Independent Suspension - K and C

Independent kinematics and compliance test suspension

Since R2022a

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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
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 For more information, see Twist-Beam Suspension - K and C.
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.

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.

$$\begin{array}{l}\tan ({\theta }_{CPSA})=f(Z_w)\\ F_{zCPSA}=F_y\tan ({\theta }_{CPSA})\end{array}$$

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

The equations use these variables.

ϴCPSA	Contact patch swing arm angle
Fy	Lateral suspension force
FzCPSA	CPSA effect on vertical suspension force
zw	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.

$$\begin{array}{l}\tan ({\theta }_{SVSA})=f(Z_w)\\ F_{zSVSA}=F_x\tan ({\theta }_{SVSA})\end{array}$$

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

The equations use these variables.

ϴSVSA	Contact patch swing arm angle
Fx	Longitudinal wheel force
FzSVSA	SVSA effect on vertical suspension force
zw	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 enable an anti-sway bar on the 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-sway bar present Suspension roll stiffness without anti-roll bar, RollStiffNoArb.

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

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

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].

  $$\mathrm{WhlPz}=z_w=\left[\begin{array}{cccc}{z}_{w_{1,1}}& z_{w_{1,2}}& z_{w_{2,1}}& z_{w_{2,2}}\end{array}\right]$$

  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].

  $$\mathrm{Whl}\mathrm{Re}=R{e}_w=\left[\begin{array}{cccc}R{e}_{w_{1,1}}& R{e}_{w_{1,2}}& R{e}_{w_{2,1}}& R{e}_{w_{2,2}}\end{array}\right]$$

  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].

  $$\mathrm{WhlVz}={\dot{z}}_w=\left[\begin{array}{cccc}{\dot{z}}_{w_{1,1}}& {\dot{z}}_{w_{1,2}}& {\dot{z}}_{w_{2,1}}& {\dot{z}}_{w_{2,2}}\end{array}\right]$$

  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].

  $$\mathrm{WhlFx}=F_{wx}=\left[\begin{array}{cccc}{F}_{w{x}_{1,1}}& F_{w{x}_{1,2}}& F_{w{x}_{2,1}}& F_{w{x}_{2,2}}\end{array}\right]$$

  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].

  $$\mathrm{WhlFy}=F_{wy}=\left[\begin{array}{cccc}{F}_{w{y}_{1,1}}& F_{w{y}_{1,2}}& F_{w{y}_{2,1}}& F_{w{y}_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{WhlM}=M_w=\left[\begin{array}{cccc}{M}_{w{x}_{1,1}}& M_{w{x}_{1,2}}& M_{w{x}_{2,1}}& M_{w{x}_{2,2}}\\ M_{w{y}_{1,1}}& M_{w{y}_{1,2}}& M_{w{y}_{2,1}}& M_{w{y}_{2,2}}\\ M_{w{z}_{1,1}}& M_{w{z}_{1,2}}& M_{w{z}_{2,1}}& M_{w{z}_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{VehP}=\left[\begin{array}{c}{x}_v\\ y_v\\ z_v\end{array}\right]=\left[\begin{array}{cccc}{x}_v{}_{{}_{1,1}}& x_v{}_{{}_{1,2}}& x_v{}_{{}_{2,1}}& x_v{}_{{}_{2,2}}\\ y_v{}_{{}_{1,1}}& y_v{}_{{}_{1,2}}& y_v{}_{{}_{2,1}}& y_v{}_{{}_{2,2}}\\ z_v{}_{{}_{1,1}}& z_v{}_{{}_{1,2}}& z_v{}_{{}_{2,1}}& z_v{}_{{}_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{VehV}=\left[\begin{array}{c}{\dot{x}}_v\\ {\dot{y}}_v\\ {\dot{z}}_v\end{array}\right]=\left[\begin{array}{cccc}{\dot{x}}_{v_{1,1}}& {\dot{x}}_{v_{1,2}}& {\dot{x}}_{v_{2,1}}& {\dot{x}}_{v_{2,2}}\\ {\dot{y}}_{v_{1,1}}& {\dot{y}}_{v_{1,2}}& {\dot{y}}_{v_{2,1}}& {\dot{y}}_{v_{2,2}}\\ {\dot{z}}_{v_{1,1}}& {\dot{z}}_{v_{1,2}}& {\dot{z}}_{v_{2,1}}& {\dot{z}}_{v_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{StrgAng}={\delta }_{steer}=\left[\begin{array}{cc}{\delta }_{stee{r}_{1,1}}& {\delta }_{stee{r}_{1,2}}\end{array}\right]$$

  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

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	$$\mathrm{WhlAng}[1,\mathrm{...}]=\xi =\left[{\xi }_{a,t}\right]$$	rad
Caster			$$\mathrm{WhlAng}[2,\mathrm{...}]=\eta =\left[{\eta }_{a,t}\right]$$
Toe			$$\mathrm{WhlAng}[3,\mathrm{...}]=\zeta =\left[{\zeta }_{a,t}\right]$$
Height	Suspension height	1D	H	m
Power	Suspension power dissipation	1D	Psusp	W
Energy	Suspension absorbed energy	1D	Esusp	J
VehF	Suspension forces applied to the vehicle	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{VehF}=F_v=\left[\begin{array}{cccc}{F}_v{}_{x_{1,1}}& F_v{}_{x_{1,2}}& F_v{}_{x_{2,1}}& F_v{}_{x_{2,2}}\\ F_v{}_{y_{1,1}}& F_v{}_{y_{1,2}}& F_v{}_{y_{2,1}}& F_v{}_{y_{2,2}}\\ F_v{}_{z_{1,1}}& F_v{}_{z_{1,2}}& F_v{}_{z_{2,1}}& F_v{}_{z_{2,2}}\end{array}\right]$$	N
VehM	Suspension moments applied to vehicle	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{VehM}=M_v=\left[\begin{array}{cccc}{M}_{v{x}_{1,1}}& M_{v{x}_{1,2}}& M_{v{x}_{2,1}}& M_{v{x}_{2,2}}\\ M_{v{y}_{1,1}}& M_{v{y}_{1,2}}& M_{v{y}_{2,1}}& M_{v{y}_{2,2}}\\ M_{v{z}_{1,1}}& M_{v{z}_{1,2}}& M_{v{z}_{2,1}}& M_{v{z}_{2,2}}\end{array}\right]$$	N·m
WhlF	Suspension force applied to wheel	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{WhlF}=F_w=\left[\begin{array}{cccc}{F}_w{}_{x_{1,1}}& F_w{}_{x_{1,2}}& F_w{}_{x_{2,1}}& F_w{}_{x_{2,2}}\\ F_w{}_{y_{1,1}}& F_w{}_{y_{1,2}}& F_w{}_{y_{2,1}}& F_w{}_{y_{2,2}}\\ F_w{}_{z_{1,1}}& F_w{}_{z_{1,2}}& F_w{}_{z_{2,1}}& F_w{}_{z_{2,2}}\end{array}\right]$$	N
WhlP	Wheel displacement	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{WhlP}=\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\end{array}\right]=\left[\begin{array}{cccc}{x}_w{}_{{}_{1,1}}& x_w{}_{{}_{1,2}}& x_w{}_{{}_{2,1}}& x_{w_{2,2}}\\ y_w{}_{{}_{1,1}}& y_w{}_{{}_{1,2}}& y_w{}_{{}_{2,1}}& y_w{}_{y_{2,2}}\\ z_{wtr}{}_{{}_{1,1}}& z_{wtr}{}_{{}_{1,2}}& z_{wtr}{}_{{}_{2,1}}& z_{wt{r}_{2,2}}\end{array}\right]$$	m
WhlV	Wheel velocity	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{WhlV}=\left[\begin{array}{c}{\dot{x}}_w\\ {\dot{y}}_w\\ {\dot{z}}_w\end{array}\right]=\left[\begin{array}{cccc}{\dot{x}}_{w_{1,1}}& {\dot{x}}_{w_{1,2}}& {\dot{x}}_{w_{2,1}}& {\dot{x}}_{w_{2,2}}\\ {\dot{y}}_{w_{{}_{1,1}}}& {\dot{y}}_{w_{1,2}}& {\dot{y}}_{w_{2,1}}& {\dot{y}}_{w_{2,2}}\\ {\dot{z}}_{w_{{}_{1,1}}}& {\dot{z}}_{w_{1,2}}& {\dot{z}}_{w_{2,1}}& {\dot{z}}_{w_{2,2}}\end{array}\right]$$	m/s
WhlAng	Wheel camber, caster, toe angles	3D	For a two-axle, two wheels per axle vehicle: $$\mathrm{WhlAng}=\left[\begin{array}{c}\xi \\ \eta \\ \zeta \end{array}\right]=\left[\begin{array}{cccc}{\xi }_{1,1}& {\xi }_{1,2}& {\xi }_{2,1}& {\xi }_{2,2}\\ {\eta }_{1,1}& {\eta }_{1,2}& {\eta }_{2,1}& {\eta }_{2,2}\\ {\zeta }_{1,1}& {\zeta }_{1,2}& {\zeta }_{2,1}& {\zeta }_{2,2}\end{array}\right]$$	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.

  $$\mathrm{VehF}=F_v=\left[\begin{array}{cccc}{F}_v{}_{x_{1,1}}& F_v{}_{x_{1,2}}& F_v{}_{x_{2,1}}& F_v{}_{x_{2,2}}\\ F_v{}_{y_{1,1}}& F_v{}_{y_{1,2}}& F_v{}_{y_{2,1}}& F_v{}_{y_{2,2}}\\ F_v{}_{z_{1,1}}& F_v{}_{z_{1,2}}& F_v{}_{z_{2,1}}& F_v{}_{z_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{VehM}=M_v=\left[\begin{array}{cccc}{M}_{v{x}_{1,1}}& M_{v{x}_{1,2}}& M_{v{x}_{2,1}}& M_{v{x}_{2,2}}\\ M_{v{y}_{1,1}}& M_{v{y}_{1,2}}& M_{v{y}_{2,1}}& M_{v{y}_{2,2}}\\ M_{v{z}_{1,1}}& M_{v{z}_{1,2}}& M_{v{z}_{2,1}}& M_{v{z}_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{WhlF}=F_w=\left[\begin{array}{cccc}{F}_w{}_{x_{1,1}}& F_w{}_{x_{1,2}}& F_w{}_{x_{2,1}}& F_w{}_{x_{2,2}}\\ F_w{}_{y_{1,1}}& F_w{}_{y_{1,2}}& F_w{}_{y_{2,1}}& F_w{}_{y_{2,2}}\\ F_w{}_{z_{1,1}}& F_w{}_{z_{1,2}}& F_w{}_{z_{2,1}}& F_w{}_{z_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{WhlV}=\left[\begin{array}{c}{\dot{x}}_w\\ {\dot{y}}_w\\ {\dot{z}}_w\end{array}\right]=\left[\begin{array}{cccc}{\dot{x}}_{w_{1,1}}& {\dot{x}}_{w_{1,2}}& {\dot{x}}_{w_{2,1}}& {\dot{x}}_{w_{2,2}}\\ {\dot{y}}_{w_{{}_{1,1}}}& {\dot{y}}_{w_{1,2}}& {\dot{y}}_{w_{2,1}}& {\dot{y}}_{w_{2,2}}\\ {\dot{z}}_{w_{{}_{1,1}}}& {\dot{z}}_{w_{1,2}}& {\dot{z}}_{w_{2,1}}& {\dot{z}}_{w_{2,2}}\end{array}\right]$$

  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.

  $$\mathrm{WhlAng}=\left[\begin{array}{c}\xi \\ \eta \\ \zeta \end{array}\right]=\left[\begin{array}{cccc}{\xi }_{1,1}& {\xi }_{1,2}& {\xi }_{2,1}& {\xi }_{2,2}\\ {\eta }_{1,1}& {\eta }_{1,2}& {\eta }_{2,1}& {\eta }_{2,2}\\ {\zeta }_{1,1}& {\zeta }_{1,2}& {\zeta }_{2,1}& {\zeta }_{2,2}\end{array}\right]$$

  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

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 axle 1 anti-sway and disables axle 2 anti-sway. Vector is 1 by the number of vehicle axles, N_a.

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, Suspension roll stiffness with anti-roll bar, RollStiffArb, and the roll stiffness parameter measured with no anti-sway bar present Suspension roll stiffness without anti-roll bar, RollStiffNoArb.

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

Suspension roll stiffness with anti-roll bar, RollStiffArb — Anti-sway bar enabled

[800 700] (default) | 1-by-2 vector

Suspension roll stiffness with anti-roll bar, specified as a 1-by-2 vector, in Nm/deg. The first element is the front axle roll stiffness. The second element is the rear axle roll stiffness.

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, Suspension roll stiffness with anti-roll bar, RollStiffArb, and the roll stiffness parameter measured with no anti-sway bar present Suspension roll stiffness without anti-roll bar, RollStiffNoArb.

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

Dependencies

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

Data Types: double

Suspension roll stiffness without anti-roll bar, RollStiffNoArb — Anti-sway bar not enabled

[0 0] (default) | 1-by-2 vector

Suspension roll stiffness without anti-roll bar, specified as a 1-by-2 vector, in Nm/deg. The first element is the front axle roll stiffness. The second element is the rear axle roll stiffness.

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, Suspension roll stiffness with anti-roll bar, RollStiffArb, and the roll stiffness parameter measured with no anti-sway bar present Suspension roll stiffness without anti-roll bar, RollStiffNoArb.

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

Dependencies

To enable this parameter, set Suspension type to Independent front and 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

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
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022a

R2022b: Parameter name change from NumTracksByAxl to NumWhlsByAxl

The Number of tracks by axle, NumTracksByAxl parameter is renamed to Number of wheels by axle, NumWhlsByAxl.

The block uses the number of wheels per axle to index the input and output block signals.

R2022b: New Suspension type and Drivetrain type Parameters

Starting from R2022b, the Independent Suspension - K and C block includes Suspension type and Drivetrain type parameters that allow you specify a suspension and drivetrain. Previously, the block was configured for front wheel drive with independent front and rear suspensions.