Twist-Beam Suspension - K and C

Twist-beam kinematics and compliance test suspension

Since R2022b

Libraries:
Vehicle Dynamics Blockset / Suspension

Description

In the Vehicle Dynamics Blockset™ library, there are two types of suspension blocks that implement the kinematics and compliance (K and C) test suspension characteristics measured from simulated or actual laboratory suspension tests.

Block Suspension type Setting Implementation

Block	Suspension type Setting	Implementation
Twist-Beam Suspension - K and C	`Independent front and twist-beam rear`	Kinematics and compliance effects of: Independent suspension on a front axle with two wheels Twist-beam suspension on a rear axle with two wheels
Independent Suspension - K and C	`Independent front and rear`	Kinematics and compliance effects of four independent suspensions on a vehicle with two axles and two wheels per axle. For more information, see Independent Suspension - K and C.

Twist-Beam Suspension - K and C

Independent front and twist-beam rear

Kinematics and compliance effects of:

Independent suspension on a front axle with two wheels
Twist-beam suspension on a rear axle with two wheels

Independent Suspension - K and C

Independent front and rear

Kinematics and compliance effects of four independent suspensions on a vehicle with two axles and two wheels per axle.

For more information, see Independent Suspension - K and C.

K and C Effects on Suspension

To determine the overall suspension forces and geometric effects on the vehicle and wheels, the block adds the individual effects from kinematic (bounce, roll, steering) and compliance (longitudinal and lateral forces, aligning moments) inputs. Specifically, the block multiplies the suspension geometry states by either gradient or table values to determine the K and C effects on wheel orientation and suspension forces.

Wheel orientation:

Camber, caster, and steer angles
Lateral wheel center displacement
Longitudinal wheel center displacement

Vertical suspension forces:

Anti-sway bar
Shock force
Wheel rate
Contact patch swing arm (CPSA) force
Longitudinal side view swing arm (SVSA) anti-effects

Camber, Caster, and Steer Angles

The block uses these parameters to account for the K and C effects on the camber, caster, and steer angles.

Bounce test– Independent suspension
Roll test– Independent suspension
Steer test
Longitudinal compliance test
Lateral compliance-opposed test
Aligning torque compliance-opposed test

Use the Static alignment settings parameters to set the initial state of the suspension.

Lateral Wheel Center Displacement

The block uses these parameters to account for the K and C effects the lateral wheel center displacement.

Bounce test
Longitudinal compliance test
Lateral compliance-opposed test

Longitudinal Wheel Center Displacement

The block uses these parameters to account for the K and C effects on the longitudinal wheel center displacement.

Bounce test
Longitudinal compliance test

Shock Force

The block uses the Shock force parameters to calculate the shock force effect on the vertical suspension force. You can specify table-based or constant parameter values.

Wheel Rate

The block uses the Bounce test parameters to calculate the wheel rate effect on the vertical suspension force.

Contact Patch Swing Arm

The block uses these equations to calculate the effect of the contact patch swing arm (CPSA) forces on vertical suspension force.

$\begin{array}{l} \tan (θ_{C P S A}) = f (Z_{w}) \\ F_{z C P S A} = F_{y} \tan (θ_{C P S A}) \end{array}$

The block also uses the Static loaded radius of wheels parameter in the CPSA force calculation.

The equations use these variables.

ϴ_CPSA	Contact patch swing arm angle
F_y	Lateral suspension force
F_zCPSA	CPSA effect on vertical suspension force
z_w	Wheel displacement

Longitudinal Side View Swing Arm Anti-Effects

The block uses these equations to calculate the effect of the side view swing arm (SVSA) forces on vertical suspension force during acceleration and braking.

$\begin{array}{l} \tan (θ_{S V S A}) = f (Z_{w}) \\ F_{z S V S A} = F_{x} \tan (θ_{S V S A}) \end{array}$

Use the Drivetrain type parameter to ensure that the block applies the acceleration anti-effects to the correct wheels.

The equations use these variables.

ϴ_SVSA	Contact patch swing arm angle
F_x	Longitudinal wheel force
F_zSVSA	SVSA effect on vertical suspension force
z_w	Wheel displacement

Anti-Sway Bar

Optionally, use the Anti-sway axle enable by axle, AntiSwayEnByAxl parameter to implement anti-sway bar reaction forces by axle.

If you do not enable an anti-sway bar, the axle roll stiffness is 0.

Front Axle

If you enable an anti-sway bar on the axle, the anti-sway bar stiffness is the difference between the anti-sway bar torque parameter, Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt, and the roll stiffness parameter measured with no anti-sway bar present Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt.

Rear Axle

If you enable an anti-sway bar on the rear axle, the block uses this equation to calculate the twist-beam roll stiffness.

$T B_{r s} = S_{r s} - \frac{π [\frac{1}{2} W R_{\nabla} T W^{2}]}{180}$

The equation uses these variables.

TB_rs	Twist beam roll stiffness
S_rs	Suspension roll stiffness without twist beam, RollStiffNoTwstRear parameter
WR_∇	Normal wheel rate gradient, calculated from NrmlWhlRates parameter and suspension displacement
TW	Track width

Examples

Double Lane Change Reference Application

Simulate a full vehicle dynamics model undergoing a double lane change maneuver standard ISO 3888-2. Use for vehicle dynamics ride and handling analysis and chassis controls development, including yaw stability and lateral acceleration limits.

Open Script

Ports

The block uses the wheel number, t, to index the input and output signals. This table summarizes the wheel, axle, and corresponding wheel number for a vehicle with:

Two axles
Two wheels per axle

Wheel	Axle	Wheel Number
Front left	Front	`1`
Front right	Front	`2`
Rear left	Rear	`1`
Rear right	Rear	`2`

Input

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WhlPz — Wheel `z`-axis displacement
array

Wheel displacement, z_w, along wheel-fixed z-axis, in m. Array dimensions are 1 by the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels per axle, the WhlPz:

Signal array dimensions are [1x4].
$WhlPz = z_{w} = [\begin{matrix} z_{w_{1, 1}} & z_{w_{1, 2}} & z_{w_{2, 1}} & z_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle 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

Wheel	Array Element	Axle	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`

WhlRe — Wheel effective radius
array

Effective wheel radius, Re_w, in m. Array dimensions are 1 by the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels per axle, the WhlRe:

Signal array dimensions are [1x4].
$Whl Re = R e_{w} = [\begin{matrix} R e_{w_{1, 1}} & R e_{w_{1, 2}} & R e_{w_{2, 1}} & R e_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle 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

Wheel	Array Element	Axle	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`

WhlVz — Wheel `z`-axis velocity
array

Wheel velocity, ż_w, along wheel-fixed z-axis, in m. Array dimensions are 1 by the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels per axle, the WhlVz:

Signal array dimensions are [1x4].
$WhlVz = {\dot{z}}_{w} = [\begin{matrix} {\dot{z}}_{w_{1, 1}} & {\dot{z}}_{w_{1, 2}} & {\dot{z}}_{w_{2, 1}} & {\dot{z}}_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle 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

Wheel	Array Element	Axle	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`

WhlFx — Longitudinal wheel force on vehicle
array

Longitudinal wheel force applied to vehicle, F_wx, along the inertial-fixed x-axis. Array dimensions are 1 by the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels per axle, the WhlFx:

Signal array dimensions are [1x4].
$WhlFx = F_{w x} = [\begin{matrix} F_{w x_{1, 1}} & F_{w x_{1, 2}} & F_{w x_{2, 1}} & F_{w x_{2, 2}} \end{matrix}]$
Wheel Array Element Axle 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

Wheel	Array Element	Axle	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`

WhlFy — Lateral wheel force on vehicle
array

Lateral wheel force applied to vehicle, F_wy, along the inertial-fixed y-axis. Array dimensions are 1 by the total number of wheels on the vehicle.

For example, for a two-axle vehicle with two wheels per axle, the WhlFy:

Signal array dimensions are [1x4].

$WhlFy = F_{w y} = [\begin{matrix} F_{w y_{1, 1}} & F_{w y_{1, 2}} & F_{w y_{2, 1}} & F_{w y_{2, 2}} \end{matrix}]$

Wheel Array Element Axle 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

Wheel	Array Element	Axle	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`

WhlM — Suspension moment on wheel
array

Longitudinal, lateral, and vertical suspension moments at axle a, wheel t, applied to the wheel at the axle wheel carrier reference coordinate, in N·m. Input array dimensions are 3 by the number of wheels on the vehicle.

WhlM(1,...) — Suspension moment applied to the wheel about the inertial-fixed x-axis (longitudinal)
WhlM(2,...) — Suspension moment applied to the wheel about the inertial-fixed y-axis (lateral)
WhlM(3,...) — Suspension moment applied to the wheel about the inertial-fixed z-axis (vertical)

For example, for a two-axle vehicle with two wheels per axle, the WhlM:

Signal dimensions are [3x4].

Signal contains suspension moments applied to four wheels according to their axle and wheel locations.

$WhlM = M_{w} = [\begin{matrix} M_{w x_{1, 1}} & M_{w x_{1, 2}} & M_{w x_{2, 1}} & M_{w x_{2, 2}} \\ M_{w y_{1, 1}} & M_{w y_{1, 2}} & M_{w y_{2, 1}} & M_{w y_{2, 2}} \\ M_{w z_{1, 1}} & M_{w z_{1, 2}} & M_{w z_{2, 1}} & M_{w z_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Moment Axis
Front left	`WhlM(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-axis (lateral)
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`	Inertial-fixed z-axis (vertical)
Front right	`WhlM(3,2)`	`1`	`2`
Rear left	`WhlM(3,3)`	`2`	`1`
Rear right	`WhlM(3,4)`	`2`	`2`

VehP — Vehicle displacement
array

Vehicle displacement from axle a, wheel t along inertial-fixed coordinate system, in m. Input array dimensions are 3 by the number of wheels on the vehicle.

VehP(1,...) — Vehicle displacement from wheel, x_v, along the inertial-fixed x-axis
VehP(2,...) — Vehicle displacement from wheel, y_v, along the inertial-fixed y-axis
VehP(3,...) — Vehicle displacement from wheel, z_v, along the inertial-fixed z-axis

For example, for a two-axle vehicle with two wheels per axle, the VehP:

Signal dimensions are [3x4].

Signal contains four displacements according to their axle and wheel locations.

$VehP = [\begin{matrix} x_{v} \\ y_{v} \\ z_{v} \end{matrix}] = [\begin{matrix} x_{v}_{_{1, 1}} & x_{v}_{_{1, 2}} & x_{v}_{_{2, 1}} & x_{v}_{_{2, 2}} \\ y_{v}_{_{1, 1}} & y_{v}_{_{1, 2}} & y_{v}_{_{2, 1}} & y_{v}_{_{2, 2}} \\ z_{v}_{_{1, 1}} & z_{v}_{_{1, 2}} & z_{v}_{_{2, 1}} & z_{v}_{_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Axis
Front left	`VehP(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-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`	inertial-fixed z-axis
Front right	`VehP(3,2)`	`1`	`2`
Rear left	`VehP(3,3)`	`2`	`1`
Rear right	`VehP(3,4)`	`2`	`2`

VehV — Vehicle velocity
array

Vehicle velocity at axle a, wheel t along inertial-fixed coordinate system, in m. Input array dimensions are 3 by the number of wheels on the vehicle.

VehV(1,...) — Vehicle velocity at wheel, x_v, along the inertial-fixed x-axis
VehV(2,...) — Vehicle velocity at wheel, y_v, along the inertial-fixed y-axis
VehV(3,...) — Vehicle velocity at wheel, z_v, along the inertial-fixed z-axis

For example, for a two-axle vehicle with two wheels per axle, the VehV:

Signal dimensions are [3x4].

Signal contains 4 velocities according to their axle and wheel locations.

$VehV = [\begin{matrix} {\dot{x}}_{v} \\ {\dot{y}}_{v} \\ {\dot{z}}_{v} \end{matrix}] = [\begin{matrix} {\dot{x}}_{v_{1, 1}} & {\dot{x}}_{v_{1, 2}} & {\dot{x}}_{v_{2, 1}} & {\dot{x}}_{v_{2, 2}} \\ {\dot{y}}_{v_{1, 1}} & {\dot{y}}_{v_{1, 2}} & {\dot{y}}_{v_{2, 1}} & {\dot{y}}_{v_{2, 2}} \\ {\dot{z}}_{v_{1, 1}} & {\dot{z}}_{v_{1, 2}} & {\dot{z}}_{v_{2, 1}} & {\dot{z}}_{v_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Axis
Front left	`VehV(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-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`	Inertial-fixed z-axis
Front right	`VehV(3,2)`	`1`	`2`
Rear left	`VehV(3,3)`	`2`	`1`
Rear right	`VehV(3,4)`	`2`	`2`

StrgAng — Steering angle, optional
array

Optional steering angle for each wheel, δ. Input array dimensions are 1 by the number of steered wheels.

For example, for a two-axle vehicle with two wheels per axle, you can input steering angles for both wheels on the first axle.

To enable the StrgAng port, set Steered axle enable by axle, StrgEnByAxl to [1 0]. The input signal array dimensions are [1x2].
The StrgAng signal contains two steering angles according to their axle and wheel locations.
$StrgAng = δ_{s t e e r} = [\begin{matrix} δ_{s t e e r_{1, 1}} & δ_{s t e e r_{1, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left StrgAng(1,1) 1 1
Front right StrgAng(1,2) 1 2

Wheel	Array Element	Axle	Wheel Number
Front left	`StrgAng(1,1)`	`1`	`1`
Front right	`StrgAng(1,2)`	`1`	`2`

Dependencies

To enable the port StrgAng, set an element of the Steered axle enable by axle, StrgEnByAxl vector to 1.

Phi — Vehicle pitch angle
`scalar`

Vehicle pitch angle about earth-fixed Y-axis, in rad.

TrckWdth — Track width
`array`

Distance between wheels on each axle. Input array dimensions are 1-by-2.

Array Element	Description
`TrckWdth(1,1)`	Distance between wheels on front axle
`TrckWdth(1,2)`	Distance between wheels on rear axle

Output

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Info — Bus signal
bus

Bus signal containing block values. The signals are arrays that depend on the wheel location.

For example, these are the indices for a two-axle, two-wheel vehicle. The total number of wheels is four.

1D array signal (1-by-4)

Wheel Array Element Axle 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

3D array signal (3-by-4)

Wheel	Array Element	Axle	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`

Signal	Description	Array Signal	Variable	Units
`Camber`	Wheel angles according to the axle and wheel location.	1D	$WhlAng [1, ...] = ξ = [ξ_{a, t}]$	rad
`Caster`			$WhlAng [2, ...] = η = [η_{a, t}]$
`Toe`			$WhlAng [3, ...] = ζ = [ζ_{a, t}]$
`Height`	Suspension height	1D	H	m
`Power`	Suspension power dissipation	1D	P_susp	W
`Energy`	Suspension absorbed energy	1D	E_susp	J
`VehF`	Suspension forces applied to the vehicle	3D	For a two-axle, two wheels per axle vehicle: $VehF = F_{v} = [\begin{matrix} F_{v}_{x_{1, 1}} & F_{v}_{x_{1, 2}} & F_{v}_{x_{2, 1}} & F_{v}_{x_{2, 2}} \\ F_{v}_{y_{1, 1}} & F_{v}_{y_{1, 2}} & F_{v}_{y_{2, 1}} & F_{v}_{y_{2, 2}} \\ F_{v}_{z_{1, 1}} & F_{v}_{z_{1, 2}} & F_{v}_{z_{2, 1}} & F_{v}_{z_{2, 2}} \end{matrix}]$	N
`VehM`	Suspension moments applied to vehicle	3D	For a two-axle, two wheels per axle vehicle: $VehM = M_{v} = [\begin{matrix} M_{v x_{1, 1}} & M_{v x_{1, 2}} & M_{v x_{2, 1}} & M_{v x_{2, 2}} \\ M_{v y_{1, 1}} & M_{v y_{1, 2}} & M_{v y_{2, 1}} & M_{v y_{2, 2}} \\ M_{v z_{1, 1}} & M_{v z_{1, 2}} & M_{v z_{2, 1}} & M_{v z_{2, 2}} \end{matrix}]$	N·m
`WhlF`	Suspension force applied to wheel	3D	For a two-axle, two wheels per axle vehicle: $WhlF = F_{w} = [\begin{matrix} F_{w}_{x_{1, 1}} & F_{w}_{x_{1, 2}} & F_{w}_{x_{2, 1}} & F_{w}_{x_{2, 2}} \\ F_{w}_{y_{1, 1}} & F_{w}_{y_{1, 2}} & F_{w}_{y_{2, 1}} & F_{w}_{y_{2, 2}} \\ F_{w}_{z_{1, 1}} & F_{w}_{z_{1, 2}} & F_{w}_{z_{2, 1}} & F_{w}_{z_{2, 2}} \end{matrix}]$	N
`WhlP`	Wheel displacement	3D	For a two-axle, two wheels per axle vehicle: $WhlP = [\begin{matrix} x_{w} \\ y_{w} \\ z_{w} \end{matrix}] = [\begin{matrix} x_{w}_{_{1, 1}} & x_{w}_{_{1, 2}} & x_{w}_{_{2, 1}} & x_{w_{2, 2}} \\ y_{w}_{_{1, 1}} & y_{w}_{_{1, 2}} & y_{w}_{_{2, 1}} & y_{w}_{y_{2, 2}} \\ z_{w t r}_{_{1, 1}} & z_{w t r}_{_{1, 2}} & z_{w t r}_{_{2, 1}} & z_{w t r_{2, 2}} \end{matrix}]$	m
`WhlV`	Wheel velocity	3D	For a two-axle, two wheels per axle vehicle: $WhlV = [\begin{matrix} {\dot{x}}_{w} \\ {\dot{y}}_{w} \\ {\dot{z}}_{w} \end{matrix}] = [\begin{matrix} {\dot{x}}_{w_{1, 1}} & {\dot{x}}_{w_{1, 2}} & {\dot{x}}_{w_{2, 1}} & {\dot{x}}_{w_{2, 2}} \\ {\dot{y}}_{w_{_{1, 1}}} & {\dot{y}}_{w_{1, 2}} & {\dot{y}}_{w_{2, 1}} & {\dot{y}}_{w_{2, 2}} \\ {\dot{z}}_{w_{_{1, 1}}} & {\dot{z}}_{w_{1, 2}} & {\dot{z}}_{w_{2, 1}} & {\dot{z}}_{w_{2, 2}} \end{matrix}]$	m/s
`WhlAng`	Wheel camber, caster, toe angles	3D	For a two-axle, two wheels per axle vehicle: $WhlAng = [\begin{matrix} ξ \\ η \\ ζ \end{matrix}] = [\begin{matrix} ξ_{1, 1} & ξ_{1, 2} & ξ_{2, 1} & ξ_{2, 2} \\ η_{1, 1} & η_{1, 2} & η_{2, 1} & η_{2, 2} \\ ζ_{1, 1} & ζ_{1, 2} & ζ_{2, 1} & ζ_{2, 2} \end{matrix}]$	rad

VehF — Suspension force on vehicle
`array`

Longitudinal, lateral, and vertical suspension force at axle a, wheel t, applied to the vehicle at the suspension connection point, in N. Array dimensions are 3 by the number of wheels on the vehicle.

VehF(1,...) — Suspension force applied to vehicle along the inertial-fixed x-axis (longitudinal)
VehF(2,...) — Suspension force applied to vehicle along the inertial-fixed y-axis (lateral)
VehF(3,...) — Suspension force applied to vehicle along the inertial-fixed z-axis (vertical)

For example, for a two-axle vehicle with two wheels per axle, the VehF:

Signal dimensions are [3x4].

Signal contains suspension forces applied to the vehicle according to the axle and wheel locations.

$VehF = F_{v} = [\begin{matrix} F_{v}_{x_{1, 1}} & F_{v}_{x_{1, 2}} & F_{v}_{x_{2, 1}} & F_{v}_{x_{2, 2}} \\ F_{v}_{y_{1, 1}} & F_{v}_{y_{1, 2}} & F_{v}_{y_{2, 1}} & F_{v}_{y_{2, 2}} \\ F_{v}_{z_{1, 1}} & F_{v}_{z_{1, 2}} & F_{v}_{z_{2, 1}} & F_{v}_{z_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Force Axis
Front left	`VehF(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-axis (lateral)
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`	Inertial-fixed z-axis (vertical)
Front right	`VehF(3,2)`	`1`	`2`
Rear left	`VehF(3,3)`	`2`	`1`
Rear right	`VehF(3,4)`	`2`	`2`

VehM — Suspension moment on vehicle
`array`

Longitudinal, lateral, and vertical suspension moment at axle a, wheel t, applied to the vehicle at the suspension connection point, in N·m. Array dimensions are 3 by the number of wheels on the vehicle.

VehM(1,...) — Suspension moment applied to the vehicle about the inertial-fixed x-axis (longitudinal)
VehM(2,...) — Suspension moment applied to the vehicle about the inertial-fixed y-axis (lateral)
VehM(3,...) — Suspension moment applied to the vehicle about the inertial-fixed z-axis (vertical)

For example, for a two-axle vehicle with two wheels per axle, the VehM:

Signal dimensions are [3x4].

Signal contains suspension moments applied to vehicle according to the axle and wheel locations.

$VehM = M_{v} = [\begin{matrix} M_{v x_{1, 1}} & M_{v x_{1, 2}} & M_{v x_{2, 1}} & M_{v x_{2, 2}} \\ M_{v y_{1, 1}} & M_{v y_{1, 2}} & M_{v y_{2, 1}} & M_{v y_{2, 2}} \\ M_{v z_{1, 1}} & M_{v z_{1, 2}} & M_{v z_{2, 1}} & M_{v z_{2, 2}} \end{matrix}]$

Array Element	Axle	Wheel Number	Moment Axis
`VehM(1,1)`	`1`	`1`	Inertial-fixed x-axis (longitudinal)
`VehM(1,2)`	`1`	`2`
`VehM(1,3)`	`2`	`1`
`VehM(1,4)`	`2`	`2`
`VehM(2,1)`	`1`	`1`	Inertial-fixed y-axis (lateral)
`VehM(2,2)`	`1`	`2`
`VehM(2,3)`	`2`	`1`
`VehM(2,4)`	`2`	`2`
`VehM(3,1)`	`1`	`1`	Inertial-fixed z-axis (vertical)
`VehM(3,2)`	`1`	`2`
`VehM(3,3)`	`2`	`1`
`VehM(3,4)`	`2`	`2`

WhlF — Suspension force on wheel
`array`

Longitudinal, lateral, and vertical suspension forces at axle a, wheel t, applied to the wheel at the axle wheel carrier reference coordinate, in N. Array dimensions are 3 by the number of wheels on the vehicle.

WhlF(1,...) — Suspension force on wheel along the inertial-fixed x-axis (longitudinal)
WhlF(2,...) — Suspension force on wheel along the inertial-fixed y-axis (lateral)
WhlF(3,...) — Suspension force on wheel along the inertial-fixed z-axis (vertical)

For example, for a two-axle vehicle with two wheels per axle, the WhlF:

Signal dimensions are [3x4].

Signal contains wheel forces applied to the vehicle according to the axle and wheel locations.

$WhlF = F_{w} = [\begin{matrix} F_{w}_{x_{1, 1}} & F_{w}_{x_{1, 2}} & F_{w}_{x_{2, 1}} & F_{w}_{x_{2, 2}} \\ F_{w}_{y_{1, 1}} & F_{w}_{y_{1, 2}} & F_{w}_{y_{2, 1}} & F_{w}_{y_{2, 2}} \\ F_{w}_{z_{1, 1}} & F_{w}_{z_{1, 2}} & F_{w}_{z_{2, 1}} & F_{w}_{z_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Force Axis
Front left	`WhlF(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-axis (lateral)
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`	Inertial-fixed z-axis (vertical)
Front right	`WhlF(3,2)`	`1`	`2`
Rear left	`WhlF(3,3)`	`2`	`1`
Rear right	`WhlF(3,4)`	`2`	`2`

WhlV — Wheel velocity
`array`

Longitudinal, lateral, and vertical wheel velocity at axle a, wheel t, in m/s. Array dimensions are 3 by the number of wheels on the vehicle.

WhlV(1,...) — Wheel velocity along the inertial-fixed x-axis (longitudinal)
WhlV(2,...) — Wheel velocity along the inertial-fixed y-axis (lateral)
WhlV(3,...) — Wheel velocity along the inertial-fixed z-axis (vertical)

For example, for a two-axle vehicle with two wheels per axle, the WhlV:

Signal dimensions are [3x4].

Signal contains wheel forces applied to the vehicle according to the axle and wheel locations.

$WhlV = [\begin{matrix} {\dot{x}}_{w} \\ {\dot{y}}_{w} \\ {\dot{z}}_{w} \end{matrix}] = [\begin{matrix} {\dot{x}}_{w_{1, 1}} & {\dot{x}}_{w_{1, 2}} & {\dot{x}}_{w_{2, 1}} & {\dot{x}}_{w_{2, 2}} \\ {\dot{y}}_{w_{_{1, 1}}} & {\dot{y}}_{w_{1, 2}} & {\dot{y}}_{w_{2, 1}} & {\dot{y}}_{w_{2, 2}} \\ {\dot{z}}_{w_{_{1, 1}}} & {\dot{z}}_{w_{1, 2}} & {\dot{z}}_{w_{2, 1}} & {\dot{z}}_{w_{2, 2}} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Force Axis
Front left	`WhlV(1,1)`	`1`	`1`	Inertial-fixed x-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`	Inertial-fixed y-axis (lateral)
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`	Inertial-fixed z-axis (vertical)
Front right	`WhlV(3,2)`	`1`	`2`
Rear left	`WhlV(3,3)`	`2`	`1`
Rear right	`WhlV(3,4)`	`2`	`2`

WhlAng — Wheel camber, caster, toe angles
`array`

Camber, caster, and toe angles at axle a, wheel t, in rad. Array dimensions are 3 by the number of wheels on the vehicle.

WhlAng(1,...) — Camber angle
WhlAng(2,...) — Caster angle
WhlAng(3,...) — Toe angle

For example, for a two-axle vehicle with two wheels per axle, the WhlAng:

Signal dimensions are [3x4].

Signal contains angles according to the axle and wheel locations.

$WhlAng = [\begin{matrix} ξ \\ η \\ ζ \end{matrix}] = [\begin{matrix} ξ_{1, 1} & ξ_{1, 2} & ξ_{2, 1} & ξ_{2, 2} \\ η_{1, 1} & η_{1, 2} & η_{2, 1} & η_{2, 2} \\ ζ_{1, 1} & ζ_{1, 2} & ζ_{2, 1} & ζ_{2, 2} \end{matrix}]$

Wheel	Array Element	Axle	Wheel Number	Angle
Front left	`WhlAng(1,1)`	`1`	`1`	Camber
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`	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`	Toe
Front right	`WhlF(3,2)`	`1`	`2`
Rear left	`WhlF(3,3)`	`2`	`1`
Rear right	`WhlF(3,4)`	`2`	`2`

Parameters

expand all

Steered axle enable by axle, StrgEnByAxl — Boolean vector to enable axle steering
`[1 0]` (default) | `vector`

Boolean vector that enables axle steering, En_steer, dimensionless. Vector is 1 by the number of vehicle axles, N_a. For example:

[1 0] — For a two-axle vehicle, enables axle 1 steering and disables axle 2 steering
[1 1] — For a two-axle vehicle, enables axle 1 and axle 2 steering

Dependencies

Setting any element of the Steered axle enable by axle, StrgEnByAxl vector to 1 creates Input port StrgAng.

Anti-sway axle enable by axle, AntiSwayEnByAxl — Boolean vector to enable axle anti-sway
`[0 0]` (default) | `vector`

Boolean vector that enables axle anti-sway for axle a, dimensionless. For example, [1 0] enables a front axle anti-sway and disables a rear axle anti-sway. Vector is 1 by the number of vehicle axles, N_a.

If you enable an anti-sway bar on the front axle, the anti-sway bar stiffness is the difference between the anti-sway bar torque parameter, Suspension roll stiffness with anti-roll bar, RollStiffArb, and the roll stiffness parameter measured with no anti-roll bar present Suspension roll stiffness without anti-roll bar, RollStiffNoArb.

If you enable an anti-sway bar on the rear axle, the block uses this equation to calculate the twist-beam roll stiffness.

$T B_{r s} = S_{r s} - \frac{π [\frac{1}{2} W R_{\nabla} T W^{2}]}{180}$

The equation uses these variables.

TB_rs	Twist beam roll stiffness
S_rs	Suspension roll stiffness without twist beam, RollStiffNoTwstRear parameter
WR_∇	Normal wheel rate gradient, calculated from NrmlWhlRates parameter and suspension displacement
TW	Track width

If you do not enable an anti-sway bar, the stiffness is 0.

Suspension Parameters

Suspension type — Type of suspension
`Independent front and rear` | `Independent front and twist beam rear`

Select type of suspension.

Drivetrain type — Type of drivetrain
`FWD` (default) | `RWD` | `AWD`

Select type of drivetrain.

AWD – All-wheel drive
FWD – Front-wheel drive
RWD – Rear-wheel drive

Directions

+ Steer angle — Positive steer angle
`Right` (default) | `Left`

Direction of positive steer angle during kinematics and compliance test.

+ Fx used in compliance tests — Positive longitudinal force
`Front` (default) | `Rear`

Direction of positive longitudinal force during kinematics and compliance test.

+ Fy used in compliance tests — Positive lateral force
`Right` (default) | `Left`

Direction of positive lateral force during kinematics and compliance test.

+ Suspension Jounce — Positive suspension jounce
`Up` (default) | `Down`

Direction of positive suspension jounce during kinematics and compliance test.

+ WhlMz used in compliance tests — Positive yaw moment
`Counter-clockwise` (default) | `Clockwise`

Direction of positive yaw moment during kinematics and compliance test.

Shock force

Shock type — Type of shock force
`Table-based` (default) | `Table-based individualConstant`

Type of shock force.

If a table-based individual setting is chosen, table-based shock force is implemented together with constant motion ratios. If a table-based setting is chosen both shock force and motion ratios are calculated from lookup tables.

Setting	Implementation
`Table-based`	Table-based shock force and motion ratios.
`Table-based individual`	Table-based shock force and constant motion ratios.
`Constant`	Constant shock force and motion ratios.

Shock force vs shock compression rate, ShckFrceVsCompRate — Table
`struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000])` (default)

Shock force versus shock compression rate, specified as a structure, in N/mm per sec.

Dependencies

To create this parameter, set Shock type to Table-based or Table-based individual.

Data Types: struct

Motion ratios by axle, MotRatios — Table
`struct('FL',[-0.1 -0.1;0 0;0.1 0.1],'FR',[-0.1 -0.1;0 0;0.1 0.1],'RL',[-0.1 -0.1;0 0;0.1 0.1],'RR',[-0.1 -0.1;0 0;0.1 0.1])` (default)

Motion ratios by axle, specified as a structure.

Data Types: struct

Bounce test

Bump steer, BumpSteer — Table
`struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Bump steer, specified as a structure, in deg/m.

Data Types: struct

Bump camber, BumpCamber — Table
`struct('FL',[-0.1 1.7189;0 0;0.1 -1.7189],'FR',[-0.1 1.7189;0 0;0.1 -1.7189],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Bump camber, specified as a structure, in deg/m.

Data Types: struct

Bump caster, BumpCaster — Table
`struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 -11.4592;0 0;0.1 11.4592],'RR',[-0.1 -11.4592;0 0;0.1 11.4592])` (default)

Bump caster, specified as a structure, in deg/m.

Data Types: struct

Lateral wheel center displacement, LatWhlCtrDisp — Table
`struct('FL',[-0.1 0.02;0 0;0.1 -0.02],'FR',[-0.1 0.02;0 0;0.1 -0.02],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Lateral wheel center displacement, specified as a structure, in mm/mm.

Data Types: struct

Longitudinal wheel center displacement, LngWhlCtrDisp — Table
`struct('FL',[-0.1 -0.002;0 0;0.1 0.002],'FR',[-0.1 -0.002;0 0;0.1 0.002],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.02;0 0;0.1 0.01])` (default)

Longitudinal wheel center displacement, specified as a structure, in mm/mm.

Data Types: struct

Normal wheel rates, NrmlWhlRates — Table
`struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000])` (default) | vector

Normal wheel rates, specified as a structure, in N/mm.

Data Types: struct

Normal wheel force offsets, NrmlWhlFrcOff — Force offset
`[0 0 0 0]` (default)

Normal wheel force offsets, specified as a vector, in N.

Dependencies

To create this parameter, specify a Normal wheel rates, NrmlWhlRates vector.

Data Types: struct

Roll test

Roll steer, RollSteer — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Rear axle roll steer, specified as a structure, in deg/deg.

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: struct

Roll camber, RollCamber — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Rear axle roll camber, specified as a structure, in deg/deg.

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: struct

Roll caster, RollCaster — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Rear axle roll caster, specified as a structure, in deg/deg.

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: struct

Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt — Anti-sway bar enabled
`800` (default) | scalar

Front axle suspension roll stiffness with anti-roll bar, specified as a scalar.

If you enable an anti-sway bar on the axle, the anti-sway bar stiffness is the difference between the anti-sway bar torque parameter, Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt, and the roll stiffness parameter measured with no anti-sway bar present, Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt.

If you do not enable an anti-sway bar, the front axle roll stiffness is 0.

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: double

Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt — Anti-sway bar not enabled
`0` (default) | scalar

Front suspension roll stiffness without an anti-roll bar, specified as a scalar, in Nm/deg.

If you enable an anti-sway bar on the axle, the anti-sway bar stiffness is the difference between the anti-sway bar torque parameter, Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt, and the roll stiffness parameter measured with no anti-sway bar present, Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt.

If you do not enable an anti-sway bar, the axle roll stiffness is 0.

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: double

Rear suspension roll stiffness without twist-beam, RollStiffNoTwstRear — Anti-sway bar not enabled
`0` (default) | scalar

Rear suspension roll stiffness without an twist beam, specified as a scalar, in Nm/deg. T

If you do not enable an anti-sway bar, the rear axle roll stiffness is 0.

If you enable an anti-sway bar on the rear axle, the block uses this equation to calculate the twist-beam roll stiffness.

$T B_{r s} = S_{r s} - \frac{π [\frac{1}{2} W R_{\nabla} T W^{2}]}{180}$

The equation uses these variables.

TB_rs	Twist beam roll stiffness
S_rs	Suspension roll stiffness without twist beam, RollStiffNoTwstRear parameter
WR_∇	Normal wheel rate gradient, calculated from NrmlWhlRates parameter and suspension displacement
TW	Track width

Dependencies

To enable this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: double

Steer test

Camber vs steer angle, CambVsSteerAng — Table
`struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Camber vs steer angle, specified as a structure, in deg/deg.

Data Types: struct

Caster vs steer angle, CastVsSteerAng — Table
`struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Caster vs steer angle, specified as a structure, in deg/deg.

Data Types: struct

Longitudinal compliance test

Longitudinal steer compliance, LngSteerCompl — Table
`struct('NegFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]),'PosFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]))` (default)

Longitudinal steer compliance, specified as a structure, in deg/kN.

Data Types: struct

Longitudinal camber compliance, LngCambCompl — Table
`struct('NegFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]),'PosFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]))` (default)

Longitudinal camber compliance, specified as a structure, in deg/kN.

Data Types: struct

Longitudinal caster compliance, LngCastCompl — Table
`struct('NegFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]),'PosFx',struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]))` (default)

Longitudinal caster compliance, specified as a structure, in deg/kN.

Data Types: struct

Longitudinal wheel center compliance, LngWhlCtrCompl — Table
`struct('NegFx',struct('FL',[-2. -10.;0 0;2. 10.],'FR',[-2. 10.;0 0;2. -10.],'RL',[-2. -10.;0 0;2. 10.],'RR',[-2. 10.;0 0;2. -10.]),'PosFx',struct('FL',[-2. -10.;0 0;2. 10.],'FR',[-2. 10.;0 0;2. -10.],'RL',[-2. -10.;0 0;2. 10.],'RR',[-2. 10.;0 0;2. -10.]))` (default)

Longitudinal wheel center compliance, specified as a structure, in mm/kN.

Data Types: struct

Lateral wheel center compliance, LatWhlCtrComplLng — Table
`struct('NegFx',struct('FL',[-2. -10.;0 0;2. 10.],'FR',[-2. 10.;0 0;2. -10.],'RL',[-2. -10.;0 0;2. 10.],'RR',[-2. 10.;0 0;2. -10.]),'PosFx',struct('FL',[-2. -10.;0 0;2. 10.],'FR',[-2. 10.;0 0;2. -10.],'RL',[-2. -10.;0 0;2. 10.],'RR',[-2. 10.;0 0;2. -10.]))` (default)

Lateral wheel center compliance, specified as a structure, in mm/kN.

Data Types: struct

Lateral compliance-opposed test

Lateral steer compliance, LatSteerCompl — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Lateral steer compliance, specified as a structure, in deg/kN.

Data Types: struct

Lateral camber compliance, LatCambCompl — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Lateral camber compliance, specified as a structure, in deg/kN.

Data Types: struct

Lateral wheel center compliance from lateral sources, LatWhlCtrComplLat — Table
`struct('FL',[-2. -5.;0 0;2. 5.],'FR',[-2. 5.;0 0;2. -5.],'RL',[-2. -5.;0 0;2. 5.],'RR',[-2. 5.;0 0;2. -5.])` (default)

Lateral wheel center compliance from lateral sources, specified as a structure, in mm/kN.

Data Types: struct

Aligning torque compliance-opposed test

Aligning torque steer compliance, AlgnTrqSteerCompl — Table
`struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.])` (default)

Aligning torque steer compliance, specified as a structure, in deg/kNm.

Data Types: struct

Aligning torque camber compliance, AlgnTrqCambCompl — Table
`struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.])` (default)

Aligning torque camber compliance, specified as a structure, in deg/kNm.

Data Types: struct

Parallel lateral force compliance test

Vertical load transfer, VrtLdTrnsfr — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Vertical load transfer, specified as a structure, in N/kN.

Dependencies

To create this parameter, set Suspension type to Independent front and twist-beam rear.

Data Types: struct

Static alignment settings

Toe, StatToe — Wheel toe angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Static toe angle for each wheel, specified as a 1-by-4 vector, in deg.

Wheel	Array Element	Axle	Wheel Location
Front left	`(1,1)`	`1`	`1`
Front right	`(1,2)`	`1`	`2`
Rear left	`(1,3)`	`2`	`1`
Rear left	`(1,4)`	`2`	`2`

Data Types: double

Camber, StatCamber — Wheel camber angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Static camber angle for each wheel, specified as a 1-by-4 vector, in deg.

Wheel	Array Element	Axle
Front left	`(1,1)`	`1`
Front right	`(1,2)`	`1`
Rear left	`(1,3)`	`2`
Rear left	`(1,4)`	`2`

Data Types: double

Caster, StatCaster — Wheel caster angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Static caster angle for each wheel, specified as a 1-by-4 vector, in deg.

Wheel	Array Element	Axle
Front left	`(1,1)`	`1`
Front right	`(1,2)`	`1`
Rear left	`(1,3)`	`2`
Rear left	`(1,4)`	`2`

Data Types: double

Wheels

Static loaded radius of wheels, StatLdWhlR — Wheel radius
`[0.3 0.3 0.3 0.3]` (default) | `1`-by-`4` vector

Static loaded radius of wheels, specified as a 1-by-4 vector, in m.

Wheel	Array Element	Axle
Front left	`(1,1)`	`1`
Front right	`(1,2)`	`1`
Rear left	`(1,3)`	`2`
Rear left	`(1,4)`	`2`

Data Types: double

References

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

Extended Capabilities

C/C++ Code Generation
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Version History

Introduced in R2022b

Twist-Beam Suspension - K and C

Description

K and C Effects on Suspension

Anti-Sway Bar

Examples

Double Lane Change Reference Application

Ports

Input

WhlPz — Wheel z-axis displacement array

WhlRe — Wheel effective radius array

WhlVz — Wheel z-axis velocity array

WhlFx — Longitudinal wheel force on vehicle array

WhlFy — Lateral wheel force on vehicle array

WhlM — Suspension moment on wheel array

VehP — Vehicle displacement array

VehV — Vehicle velocity array

StrgAng — Steering angle, optional array

Dependencies

Phi — Vehicle pitch angle scalar

TrckWdth — Track width array

Output

Info — Bus signal bus

VehF — Suspension force on vehicle array

VehM — Suspension moment on vehicle array

WhlF — Suspension force on wheel array

WhlV — Wheel velocity array

WhlAng — Wheel camber, caster, toe angles array

Parameters

Steered axle enable by axle, StrgEnByAxl — Boolean vector to enable axle steering [1 0] (default) | vector

Dependencies

Anti-sway axle enable by axle, AntiSwayEnByAxl — Boolean vector to enable axle anti-sway [0 0] (default) | vector

Suspension Parameters

Suspension type — Type of suspension Independent front and rear | Independent front and twist beam rear

Drivetrain type — Type of drivetrain FWD (default) | RWD | AWD

+ Steer angle — Positive steer angle Right (default) | Left

+ Fx used in compliance tests — Positive longitudinal force Front (default) | Rear

+ Fy used in compliance tests — Positive lateral force Right (default) | Left

+ Suspension Jounce — Positive suspension jounce Up (default) | Down

+ WhlMz used in compliance tests — Positive yaw moment Counter-clockwise (default) | Clockwise

Shock type — Type of shock force Table-based (default) | Table-based individualConstant

Shock force vs shock compression rate, ShckFrceVsCompRate — Table struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000]) (default)

Dependencies

Motion ratios by axle, MotRatios — Table struct('FL',[-0.1 -0.1;0 0;0.1 0.1],'FR',[-0.1 -0.1;0 0;0.1 0.1],'RL',[-0.1 -0.1;0 0;0.1 0.1],'RR',[-0.1 -0.1;0 0;0.1 0.1]) (default)

Bump steer, BumpSteer — Table struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.]) (default)

Bump camber, BumpCamber — Table struct('FL',[-0.1 1.7189;0 0;0.1 -1.7189],'FR',[-0.1 1.7189;0 0;0.1 -1.7189],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.]) (default)

Bump caster, BumpCaster — Table struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 -11.4592;0 0;0.1 11.4592],'RR',[-0.1 -11.4592;0 0;0.1 11.4592]) (default)

Lateral wheel center displacement, LatWhlCtrDisp — Table struct('FL',[-0.1 0.02;0 0;0.1 -0.02],'FR',[-0.1 0.02;0 0;0.1 -0.02],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.]) (default)

Longitudinal wheel center displacement, LngWhlCtrDisp — Table struct('FL',[-0.1 -0.002;0 0;0.1 0.002],'FR',[-0.1 -0.002;0 0;0.1 0.002],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.02;0 0;0.1 0.01]) (default)

Normal wheel rates, NrmlWhlRates — Table struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000]) (default) | vector

Normal wheel force offsets, NrmlWhlFrcOff — Force offset [0 0 0 0] (default)

Dependencies

Roll steer, RollSteer — Table struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.]) (default)

Dependencies

Roll camber, RollCamber — Table struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.]) (default)

Dependencies

Roll caster, RollCaster — Table struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.]) (default)

Dependencies

Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt — Anti-sway bar enabled 800 (default) | scalar

Dependencies

Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt — Anti-sway bar not enabled 0 (default) | scalar

Dependencies

Rear suspension roll stiffness without twist-beam, RollStiffNoTwstRear — Anti-sway bar not enabled 0 (default) | scalar

Dependencies

Camber vs steer angle, CambVsSteerAng — Table struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.]) (default)

Caster vs steer angle, CastVsSteerAng — Table struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.]) (default)

Lateral steer compliance, LatSteerCompl — Table struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]) (default)

Lateral camber compliance, LatCambCompl — Table struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]) (default)

Lateral wheel center compliance from lateral sources, LatWhlCtrComplLat — Table struct('FL',[-2. -5.;0 0;2. 5.],'FR',[-2. 5.;0 0;2. -5.],'RL',[-2. -5.;0 0;2. 5.],'RR',[-2. 5.;0 0;2. -5.]) (default)

Aligning torque steer compliance, AlgnTrqSteerCompl — Table struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.]) (default)

Aligning torque camber compliance, AlgnTrqCambCompl — Table struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.]) (default)

Vertical load transfer, VrtLdTrnsfr — Table struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.]) (default)

Dependencies

Toe, StatToe — Wheel toe angle [0 0 0 0] (default) | 1-by-4 vector

Camber, StatCamber — Wheel camber angle [0 0 0 0] (default) | 1-by-4 vector

Caster, StatCaster — Wheel caster angle [0 0 0 0] (default) | 1-by-4 vector

Static loaded radius of wheels, StatLdWhlR — Wheel radius [0.3 0.3 0.3 0.3] (default) | 1-by-4 vector

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

WhlPz — Wheel `z`-axis displacement
array

WhlRe — Wheel effective radius
array

WhlVz — Wheel `z`-axis velocity
array

WhlFx — Longitudinal wheel force on vehicle
array

WhlFy — Lateral wheel force on vehicle
array

WhlM — Suspension moment on wheel
array

VehP — Vehicle displacement
array

VehV — Vehicle velocity
array

StrgAng — Steering angle, optional
array

Phi — Vehicle pitch angle
`scalar`

TrckWdth — Track width
`array`

Info — Bus signal
bus

VehF — Suspension force on vehicle
`array`

VehM — Suspension moment on vehicle
`array`

WhlF — Suspension force on wheel
`array`

WhlV — Wheel velocity
`array`

WhlAng — Wheel camber, caster, toe angles
`array`

Steered axle enable by axle, StrgEnByAxl — Boolean vector to enable axle steering
`[1 0]` (default) | `vector`

Anti-sway axle enable by axle, AntiSwayEnByAxl — Boolean vector to enable axle anti-sway
`[0 0]` (default) | `vector`

Suspension type — Type of suspension
`Independent front and rear` | `Independent front and twist beam rear`

Drivetrain type — Type of drivetrain
`FWD` (default) | `RWD` | `AWD`

+ Steer angle — Positive steer angle
`Right` (default) | `Left`

+ Fx used in compliance tests — Positive longitudinal force
`Front` (default) | `Rear`

+ Fy used in compliance tests — Positive lateral force
`Right` (default) | `Left`

+ Suspension Jounce — Positive suspension jounce
`Up` (default) | `Down`

+ WhlMz used in compliance tests — Positive yaw moment
`Counter-clockwise` (default) | `Clockwise`

Shock type — Type of shock force
`Table-based` (default) | `Table-based individualConstant`

Shock force vs shock compression rate, ShckFrceVsCompRate — Table
`struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000])` (default)

Motion ratios by axle, MotRatios — Table
`struct('FL',[-0.1 -0.1;0 0;0.1 0.1],'FR',[-0.1 -0.1;0 0;0.1 0.1],'RL',[-0.1 -0.1;0 0;0.1 0.1],'RR',[-0.1 -0.1;0 0;0.1 0.1])` (default)

Bump steer, BumpSteer — Table
`struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Bump camber, BumpCamber — Table
`struct('FL',[-0.1 1.7189;0 0;0.1 -1.7189],'FR',[-0.1 1.7189;0 0;0.1 -1.7189],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Bump caster, BumpCaster — Table
`struct('FL',[-0.1 1.1459;0 0;0.1 -1.1459],'FR',[-0.1 1.1459;0 0;0.1 -1.1459],'RL',[-0.1 -11.4592;0 0;0.1 11.4592],'RR',[-0.1 -11.4592;0 0;0.1 11.4592])` (default)

Lateral wheel center displacement, LatWhlCtrDisp — Table
`struct('FL',[-0.1 0.02;0 0;0.1 -0.02],'FR',[-0.1 0.02;0 0;0.1 -0.02],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.;0 0;0.1 0.])` (default)

Longitudinal wheel center displacement, LngWhlCtrDisp — Table
`struct('FL',[-0.1 -0.002;0 0;0.1 0.002],'FR',[-0.1 -0.002;0 0;0.1 0.002],'RL',[-0.1 0.;0 0;0.1 0.],'RR',[-0.1 0.02;0 0;0.1 0.01])` (default)

Normal wheel rates, NrmlWhlRates — Table
`struct('FL',[-100. -5000;0 0;100. 5000],'FR',[-100. -5000;0 0;100. 5000],'RL',[-100. -5000;0 0;100. 5000],'RR',[-100. -5000;0 0;100. 5000])` (default) | vector

Normal wheel force offsets, NrmlWhlFrcOff — Force offset
`[0 0 0 0]` (default)

Roll steer, RollSteer — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Roll camber, RollCamber — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Roll caster, RollCaster — Table
`struct('RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Front suspension roll stiffness with anti-roll bar, RollStiffArbFrnt — Anti-sway bar enabled
`800` (default) | scalar

Front suspension roll stiffness without anti-roll bar, RollStiffNoArbFrnt — Anti-sway bar not enabled
`0` (default) | scalar

Rear suspension roll stiffness without twist-beam, RollStiffNoTwstRear — Anti-sway bar not enabled
`0` (default) | scalar

Camber vs steer angle, CambVsSteerAng — Table
`struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Caster vs steer angle, CastVsSteerAng — Table
`struct('FL',[-10. -1.;0 0;10. 1.],'FR',[-10. 1.;0 0;10. -1.],'RL',[-10. -1.;0 0;10. 1.],'RR',[-10. 1.;0 0;10. -1.])` (default)

Lateral steer compliance, LatSteerCompl — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Lateral camber compliance, LatCambCompl — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Lateral wheel center compliance from lateral sources, LatWhlCtrComplLat — Table
`struct('FL',[-2. -5.;0 0;2. 5.],'FR',[-2. 5.;0 0;2. -5.],'RL',[-2. -5.;0 0;2. 5.],'RR',[-2. 5.;0 0;2. -5.])` (default)

Aligning torque steer compliance, AlgnTrqSteerCompl — Table
`struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.])` (default)

Aligning torque camber compliance, AlgnTrqCambCompl — Table
`struct('FL',[-0.2 -1.;0 0;0.2 1.],'FR',[-0.2 1.;0 0;0.2 -1.],'RL',[-0.2 -1.;0 0;0.2 1.],'RR',[-0.2 1.;0 0;0.2 -1.])` (default)

Vertical load transfer, VrtLdTrnsfr — Table
`struct('FL',[-2. -1.;0 0;2. 1.],'FR',[-2. 1.;0 0;2. -1.],'RL',[-2. -1.;0 0;2. 1.],'RR',[-2. 1.;0 0;2. -1.])` (default)

Toe, StatToe — Wheel toe angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Camber, StatCamber — Wheel camber angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Caster, StatCaster — Wheel caster angle
`[0 0 0 0]` (default) | `1`-by-`4` vector

Static loaded radius of wheels, StatLdWhlR — Wheel radius
`[0.3 0.3 0.3 0.3]` (default) | `1`-by-`4` vector

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.