Solid Axle Suspension - Leaf Spring

Solid axle suspension with leaf spring

• Library:

• Vehicle Dynamics Blockset / Suspension

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Description

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

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

For Each	You Can Specify
Axle	Multiple tracks. Suspension parameters.
Track	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 tracks per axle.

• Steering angle input for both tracks on the front axle.

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

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 track. Vertical wheel forces applied to the vehicle.	Suspension forces applied to the axle center. Vertical displacements and velocities of the vehicle and track. 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 tracks.

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

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 track location, the block implements a stiff spring-damper.

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

The equations use these variables.

Fwza,t, Mwza,t	Suspension force and moment applied to the wheel on axle a, track t along wheel-fixed z-axis
Fwxa,t, Mwxa,t	Suspension force and moment applied to the wheel on axle a, track t along wheel-fixed x-axis
Fwya,t, Mwya,t	Suspension force and moment applied to the wheel on axle a, track t along wheel-fixed y-axis
Fvza,t, Mvza,t	Suspension force and moment applied to the vehicle on axle a, track t along wheel-fixed z-axis
Fvxa,t, Mvxa,t	Suspension force and moment applied to the vehicle on axle a, track t along wheel-fixed x-axis
Fvya,t, Mvya,t	Suspension force and moment applied to the vehicle on axle a, track 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 tracks on axle a
mhsteera	Steering angle to vertical force slope applied at wheel carrier for tracks on axle a
δsteera,t	Steering angle input for axle a, track t
cza	Vertical damping constant applied to tracks on axle a
Rewa,t	Effective wheel radius for axle a, track t
Fzhstopa,t	Vertical hardstop force at axle a, track t, along the vehicle-fixed z-axis
Fzaswya,t	Vertical anti-sway force at axle a, track t, along the vehicle-fixed z-axis
zva,t, żva,t	Vehicle displacement and velocity at axle a, track t, along the vehicle-fixed z-axis
zwa,t, żwa,t	Track displacement and velocity at axle a, track t, along the vehicle-fixed z-axis
xva,t, ẋva,t	Vehicle displacement and velocity at axle a, track t, along the vehicle-fixed z-axis
xwa,t, ẋwa,t	Track displacement and velocity at axle a, track t, along the vehicle-fixed z-axis
yva,t, ẏva,t	Vehicle displacement and velocity at axle a, track t, along the vehicle-fixed y-axis
ywa,t, ẏwa,t	Track displacement and velocity at axle a, track t, along the vehicle-fixed y-axis
Ha,t	Suspension height at axle a, track t
Rewa,t	Effective wheel radius at axle a, track 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, track t
ηa,t	Caster angle of wheel on axle a, track t
ζa,t	Toe angle of wheel on axle a, track 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, track t
zva,t	Vehicle displacement at axle a, track t, along the vehicle-fixed z-axis
zwa,t	Track displacement at axle a, track t, along the vehicle-fixed z-axis

Steering Angles

Optionally, you can input steering angles for the tracks. 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, track t
δsteera,t	Steering angle input for axle a, track t
zva,t	Vehicle displacement at axle a, track t, along the vehicle-fixed z-axis
zwa,t	Track displacement at axle a, track t, along the vehicle-fixed z-axis

Power and Energy

The block calculates these suspension characteristics for each axle, a, track, 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 tracks on axle a
δsteera,t	Steering angle input for axle a, track t
Rewa,t	Axle a, track 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 vehicle-fixed z-axis
zva,t, żva,t	Vehicle displacement and velocity at axle a, track t, along the vehicle-fixed z-axis
zwa,t, żwa,t	Track displacement and velocity at axle a, track t, along the vehicle-fixed z-axis

Ports

Input

WhlPz — Track z-axis displacement

array

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

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

• Signal array dimensions are [1x4].

• Array dimensions are axle by track.

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

  Array Element	Axle	Track
  WhlPz(1,1)	1	1
  WhlPz(1,2)	1	2
  WhlPz(1,3)	2	1
  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 tracks on the vehicle.

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

• Signal array dimensions are [1x4].

• Array dimensions are axle by track.

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

  Array Element	Axle	Track
  WhlRe(1,1)	1	1
  WhlRe(1,2)	1	2
  WhlRe(1,3)	2	1
  WhlRe(1,4)	2	2

WhlVz — Track z-axis velocity

array

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

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

• Signal array dimensions are [1x4].

• Array dimensions are axle by track.

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

  Array Element	Axle	Track
  WhlVz(1,1)	1	1
  WhlVz(1,2)	1	2
  WhlVz(1,3)	2	1
  WhlVz(1,4)	2	2

WhlFx — Longitudinal wheel force on vehicle

array

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

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

• Signal array dimensions are [1x4].

• Array dimensions are axle by track.

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

  Array Element	Axle	Track
  WhlFx(1,1)	1	1
  WhlFx(1,2)	1	2
  WhlFx(1,3)	2	1
  WhlFx(1,4)	2	2

WhlFy — Lateral wheel force on vehicle

array

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

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

• Signal array dimensions are [1x4].

• Array dimensions are axle by track.

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

  Array Element	Axle	Track
  WhlFy(1,1)	1	1
  WhlFy(1,2)	1	2
  WhlFy(1.3)	2	1
  WhlFy(1,4)	2	2

WhlM — Suspension moment on wheel

array

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

• WhlM(1,...) — Suspension moment applied to the wheel about the vehicle-fixed x-axis (longitudinal)

• WhlM(2,...) — Suspension moment applied to the wheel about the vehicle-fixed y-axis (lateral)

• WhlM(3,...) — Suspension moment applied to the wheel about the vehicle-fixed z-axis (vertical)

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

• Signal dimensions are [3x4].

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

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

  Array Element	Axle	Track	Moment Axis
  WhlM(1,1)	1	1	Vehicle-fixed x-axis (longitudinal)
  WhlM(1,2)	1	2
  WhlM(1,3)	2	1
  WhlM(1,4)	2	2
  WhlM(2,1)	1	1	Vehicle-fixed y-axis (lateral)
  WhlM(2,2)	1	2
  WhlM(2,3)	2	1
  WhlM(2,4)	2	2
  WhlM(3,1)	1	1	Vehicle-fixed z-axis (vertical)
  WhlM(3,2)	1	2
  WhlM(3,3)	2	1
  WhlM(3,4)	2	2

VehP — Vehicle displacement

array

Vehicle displacement from axle a, track t along vehicle-fixed coordinate system, in m. Array dimensions are 3 by the total number of tracks on the vehicle.

• VehP(1,...) — Vehicle displacement from track, x_v, along the vehicle-fixed x-axis

• VehP(2,...) — Vehicle displacement from track, y_v, along the vehicle-fixed y-axis

• VehP(3,...) — Vehicle displacement from track, z_v, along the vehicle-fixed z-axis

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

• Signal dimensions are [3x4].

• Signal contains four track displacements according to their axle and track locations.

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

  Array Element	Axle	Track	Axis
  VehP(1,1)	1	1	Vehicle-fixed x-axis
  VehP(1,2)	1	2
  VehP(1,3)	2	1
  VehP(1,4)	2	2
  VehP(2,1)	1	1	Vehicle-fixed y-axis
  VehP(2,2)	1	2
  VehP(2,3)	2	1
  VehP(2,4)	2	2
  VehP(3,1)	1	1	Vehicle-fixed z-axis
  VehP(3,2)	1	2
  VehP(3,3)	2	1
  VehP(3,4)	2	2

VehV — Vehicle velocity

array

Vehicle velocity at axle a, track t along vehicle-fixed coordinate system, in m. Input array dimensions are 3 by a*t.

• VehV(1,...) — Vehicle velocity at track, x_v, along the vehicle-fixed x-axis

• VehV(2,...) — Vehicle velocity at track, y_v, along the vehicle-fixed y-axis

• VehV(3,...) — Vehicle velocity at track, z_v, along the vehicle-fixed z-axis

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

• Signal dimensions are [3x4].

• Signal contains 4 track velocities according to their axle and track locations.

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

  Array Element	Axle	Track	Axis
  VehV(1,1)	1	1	Vehicle-fixed x-axis
  VehV(1,2)	1	2
  VehV(1,3)	2	1
  VehV(1,4)	2	2
  VehV(2,1)	1	1	Vehicle-fixed y-axis
  VehV(2,2)	1	2
  VehV(2,3)	2	1
  VehV(2,4)	2	2
  VehV(3,1)	1	1	Vehicle-fixed z-axis
  VehV(3,2)	1	2
  VehV(3,3)	2	1
  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 tracks.

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

• To create 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 track locations.

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

  Array Element	Axle	Track
  StrgAng(1,1)	1	1
  StrgAng(1,2)	1	2

Dependencies

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

• Input port StrgAng.

• 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

Output

Info — Bus signal

bus

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

For example, here are the indices for a two-axle, two-track vehicle. The total number of tracks is four.

• 1D array signal (1-by-4)

  Array Element	Axle	Track
  (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	Track
  (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 tracks 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 tracks 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 tracks 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	Track displacement	3D	For a two-axle, two tracks 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	Track velocity	3D	For a two-axle, two tracks 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 tracks 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, track t, applied to the vehicle at the suspension connection point, in N. Array dimensions are 3 by the total number of tracks on the vehicle.

• VehF(1,...) — Suspension force applied to vehicle along the vehicle-fixed x-axis (longitudinal)

• VehF(2,...) — Suspension force applied to vehicle along the vehicle-fixed y-axis (lateral)

• VehF(3,...) — Suspension force applied to vehicle along the vehicle-fixed z-axis (vertical)

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

• Signal dimensions are [3x4].

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

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

  Array Element	Axle	Track	Force Axis
  VehF(1,1)	1	1	Vehicle-fixed x-axis (longitudinal)
  VehF(1,2)	1	2
  VehF(1,3)	2	1
  VehF(1,4)	2	2
  VehF(2,1)	1	1	Vehicle-fixed y-axis (lateral)
  VehF(2,2)	1	2
  VehF(2,3)	2	1
  VehF(2,4)	2	2
  VehF(3,1)	1	1	Vehicle-fixed z-axis (vertical)
  VehF(3,2)	1	2
  VehF(3,3)	2	1
  VehF(3,4)	2	2

VehM — Suspension moment on vehicle

array

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

• VehM(1,...) — Suspension moment applied to the vehicle about the vehicle-fixed x-axis (longitudinal)

• VehM(2,...) — Suspension moment applied to the vehicle about the vehicle-fixed y-axis (lateral)

• VehM(3,...) — Suspension moment applied to the vehicle about the vehicle-fixed z-axis (vertical)

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

• Signal dimensions are [3x4].

• Signal contains suspension moments applied to vehicle according to the axle and track 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	Track	Moment Axis
  VehM(1,1)	1	1	Vehicle-fixed x-axis (longitudinal)
  VehM(1,2)	1	2
  VehM(1,3)	2	1
  VehM(1,4)	2	2
  VehM(2,1)	1	1	Vehicle-fixed y-axis (lateral)
  VehM(2,2)	1	2
  VehM(2,3)	2	1
  VehM(2,4)	2	2
  VehM(3,1)	1	1	Vehicle-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, track t, applied to the wheel at the axle wheel carrier reference coordinate, in N. Array dimensions are 3 by the total number of tracks on the vehicle.

• WhlF(1,...) — Suspension force on wheel along the vehicle-fixed x-axis (longitudinal)

• WhlF(2,...) — Suspension force on wheel along the vehicle-fixed y-axis (lateral)

• WhlF(3,...) — Suspension force on wheel along the vehicle-fixed z-axis (vertical)

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

• Signal dimensions are [3x4].

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

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

  Array Element	Axle	Track	Force Axis
  WhlF(1,1)	1	1	Vehicle-fixed x-axis (longitudinal)
  WhlF(1,2)	1	2
  WhlF(1,3)	2	1
  WhlF(1,4)	2	2
  WhlF(2,1)	1	1	Vehicle-fixed y-axis (lateral)
  WhlF(2,2)	1	2
  WhlF(2,3)	2	1
  WhlF(2,4)	2	2
  WhlF(3,1)	1	1	Vehicle-fixed z-axis (vertical)
  WhlF(3,2)	1	2
  WhlF(3,3)	2	1
  WhlF(3,4)	2	2

WhlV — Track velocity

array

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

• WhlV(1,...) — Track velocity along the vehicle-fixed x-axis (longitudinal)

• WhlV(2,...) — Track velocity along the vehicle-fixed y-axis (lateral)

• WhlV(3,...) — Track velocity along the vehicle-fixed z-axis (vertical)

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

• Signal dimensions are [3x4].

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

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

  Array Element	Axle	Track	Force Axis
  WhlV(1,1)	1	1	Vehicle-fixed x-axis (longitudinal)
  WhlV(1,2)	1	2
  WhlV(1,3)	2	1
  WhlV(1,4)	2	2
  WhlV(2,1)	1	1	Vehicle-fixed y-axis (lateral)
  WhlV(2,2)	1	2
  WhlV(2,3)	2	1
  WhlV(2,4)	2	2
  WhlV(3,1)	1	1	Vehicle-fixed z-axis (vertical)
  WhlV(3,2)	1	2
  WhlV(3,3)	2	1
  WhlV(3,4)	2	2

WhlAng — Wheel camber, caster, toe angles

array

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

• WhlAng(1,...) — Camber angle

• WhlAng(2,...) — Caster angle

• WhlAng(3,...) — Toe angle

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

• Signal dimensions are [3x4].

• Signal contains wheel angles according to the axle and track locations.

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

  Array Element	Axle	Track	Angle
  WhlAng(1,1)	1	1	Camber
  WhlAng(1,2)	1	2
  WhlAng(1,3)	2	1
  WhlAng(1,4)	2	2
  WhlAng(2,1)	1	1	Caster
  WhlAng(2,2)	1	2
  WhlAng(2,3)	2	1
  WhlAng(2,4)	2	2
  WhlAng(3,1)	1	1	Toe
  WhlF(3,2)	1	2
  WhlF(3,3)	2	1
  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 tracks by axle, NumTracksByAxl — Number of tracks per axle

[2 2] (default) | vector

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

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 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 tracks per axle, you can input steering angles for both wheels on the first axle.

• To create 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 track locations.

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

  Array Element	Axle	Track
  StrgAng(1,1)	1	1
  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 tracks per axle, the TrackCoords array:

• Dimensions are [3x4].

• Contains four track hardpoint coordinates according to their axle and track 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	Track	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 tracks 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, K_z, in N/m.

Wheel and axle interface compliance preload, F0zWhlAxl — Spring rate

9810 (default) | scalar

Wheel and axle interface compliance preload, F_0z, in N.

Wheel and axle interface damping constant, CzWhlAxl — Damping

10000 (default) | scalar

Wheel and axle interface damping constant, C_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 tracks 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 vehicle-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 tracks 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

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

• Input port StrgAng.

• 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

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

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

• Input port StrgAng.

• 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

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

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

• Input port StrgAng.

• 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

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

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

• Input port StrgAng.

• 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

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.

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