Solid Axle Suspension - Air Spring

Air spring solid axle suspension

Since R2023b

Libraries:
Vehicle Dynamics Blockset / Suspension

Description

The Solid Axle Suspension - Air Spring block implements an air spring solid axle suspension with multiple axles and 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.

Illustration of a solid axle

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

Suspension Element	Setting
Axle	Multiple wheels Suspension parameters
Wheel	Steering angles

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

When you set the Model type parameter as Mapped, the block uses a lookup table that relates the vertical damping and compliance to the suspension height, air spring pressure, and steering angle. You can calibrate the wheel force lookup table so that steering angle changes from the nominal center position generate a force that increases the vehicle height.

The block implements these equations.

$\begin{array}{l} F_{w z l o o k u p_{a}} = f (z_{v_{a, t}} - z_{w_{a, t}}, {\dot{z}}_{v_{a, t}} - {\dot{z}}_{w_{a, t}}, δ_{s t e e r_{a, t}}) \\ F_{w z_{a, t}} = F_{w z l o o k u p_{a}} + F_{z a s w y_{a, t}} \end{array}$

The block assumes that the suspension elements have no mass. Therefore, the suspension forces and moments applied to the vehicle are equal to the suspension forces and moments applied to the wheel.

$\begin{array}{l} F_{v x_{a, t}} = F_{w x_{a, t}} \\ F_{v y_{a, t}} = F_{w y_{a, t}} \\ F_{v z_{a, t}} = - F_{w z_{a, t}} \\ M_{v x_{a, t}} = M_{w x_{a, t}} + F_{w y_{a, t}} (R e_{w y_{a, t}} + H_{a, t}) \\ M_{v y_{a, t}} = M_{w y_{a, t}} + F_{w x_{a, t}} (R e_{w x_{a, t}} + H_{a, t}) \\ M_{v z_{a, t}} = M_{w z_{a, t}} \end{array}$

The block sets the wheel positions and velocities equal to the vehicle lateral and longitudinal positions and velocities.

$\begin{array}{l} x_{w_{a, t}} = x_{v_{a, t}} \\ y_{w_{a, t}} = y_{v_{a, t}} \\ {\dot{x}}_{w_{a, t}} = {\dot{x}}_{v_{a, t}} \\ {\dot{y}}_{w_{a, t}} = {\dot{y}}_{v_{a, t}} \end{array}$

The equations use these variables.

F_{wz_a,t}, M_{wz_a,t}	Suspension force and moment applied to the wheel on axle `a`, wheel `t` along wheel-fixed z-axis
F_{wx_a,t}, M_{wx_a,t}	Suspension force and moment applied to the wheel on axle `a`, wheel `t` along wheel-fixed x-axis
F_{wy_a,t}, M_{wy_a,t}	Suspension force and moment applied to the wheel on axle `a`, wheel `t` along wheel-fixed y-axis
F_{vz_a,t}, M_{vz_a,t}	Suspension force and moment applied to the vehicle on axle `a`, wheel `t` along wheel-fixed z-axis
F_{vx_a,t}, M_{vx_a,t}	Suspension force and moment applied to the vehicle on axle `a`, wheel `t` along wheel-fixed x-axis
F_{vy_a,t}, M_{vy_a,t}	Suspension force and moment applied to the vehicle on axle `a`, wheel `t` along wheel-fixed y-axis
F_{z0_a}	Vertical suspension spring preload force applied to the wheels on axle `a`
k_{z_a}	Vertical spring constant applied to wheels on axle `a`
kwa_z	Wheel and axle interface compliance constant
m_{hsteer_a}	Steering angle to vertical force slope applied at wheel carrier for wheels on axle `a`
δ_{steer_a,t}	Steering angle input for axle `a`, wheel `t`
c_{z_a}	Vertical damping constant applied to wheels on axle `a`
cwa_z	Wheel and axle interface damping constant
Re_{w_a,t}	Effective wheel radius for axle `a`, wheel `t`
F_{zhstop_a,t}	Vertical hardstop force at axle `a`, wheel `t`, along the inertial-fixed z-axis
F_{zaswy_a,t}	Vertical anti-sway force at axle `a`, wheel `t`, along the inertial-fixed z-axis
Fwa_z0	Wheel and axle interface compliance constant
z_{v_a,t}, ż_{v_a,t}	Vehicle displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis
z_{w_a,t}, ż_{w_a,t}	Wheel displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis
x_{v_a,t}, ẋ_{v_a,t}	Vehicle displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis
x_{w_a,t}, ẋ_{w_a,t}	Wheel displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis
y_{v_a,t}, ẏ_{v_a,t}	Vehicle displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed y-axis
y_{w_a,t}, ẏ_{w_a,t}	Wheel displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed y-axis
H_a,t	Suspension height at axle `a`, wheel `t`
Re_{w_a,t}	Effective wheel radius at axle `a`, wheel `t`

When you set the Model type parameter as Physical, the block calculates spring force as a function of spring deflection.

$\begin{array}{l} F = p_{0} A_{w} {(\frac{V_{0}}{V_{0} - V s})}^{x} \\ where \\ V = \frac{π}{4} (0.4 D_{A}^{2} - 0.6 D_{K}^{2}) \end{array}$

The block calculates spring rate as a function of the effective area and the internal volume.

$k = \frac{x (1 + p_{0}) A_{w}^{2}}{V_{0}}$

The equations use these variables.

p₀	Static operating pressure
A_w	Effective area
V₀	Volume in design position
V	Volume gradient of the air spring
s	Spring deflection
X	Isentropic exponent

Hardstop Forces

The hardstop feedback force, F_{zhstop_a,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, the block uses a lookup table, G_alookup, that is a function of the suspension height and steering angle.

$[\begin{matrix} ξ_{a, t} & η_{a, t} & ζ_{a, t} \end{matrix}] = G_{a l o o k u p} f (z_{w_{a, t}} - z_{v_{a, t}}, δ_{s t e e r_{a, t}})$

The equations use these variables.

ξ_a,t	Camber angle of wheel on axle `a`, wheel `t`
η_a,t	Caster angle of wheel on axle `a`, wheel `t`
ζ_a,t	Toe angle of wheel on axle `a`, wheel `t`
δ_{steer_a,t}	Steering angle input for axle `a`, wheel `t`
z_{v_a,t}	Vehicle displacement at axle `a`, wheel `t`, along inertial-fixed z-axis
z_{w_a,t}	Wheel displacement at axle `a`, wheel `t`, along inertial-fixed z-axis

Steering Angles

Optionally, you can input steering angles for the wheels. To calculate the steering angles for the wheels, the block offsets the input steering angles as a function of the suspension height. For the calculation, the block uses a lookup table, G_alookup, that is a function of the suspension position and steering angle.

$δ_{w h l s t e e r_{a, t}} = δ_{s t e e r_{a, t}} + G_{a l o o k u p} f (z_{w_{a, t}} - z_{v_{a, t}}, δ_{s t e e r_{a, t}})$

The equation uses these variables.

δ_{whlsteer_a,t}	Wheel steering angle for axle `a`, wheel `t`
δ_{steer_a,t}	Steering angle input for axle `a`, wheel `t`
z_{v_a,t}	Vehicle displacement at axle `a`, wheel `t`, along the inertial-fixed z-axis
z_{w_a,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, and wheel, t.

Calculation	Equation
Dissipated power, P_{susp_a,t}	$P_{s u s p_{a, t}} = F_{w z l o o k u p_{a}} ({\dot{z}}_{v_{a, t}} - {\dot{z}}_{w_{a, t}}, {\dot{z}}_{v_{a, t}} - {\dot{z}}_{w_{a, t}}, δ_{s t e e r_{a, t}})$
Absorbed energy, E_{susp_a,t}	$E_{s u s p_{a, t}} = F_{w z l o o k u p_{a}} ({\dot{z}}_{v_{a, t}} - {\dot{z}}_{w_{a, t}}, {\dot{z}}_{v_{a, t}} - {\dot{z}}_{w_{a, t}}, δ_{s t e e r_{a, t}})$
Suspension height, H_a,t	$H_{a, t} = - (z_{v_{a, t}} - z_{w_{a, t}} - median (f_s u s p_d z_b p))$
Distance from wheel carrier center to tire/road interface	$z_{w t r_{a, t}} = R e_{w_{a, t}} + H_{a, t}$

The equations use these variables.

m_{hsteer_a}	Steering angle to vertical force slope applied at wheel carrier for wheels on axle `a`
δ_{steer_a,t}	Steering angle input for axle `a`, wheel `t`
Re_{w_a,t}	Axle `a`, wheel `t` effective wheel radius from wheel carrier center to tire/road interface
f_susp_dz_bp	Vertical axis suspension height breakpoints
z_{wtr_a,t}	Distance from wheel carrier center to tire/road interface, along the inertial-fixed z-axis
z_{v_a,t}, ż_{v_a,t}	Vehicle displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis
z_{w_a,t}, ż_{w_a,t}	Wheel displacement and velocity at axle `a`, wheel `t`, along the inertial-fixed z-axis

Ports

Input

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WhlPz — Wheel `z`-axis displacement
array

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

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

Signal array dimensions are [1x4].
$WhlPz = z_{w} = [\begin{matrix} z_{w_{1, 1}} & z_{w_{1, 2}} & z_{w_{2, 1}} & z_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left WhlPz(1,1) 1 1
Front right WhlPz(1,2) 1 2
Rear left WhlPz(1,3) 2 1
Rear right WhlPz(1,4) 2 2

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

WhlRe — Wheel effective radius
array

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

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

Signal array dimensions are [1x4].
$Whl Re = R e_{w} = [\begin{matrix} R e_{w_{1, 1}} & R e_{w_{1, 2}} & R e_{w_{2, 1}} & R e_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left WhlRe(1,1) 1 1
Front right WhlRe(1,2) 1 2
Rear left WhlRe(1,3) 2 1
Rear right WhlRe(1,4) 2 2

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

WhlVz — Wheel `z`-axis velocity
array

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

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

Signal array dimensions are [1x4].
$WhlVz = {\dot{z}}_{w} = [\begin{matrix} {\dot{z}}_{w_{1, 1}} & {\dot{z}}_{w_{1, 2}} & {\dot{z}}_{w_{2, 1}} & {\dot{z}}_{w_{2, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left WhlVz(1,1) 1 1
Front right WhlVz(1,2) 1 2
Rear left WhlVz(1,3) 2 1
Rear right WhlVz(1,4) 2 2

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

WhlFx — Longitudinal wheel force on vehicle
array

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

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

Signal array dimensions are [1x4].
$WhlFx = F_{w x} = [\begin{matrix} F_{w x_{1, 1}} & F_{w x_{1, 2}} & F_{w x_{2, 1}} & F_{w x_{2, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left WhlFx(1,1) 1 1
Front right WhlFx(1,2) 1 2
Rear left WhlFx(1,3) 2 1
Rear right WhlFx(1,4) 2 2

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

WhlFy — Lateral wheel force on vehicle
array

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

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

Signal array dimensions are [1x4].

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

Wheel Array Element Axle Wheel Number
Front left WhlFy(1,1) 1 1
Front right WhlFy(1,2) 1 2
Rear left WhlFy(1.3) 2 1
Rear right WhlFy(1,4) 2 2

Wheel	Array Element	Axle	Wheel Number
Front left	`WhlFy(1,1)`	`1`	`1`
Front right	`WhlFy(1,2)`	`1`	`2`
Rear left	`WhlFy(1.3)`	`2`	`1`
Rear right	`WhlFy(1,4)`	`2`	`2`

WhlM — Suspension moment on wheel
array

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

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

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

Signal dimensions are [3x4].

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

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

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

VehP — Vehicle displacement
array

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

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

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

Signal dimensions are [3x4].

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

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

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

VehV — Vehicle velocity
array

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

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

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

Signal dimensions are [3x4].

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

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

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

StrgAng — Steering angle, optional
array

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

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

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

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

Dependencies

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

Pressure — Pressure in air spring
array

Pressure in air spring, p, in bar. Input array dimensions are 1 by the total number of wheels on the vehicle.

Output

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Info — Bus signal
bus

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

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

1D array signal (1-by-4)

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

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

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

VehF — Suspension force on vehicle
`array`

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

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

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

Signal dimensions are [3x4].

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

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

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

VehM — Suspension moment on vehicle
`array`

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

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

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

Signal dimensions are [3x4].

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

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

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

WhlF — Suspension force on wheel
`array`

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

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

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

Signal dimensions are [3x4].

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

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

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

WhlV — Wheel velocity
`array`

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

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

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

Signal dimensions are [3x4].

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

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

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

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

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

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

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

Signal dimensions are [3x4].

Signal contains angles according to the axle and wheel locations.

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

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

Parameters

expand all

Model type — Air suspension model type
`Physical` (default) | `Mapped`

Air suspension model type, specified as Physical or Mapped. Use the Mapped model type if you have data available for your suspension. Use the Physical model type if you don't not have data for the suspension.

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 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:

Enables the port StrgAng.
Enables 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.
$StrgAng = δ_{s t e e r} = [\begin{matrix} δ_{s t e e r_{1, 1}} & δ_{s t e e r_{1, 2}} \end{matrix}]$
Wheel Array Element Axle Wheel Number
Front left StrgAng(1,1) 1 1
Front right StrgAng(1,2) 1 2

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

Solid Axle Parameters

Axle and wheels lumped principal moment of inertia about longitudinal axis, AxlIxx — Principal moment of inertia about longitudinal axis
`200` (default)

Axle and wheels lumped principal moment of inertia about longitudinal axis, Axllxx, in kg*m^2.

Axle and wheels lumped mass, AxlM — Axle and wheels lumped mass
`300` (default)

Axle and wheels lumped mass, AxlM, in kg.

Track hardpoint coordinates relative to axle center, TrackCoords — Track hardpoint coordinates
`[0 0 0 0;-1 1 -1 1;0 0 0 0]` (default)

Track hardpoint coordinates relative to axle center, TrackCoords, in m.

Suspension hardpoint coordinates relative to axle center, SuspCoords — Suspension hardpoint coordinates
`[0 0 0 0;-1 1 -1 1;0 0 0 0]` (default)

Suspension hardpoint coordinates relative to axle center, SuspCoords, in m.

Wheel and axle interface compliance constant, KzWhlAxl — Wheel and axle interface compliance constant
`6437000` (default)

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

Wheel and axle interface compliance preload, F0zWhlAxl — Wheel and axle interface compliance preload
`9810` (default)

Wheel and axle interface compliance preload, F0zWhlAxl, in N.

Wheel and axle interface damping constant, CzWhlAxl [Ns/m] — Wheel and axle interface damping constant
`10000` (default)

Wheel and axle interface damping constant, CzWhlAxl, in Ns/m.

Physical

Air suspension spring preload, F0z — Air suspension spring preload
`9810` (default) | scalar

Air suspension spring load, F0z, in N.

Dependencies

To enable the parameter, set Model Type to Physical.

Air suspension shock damping constant, Cz — Air suspension shock damping constant
`10000` (default) | scalar

Air suspension shock damping constant, Cz, in Ns/m.

Dependencies

To enable the parameter, set Model Type to Physical.

Air spring effective area, EffctArea — Air spring effective area
`0.21993` (default) | scalar

Air spring effective area, EffctArea, in m^2.

Dependencies

To enable the parameter, set Model Type to Physical.

Air spring volume in design position, VolDgnPos — Air spring volume in design position
`0.08` (default) | scalar

Air spring volume in design position, VolDngPos, in m^3.

Dependencies

To enable the parameter, set Model Type to Physical.

Air spring isentropic exponent, IstpExp — Air spring isentropic exponent
`1.4` (default) | scalar

Air spring isentropic exponent, IstpExp, unitless.

Dependencies

To enable the parameter, set Model Type to Physical.

Air spring outer diameter, OuterDiam — Air spring outer diameter
`0.6199` (default) | scalar

Air spring outer diameter, OuterDiam, in m.

Dependencies

To enable the parameter, set Model Type to Physical.

Air spring piston diameter, PistDiam — Air spring piston diameter
`0.236` (default) | scalar

Air spring piston diameter, PistDiam, in m.

Dependencies

To enable the parameter, set Model Type to Physical.

Air suspension maximum height, Hmax — Air suspension maximum height
`0.5` (default) | scalar

Air suspension maximum height, Hmax, in m.

Dependencies

To enable the parameter, set Model Type to Physical.

Toe angle at steering center, Toe — Toe angle
`0.0349` (default) | scalar

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

Dependencies

To enable the parameter, set Model Type to Physical.

Roll steer vs suspension height slope, RollStrgSlp — Steer angle suspension slope
`-0.2269` (default) | scalar | `vector`

Roll steer angle versus suspension height, m_{htoe_a}, 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.

Dependencies

To enable the parameter, set Model Type to Physical.

Toe angle vs steering angle slope, ToeStrgSlp — Toe angle steering slope
`0.01` (default) | scalar | vector

Toe angle versus steering angle slope, m_{toesteer_a}, 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.

To create this parameter, set Model Type to Physical.

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.

Dependencies

To enable the parameter, set Model Type to Physical.

Caster angle vs suspension height slope, CasterHslp — Caster angle versus suspension height slope
`-0.2269` (default) | scalar | vector

Caster angle versus suspension height, m_{hcaster_a}, 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.

Dependencies

To enable the parameter, set Model Type to Physical.

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_{castersteer_a}, 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.

To create this parameter, set Model Type to Physical.

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.

Dependencies

To enable the parameter, set Model Type to Physical.

Camber angle vs suspension height slope, CamberHslp — Camber angle versus suspension height slope
`-0.2269` (default) | scalar | vector

Camber angle versus suspension height, m_{hcamber_a}, 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.

Dependencies

To enable the parameter, set Model Type to Physical.

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_{cambersteer_a}, 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.

To create this parameter, set Model Type to Physical.

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_{hsteer_a}, 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.

To create this parameter, set Model Type to Physical.

Mapped

Axle breakpoints, f_susp_axl_bp — Breakpoints
`[1 2]` (default) | `1`-by-`P` array

Axle breakpoints, f_susp_axl_bp, dimensionless.

Dependencies

To enable this parameter, set Model type to Mapped.

Vertical axis suspension height breakpoints, f_susp_dz_bp — Breakpoints
`1`-by-`M` array

Vertical axis suspension height breakpoints, f_susp_dz_bp, in m.

Dependencies

To enable this parameter, set Model type to Mapped.

Vertical axis air suspension pressure breakpoints, f_susp_press_bp — Vertical axis air suspension pressure breakpoints
`[0.50 7]` (default) | `1`-by-`M` array

Vertical axis air suspension pressure breakpoints, f_susp_press_bp, in m/s.

Dependencies

To enable this parameter, set Model type to Mapped.

Vertical air axis suspension force and moment responses, f_susp_fmz — Output array
`zeros(31,31,61,2,4)` (default) | `M`-by-`N`-by-`O`-by-`P`-by-`4` array

Array of output values as a function of:

Vertical suspension height, M
Vertical suspension height velocity, N
Steering angle, O
Axle, P
Four output types:
- 1 — Vertical force, in N
- 2 — User-defined output
- 3 — Stored energy, in J
- 4 — Absorbed power, in W

The array dimensions must match the breakpoint dimensions.

Dependencies

To enable this parameter, set Model type to Mapped.

Air suspension shock damping constant, c_airSusp — Air suspension shock damping constant
`6e6` (default) | scalar

Air suspension shock damping constant, c_airSusp, in Ns/m.

Dependencies

To enable this parameter, set Model type to Mapped.

Suspension geometry responses, f_susp_geom — Suspension geometry responses
`zeros(31,61,2,3)` (default) | `M`-by-`O`-by-`P`-by-`3` array

Array of geometric suspension values as a function of:

Vertical suspension height, M
Steering angle, O
Axle, P
Three output types:
- 1 — Camber angle, in rad
- 2 — Caster angle, in rad
- 3 — Toe angle, in rad

The array dimensions must match the breakpoint dimensions

Dependencies

To enable this parameter, set Model type to Mapped.

Steering angle breakpoints, f_susp_strgdelta_bp — Steering angle breakpoints
`1`-by-`O` array

Steering angle breakpoints, in rad.

Dependencies

To enable this parameter, set Model type to Mapped.

Extended Capabilities

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

Version History

Introduced in R2023b

Solid Axle Suspension - Air Spring

Description

Suspension Compliance and Damping

Hardstop Forces

Camber, Caster, and Toe Angles

Steering Angles

Power and Energy

Ports

Input

WhlPz — Wheel z-axis displacement array

WhlRe — Wheel effective radius array

WhlVz — Wheel z-axis velocity array

WhlFx — Longitudinal wheel force on vehicle array

WhlFy — Lateral wheel force on vehicle array

WhlM — Suspension moment on wheel array

VehP — Vehicle displacement array

VehV — Vehicle velocity array

StrgAng — Steering angle, optional array

Dependencies

Pressure — Pressure in air spring array

Output

Info — Bus signal bus

VehF — Suspension force on vehicle array

VehM — Suspension moment on vehicle array

WhlF — Suspension force on wheel array

WhlV — Wheel velocity array

WhlAng — Wheel camber, caster, toe angles array

Parameters

Model type — Air suspension model type Physical (default) | Mapped

Number of axles, NumAxl — Number of axles 2 (default) | scalar

Number of wheels by axle, NumWhlsByAxl — Number of wheels per axle [2 2] (default) | vector

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

Dependencies

Axle and wheels lumped principal moment of inertia about longitudinal axis, AxlIxx — Principal moment of inertia about longitudinal axis 200 (default)

Axle and wheels lumped mass, AxlM — Axle and wheels lumped mass 300 (default)

Track hardpoint coordinates relative to axle center, TrackCoords — Track hardpoint coordinates [0 0 0 0;-1 1 -1 1;0 0 0 0] (default)

Suspension hardpoint coordinates relative to axle center, SuspCoords — Suspension hardpoint coordinates [0 0 0 0;-1 1 -1 1;0 0 0 0] (default)

Wheel and axle interface compliance constant, KzWhlAxl — Wheel and axle interface compliance constant 6437000 (default)

Wheel and axle interface compliance preload, F0zWhlAxl — Wheel and axle interface compliance preload 9810 (default)

Wheel and axle interface damping constant, CzWhlAxl [Ns/m] — Wheel and axle interface damping constant 10000 (default)

Air suspension spring preload, F0z — Air suspension spring preload 9810 (default) | scalar

Dependencies

Air suspension shock damping constant, Cz — Air suspension shock damping constant 10000 (default) | scalar

Dependencies

Air spring effective area, EffctArea — Air spring effective area 0.21993 (default) | scalar

Dependencies

Air spring volume in design position, VolDgnPos — Air spring volume in design position 0.08 (default) | scalar

Dependencies

Air spring isentropic exponent, IstpExp — Air spring isentropic exponent 1.4 (default) | scalar

Dependencies

Air spring outer diameter, OuterDiam — Air spring outer diameter 0.6199 (default) | scalar

Dependencies

Air spring piston diameter, PistDiam — Air spring piston diameter 0.236 (default) | scalar

Dependencies

Air suspension maximum height, Hmax — Air suspension maximum height 0.5 (default) | scalar

Dependencies

Toe angle at steering center, Toe — Toe angle 0.0349 (default) | scalar

Dependencies

Roll steer vs suspension height slope, RollStrgSlp — Steer angle suspension slope -0.2269 (default) | scalar | vector

Dependencies

Toe angle vs steering angle slope, ToeStrgSlp — Toe angle steering slope 0.01 (default) | scalar | vector

Dependencies

Caster angle at steering center, Caster — Caster angle at steering center 0.0698 (default) | scalar

Dependencies

Caster angle vs suspension height slope, CasterHslp — Caster angle versus suspension height slope -0.2269 (default) | scalar | vector

Dependencies

Caster angle vs steering angle slope, CasterStrgSlp — Caster angle versus steering angle slope 0.01 (default) | scalar | vector

Dependencies

Camber angle at steering center, Camber — Camber angle at steering center 0.0698 (default) | scalar

Dependencies

Camber angle vs suspension height slope, CamberHslp — Camber angle versus suspension height slope -0.2269 (default) | scalar | vector

Dependencies

Camber angle vs steering angle slope, CamberStrgSlp — Camber angle versus steering angle slope 0.01 (default) | scalar | vector

Dependencies

Suspension height vs steering angle slope, StrgHgtSlp — Suspension height versus steering angle slope 0.1432 (default) | scalar | vector

Dependencies

Axle breakpoints, f_susp_axl_bp — Breakpoints [1 2] (default) | 1-by-P array

Dependencies

Vertical axis suspension height breakpoints, f_susp_dz_bp — Breakpoints 1-by-M array

Dependencies

WhlPz — Wheel `z`-axis displacement
array

WhlRe — Wheel effective radius
array

WhlVz — Wheel `z`-axis velocity
array

WhlFx — Longitudinal wheel force on vehicle
array

WhlFy — Lateral wheel force on vehicle
array

WhlM — Suspension moment on wheel
array

VehP — Vehicle displacement
array

VehV — Vehicle velocity
array

StrgAng — Steering angle, optional
array

Pressure — Pressure in air spring
array

Info — Bus signal
bus

VehF — Suspension force on vehicle
`array`

VehM — Suspension moment on vehicle
`array`

WhlF — Suspension force on wheel
`array`

WhlV — Wheel velocity
`array`

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

Model type — Air suspension model type
`Physical` (default) | `Mapped`

Number of axles, NumAxl — Number of axles
`2` (default) | scalar

Number of wheels by axle, NumWhlsByAxl — Number of wheels per axle
`[2 2]` (default) | vector

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

Axle and wheels lumped principal moment of inertia about longitudinal axis, AxlIxx — Principal moment of inertia about longitudinal axis
`200` (default)

Axle and wheels lumped mass, AxlM — Axle and wheels lumped mass
`300` (default)

Track hardpoint coordinates relative to axle center, TrackCoords — Track hardpoint coordinates
`[0 0 0 0;-1 1 -1 1;0 0 0 0]` (default)

Suspension hardpoint coordinates relative to axle center, SuspCoords — Suspension hardpoint coordinates
`[0 0 0 0;-1 1 -1 1;0 0 0 0]` (default)

Wheel and axle interface compliance constant, KzWhlAxl — Wheel and axle interface compliance constant
`6437000` (default)

Wheel and axle interface compliance preload, F0zWhlAxl — Wheel and axle interface compliance preload
`9810` (default)

Wheel and axle interface damping constant, CzWhlAxl [Ns/m] — Wheel and axle interface damping constant
`10000` (default)

Air suspension spring preload, F0z — Air suspension spring preload
`9810` (default) | scalar

Air suspension shock damping constant, Cz — Air suspension shock damping constant
`10000` (default) | scalar

Air spring effective area, EffctArea — Air spring effective area
`0.21993` (default) | scalar

Air spring volume in design position, VolDgnPos — Air spring volume in design position
`0.08` (default) | scalar

Air spring isentropic exponent, IstpExp — Air spring isentropic exponent
`1.4` (default) | scalar

Air spring outer diameter, OuterDiam — Air spring outer diameter
`0.6199` (default) | scalar

Air spring piston diameter, PistDiam — Air spring piston diameter
`0.236` (default) | scalar

Air suspension maximum height, Hmax — Air suspension maximum height
`0.5` (default) | scalar

Toe angle at steering center, Toe — Toe angle
`0.0349` (default) | scalar

Roll steer vs suspension height slope, RollStrgSlp — Steer angle suspension slope
`-0.2269` (default) | scalar | `vector`

Toe angle vs steering angle slope, ToeStrgSlp — Toe angle steering slope
`0.01` (default) | scalar | vector

Caster angle at steering center, Caster — Caster angle at steering center
`0.0698` (default) | scalar

Caster angle vs suspension height slope, CasterHslp — Caster angle versus suspension height slope
`-0.2269` (default) | scalar | vector

Caster angle vs steering angle slope, CasterStrgSlp — Caster angle versus steering angle slope
`0.01` (default) | scalar | vector

Camber angle at steering center, Camber — Camber angle at steering center
`0.0698` (default) | scalar

Camber angle vs suspension height slope, CamberHslp — Camber angle versus suspension height slope
`-0.2269` (default) | scalar | vector

Camber angle vs steering angle slope, CamberStrgSlp — Camber angle versus steering angle slope
`0.01` (default) | scalar | vector

Suspension height vs steering angle slope, StrgHgtSlp — Suspension height versus steering angle slope
`0.1432` (default) | scalar | vector

Axle breakpoints, f_susp_axl_bp — Breakpoints
`[1 2]` (default) | `1`-by-`P` array

Vertical axis suspension height breakpoints, f_susp_dz_bp — Breakpoints
`1`-by-`M` array

Vertical axis air suspension pressure breakpoints, f_susp_press_bp — Vertical axis air suspension pressure breakpoints
`[0.50 7]` (default) | `1`-by-`M` array

Vertical air axis suspension force and moment responses, f_susp_fmz — Output array
`zeros(31,31,61,2,4)` (default) | `M`-by-`N`-by-`O`-by-`P`-by-`4` array

Air suspension shock damping constant, c_airSusp — Air suspension shock damping constant
`6e6` (default) | scalar

Suspension geometry responses, f_susp_geom — Suspension geometry responses
`zeros(31,61,2,3)` (default) | `M`-by-`O`-by-`P`-by-`3` array

Steering angle breakpoints, f_susp_strgdelta_bp — Steering angle breakpoints
`1`-by-`O` array

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