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

wrStoredGrvtyRate 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
InertFrmCgDispXVehicle CG displacement along earth-fixed X-axis

Computed

m
YVehicle CG displacement along earth-fixed Y-axis0

m

ZVehicle CG displacement along earth-fixed Z-axis

Computed

m
VelXdotVehicle CG velocity along earth-fixed X-axis

Computed

m/s

YdotVehicle CG velocity along earth-fixed Y-axis0m/s
ZdotVehicle CG velocity along earth-fixed Z-axis

Computed

m/s
thetaRotation of vehicle-fixed frame about the earth-fixed Y-axis (pitch)

Computed

BdyFrmCgDispxVehicle CG displacement along the vehicle-fixed x-axis

Computed

m
yVehicle CG displacement along the vehicle-fixed y-axis0m
zVehicle CG displacement along the vehicle-fixed z-axis0m
VelxdotVehicle CG velocity along the vehicle-fixed x-axis

Computed

m/s
ydotVehicle CG velocity along the vehicle-fixed y-axis0m/s
zdotVehicle CG velocity along the vehicle-fixed z-axis0m/s
AccaxVehicle CG acceleration along the vehicle-fixed x-axis

Computed

gn
ayVehicle CG acceleration along the vehicle-fixed y-axis0gn
azVehicle CG acceleration along the vehicle-fixed z-axis0gn
ForcesBodyFxNet force on vehicle CG along the vehicle-fixed x-axis

Computed

N
FyNet force on vehicle CG along the vehicle-fixed y-axis0N
FzNet force on vehicle CG along the vehicle-fixed z-axis0N
ExtFxExternal force on vehicle CG along the vehicle-fixed x-axis

Computed

N
FyExternal force on vehicle CG along the vehicle-fixed y-axis0N
FzExternal force on vehicle CG along the vehicle-fixed z-axis0N
DragFxDrag force on vehicle CG along the vehicle-fixed x-axis

Computed

N
FyDrag force on vehicle CG along the vehicle-fixed y-axis0N
FzDrag force on vehicle CG along the vehicle-fixed z-axis0N
GrvtyFxGravity force on vehicle CG along the vehicle-fixed x-axis

Computed

N
FyGravity force on vehicle CG along the vehicle-fixed y-axis0N
FzGravity force on vehicle CG along the vehicle-fixed z-axis

Computed

N
PwrPwrExtApplied external power

Computed

W
DragPower loss due to drag

Computed

W
PwrInfoPwrTrnsfrd

PwrFxExt

Externally applied force power

PFxExt

W
PwrNotTrnsfrdPwrFxDrag

Drag force power

PD

W
PwrStoredwrStoredGrvtyRate 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

expand all

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.