Copyright © 2012 Mahindra & Mahindra Ltd. All rights reserved.

Energy Requirement Calculator for Passenger Vehicles Using Parameter Based Vehicle Model

Developed in MATLAB

Lakshmi Nair

Mahindra Research Valley

Mahindra and Mahindra Ltdlakshmi.nair@mahindra.com

Copyright © 2012 Mahindra & Mahindra Ltd. All rights reserved.

Introduction

Vehicle Energy Calculations

Approach to Problem Statement

MATLAB Application Interface

Results and Representative Plots

Use of MATLAB Tools

Conclusions

Contents

Introduction

03

Vehicle mass Inertias

AerodynamicsRolling resistance

Drive cycles

Aerodynamic DragRolling Resistance

Inertial Force

Total energy consumption

Vehicle Design Parameters

Forces acting during Drive cycle

Automotive Product

Development

Inputs to the application

Outputs from the application

05

Vehicle Energy Calculations

where, Ftot = total (resultant) forceFRR = force due to tire rolling resistanceFAD = force due to aerodynamic dragFI = force necessary to overcome inertia (acceleration, deceleration, and traversing a grade)

Tire rolling resistance

where, m = vehicle mass (kg) g = 9.81 m/s2 (gravitational constant) CRR = coefficient of rolling resistance (dimensionless)

Source: http://www.virtual-car.org/wheels/hybrid_road_load_model.htmlhttps://www.carswithcords.net/2015/01/rolling-resistance.html

Total Tractive Force and its components

𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐹𝐹𝑅𝑅𝑅𝑅 + 𝐹𝐹𝐴𝐴𝐴𝐴 + 𝐹𝐹𝐼𝐼

𝐹𝐹𝑅𝑅𝑅𝑅 = 𝑚𝑚𝑚𝑚𝐶𝐶𝑟𝑟𝑟𝑟

06

Aerodynamic Drag

where, rho = density of air (kg/m3)CD = drag coefficient (dimensionless)AF = projected frontal area (m2)v = average velocity during a time increment of the driving cycle (m/s)

Inertia Force

where, m = vehicle mass (kg)dv/dt = acceleration (or deceleration) rateg = 9.81 m/s2 (gravitational constant)

= grade of the road

Vehicle Energy Calculations

Source: http://www.virtual-car.org/wheels/hybrid_road_load_model.htmlhttps://gr8autotech.wordpress.com/2013/06/16/vehicular-aerodynamics/

Total Tractive Force and its components

Aero Drag

𝐹𝐹𝐼𝐼 = 𝑚𝑚 �d𝑣𝑣d𝑡𝑡 + 𝑚𝑚𝑚𝑚 sin𝛼𝛼

𝛼𝛼

𝐹𝐹𝐴𝐴𝐴𝐴 =12𝜌𝜌𝐶𝐶𝑑𝑑𝐴𝐴𝑓𝑓𝑣𝑣2

07

Source: http://www.virtual-car.org/wheels/hybrid_road_load_model.html

Tractive Power

where, v = average velocity during a time increment of the driving cycle (m/s)

Vehicle Energy Calculations

𝑃𝑃 = 𝐹𝐹𝑅𝑅𝑅𝑅 + 𝐹𝐹𝐴𝐴𝐴𝐴 + 𝐹𝐹𝐼𝐼 𝑣𝑣

08

Approach to Problem StatementComputation Procedure

Acceleration Mode

Cruising

Braking

09

Identification of driving modes

Approach to Problem Statement

Total Tractive Force

Positive Inertia Force

Positive Positive Acceleration

Zero Cruising

Negative Powered Deceleration

Zero Coast Down

Negative Braking

11

MATLAB Application Interface

14 standard drive cycles stored as .mat files

Option to input custom drive cycle

Input Tab

12

ResultsEnergy Analysis Time Split

47%

37%

16%

Energy Consumption in %

Energy Consumed inAerodynamic Drag

Energy Consumed in RollingResistance

Energy Consumed inOvercoming Inertia

44%

1%16%

26%

13%

Time Split

Acceleration

Idle

Cruising

PoweredDecelerationBraking

13

Representative Plots- Total Power

14

Representative Plots- Inertia Power

15

Representative Plots- Aerodynamic Drag

16

Representative Plots- Rolling Resistance

17

Representative Plots- Brake Power

18

Use of MATLAB ToolsApplication was created with the help of App Designer

interface in MATLAB

Executable (.exe) file for the application created with

MATLAB Application Compiler

This application has been deployed in our Mahindra

server based centralized application platform, MathApps

19

Quick and easy to use calculator , beneficial to design and

platform engineers

The designers can evaluate multiple design iterations

The results can be further used for feasibility analysis

Plots can help to visualize the performance of the vehicle

and can aid the designer in his decision-making process

Conclusions

19

Questions?