Solid Axle Suspension - Coil Spring

Solid axle suspension with coil spring

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Libraries:
Vehicle Dynamics Blockset / Suspension

Description

The Solid Axle Suspension - Coil Spring block implements a solid axle suspension with a coil spring for multiple axles with multiple wheels per axle.

The block models the suspension compliance, damping, and geometric effects as functions of the wheel positions and velocities, with axle-specific compliance and damping parameters. Using the wheel position and velocity, the block calculates the vertical wheel position and suspension forces on the vehicle and wheel. The block uses the Z-down coordinate system (defined in SAE J670) and a solid axle coordinate system. The solid axle coordinate system is aligned with the Z-down vehicle coordinate system, with the x-axis in the direction of forward vehicle motion.

This table describes the settings you can specify for each suspension element.

Suspension Element	Setting
Axle	Multiple wheels Suspension parameters
Wheel	Steering angles

The block contains energy-storing spring elements and energy-dissipating damper elements. The block also stores energy via the axle roll angular acceleration and axle center of mass vertical and lateral acceleration.

This table summarizes the block parameter settings for a vehicle with:

• Two axles

• Two wheels per axle

• Steering angle input for both wheels on the front axle

Parameter	Setting
Number of axles, NumAxl	2
Number of wheels by axle, NumWhlsByAxl	[2 2]
Steered axle enable by axle, StrgEnByAxl	[1 0]

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

Suspension Compliance and Damping

The block uses a linear spring and damper to model the vertical dynamic effects of the suspension system on the vehicle and wheel. Specifically, the block:

Uses	To Calculate
Longitudinal and lateral displacement and velocity of the vehicle. Longitudinal and lateral displacement and velocity of the wheel. Vertical wheel forces applied to the vehicle.	Suspension forces applied to the axle center. Vertical displacements and velocities of the vehicle and wheel. Longitudinal, lateral and vertical suspension forces and moments applied to the vehicle. Longitudinal, lateral and vertical suspension forces and moments applied to the wheel.

To calculate the dynamics of the axle, the block implements these equations. The block neglects the effects of:

• Lateral and longitudinal translational velocity.

• Angular velocity about the vertical and lateral axes.

$\begin{array}{l}\left[\begin{array}{c}{\ddot{x}}_a\\ {\ddot{y}}_a\\ {\ddot{z}}_a\end{array}\right]=\frac{1}{M_a}\left[\begin{array}{c}{F}_{xa}\\ F_{ya}\\ F_{za}\end{array}\right]+\left[\begin{array}{c}{\dot{x}}_a\\ {\dot{y}}_a\\ {\dot{z}}_a\end{array}\right]\times \left[\begin{array}{c}p\\ q\\ r\end{array}\right]=\frac{1}{M_a}\left[\begin{array}{c}0\\ 0\\ F_{za}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ {\dot{z}}_a\end{array}\right]\times \left[\begin{array}{c}p\\ 0\\ 0\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ g\end{array}\right]=\left[\begin{array}{c}0\\ p{\dot{z}}_a\\ \frac{F_{za}}{M_a}+g\end{array}\right]\\ \\ \left[\begin{array}{c}\dot{p}\\ \dot{q}\\ \dot{r}\end{array}\right]=\left[\left[\begin{array}{c}{M}_x\\ M_y\\ M_z\end{array}\right]-\left[\begin{array}{c}p\\ q\\ r\end{array}\right]\times \left[\begin{array}{ccc}{I}_{xx}& 0& 0\\ 0& I_{yy}& 0\\ 0& 0& I_{zz}\end{array}\right]\left[\begin{array}{c}p\\ q\\ r\end{array}\right]\right]{\left[\begin{array}{ccc}{I}_{xx}& 0& 0\\ 0& I_{yy}& 0\\ 0& 0& I_{zz}\end{array}\right]}^{-1}\\ =\left[\left[\begin{array}{c}{M}_x\\ 0\\ 0\end{array}\right]-\left[\begin{array}{c}p\\ q\\ 0\end{array}\right]\times \left[\begin{array}{ccc}{I}_{xx}& 0& 0\\ 0& I_{yy}& 0\\ 0& 0& I_{zz}\end{array}\right]\left[\begin{array}{c}p\\ 0\\ 0\end{array}\right]\right]{\left[\begin{array}{ccc}{I}_{xx}& 0& 0\\ 0& I_{yy}& 0\\ 0& 0& I_{zz}\end{array}\right]}^{-1}=\left[\begin{array}{c}\frac{M_x}{I_{xx}}\\ 0\\ 0\end{array}\right]\end{array}$

The net vertical force on the axle center of mass is the sum of the wheel and suspension forces acting on the axle.

$F_{za}={\displaystyle \sum }_{t=1}^{Nta}\left(F_{w{z}_{a,t}}+F_{z{0}_a}+k_{z_a}\left(z_{v_{a,t}}-z_{s_{a,t}}+m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+c_{z_a}\left({\dot{z}}_{v_{a,t}}-{\dot{z}}_{s_{a,t}}\right)\right)$

The net moment about the roll axis of the solid axle suspension accounts for the hardpoint coordinates of the suspension and wheels.

$M_x={\displaystyle \sum }_{t=1}^{Nta}\left(F_{w{z}_{a,t}}{y}_{w_t}+\left(F_{z{0}_a}+k_{z_a}\left(z_{v_{a,t}}-z_{s_{a,t}}+m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+c_{z_a}\left({\dot{z}}_{v_{a,t}}-{\dot{z}}_{s_{a,t}}\right)\right)y_{s_t}+M_{w{x}_{a,t}}\frac{I_{xx}}{I_{xx}+M_a{y}_{w_t}}\right)$

Block parameters provide the track and suspension hardpoints coordinates.

$$\begin{array}{l} T{c}_t=\left[\begin{array}{ccc}{x}_{w_1}& x_{w_2}& \dots \\ y_{w_1}& y_{w_2}& \dots \\ z_{w_1}& z_{w_2}& \dots \end{array}\right]\\ S{c}_t=\left[\begin{array}{ccc}{x}_{s_1}& x_{s_2}& \dots \\ y_{s_1}& y_{s_2}& \dots \\ z_{s_1}& z_{s_2}& \dots \end{array}\right]\end{array}$$

The block uses Euler angles to transform the track and suspension displacements, velocities, and accelerations to the vehicle coordinate system.

To calculate the suspension forces applied to the vehicle, the block implements this equation.

$F_{v{z}_{a,t}=-}\left(F_{z{0}_a}+k_{z_a}\left(z_{v_{a,t}}-z_{s_{a,t}}+m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+c_{z_a}\left({\dot{z}}_{v_{a,t}}-{\dot{z}}_{s_{a,t}}\right)+F_{zhsto{p}_{a,t}}\right)$

The suspension forces and moments applied to the vehicle are equal to the suspension forces and moments applied to the wheel.

$$\begin{array}{l}{F}_{v{x}_{a,t}}=F_{w{x}_{a,t}}\\ F_{v{y}_{a,t}}=F_{w{y}_{a,t}}\\ F_{v{z}_{a,t}}=-F_{w{z}_{a,t}}\\ \\ M_{v{x}_{a,t}}=M_{w{x}_{a,t}}+F_{w{y}_{a,t}}(R{e}_{w{y}_{a,t}}+H_{a,t})\\ M_{v{y}_{a,t}}=M_{w{y}_{a,t}}+F_{w{x}_{a,t}}\left(R{e}_{w{x}_{a,t}}+H_{a,t}\right)\\ M_{v{z}_{a,t}}=M_{w{z}_{a,t}}\end{array}$$

To calculate the vertical force applied to the suspension at the wheel location, the block implements a stiff spring-damper, shown here.

The block uses this equation.

$F_{w{z}_{a,t}}=-Fw{a}_{z0}-kw{a}_z\left(z_{w_{a,t}}-z_{s_{a,t}}\right)-cw{a}_z\left({\dot{z}}_{w_{a,t}}-{\dot{z}}_{s_{a,t}}\right)$

The equations use these variables.

Fwza,t, Mwza,t	Suspension force and moment applied to the wheel on axle a, wheel t along wheel-fixed z-axis
Fwxa,t, Mwxa,t	Suspension force and moment applied to the wheel on axle a, wheel t along wheel-fixed x-axis
Fwya,t, Mwya,t	Suspension force and moment applied to the wheel on axle a, wheel t along wheel-fixed y-axis
Fvza,t, Mvza,t	Suspension force and moment applied to the vehicle on axle a, wheel t along wheel-fixed z-axis
Fvxa,t, Mvxa,t	Suspension force and moment applied to the vehicle on axle a, wheel t along wheel-fixed x-axis
Fvya,t, Mvya,t	Suspension force and moment applied to the vehicle on axle a, wheel t along wheel-fixed y-axis
Fz0a	Vertical suspension spring preload force applied to the wheels on axle a
kza	Vertical spring constant applied to wheels on axle a
kwaz	Wheel and axle interface compliance constant
mhsteera	Steering angle to vertical force slope applied at wheel carrier for wheels on axle a
δsteera,t	Steering angle input for axle a, wheel t
cza	Vertical damping constant applied to wheels on axle a
cwaz	Wheel and axle interface damping constant
Rewa,t	Effective wheel radius for axle a, wheel t
Fzhstopa,t	Vertical hardstop force at axle a, wheel t, along the inertial-fixed z-axis
Fzaswya,t	Vertical anti-sway force at axle a, wheel t, along the inertial-fixed z-axis
Fwaz0	Wheel and axle interface compliance constant
zva,t, żva,t	Vehicle displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis
zwa,t, żwa,t	Wheel displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis
xva,t, ẋva,t	Vehicle displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis
xwa,t, ẋwa,t	Wheel displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis
yva,t, ẏva,t	Vehicle displacement and velocity at axle a, wheel t, along the inertial-fixed y-axis
ywa,t, ẏwa,t	Wheel displacement and velocity at axle a, wheel t, along the inertial-fixed y-axis
Ha,t	Suspension height at axle a, wheel t
Rewa,t	Effective wheel radius at axle a, wheel t

Hardstop Forces

The hardstop feedback force, F_zhstopa,t, that the block applies depends on whether the suspension is compressing or extending. The block applies the force:

• In compression, when the suspension is compressed more than the maximum distance specified by the Suspension maximum height, Hmax parameter

• In extension, when the suspension extension is greater than maximum extension specified by the Suspension maximum height, Hmax parameter

To calculate the force, the block uses a stiffness based on a hyperbolic tangent and exponential scaling.

Camber, Caster, and Toe Angles

To calculate the camber, caster, and toe angles, block uses linear functions of the suspension height and steering angle.

$$\begin{array}{l}{\xi }_{a,t}={\xi }_{0a}+m_{hcambe{r}_a}\left(z_{w_{a,t}}-z_{v_{a,t}}-m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+m_{camberstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\\ {\eta }_{a,t}={\eta }_{0a}+m_{hcaste{r}_a}\left(z_{w_{a,t}}-z_{v_{a,t}}-m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+m_{casterstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\\ {\zeta }_{a,t}={\zeta }_{0a}+m_{hto{e}_a}\left(z_{w_{a,t}}-z_{v_{a,t}}-m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+m_{toestee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\\ \end{array}$$

The equations use these variables.

ξa,t	Camber angle of wheel on axle a, wheel t
ηa,t	Caster angle of wheel on axle a, wheel t
ζa,t	Toe angle of wheel on axle a, wheel t
ξ0a, η0a, ζ0a	Nominal suspension axle a camber, caster, and toe angles, respectively, at zero steering angle
mhcambera, mhcastera, mhtoea	Camber, caster, and toe angles, respectively, versus suspension height slope for axle a
mcambersteera, mcastersteera, mtoesteera	Camber, caster, and toe angles, respectively, versus steering angle slope for axle a
mhsteera	Steering angle versus vertical force slope for axle a
δsteera,t	Steering angle input for axle a, wheel t
zva,t	Vehicle displacement at axle a, wheel t, along the inertial-fixed z-axis
zwa,t	Wheel displacement at axle a, wheel t, along the inertial-fixed z-axis

Steering Angles

Optionally, use the Steered axle enable by axle, StrgEnByAxl parameter to input steering angles for the wheels. To calculate the steering angles for the wheels, the block offsets the input steering angles with a linear function of the suspension height.

${\delta }_{whlstee{r}_{a,t}}={\delta }_{stee{r}_{a,t}}+m_{hto{e}_a}\left(z_{w_{a,t}}-z_{v_{a,t}}-m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)+m_{toestee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|$

The equation uses these variables.

mtoesteera	Axle a toe angle versus steering angle slope
mhsteera	Axle a steering angle versus vertical force slope
mhtoea	Axle a toe angle versus suspension height slope
δwhlsteera,t	Wheel steering angle for axle a, wheel t
δsteera,t	Steering angle input for axle a, wheel t
zva,t	Vehicle displacement at axle a, wheel t, along the inertial-fixed z-axis
zwa,t	Wheel displacement at axle a, wheel t, along the inertial-fixed z-axis

Power and Energy

The block calculates these suspension characteristics for each axle, a, wheel, t.

Calculation	Equation
Dissipated power, Psuspa,t	$$P_{sus{p}_{a,t}}=F_{wzlooku{p}_a}\left({\dot{z}}_{v_{a,t}}-{\dot{z}}_{w_{a,t}},{\dot{z}}_{v_{a,t}}-{\dot{z}}_{w_{a,t}},{\delta }_{stee{r}_{a,t}}\right)$$
Absorbed energy, Esuspa,t	$$E_{sus{p}_{a,t}}=F_{wzlooku{p}_a}\left({\dot{z}}_{v_{a,t}}-{\dot{z}}_{w_{a,t}},{\dot{z}}_{v_{a,t}}-{\dot{z}}_{w_{a,t}},{\delta }_{stee{r}_{a,t}}\right)$$
Suspension height, Ha,t	$$H_{a,t}=-\left(z_{v_{a,t}}-z_{w_{a,t}}+\frac{F_{z{0}_a}}{k_{z_a}}+m_{hstee{r}_a}\left|{\delta }_{stee{r}_{a,t}}\right|\right)$$
Distance from wheel carrier center to tire/road interface	$$z_{wt{r}_{a,t}}=R{e}_{w_{a,t}}+H_{a,t}$$

The equations use these variables.

mhsteera	Steering angle to vertical force slope applied at wheel carrier for wheels on axle a
δsteera,t	Steering angle input for axle a, wheel t
Rewa,t	Axle a, wheel t effective wheel radius from wheel carrier center to tire/road interface
Fz0a	Vertical suspension spring preload force applied to the wheels on axle a
zwtra,t	Distance from wheel carrier center to tire/road interface, along the inertial-fixed z-axis
zva,t, żva,t	Vehicle displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis
zwa,t, żwa,t	Wheel displacement and velocity at axle a, wheel t, along the inertial-fixed z-axis

Examples

Kinematics and Compliance Virtual Test Laboratory Reference Application

Generate optimized suspension parameters for the vehicle dynamics mapped suspension blocks.

• Open Script

Ports

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.

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)

  Array Element	Axle	Wheel Number
  (1,1)	1	1
  (1,2)	1	2
  (1,3)	2	1
  (1,4)	2	2

• 3D array signal (3-by-4)

  Array Element	Axle	Wheel Number
  (1,1)	1	1
  (1,2)	1	2
  (1,3)	2	1
  (1,4)	2	2
  (2,1)	1	1
  (2,2)	1	2
  (2,3)	2	1
  (2,4)	2	2
  (3,1)	1	1
  (3,2)	1	2
  (3,3)	2	1
  (3,4)	2	2

Signal	Description	Array Signal	Variable	Units
Camber	Wheel angles according to the axle.	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

Axles

Number of axles, NumAxl — Number of axles

2 (default) | scalar

Number of axles, N_a, dimensionless.

Number of wheels by axle, NumWhlsByAxl — Number of wheels per axle

[2 2] (default) | vector

Number of wheels per axle, Nt_a, dimensionless. Vector is 1 by the number of vehicle axles, N_a. For example, [1,2] represents one wheel on axle one and two wheels on axle two.

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 one steering and disables axle two steering

• [1 1]—For a two-axle vehicle, enables axle one and axle two steering

Dependencies

Setting an element of the Steered axle enable by axle, StrgEnByAxl vector to 1:

• Creates input port StrgAng.

• Creates these parameters

  • 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

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

Axle and wheels lumped principal moments of inertia about longitudinal axis, AxlIxx — Inertia

300 (default) | vector

Axle and wheels lumped principal moments of inertia about longitudinal axis, AxleIxx a, in kg*m^2.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Axle and wheels lumped mass, AxlM — Mass

[2 2] (default) | vector

Axle and wheels lumped mass, a, in kg.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Track hardpoint coordinates relative to axle center, TrackCoords — Point

[0 0 0 0;-1 1 -1 1;0 0 0 0] (default) | array

Track hardpoint coordinates, Tc_t, along the solid axle x, y, and z-axes, in m.

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

• Dimensions are [3x4].

• Contains four track hardpoint coordinates according to their axle and wheel locations.

  $$T{c}_t=\left[\begin{array}{cccc}{x}_{w_{1,1}}& x_{w_{1,2}}& x_{w_{2,1}}& x_{w_{2,2}}\\ y_{w_{1,1}}& y_{w_{1,2}}& y_{w_{2,1}}& y_{w_{2,2}}\\ z_{w_{1,1}}& z_{w_{1,2}}& z_{w_{2,1}}& z_{w_{2,2}}\end{array}\right]$$

  Array Element	Axle	Wheel Number	Axis
  TrackCoords(1,1)	1	1	Solid axle x-axis
  TrackCoords(1,2)	1	2
  TrackCoords(1,3)	2	1
  TrackCoords(1,4)	2	2
  TrackCoords(2,1)	1	1	Solid axle y-axis
  TrackCoords(2,2)	1	2
  TrackCoords(2,3)	2	1
  TrackCoords(2,4)	2	2
  TrackCoords(3,1)	1	1	Solid axle z-axis
  TrackCoords(3,2)	1	2
  TrackCoords(3,3)	2	1
  TrackCoords(3,4)	2	2

Suspension hardpoint coordinates relative to axle center, SuspCoords — Point

[0 0 0 0;-1 1 -1 1;0 0 0 0] (default) | array

Suspension hardpoint coordinates, Sc_t, along the solid axle x-, y-, and z-axes, in m.

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

• Dimensions are [3x4].

• Contains four track hardpoint coordinates according to their axle and track locations.

  $$S{c}_t=\left[\begin{array}{cccc}{x}_{s_{1,1}}& x_{s_{1,2}}& x_{s_{2,1}}& x_{s_{2,2}}\\ y_{s_{1,1}}& y_{s_{1,2}}& y_{s_{2,1}}& y_{s_{2,2}}\\ z_{s_{1,1}}& z_{s_{1,2}}& z_{s_{2,1}}& z_{s_{2,2}}\end{array}\right]$$

  Array Element	Axle	Track	Axis
  SuspCoords(1,1)	1	1	Solid axle x-axis
  SuspCoords(1,2)	1	2
  SuspCoords(1,3)	2	1
  SuspCoords(1,4)	2	2
  SuspCoords(2,1)	1	1	Solid axle y-axis
  SuspCoords(2,2)	1	2
  SuspCoords(2,3)	2	1
  SuspCoords(2,4)	2	2
  SuspCoords(3,1)	1	1	Solid axle z-axis
  SuspCoords(3,2)	1	2
  SuspCoords(3,3)	2	1
  SuspCoords(3,4)	2	2

Wheel and axle interface compliance constant, KzWhlAxl — Spring rate

6437000 (default) | scalar

Wheel and axle interface compliance constant, kwa_z, in N/m.

Wheel and axle interface compliance preload, F0zWhlAxl — Spring rate

9810 (default) | scalar

Wheel and axle interface compliance preload, Fwa_z0, in N.

Wheel and axle interface damping constant, CzWhlAxl — Damping

10000 (default) | scalar

Wheel and axle interface damping constant, cwa_z, in m.

Suspension

Compliance and Damping - Passive

Suspension spring constant, Kz — Suspension spring constant

64370 (default) | scalar | vector

Linear vertical spring constant for independent suspension wheels on axle a, k_za, in N/m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Suspension spring preload, F0z — Suspension spring preload

9810 (default) | scalar | vector

Vertical preload spring force applied to the wheels on the axle at wheel carrier reference coordinates, F_z0a, in N. Positive preload forces:

• Cause the vehicle to lift.

• Point along the negative inertial-fixed z-axis.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Suspension shock damping constant, Cz — Suspension shock damping constant

10000 (default) | scalar | vector

Linear vertical damping constant for independent suspension wheels on axle a, c_za, in Ns/m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Dependencies

To create this parameter, clear Enable active damping.

Suspension maximum height, Hmax — Height

0.5 (default) | scalar | vector

Maximum suspension extension or minimum suspension compression height, H_max, for axle a before the suspension reaches a hardstop, in m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Geometry

Toe angle at steering center, Toe — Toe angle

0.0349 (default) | scalar

Nominal suspension toe angle at zero steering angle, ζ_0a, in rad.

Roll steer vs suspension height slope, RollStrgSlp — Steer angle suspension slope

-0.2269 (default) | scalar | vector

Roll steer angle versus suspension height, m_htoea, in rad/m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Toe angle vs steering angle slope, ToeStrgSlp — Toe angle steering slope

0.01 (default) | scalar | vector

Toe angle versus steering angle slope, m_toesteera, dimensionless.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Dependencies

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

Caster angle at steering center, Caster — Caster angle at steering center

0.0698 (default) | scalar

Nominal suspension caster angle at zero steering angle, η_0a, in rad.

Caster angle vs suspension height slope, CasterHslp — Caster angle versus suspension height slope

-0.2269 (default) | scalar | vector

Caster angle versus suspension height, m_hcastera, in rad/m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Caster angle vs steering angle slope, CasterStrgSlp — Caster angle versus steering angle slope

0.01 (default) | scalar | vector

Caster angle versus steering angle slope, m_castersteera, dimensionless.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Dependencies

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

Camber angle at steering center, Camber — Camber angle at steering center

0.0698 (default) | scalar

Nominal suspension camber angle at zero steering angle, ξ_0a, in rad.

Camber angle vs suspension height slope, CamberHslp — Camber angle versus suspension height slope

-0.2269 (default) | scalar | vector

Camber angle versus suspension height, m_hcambera, in rad/m.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Camber angle vs steering angle slope, CamberStrgSlp — Camber angle versus steering angle slope

0.01 (default) | scalar | vector

Camber angle versus steering angle slope, m_cambersteera, dimensionless.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Dependencies

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

Suspension height vs steering angle slope, StrgHgtSlp — Suspension height versus steering angle slope

0.1432 (default) | scalar | vector

Steering angle to vertical force slope applied at suspension wheel carrier reference point, m_hsteera, in m/rad.

Vector is 1 by the number of vehicle axles, N_a. If you provide a scalar value, the block uses that value for all axles.

Dependencies

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

References

[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.

Extended Capabilities

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

Version History

Introduced in R2018a

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.