each axle And the wheels :

  • Power dissipation :

    where — the angle of rotation for the axis And the wheels ;

  • Absorbed energy :

  • Suspension height :

    where

    • — movement and speed of the vehicle on the axle and the wheel along the inertial axis ;

    • — movement and speed of the wheel on the axis along the inertial axis ;

    • — the preload force of the vertical suspension spring applied to the wheels on the axle ;

    • — the angle of rotation relative to the vertical force applied to the wheel hubs on the axle .

  • The distance from the center of the wheel hub to the point of contact of the tire with the road:

    where — effective wheel radius on the axis from the center of the wheel hub to the point of contact of the tire with the road.

Ports

Input

WhlPz

# —

moving the wheel along the axis 

+

array

Details

Moving the wheel along the axis , mounted on a wheel, measured in meters. Size of the array: 1 for the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels on each axle, the signal array WhlPz has the size 1 on 4:


Wheel Array element The axis Wheel number

Front left

WhlPz[1, 1]

1

1

Front right

WhlPz[1, 2]

1

2

Rear left

WhlPz[1, 3]

2

1

Rear right

WhlPz[1, 4]

2

2
Data types

Float64
Complex numbers support

No

WhlRe

# —

effective wheel radius

array

Details

Effective wheel radius , measured in meters. Size of the array: 1 for the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels on each axle, the signal array WhlRe has the size 1 on 4:



Wheel Array element The axis Wheel number

Front left

WhlRe[1, 1]

1

1

Front right

WhlRe[1, 2]

1

2

Rear left

WhlRe[1, 3]

2

1

Rear right

WhlRe[1, 4]

2

2
Data types

Float64
Complex numbers support

No

# WhlVz —

the speed of rotation of the wheel on the axis 

 +
`array`
Details

Wheel speed along the axis , mounted on the wheel, measured in m/s. Size of the array: 1 for the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels on each axle, the signal array WhlVz has the size 1 on 4:



Wheel Array element The axis Wheel number

Front left

WhlVz[1, 1]

1

1

Front right

WhlVz[1, 2]

1

2

Rear left

WhlVz[1, 3]

2

1

Rear right

WhlVz[1, 4]

2

2
Data types

Float64
Complex numbers support

No

WhlFx

# —

the longitudinal force acting on the wheel of the vehicle

+

array

Details

Longitudinal force acting on the vehicle along the inertial axis . Size of the array: 1 for the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels on each axle, the WhlFx signal array has the size 1 on 4:



Wheel Array element The axis Wheel number

Front left

WhlFx[1, 1]

1

1

Front right

WhlFx[1, 2]

1

2

Rear left

WhlFx[1, 3]

2

1

Rear right

WhlFx[1, 4]

2

2
Data types

Float64
Complex numbers support

No

WhlFy

# —

the lateral force acting on the wheel of the vehicle

+

array

Details

Transverse force acting on the vehicle along the inertial axis . Size of the array: 1 for the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels on each axle, the signal array WhlFy has the size 1 on 4:


Wheel Array element The axis Wheel number

Front left

WhlFy[1, 1]

1

1

Front right

WhlFy[1, 2]

1

2

Rear left

WhlFy[1, 3]

2

1

Rear right

WhlFy[1, 4]

2

2
Data types

Float64
Complex numbers support

No

WhlM

# —

the moment acting on the wheel from the suspension side

+

array

Details

Longitudinal, transverse and vertical moments on the axis and the wheel , acting on the wheel from the suspension side in the reference coordinate of the wheel hub, measured in nm. Size of the array: 3 the number of wheels on the vehicle.

  • WhlM[1,…​] — the moment acting on the wheel from the suspension side along the inertial axis (longitudinal);

  • WhlM[2,…​] — the moment acting on the wheel from the suspension side along the inertial axis (transverse);

  • WhlM[3,…​] — the moment acting on the wheel from the suspension side along the inertial axis (vertical).

For example, for a two-axle vehicle with two wheels on each axle, an array of WhlM signals:

  • It has a size 3 on 4;

  • It contains the moments acting on the four wheels from the suspension side in accordance with the location of the axles and wheels:


    Wheel Array element The axis Wheel number The axis of the moment

    Front left

    WhlM[1, 1]

    1

    1

    The inertial axis (longitudinal)

    Front right

    WhlM[1, 2]

    1

    2

    Rear left

    WhlM[1, 3]

    2

    1

    Rear right

    WhlM[1, 4]

    2

    2

    Front left

    WhlM[2, 1]

    1

    1

    The inertial axis (transverse)

    Front right

    WhlM[2, 2]

    1

    2

    Rear left

    WhlM[2, 3]

    2

    1

    Rear right

    WhlM[2, 4]

    2

    2

    Front left

    WhlM[3, 1]

    1

    1

    The inertial axis (vertical)

    Front right

    WhlM[3, 2]

    1

    2

    Rear left

    WhlM[3, 3]

    2

    1

    Rear right

    WhlM[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

VehP

# —

moving the vehicle

+

array

Details

Moving the vehicle away from the axle And the wheels along the inertial coordinate system, measured in meters. The size of the input data array: 3 the number of wheels on the vehicle.

  • VehP[1,…​] — moving moving the vehicle away from the wheel along the inertial axis ;

  • VehP[2,…​] — moving moving the vehicle away from the wheel along the inertial axis ;

  • VehP[3,…​] — moving moving the vehicle away from the wheel along the inertial axis .

For example, for a two-axle vehicle with two wheels on each axle, an array of VehP signals:

  • Has a size of 3 on 4;

  • It contains four movements according to the position of the axles and wheels:


    Wheel Array element The axis Wheel number The axis

    Front left

    VehP[1, 1]

    1

    1

    The inertial axis

    Front right

    VehP[1, 2]

    1

    2

    Rear left

    VehP[1, 3]

    2

    1

    Rear right

    VehP[1, 4]

    2

    2

    Front left

    VehP[2, 1]

    1

    1

    The inertial axis

    Front right

    VehP[2, 2]

    1

    2

    Rear left

    VehP[2, 3]

    2

    1

    Rear right

    VehP[2, 4]

    2

    2

    Front left

    VehP[3, 1]

    1

    1

    The inertial axis

    Front right

    VehP[3, 2]

    1

    2

    Rear left

    VehP[3, 3]

    2

    1

    Rear right

    VehP[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

VehV

# —

vehicle speed

+

array

Details

Vehicle speed on the axle and the wheel along the inertial coordinate system, measured in m/s. The size of the input data array: 3 the number of wheels on the vehicle.

  • VehV[1,…​] — speed vehicle wheels along the inertial axis ;

  • VehV[2,…​] — speed vehicle wheels along the inertial axis ;

  • VehV[3,…​] — speed vehicle wheels along the inertial axis .

For example, for a two-axle vehicle with two wheels on each axle, an array of VehV signals:

  • It has a size 3 on 4;

  • It contains four speeds according to the position of the axles and wheels:


    Wheel Array element The axis Wheel number The axis

    Front left

    VehV[1, 1]

    1

    1

    The inertial axis

    Front right

    VehV[1, 2]

    1

    2

    Rear left

    VehV[1, 3]

    2

    1

    Rear right

    VehV[1, 4]

    2

    2

    Front left

    VehV[2, 1]

    1

    1

    The inertial axis

    Front right

    VehV[2, 2]

    1

    2

    Rear left

    VehV[2, 3]

    2

    1

    Rear right

    VehV[2, 4]

    2

    2

    Front left

    VehV[3, 1]

    1

    1

    The inertial axis

    Front right

    VehV[3, 2]

    1

    2

    Rear left

    VehV[3, 3]

    2

    1

    Rear right

    VehV[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

StrgAng

# —

optional rotation angle

array

Details

Optional rotation angle for each wheel. Size of the input array: 1 the number of steerable wheels.

For example, for a two-axle vehicle with two wheels on each axle, you can enter the turning angles for both wheels on the first axle.:

  • The input data array has the size 1 on 2;

  • The StrgAng signal array contains two rotation angles according to the position of the axles and wheels:


    Wheel Array element The axis Wheel number

    Front left

    StrgAng[1, 1]

    1

    1

    Front right

    StrgAng[1, 2]

    1

    2

Dependencies

To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning [1 0].

Data types

Float64
Complex numbers support

No

Output

Info

# —

information signal

+

the tire

Details

The bus signal containing the block values. The signals are arrays that depend on the position of the wheel.

For example, these are indexes for a two-axle vehicle with two wheels. The total number of wheels is four.

  • One-dimensional array of signals (1 on 4)

    Wheel Array element The axis Wheel number

    Front left

    [1, 1]

    1

    1

    Front right

    [1, 2]

    1

    2

    Rear left

    [1, 3]

    2

    1

    Rear right

    [1, 4]

    2

    2

  • Three-dimensional array of signals (3 on 4)

    Wheel Array element The axis Wheel number

    Front left

    [1, 1]

    1

    1

    Front right

    [1, 2]

    1

    2

    Rear left

    [1, 3]

    2

    1

    Rear right

    [1, 4]

    2

    2

    Front left

    [2, 1]

    1

    1

    Front right

    [2, 2]

    1

    2

    Rear left

    [2, 3]

    2

    1

    Rear right

    [2, 4]

    2

    2

    Front left

    [3, 1]

    1

    1

    Front right

    [3, 2]

    1

    2

    Rear left

    [3, 3]

    2

    1

    Rear right

    [3, 4]

    2

    2
The signal Description Array of signals Variable Units of measurement

Camber

Wheel tilt angles depending on the location of the axle and wheel

One-dimensional

glad

Caster

Toe

Height

Suspension height

One-dimensional

m

Power

Dissipated suspension power

One-dimensional

Tue

Energy

Absorbed suspension energy

One-dimensional

J

VehF

Forces acting on the vehicle from the suspension side

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

N

VehM

The moments acting on the vehicle from the suspension side

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

N⋅m

WhlF

Force acting on the wheel from the suspension side

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

N

WhlP

Moving the wheel

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

m

WhlV

Wheel speed

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

m/s

WhlAng

Angles of camber, tilt and convergence of the wheel

Three-dimensional

For a two-axle vehicle with two wheels on the axle:

glad
Data types

Float64
Complex numbers support

No

VehF

# —

the force acting on the vehicle from the suspension side

+

array

Details

Longitudinal, transverse and vertical forces on the axis and the wheel , acting on the vehicle from the suspension side at the suspension junction point, measured in Newtons. Size of the array: 3 the number of wheels on the vehicle.

  • VehF[1,…​] — the force acting on the vehicle from the suspension side along the inertial axis (longitudinal);

  • VehF[2,…​] — the force acting on the vehicle from the suspension side along the inertial axis (transverse);

  • VehF[3,…​] — the force acting on the vehicle from the suspension side along the inertial axis (vertical).

For example, for a two-axle vehicle with two wheels on each axle, an array of VehF signals:

  • It has a size 3 on 4;

  • It contains forces acting on the vehicle from the suspension side in accordance with the location of the axles and wheels:



    Wheel Array element The axis Wheel number The axis of power

    Front left

    VehF[1, 1]

    1

    1

    The inertial axis (longitudinal)

    Front right

    VehF[1, 2]

    1

    2

    Rear left

    VehF[1, 3]

    2

    1

    Rear right

    VehF[1, 4]

    2

    2

    Front left

    VehF[2, 1]

    1

    1

    The inertial axis (transverse)

    Front right

    VehF[2, 2]

    1

    2

    Rear left

    VehF[2, 3]

    2

    1

    Rear right

    VehF[2, 4]

    2

    2

    Front left

    VehF[3, 1]

    1

    1

    The inertial axis (vertical)

    Front right

    VehF[3, 2]

    1

    2

    Rear left

    VehF[3, 3]

    2

    1

    Rear right

    VehF[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

VehM

# —

the moment acting on the vehicle from the suspension side

+

array

Details

Longitudinal, transverse and vertical moments on the axis and the wheel , acting on the vehicle from the suspension side at the suspension connection point, measured in Nm. Size of the array: 3 the number of wheels on the vehicle.

  • VehM[1,…​] — the moment acting on the vehicle from the suspension side along the inertial axis (longitudinal);

  • VehM[2,…​] — the moment acting on the vehicle from the suspension side along the inertial axis (transverse);

  • VehM[3,…​] — the moment acting on the vehicle from the suspension side along the inertial axis (vertical).

For example, for a two-axle vehicle with two wheels on each axle, an array of VehM signals:

  • It has a size 3 on 4;

  • It contains the moments acting on the vehicle from the suspension side in accordance with the location of the axles and wheels:



    Wheel Array element The axis Wheel number The axis of the moment

    Front left

    VehM[1, 1]

    1

    1

    The inertial axis (longitudinal)

    Front right

    VehM[1, 2]

    1

    2

    Rear left

    VehM[1, 3]

    2

    1

    Rear right

    VehM[1, 4]

    2

    2

    Front left

    VehM[2, 1]

    1

    1

    The inertial axis (transverse)

    Front right

    VehM[2, 2]

    1

    2

    Rear left

    VehM[2, 3]

    2

    1

    Rear right

    VehM[2, 4]

    2

    2

    Front left

    VehM[3, 1]

    1

    1

    The inertial axis (vertical)

    Front right

    VehM[3, 2]

    1

    2

    Rear left

    VehM[3, 3]

    2

    1

    Rear right

    VehM[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

WhlF

# —

force acting on the wheel from the suspension side

array

Details

Longitudinal, transverse and vertical forces on the axis and the wheel , acting on the wheel from the suspension side in the reference coordinate of the wheel hub, measured in Newtons. Size of the array: 3 the number of wheels on the vehicle.

  • WhlF[1,…​] — the force acting on the wheel from the suspension side along the inertial axis (longitudinal);

  • WhlF[2,…​] — the force acting on the wheel from the suspension side along the inertial axis (transverse);

  • WhlF[3,…​] — the force acting on the wheel from the suspension side along the inertial axis (vertical).

For example, for a two-axle vehicle with two wheels on each axle, an array of WhlF signals:

  • Has a size of 3 on 4;

  • It contains the forces acting on the wheel from the suspension side in accordance with the location of the axles and wheels:



    Wheel Array element The axis Wheel number The axis of power

    Front left

    WhlF[1, 1]

    1

    1

    The inertial axis (longitudinal)

    Front right

    WhlF[1, 2]

    1

    2

    Rear left

    WhlF[1, 3]

    2

    1

    Rear right

    WhlF[1, 4]

    2

    2

    Front left

    WhlF[2, 1]

    1

    1

    The inertial axis (transverse)

    Front right

    WhlF[2, 2]

    1

    2

    Rear left

    WhlF[2, 3]

    2

    1

    Rear right

    WhlF[2, 4]

    2

    2

    Front left

    WhlF[3, 1]

    1

    1

    The inertial axis (vertical)

    Front right

    WhlF[3, 2]

    1

    2

    Rear left

    WhlF[3, 3]

    2

    1

    Rear right

    WhlF[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

WhlV

# —

wheel rotation speed

array

Details

Longitudinal, transverse and vertical rotation speeds of the wheel on the axis , measured in m/s. Size of the array: 3 the number of wheels on the vehicle.

  • WhlV[1,…​] — the speed of rotation of the wheel along the inertial axis (longitudinal);

  • WhlV[2,…​] — the speed of rotation of the wheel along the inertial axis (transverse);

  • WhlV[3,…​] — the speed of rotation of the wheel along the inertial axis (vertical).

For example, for a two-axle vehicle with two wheels on each axle, an array of WhlV signals:

  • Has a size of 3 on 4;

  • Contains the rotation speeds of the wheel according to the position of the axles and wheels:



    Wheel Array element The axis Wheel number The axis of power

    Front left

    WhlV[1, 1]

    1

    1

    The inertial axis (longitudinal)

    Front right

    WhlV[1, 2]

    1

    2

    Rear left

    WhlV[1, 3]

    2

    1

    Rear right

    WhlV[1, 4]

    2

    2

    Front left

    WhlV[2, 1]

    1

    1

    The inertial axis (transverse)

    Front right

    WhlV[2, 2]

    1

    2

    Rear left

    WhlV[2, 3]

    2

    1

    Rear right

    WhlV[2, 4]

    2

    2

    Front left

    WhlV[3, 1]

    1

    1

    The inertial axis (vertical)

    Front right

    WhlV[3, 2]

    1

    2

    Rear left

    WhlV[3, 3]

    2

    1

    Rear right

    WhlV[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

WhlAng

# —

angles of camber, tilt and convergence of the wheel

array

Details

Angles of camber, tilt and convergence of the wheel on the axle and the wheel , measured in radians. Size of the array: 3 the number of wheels on the vehicle.

  • WhlAng[1,…​] — camber angle;

  • WhlAng[2,…​] — tilt angle;

  • WhlAng[3,…​] — angle of convergence.

For example, for a two-axle vehicle with two wheels on each axle, an array of WhlAng signals:

  • Has a size of 3 on 4;

  • Contains angles according to the position of the axles and wheels:



    Wheel Array element The axis Wheel number Corner

    Front left

    WhlAng[1, 1]

    1

    1

    Camber Angle

    Front right

    WhlAng[1, 2]

    1

    2

    Rear left

    WhlAng[1, 3]

    2

    1

    Rear right

    WhlAng[1, 4]

    2

    2

    Front left

    WhlAng[2, 1]

    1

    1

    Tilt Angle (Caster)

    Front right

    WhlAng[2, 2]

    1

    2

    Rear left

    WhlAng[2, 3]

    2

    1

    Rear right

    WhlAng[2, 4]

    2

    2

    Front left

    WhlAng[3, 1]

    1

    1

    Angle of Convergence (Toe)

    Front right

    WhlAng[3, 2]

    1

    2

    Rear left

    WhlAng[3, 3]

    2

    1

    Rear right

    WhlAng[3, 4]

    2

    2
Data types

Float64
Complex numbers support

No

Parameters

Main group

# Enable active damping — enable damping

Details

Enable damping.

Dependencies

After checking this box, the options appear:

  • Damping coefficient map [f_act_susp_cz], Ns/m;

  • Damping actuator duty cycle breakpoints [f_act_susp_duty_bpt];

  • Damping actuator velocity breakpoints [f_act_susp_zdot_bpt], m/s.

Default value

false (switched off)
Program usage name

ActiveDampEn
Tunable

No
Evaluatable

Yes

# Number of axles NumAxl — number of axes

Details

Number of axes , a dimensionless parameter.

Default value

2
Program usage name

NumAxl
Tunable

No
Evaluatable

Yes

# Number of wheels per axle [NumWhlsByAxl] — number of wheels per axle

Details

Number of wheels per axle , a dimensionless parameter. The vector is equal to the value 1 multiplied by the number of axes the vehicle. For example, [1, 2] indicates one wheel on the first axle and two wheels on the second axle.

Default value

[2 2]
Program usage name

NumWhlsByAxl
Tunable

No
Evaluatable

Yes

# Steered axle enable by axle [StrgEnByAxl] — a logical vector for activating axis control

Details

A logical dimensionless vector , which activates the axis control. The vector is equal to the value 1 multiplied by the number of axes the vehicle. For example, for a two-axle vehicle, the value:

  • [1 0] — activates axis 1 control and disables axis 2 control;

  • [1 1] — activates the control of axes 1 and 2.

Dependencies

When setting the value for this parameter 1:

  • The StrgAng port is activated.

  • The following parameters appear:

    • Toe angle vs steering angle slope ToeStrgSlp;

    • Caster angle vs steering angle slope CasterStrgSlp;

    • Camber angle vs steering angle slope CamberStrgSlp;

    • Suspension height vs steering angle slope StrgHgtSlp, m/rad.

For example, for a two-axle vehicle with two wheels on each axle, you can enter the turning angles for both wheels on the first axle.:

  • To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning [1 0]. The input data array has the size 1 on 2.

  • The StrgAng signal array contains two rotation angles according to the position of the axles and wheels:

    Wheel Array element The axis Wheel number

    Front left

    StrgAng[1, 1]

    1

    1

    Front right

    StrgAng[1, 2]

    1

    2
Default value

[1 0]
Program usage name

StrgEnByAxl
Tunable

No
Evaluatable

Yes

# Anti-sway axle enable by axle [AntiSwayEnByAxl] — a logical vector for activating axis stabilization

Details

A logical dimensionless vector that activates axis stabilization . For example, the value [1 0] activates axis 1 stabilization and disables axis 2 stabilization. The vector is equal to 1 multiplied by the number of axes the vehicle.

Dependencies

When setting the value for this parameter 1 The following parameters appear:

  • Anti-sway arm radius AntiSwayR, m;

  • Anti-sway arm neutral angle AntiSwayNtrlAng, rad;

  • Anti-sway torsion spring constant AntiSwayTrsK, Nm/rad.

Default value

[0 0]
Program usage name

AntiSwayEnByAxl
Tunable

No
Evaluatable

Yes

Compliance and damping

# Suspension spring constant Kz, N/m — stiffness coefficient of the suspension spring

Details

Linear stiffness coefficient vertical springs for independent suspension wheels on the axle , measured in N/m.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

64370.0
Program usage name

Kz
Tunable

No
Evaluatable

Yes

# Suspension spring preload F0z, N — preload on suspension springs

Details

Vertical force the preload of the springs applied to the wheels on the axle in the reference coordinates of the wheel hub, measured in Newtons. Positive preload forces:

  • Causing the vehicle to lift;

  • Directed along the negative inertial axis .

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

9810.0
Program usage name

F0z
Tunable

No
Evaluatable

Yes

# Suspension shock damping constant Cz, Ns/m — damping coefficient of suspension shock absorbers

Details

Linear coefficient vertical damping for independent suspension wheels on the axle , measured in N⋅s/m .

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

To use this option, uncheck the box. Enable active damping.

Default value

10000.0
Program usage name

Cz
Tunable

No
Evaluatable

Yes

# Suspension maximum height Hmax, m — maximum suspension height

Details

Maximum suspension extension or minimum suspension compression height for the axis before the suspension reaches a rigid stop, measured in meters.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

0.5
Program usage name

Hmax
Tunable

No
Evaluatable

Yes

Active damping

# Damping coefficient map [f_act_susp_cz], Ns/m — interpolation table of the fill factor

Details

Table of damping coefficients as a function of the active filling factor and the compression rate of the drive, in N⋅s/m. Each value determines the damping for a specific combination of fill factor and drive speed. The dimensions of the array must correspond to the dimensions of the vector of reference points of the fill factor. and drive speeds .

Dependencies

To use this option, uncheck the box. Enable active damping.

Default value

[10000 10000; 10000 10000]
Program usage name

f_act_susp_cz
Tunable

No
Evaluatable

Yes

# Damping actuator duty cycle breakpoints [f_act_susp_duty_bpt] — fill factor reference points

Details

Reference points of the fill factor of the damping drive, a dimensionless parameter.

Dependencies

To use this option, uncheck the box. Enable active damping.

Default value

[0 1]
Program usage name

f_act_susp_duty_bpt
Tunable

No
Evaluatable

Yes

# Damping actuator velocity breakpoints [f_act_susp_zdot_bpt], m/s — speed reference points

Details

Reference points of the damping drive speed, measured in m/s.

Dependencies

To use this option, uncheck the box. Enable active damping.

Default value

[-1 1]
Program usage name

f_act_susp_zdot_bpt
Tunable

No
Evaluatable

Yes

Geometry settings and effects

# Toe angle at steering center Toe, rad — angle of convergence

Details

Nominal angle suspension convergence at zero angle of rotation, measured in radians.

Default value

0.0349
Program usage name

Toe
Tunable

No
Evaluatable

Yes

# Roll steer angle vs suspension height slope RollStrgSlp, rad/m — angle of rotation of the suspension

Details

Angle of rotation depending on the height of the suspension, measured in rad/m.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

-0.2269
Program usage name

RollStrgSlp
Tunable

No
Evaluatable

Yes

# Toe angle vs steering angle slope ToeStrgSlp — the angle of convergence depends on the angle of rotation of the wheel

Details

Wheel convergence angle depending on the angle of rotation, a dimensionless parameter.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning 1.

Default value

0.01
Program usage name

ToeStrgSlp
Tunable

No
Evaluatable

Yes

# Caster angle at steering center Caster, rad — the angle of the axis of rotation of the wheel in the center of the wheel

Details

Nominal tilt angle the axis of rotation of the wheel at zero angle of rotation, measured in radians.

Default value

0.0698
Program usage name

Caster
Tunable

No
Evaluatable

Yes

# Caster angle vs suspension height slope CasterHslp, rad/m — the angle of inclination of the axis of rotation of the wheel depending on the height of the suspension

Details

Tilt angle the axis of rotation of the wheel depends on the height of the suspension, measured in rad/m.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

-0.2269
Program usage name

CasterHslp
Tunable

No
Evaluatable

Yes

# Caster angle vs steering angle slope CasterStrgSlp — the angle of inclination of the axis of rotation of the wheel depending on the angle of rotation of the wheel

Details

Tilt angle the axis of rotation of the wheel depends on the angle of rotation, a dimensionless parameter.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning 1.

Default value

0.01
Program usage name

CasterStrgSlp
Tunable

No
Evaluatable

Yes

# Camber angle at steering center Camber, rad — camber angle in the center of the wheel

Details

Nominal camber angle suspension at zero angle of rotation, measured in radians.

Default value

0.0698
Program usage name

Camber
Tunable

No
Evaluatable

Yes

# Camber angle vs suspension height slope CamberHslp, rad/m — camber angle depending on suspension height

Details

Camber angle depending on the height of the suspension, measured in rad/m.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Default value

-0.2269
Program usage name

CamberHslp
Tunable

No
Evaluatable

Yes

# Camber angle vs steering angle slope CamberStrgSlp — camber angle depending on the angle of rotation of the wheel

Details

Camber angle depending on the angle of rotation, a dimensionless parameter.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning 1.

Default value

0.01
Program usage name

CamberStrgSlp
Tunable

No
Evaluatable

Yes

# Suspension height vs steering angle slope StrgHgtSlp, m/rad — suspension height depending on the angle of rotation of the wheel

Details

Deviation of the rotation angle of the vertical force applied to the bearing point of the suspension wheel hub, measured in m/rad.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

To use the StrgAng port, set the parameter Steered axle enable by axle [StrgEnByAxl] meaning 1.

Default value

0.1432
Program usage name

StrgHgtSlp
Tunable

No
Evaluatable

Yes

Anti-sway parameters

# Anti-sway arm radius AntiSwayR, m — radius of the stabilizer bar

Details

Radius the lever of the stabilizer bar, measured in meters.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

When setting the value for this parameter 1 The following parameters appear:

  • Anti-sway arm neutral angle AntiSwayNtrlAng, rad;

  • Anti-sway torsion spring constant AntiSwayTrsK, Nm/rad.

Default value

0.2
Program usage name

AntiSwayR
Tunable

No
Evaluatable

Yes

# Anti-sway arm neutral angle AntiSwayNtrlAng, rad — neutral angle of the stabilizer bar

Details

Neutral angle the lever of the stabilizer bar at the nominal height of the suspension, measured in radians.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

When setting the value for this parameter 1 The following parameters appear:

  • Anti-sway arm radius AntiSwayR, m;

  • Anti-sway torsion spring constant AntiSwayTrsK, Nm/rad.

Default value

0.5236
Program usage name

AntiSwayNtrlAng
Tunable

No
Evaluatable

Yes

# Anti-sway torsion spring constant AntiSwayTrsK, Nm/rad — torsional stiffness of the stabilizer bar

Details

Torsional rigidity stabilizer bar, measured in nm/rad.

The vector is equal to the value 1 multiplied by the number of axes the vehicle. If you specify a scalar value, the block uses this value for all axes.

Dependencies

When setting the value for this parameter 1 The following parameters appear:

  • Anti-sway arm radius AntiSwayR, m;

  • Anti-sway arm neutral angle AntiSwayNtrlAng, rad.

Default value

5729.6
Program usage name

AntiSwayTrsK
Tunable

No
Evaluatable

Yes

Literature

  1. Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

  2. Vehicle Dynamics Standards Committee. Vehicle Dynamics Terminology. SAE J670. Warrendale, PA: Society of Automotive Engineers, 2008.

  3. Technical Committee. Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary. ISO 8855:2011. Geneva, Switzerland: International Organization for Standardization, 2011.