Vehicle motion using coast-down testing coefficients

• Library:
• Powertrain Blockset / Vehicle Dynamics

Vehicle Dynamics Blockset / Vehicle Body

## Description

The Vehicle Body Total Road Load block implements a one degree-of-freedom (1DOF) rigid vehicle model using coast-down testing coefficients. You can use this block in a vehicle model to represent the load that the driveline and chassis applies to a transmission or engine. It is suitable for system-level performance, component sizing, fuel economy, or drive cycle tracking studies. The block calculates the dynamic powertrain load with minimal parameterization or computational cost.

You can configure the block for kinematic, force, or total power input.

• Kinematic — Block uses the vehicle longitudinal velocity and acceleration to calculate the tractive force and power.

• Force — Block uses the tractive force to calculate the vehicle longitudinal displacement and velocity.

• Power — Block uses the engine or transmission power to calculate the vehicle longitudinal displacement and velocity.

### Dynamics

To calculate the total road load acting on the vehicle, the block implements this equation.

`${F}_{road}=a+b\stackrel{˙}{x}+c{\stackrel{˙}{x}}^{2}+mg\mathrm{sin}\left(\theta \right)$`

To determine the coefficients a, b, and c, you can use a test procedure similar to the one described in Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. You can also use Simulink® Design Optimization™ to fit the coefficients to measured data.

To calculate the vehicle motion, the block uses Newton’s law for rigid bodies.

`${F}_{total}=m\stackrel{¨}{x}+{F}_{road}$`

Total power input is a product of the total force and longitudinal velocity. Power due to road and gravitational forces is a product of the road force and longitudinal velocity.

`$\begin{array}{l}{P}_{total}={F}_{total}\stackrel{˙}{x}\\ {P}_{road}={F}_{road}\stackrel{˙}{x}\end{array}$`

### Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

`PwrInfo`

`PwrTrnsfrd` — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

`PwrFxExt`

Externally applied force power

PFxExt

${P}_{FxExt}={F}_{total}\stackrel{˙}{x}$

`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrFxDrag`

Drag force power

PD

${P}_{d}=-\left(a+b\stackrel{˙}{x}+c{\stackrel{˙}{x}}^{2}\right)\stackrel{˙}{x}$

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`wrStoredGrvty`Rate change in gravitational potential energy

Pg

${P}_{g}=-mg\stackrel{˙}{Z}$

`PwrStoredxdot`

Rate in change of longitudinal kinetic energy

Pxdot

${P}_{\stackrel{˙}{x}}=m\stackrel{¨}{x}\stackrel{˙}{x}$

The equations use these variables.

 a Steady-state rolling resistance coefficient b Viscous driveline and rolling resistance coefficient c Aerodynamic drag coefficient g Gravitational acceleration x Vehicle longitudinal displacement with respect to ground, in the vehicle-fixed frame $\stackrel{˙}{x}$ Vehicle longitudinal velocity with respect to ground, in the vehicle-fixed frame $\stackrel{¨}{x}$ Vehicle longitudinal acceleration with respect to ground, vehicle-fixed frame m Vehicle body mass Θ Road grade angle Ftotal Total force acting on vehicle Froad Resistive road load due to losses and gravitational load Ptotal Total tractive input power Proad Total power due to losses and gravitational load $\stackrel{˙}{Z}$ Vehicle vertical velocity along the vehicle-fixed `z`-axis

## Ports

### Input

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Vehicle total longitudinal velocity, $\stackrel{˙}{x}$, in m/s.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Kinematic`.

Vehicle total longitudinal acceleration, $\stackrel{¨}{x}$, in m/s^2.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Kinematic`.

Tractive input power, Ptotal, in W.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Power`.

Tractive input force, Ftotal, in N.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Force`.

### Output

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Bus signal containing these block calculations.

SignalDescriptionValueUnits
`InertFrm``Cg``Disp``X`Vehicle CG displacement along earth-fixed `X`-axis

Computed

m
`Y`Vehicle CG displacement along earth-fixed `Y`-axis`0`

m

`Z`Vehicle CG displacement along earth-fixed `Z`-axis

Computed

m
`Vel``Xdot`Vehicle CG velocity along earth-fixed `X`-axis

Computed

m/s

`Ydot`Vehicle CG velocity along earth-fixed `Y`-axis`0`m/s
`Zdot`Vehicle CG velocity along earth-fixed `Z`-axis

Computed

m/s
`Ang``phi`Rotation of vehicle-fixed frame about the earth-fixed `X`-axis (roll)`0`rad
`theta`Rotation of vehicle-fixed frame about the earth-fixed `Y`-axis (pitch)

Computed

`psi`Rotation of vehicle-fixed frame about the earth-fixed `Z`-axis (yaw)`0`rad
`BdyFrm``Cg``Disp``x`Vehicle CG displacement along the vehicle-fixed `x`-axis

Computed

m
`y`Vehicle CG displacement along the vehicle-fixed `y`-axis`0`m
`z`Vehicle CG displacement along the vehicle-fixed `z`-axis`0`m
`Vel``xdot`Vehicle CG velocity along the vehicle-fixed `x`-axis

Computed

m/s
`ydot`Vehicle CG velocity along the vehicle-fixed `y`-axis`0`m/s
`zdot`Vehicle CG velocity along the vehicle-fixed `z`-axis`0`m/s
`Acc``ax`Vehicle CG acceleration along the vehicle-fixed `x`-axis

Computed

gn
`ay`Vehicle CG acceleration along the vehicle-fixed `y`-axis`0`gn
`az`Vehicle CG acceleration along the vehicle-fixed `z`-axis`0`gn
`Forces``Body``Fx`Net force on vehicle CG along the vehicle-fixed `x`-axis

Computed

N
`Fy`Net force on vehicle CG along the vehicle-fixed `y`-axis`0`N
`Fz`Net force on vehicle CG along the vehicle-fixed `z`-axis`0`N
`Ext``Fx`External force on vehicle CG along the vehicle-fixed `x`-axis

Computed

N
`Fy`External force on vehicle CG along the vehicle-fixed `y`-axis`0`N
`Fz`External force on vehicle CG along the vehicle-fixed `z`-axis`0`N
`Drag``Fx`Drag force on vehicle CG along the vehicle-fixed `x`-axis

Computed

N
`Fy`Drag force on vehicle CG along the vehicle-fixed `y`-axis`0`N
`Fz`Drag force on vehicle CG along the vehicle-fixed `z`-axis`0`N
`Grvty``Fx`Gravity force on vehicle CG along the vehicle-fixed `x`-axis

Computed

N
`Fy`Gravity force on vehicle CG along the vehicle-fixed `y`-axis`0`N
`Fz`Gravity force on vehicle CG along the vehicle-fixed `z`-axis

Computed

N
`Pwr``PwrExt`Applied external power

Computed

W
`Drag`Power loss due to drag

Computed

W
`PwrInfo``PwrTrnsfrd`

`PwrFxExt`

Externally applied force power

PFxExt

W
`PwrNotTrnsfrd``PwrFxDrag`

Drag force power

PD

W
`PwrStored``wrStoredGrvty`Rate change in gravitational potential energy

Pg

W
`PwrStoredxdot`

Rate in change of longitudinal kinetic energy

Pxdot

W

Vehicle total longitudinal velocity, $\stackrel{˙}{x}$, in m/s.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Power` or `Force`.

Tractive input force, Ftotal, in N.

#### Dependencies

To enable this port, for the Input Mode parameter, select `Kinematic`.

## Parameters

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Specify the input type.

• `Kinematic` — Block uses the vehicle longitudinal velocity and acceleration to calculate the tractive force and power. Use this configuration for powertrain, driveline, and braking system design, or component sizing.

• `Force` — Block uses the tractive force to calculate the vehicle longitudinal displacement and velocity. Use this configuration for system-level performance, fuel economy, or drive cycle tracking studies.

• `Power` — Block uses the engine or transmission power to calculate the vehicle longitudinal displacement and velocity. Use this configuration for system-level performance, fuel economy, or drive cycle tracking studies.

#### Dependencies

This table summarizes the port and input mode configurations.

Input ModeCreates Ports
`Kinematic`

`xdot`

`xddot`

`Force`

`Force`

`Power`

`Power`

Vehicle body mass, m, in kg.

Steady-state rolling resistance coefficient, a, in N.

Viscous driveline and rolling resistance coefficient, b, in N*s/m.

Aerodynamic drag coefficient, c, in N·s^2/m.

Gravitational acceleration, g, in m/s^2.

Vehicle longitudinal initial position, in m.

Vehicle longitudinal initial velocity with respect to ground, in m/s.

## References

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

[2] Light Duty Vehicle Performance And Economy Measure Committee. Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. Standard J1263_201003. SAE International, March 2010.