DESIGN & ANALYSIS OF A TENSIONER FOR A BELT-DRIVEN

DESIGN & ANALYSIS OF A TENSIONER FOR A

BELT-DRIVEN INTEGRATED STARTER-

GENERATOR SYSTEM

OF MICRO-HYBRID VEHICLES

by

Adebukola O. Olatunde

A Thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

Copyright by Adebukola O. Olatunde 2008

ii

ABSTRACT

DESIGN AND ANALYSIS OF A TENSIONER FOR A BELT-DRIVEN INTEGRATED

STARTER-GENERATOR SYSTEM OF MICRO-HYBRID VEHICLES

Adebukola O. Olatunde

Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto 2008

The thesis presents the design and analysis of a Twin Tensioner for a Belt-driven Integrated

Starter-generator (B-ISG) system. The B-ISG is an emerging hybrid transmission closely

resembling conventional serpentine belt drives. Models of the B-ISG systems geometric

properties and dynamic and static states are derived and simulated. The objective is to reduce

the magnitudes of static tension in the belt for the ISG-driving phase. A literature review of

hybrid systems, serpentine belt drive modeling and automotive tensioners is included. A

parametric study evaluates tensioner parameters with respect to their impact on static tensions.

Design variables are selected from these for an optimization study. The optimization uses a

genetic algorithm (GA) and a hybrid GA. Results of the optimization indicate the optimal

system contains spans with static tensions that are significantly lower in magnitude than that of

the original design. Implications of the research on future work are discussed in closing.

iii

A testament unto the LORD God who answered me in the day of my distress, and was with me in

the way which I went.

To my parents, Joseph and Beatrice, for your strength and persistent prayers.

To my siblings, Shade, Charlene and Kevin, for being a listener, an editor and a relief when I

needed it.

To my friends, Samantha, Esther and Yasmin, who kept me motivated.

&

With love to my sweetheart Nana whose patience, support and companionship has made life

sweeter.

iv

ACKNOLOWEDGEMENTS

I would like to express deep gratitude to Dr. Jean Zu for her guidance throughout the duration of

my studies and for providing me with the opportunity to conduct this thesis.

I wish to thank the individuals of Litens Automotive who have provided guidance and data for

the research work. Special thanks to Mike Clark, Seeva Karuendiran and Dr. Qiu for their time

and help.

I thank my committee members Dr. Naguib and Dr. Sun for contributing their time to my

research work.

My sincerest thanks, to my research colleague David for his knowledge and support. Many

thanks to my lab mates Qiming, Hansong, Ali, Ming, Andrew and Peyman for their guidance.

I want to especially thank Dr. Cleghorn, Leslie Sinclair, and Dr. Zu for the opportunities to

teach! These experiences have served to enrich my graduate studies. As well, thank you to Dr.

Cleghorn for guidance in my research work.

I am also in debt to my classmates and teaching colleagues throughout my time at the University

of Toronto, especially Aaron and Mohammed, for their support in my development as a graduate

researcher and teacher.

v

CONTENTS

ABSTRACT .......................................................................................................................................... ii

DEDICATION ..................................................................................................................................... iii

ACKNOWLEDGEMENTS ................................................................................................................. iv

CONTENTS .......................................................................................................................................... v

LIST OF TABLES ............................................................................................................................... ix

LIST OF FIGURES ............................................................................................................................. xi

LIST OF SYMBOLS .......................................................................................................................... xvi

Chapter 1: INTRODUCTION .............................................................................................................. 1

1.1 Background .................................................................................................................................. 1

1.2 Motivation .................................................................................................................................... 3

1.3 Thesis Objectives and Scope of Research ...................................................................................... 4

1.4 Organization and Content of Thesis .............................................................................................. 5

Chapter 2: LITERATURE REVIEW................................................................................................... 7

2.1 Introduction .................................................................................................................................. 7

2.2 B-ISG System ............................................................................................................................... 8

2.2.1 ISG in Hybrids ................................................................................................................... 8

2.2.1.1 Full Hybrids ........................................................................................................... 9

2.2.1.2 Power Hybrids...................................................................................................... 10

2.2.1.3 Mild Hybrids ........................................................................................................ 11

2.2.1.4 Micro Hybrids ...................................................................................................... 11

2.2.2 B-ISG: Structure, Location and Function .......................................................................... 13

2.2.2.1 Structure and Location.......................................................................................... 13

2.2.2.2 Functionalities ...................................................................................................... 14

2.3 Belt Drive Modeling ................................................................................................................... 15

2.4 Tensioners for B-ISG System...................................................................................................... 18

2.4.1 Tensioners: Structures, Function and Location .................................................................. 18

2.4.2 Systematic Review of Tensioner Designs for a B-ISG System ........................................... 20

2.5 Summary .................................................................................................................................... 24

vi

Chapter 3: MODELING OF B-ISG SYSTEM ................................................................................... 25

3.1 Overview .................................................................................................................................... 25

3.2 B-ISG Tensioner Design ............................................................................................................. 25

3.3 Geometric Model of a B-ISG System with a Twin Tensioner ...................................................... 27

3.4 Equations of Motion for a B-ISG System with a Twin Tensioner ................................................ 32

3.4.1 Dynamic Model of the B-ISG System ............................................................................... 32

3.4.1.1 Derivation of Equations of Motion........................................................................ 32

3.4.1.2 Modeling of Phase Change ................................................................................... 41

3.4.1.3 Natural Frequencies, Mode Shapes and Dynamic Responses ................................. 42

3.4.1.4 Crankshaft Pulley: Driving Torque, Acceleration and Displacement ..................... 44

3.4.1.5 ISG Pulley: Driving Torque, Acceleration and Displacement ................................ 46

3.4.1.6 Tensioner Arms: Dynamic Torques ...................................................................... 48

3.4.1.7 Dynamic Belt Span Tensions ................................................................................ 49

3.4.2 Static Model of the B-ISG System .................................................................................... 49

3.5 Simulations ................................................................................................................................. 50

3.5.1 Geometric Analysis .......................................................................................................... 51

3.5.2 Dynamic Analysis............................................................................................................. 52

3.5.2.1 Natural Frequency and Mode Shape ..................................................................... 54

3.5.2.2 Dynamic Response ............................................................................................... 58

3.5.2.3 ISG Pulley and Crankshaft Pulley Torque Requirement ........................................ 61

3.5.2.4 Tensioner Arm Torque Requirement ..................................................................... 62

3.5.2.5 Dynamic Belt Span Tension ................................................................................. 63

3.5.3 Static Analysis .................................................................................................................. 66

3.6 Summary .................................................................................................................................... 69

Chapter 4: PARAMETRIC ANALYSIS OF A B-ISG TWIN TENSIONER .................................... 71

4.1 Introduction ................................................................................................................................ 71

4.2 Methodology .............................................................................................................................. 71

4.3 Results and Discussion ............................................................................................................... 74

4.3.1 Influence of Tensioner Arm Stiffness on Static Tension .................................................... 74

4.3.2 Influence of Tensioner Pulley Diameter on Static Tension ................................................ 78

4.3.3 Influence of Tensioner Pulley 1 Coordinates on Static Tension ......................................... 80

4.3.4 Influence of Tensioner Pulley 2 Coordinates on Static Tension ......................................... 86

vii

4.4 Conclusion ................................................................................................................................. 92

Chapter 5: OPTIMIZATION OF A B-ISG TWIN TENSIONER ..................................................... 95

5.1 Optimization Problem ................................................................................................................. 95

5.1.1 Selection of Design Variables ........................................................................................... 95

5.1.2 Objective Function & Constraints ..................................................................................... 97

5.2 Optimization Method .................................................................................................................100

5.2.1 Genetic Algorithm ...........................................................................................................100

5.2.2 Hybrid Optimization Algorithm .......................................................................................101

5.3 Results and Discussion ..............................................................................................................101

5.3.1 Parameter Settings & Stopping Criteria for Simulations ...................................................101

5.3.2 Optimization Simulations ................................................................................................102

5.3.3 Discussion .......................................................................................................................106

5.4 Conclusion ................................................................................................................................109

Chapter 6: CONCLUSION AND RECOMMENDATIONS.............................................................111

6.1 Summary ...................................................................................................................................111

6.2 Conclusion ................................................................................................................................112

6.3 Recommendations for Future Work ...........................................................................................113

REFERENCES ...................................................................................................................................116

APPENDICIES ..................................................................................................................................123

A Passive Dual Tensioner Designs from Patent Literature ................................................................123

B B-ISG Serpentine Belt Drive with Single Tensioner: Equation of Motion .....................................138

C MathCAD Scripts ........................................................................................................................145

C.1 Geometric Analysis .............................................................................................................145

C.2 Dynamic Analysis ...............................................................................................................152

C.3 Static Analysis ....................................................................................................................161

D MATLAB Functions & Scripts ....................................................................................................162

D.1 Parametric Analysis ............................................................................................................162

D.1.1 TwinMain.m .............................................................................................................162

D.1.2 TwinTenStaticTension.m ..........................................................................................168

D.2 Optimization .......................................................................................................................168

D.2.1 OptimizationTwin.m - Optimization Function ...........................................................168

viii

D.2.2 confunTwin.m ..........................................................................................................169

D.2.3 objfunTwin.m ...........................................................................................................170

VITA ...................................................................................................................................................171

ix

LIST OF TABLES

2.1 Passive Dual Tensioner Designs from Patent Literature

3.1 Selected Contact Point Types on the ith Pulley and Types for the ith Belt Span

3.2 Coordinate Points for Pulley Centres and Twin Tensioner Pivot

3.3 Geometric Results of B-ISG System with Twin Tensioner

3.4 Data for Input Parameters used in Dynamic and Static Computations

3.5 Static Solution for Belt Span Tensions in Crankshaft and ISG Driving Cases for a B-ISG

Serpentine Belt Drive with a Single Tensioner

3.6 Static Solution for Belt Span Tensions in Crankshaft and ISG Driving Cases for a B-ISG

Serpentine Belt Drive with a Twin Tensioner

4.1 Initial Values, Increments and Ranges for Parameters of Twin Tensioner

5.1 Summary of Parametric Analysis Data for Twin Tensioner Properties

5.2a GA Optimization Results for Twin Tensioner Parameters and Objective Function

5.2b Computations for Tensions and Angles from GA Optimization Results

5.3a Hybrid Optimization Results for Twin Tensioner Parameters and Objective Function

5.3b Computations for Tensions and Angles from Hybrid Optimization Results

5.4a Non-Weighted Optimization Results for Twin Tensioner Parameters and Objective

Function

5.4b Computations for Tensions and Angles from Non-Weighted Optimizations

x

5.5 Weighted Optimization Results for Static Tensions for Optimal B-ISG System with a

Twin Tensioner

5.6 Non-Weighted Optimization Results for Static Tensions for Optimal B-ISG System with a

Twin Tensioner

xi

LIST OF FIGURES

2.1 Hybrid Functions

3.1 Schematic of the Twin Tensioner

3.2 B-ISG Serpentine Belt Drive with Twin Tensioner

3.3 Angles, Coordinates and Possible Belt Contact Points for the ith and i+1th Pulleys

3.4 Twin Tensioner: Free Body Diagram of a Four-Degree of Freedom System

3.5 Free Body Diagram for Non-Tensioner Pulleys

3.6a ISG Driving Case: Natural Frequency of System and Mode Shapes for Responsive Rigid

Bodies

3.6b ISG Driving Case: First Mode Responses

3.6c ISG Driving Case: Second Mode Responses

3.7a Crankshaft Driving Case: Natural Frequency of System and Mode Shapes for Responsive

Rigid Bodies

3.7b Crankshaft Driving Case: First Mode Responses

3.7c Crankshaft Driving Case: Second Mode Responses

3.8 Crankshaft Pulley Dynamic Response (for crankshaft driven case)

3.9 ISG Pulley Dynamic Response (for ISG driven case)

3.10 Air Conditioner Pulley Dynamic Response

3.11 Tensioner Pulley 1 Dynamic Response

xii

3.12 Tensioner Pulley 2 Dynamic Response

3.13 Tensioner Arm 1 Dynamic Response

3.14 Tensioner Arm 2 Dynamic Response

3.15 Required Driving Torque for the ISG Pulley

3.16 Required Driving Torque for the Crankshaft Pulley

3.17 Dynamic Torque for Tensioner Arm 1

3.18 Dynamic Torque for Tensioner Arm 2

3.19 Span 1 (between crankshaft and air conditioner) Dynamic Belt Span Tension

3.20 Span 2 (between air conditioner and tensioner 1) Dynamic Belt Span Tension

3.21 Span 3 (between tensioner 1 and ISG) Dynamic Belt Span Tension

3.22 Span 4 (between ISG and tensioner 2) Dynamic Belt Span Tension

3.23 Span 5 (between tensioner 2 and crankshaft) Dynamic Belt Span Tension

3.24 B-ISG Serpentine Belt Drive with Single Tensioner

4.1a Regions 1 and 2, and their Associated Guidelines, for Coordinates of Tensioner Pulleys 1

& 2

4.1b Regions 1 and 2 in Cartesian Space

4.2 Parametric Analysis for Coupled Stiffness Arm Constant, kt (Nm/rad)

4.3 Parametric Analysis for Stiffness of Arm 1, kt1 (Nm/rad)

4.4 Parametric Analysis for Stiffness of Arm 2, kt2 (Nm/rad)

xiii

4.5 Parametric Analysis for Pulley 1 Diameter, D3 (m)

4.6 Parametric Analysis for Pulley 2 Diameter, D5 (m)

4.7 Parametric Analysis for Tensioner Pulley 1 Coordinates, [X3,Y3] and Tautest Span

Tension in Crankshaft Driving Case

4.8 Parametric Analysis for Tensioner Pulley 1 Coordinates, [X3,Y3] and Slackest Span



Tension in ISG Driving Case









4.14 Parametric Analysis for Tensioner Pulley 2 Coordinates, [X5,Y5], and Slackest Span


5.1 Static Stability of the B-ISG Twin Tensioner Based on the Angular Displacement of

Tensioner Arms 1 and 2

A.1 Proposed design by Bayerische Motoren Werke AG corresponding to patent nos.

EP1420192-A2 and DE10253450-A1.

A.2a First of four proposed designs (and its various configurations) by Bosch GMBH

corresponding to patent no. WO0026532-A1

A.2b Second of four proposed designs by Bosch GMBH corresponding to patent no.

WO0026532-A1

A.2c Third of four proposed designs (and its various configurations) by Bosch GMBH


A.2d Fourth of four proposed designs (and its various configurations) by Bosch GMBH


A.3 Proposed design by Daimler Chrysler AG corresponding to patent no. DE10324268-A1

A.4 Proposed design by Dayco Products LLC corresponding to patent no. US6942589-B2

xiv

A.5 Proposed design by Gates Corp. corresponding to patent no. WO2003038309-A

A.6 Proposed design by General Motors Corp. corresponding to patent no. US20060287146-

A1

A.7 Proposed design by INA Schaeffler KG corresponding to patent no. DE10044645-A1

A.8a First of three proposed designs by INA Schaeffler KG corresponding to patent no.

DE10159073-A1

A.8b Second of three proposed designs by INA Schaeffler KG corresponding to patent no.

DE10159073-A1

A.8c Third of three proposed designs by INA Schaeffler KG corresponding to patent no.

DE10159073-A1

A.9 Proposed design by INA Schaeffler KG corresponding to patent no. DE10359641-A1

A.10 Proposed design by INA Schaeffler KG corresponding to patent no. EP1723350-A1

A.11 Proposed design by INA Schaeffler KG corresponding to patent no. EP1738093-A1

A.12 Proposed design by INA Schaeffler KG corresponding to patent no. DE102004012395-

A1

A.13 Proposed design by INA Schaeffler KG corresponding to patent nos. DE102005017038-

A1and WO2006108461-A1

A.14 Proposed design by Litens Automotive GMBH et al. corresponding to patent no.

US20010007839-A1

A.15 Proposed design by Mitsubishi Jidosha Eng KK and Mitsubishi Motor Corp.

corresponding to patent no. JP2005083514-A

A.16 Proposed design by Nissan Motor Co. Ltd. corresponding to patent no. JP3565040-B2

A.17 Proposed design by NTN Corp. corresponding to patent no. JP2006189073-A

A.18 Proposed design by Valeo Equipment Electriques Moteur corresponding to patent nos.

EP1658432 and WO2005015007

B.1 Single Tensioner B-ISG System

B.2 Free-body Diagram of ith Pulley

xv

B.3 Free-body Diagram of Single Tensioner

C.1 Schematic of B-ISG System with Twin Tensioner

C.2 Possible Contact Points

xvi

LIST OF SYMBOLS

Latin Letters

A Belt cord cross-sectional area

C Damping matrix of the system

cb Belt damping

Belt damping constant of the ith belt span

Damping matrix element in the ith row and ith column

ct Damping acting between tensioner arms 1 and 2

cti Damping of the ith tensioner arm

DCS Diameter of crankshaft pulley

DISG Diameter of ISG pulley

ft Belt transition frequency

H(n) Phase change function

I Inertial matrix of the system

Inertial matrix under ISG driving phase

Inertial matrix under crankshaft driving phase

Ii Inertia of the ith pulley

Iti Inertia of the ith tensioner arm

Submatrix of inertial matrix I

j Imaginary coordinate (i.e. (-1)1/2

)

K Stiffness matrix of the system

xvii

Belt factor

Belt cord stiffness

Belt stiffness constant of the ith belt span

kt Spring stiffness acting between tensioner arms 1 and 2

kti Coil spring of the ith tensioner arm

Submatrix of stiffness matrix K

Lfi, Lbi Lengths of possible belt span connections from the ith pulley

Lti Length of the ith tensioner arm

Modeia Mode shape of the ith rigid body in the ISG driving phase

Modeic Mode shape of the ith rigid body in the crankshaft driving phase

n Engine speed

N Motor speed

nCS rpm of crankshaft pulley

NF Motor speed without load

nISG rpm of ISG pulley

Q Required torque matrix

qc Amplitude of the required crankshaft torque

Qcs/ISG Required torque of the driving pulley (crankshaft or ISG)

Qm Required torque matrix of driven rigid bodies

Qti Dynamic torque of the ith tensioner arm

Ri Radius of the ith pulley

T Matrix of belt span static tensions

xviii

T Dynamic belt tension matrix

Damping matrix due to the belt

Stiffness matrix due to the belt

Ti Tension of the ith belt span

To Initial belt tension for the system

Ts Stall torque

Tti Tension for the neighbouring belt spans of the ith tensioner pulley

(Xi,Yi) Coordinates of the ith pulley centre

XYfi, XYbi, XYfbi,

XYbfi Possible connection points on the ith pulley leading to the ith belt span

XYf2i, XYb2i,

XYfb2i, XYbf2i Possible connection points on the ith pulley leading to the (i-1)th belt span

Greek Letters

i Angle between the datum and the line connecting the ith and (i+1)th pulley

centres

ji Angle of orientation for the ith belt span

ti(t), ti(t),

ti(t)

Angular displacement, velocity and acceleration (rotational coordinate) of the

ith tensioner arm

General coordinate matrix under ISG driving phase

General coordinate matrix under crankshaft driving phase

fi, bi Angles between the datum and the belt connection spans with lengths Lfi and

Lbi respectively

i Amplitude of displacement of the ith pulley

xix

i(t), i(t), i(t) Angular position, velocity and acceleration (rotational coordinate) of the ith

pulley

ti Angle of the ith tensioner arm

toi Initial pivot angle of the ith tensioner arm

m Angular displacement matrix of driven rigid bodies

m Amplitude of displacement of driven rigid bodies

Belt cord density

Belt wrap angle on the ith pulley

max Belt maximum phase angle

0deg Belt phase angle at zero frequency

Frequency of the system

cs Angular frequency of crankshaft pulley

ISG Angular frequency of the ISG pulley

Natural frequency of system

1

CHAPTER 1: INTRODUCTION

1.1 Background

Belt drive systems are the means of power transmission in conventional automobiles. The

emergence of hybrid technologies, specifically the Belt-driven Integrated Starter-generator (B-

ISG), has placed higher demands on belt drives than ever before. The presence of an integrated

starter-generator (ISG) in a belt transmission places excessive strain on the belt, leading to

premature belt failure. This phenomenon has motivated automotive makers to design a tensioner

that is suitable for the B-ISG system.

The belt drive is also known interchangeably as the front-end accessory drive-belt (FEAD), the

belt accessory-drive system (BAS), or the belt transmission system. In a traditional setting, the

role of this system is to transmit torque generated by an internal combustion engine (ICE) in

order to reliably drive multiple peripheral devices mounted on the engine block. The high speed

torque is transmitted through a crankshaft pulley to a serpentine belt. The serpentine belt is a

single continuous member that winds around the driving and driven accessory pulleys of the

drive system. Serpentine belts used in automotive applications consist of several layers. The

load-bearing layer is a flexible member consisting of high stiffness fibers [1]. It is covered by a

protective layer to guard against mechanical damage, and is bound below by a visco-elastic layer

that provides the required shock absorption and grip against the rigid pulleys [1]. The accessory

devices may include an alternator, power steering pump, water pump and air conditioner

compressor among others.

Introduction 2

The B-ISG system is a transmission system characteristic to micro-hybrid automobiles. It is akin

to traditional belt drives, differing in the fact that an electric motor, called an integrated starter-

generator (ISG), replaces the original alternator, re-starts the engine from idle speed and provides

braking regeneration [2]. The re-start function of the micro-hybrid transmission is known as

stop-start. In the B-ISG setting the ISG is mounted on the belt drive. The ISG produces a speed

of approximately 2000 to 2500rpm in order to spin the engine at approximately 750rpm and

upwards to produce an instantaneous start in the start-stop process [3]. The high rotations per

minute (rpm) produced by the ISG consistently places much higher tension requirements on the

belt than when the crankshaft is driving the belt. It is preferable not to exceed a range of 600N to

800N of tension on the belt since this exceeds the safe operating conditions of belts used in most

traditional drive systems [4]. The traditional belt drive systems tensioner, a single-arm

tensioner, does not suitably reduce the high belt tension nor provide enough tension in the slack

belts spans occurring in the ISG phase of operation for the B-ISG system.

In order for the belt to transfer torque in a drive system its initial tension must be set to a value

that is sufficient to keep all spans rigid. This value must not be too low, as to allow any one span

to be slack during the drives phases of operation. Furthermore, the belt must not be installed

with too high a tension since this can lead to premature failure of the bearings supporting the

drive and driven pulleys and of the belt itself [5]. The presence of a tensioning mechanism in

an automotive belt drive allows for an enhanced belt life and performance, since pre-tensioning

of the belt is normally not sufficient for all phases of belt drive operation. A tensioner allows for

the system to cope with moderate to severe changes in belt span tensions.

Introduction 3

Traditional automotive tensioners, for belt drives of an ICE, consist of a single spring-loaded

arm. This type of tensioner is normally designed to provide a passive response to changes in belt

span tension. The introduction of the ISG electric motor into the traditional belt drive with a

single-arm tensioner, results in the presence of excessively slack spans and excessively tight

spans in the belt. The tension requirements in the ISG-driving phase, which differ from the

crankshaft-driving phase, are poorly met by a traditional single-arm passive tensioner.

Tensioners can be divided into two general classes: passive and active. In both classes, the

single-arm tensioner design approach is the norm. The passive class of tensioners, employ purely

mechanical power to achieve tensioning of the belt, while the active class, also known as

automatic tensioners, typically use some sort of electronic actuation. Automatic tensioners have

been employed by various automotive manufacturers, however such devices add mass,

complication and cost to each engine [5].

1.2 Motivation

The motivation for the research undertaken arises from the undesirable presence of high belt

tension in automotive belt drives. Manufacturers of automotive belt drives have presented

numerous approaches for tension mechanism designs. As mentioned in the preceding section,

the automation of the traditional single-arm tensioner has disadvantages for manufacturers. A

survey of the literature reveals that few quantitative investigations in comparison to the

qualitative investigations, provided through patent literature, have been conducted in the area of

passive and dual tensioner configurations. As such the author of the research project has selected

to investigate the performance of a passive twin-arm tensioner design. The theoretical tensioner

Introduction 4

configuration is motivated by research and developments of industry partner, Litens

Automotive a manufacturer of automotive belt drive systems and components. Litens

specialty in automotive tensioners has provided a basis for the research work conducted.

1.3 Thesis Objectives and Scope of Research

The objective of this project is to model and investigate a system containing a passive twin-arm

tensioner in a B-ISG serpentine belt drive, where the driving pulley alternates between a

crankshaft pulley and an ISG pulley. The modeling of a serpentine belt drive system is in

continuation of the work done by post-doctoral fellow Zhen Mu in development of the priority

software known as FEAD at the University of Toronto. Firstly, for the B-ISG system with a

twin-arm tensioner, the geometric state and its equations of motion (EOM) describing the

dynamic and static states are derived. The modeling approach was verified by deriving the

geometric properties and the EOM of the system with a single tensioner arm and comparing its

crankshaft-phases simulation results with FEAD software simulations. This also provides

comparison of the new twin-arm tensioner belt drive model with the former single-arm tensioner

equipped belt drive model. Secondly, the model for the static system is investigated through

analysis of the tensioner parameters. Thirdly, the design variables selected from the parametric

analysis are used for optimization of the new system with respect to its criteria for desired

performance.

Introduction 5

1.4 Organization and Content of the Thesis

This thesis presents the investigation of a passive twin-arm tensioner design in a B-ISG

serpentine belt drive system, which is distinguished by having its driving pulley alternate

between a crankshaft pulley and an ISG pulley.

Chapter 2 presents the literature reviewed relevant to the area of the thesis topic. The context of

the research discusses the function and location of the ISG in hybrid technologies in order to

provide a background for the B-ISG system. The attributes of the B-ISG are then discussed.

Subsequently, a description is given of the developments made in modeling belt drive systems.

At the close of the chapter the prior art in tensioner designs and investigations are discussed.

The third chapter describes the system models and theory for the B-ISG system with a twin-arm

tensioner. Models for the geometric properties and the static and dynamic cases are derived. The

simulation results of the system model are presented.

Then the fourth chapter contains the parametric analysis. The methodologies employed, results

and a discussion are provided. The design variables of the system to be considered in the

optimization are also discussed.

The optimization of a B-ISG system with a passive twin-arm tensioner is presented in Chapter 5.

The evaluation of optimization methods, results of optimization and discussion of the results are

included. Chapter 6 concludes the thesis work in summarizing the response to the thesis

Introduction 6

objectives and concluding the results of the investigation of the objectives. Recommendations for

future work in the design and analysis of a B-ISG tensioner design are also described.

7

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

This literature review justifies the study of the thesis research, the significance of the topic and

provides the overall framework for the project. The design of a tensioner for a Belt-driven

Integrated Starter-generator (B-ISG) system is a link in the chain of power transmission

developments in hybrid automobiles. This chapter will begin with the context of the B-ISG

followed by a review of the hybrid classifications and the critical role of the ISG for each type.

The function, location and structure of the B-ISG system are then discussed. Then a discussion

of the modeling of automotive belt transmissions is presented. A systematic review of the prior

art and current state of tensioning mechanisms for B-ISG systems amalgamates the literature and

research evidence relevant to the thesis topic, which is the design of a B-ISG tensioner.

The Belt-driven Integrated Starter-generator (B-ISG) system is a part of a hybrid class that is

distinguished from other hybrid classes by the structure, functions and location of its ISG. The

B-ISG unit is a hybrid technology applied to traditional automotive belt drives. The use of a B-

ISG system to achieve a start-stop function in the car engine is estimated to cut fuel consumption

in conventional automobiles by up to ten percent and thus reduce CO2 emissions [6].

Environmental and legislative standards for reducing CO2 emissions in vehicles, have called for

carmakers to produce less polluting and more efficient vehicle powertrain systems [7]. The

transition to cleaner cars makes room for the introduction of the ISG machine into conventional

automotive belt drives [8]. The reduction of CO2 emissions and the similarity of the B-ISG

Literature Review 8

transmission to that of conventional cars provide the motivation for the thesis research.

Consequently the micro-hybrid class of cars is especially discussed in the literature review since

it contains the B-ISG type of transmission system. The micro-hybrid class is one of several

hybrid classes.

A look at the performance of a belt-drive under the influence of an ISG is rooted in the

developments of hybrid technology. The distinction of the ISG function and its location in each

hybrid class is discussed in the following section.

2.2 B-ISG System

2.2.1 ISG in Hybrids

This section of the review discusses the standard classes of hybrid cars, which are full, power,

mild and micro- hybrids. Special attention is given to hybrid vehicle architectures involving

internal combustion engines (ICEs) as the main power source. This is done for the sake of

comparison between hybrid classes since the ICE is the standard power source for B-ISG micro-

hybrids which is the focus of the research. The term conventional car, vehicle or automobile

henceforth refers to a vehicle powered solely by a gas or diesel ICE.

A hybrid vehicle has a drive system that uses a combination of energy devices. This may include

an ICE, a battery and an electric motor, typically an ISG. Two systems exist in the classification

of hybrid vehicles. The older system of classification separates hybrids into two classes: series

hybrids and parallel hybrids. In the older system many modern hybrid vehicles have modes of

operation matching both categories, classifying them under either of the two classes [9]. The

Literature Review 9

new system of classification has four classes: full, power, mild and micro. Under these classes,

vehicles are more often under a sole category [9]. In both systems an ICE may act as the primary

source of power, otherwise it may be a fuel cell. The fuel used by the ICE may be gas (petrol),

diesel or an alternative fuel, such as ethanol, bio-diesel or natural gas.

2.2.1.1 Full Hybrids

In a full hybrid car, the ICE is used to power the integrated starter-generator (ISG), which stores

electrical energy in the batteries to be used to power an electric traction motor [8]. The electric

traction motor is akin to a second ISG as it generates power and provides torque output. It also

supplies an extra boost to the wheels during acceleration and drives up steep inclines. A full

hybrid vehicle is able to move by electrical power only. It can be driven by the ISG powering

the electric traction motor without the engine running. This silent acceleration, known as electric

launch, is normally employed when accelerating from standstill [9]. Full hybrids can generate

and consume energy at the same time. Full hybrid vehicles also use regenerative braking [8].

The ISG allows this by converting from an electric traction motor to a generator when braking or

decelerating. The kinetic energy from the cars motion is then turned into electricity and stored

in the batteries. For full hybrids to achieve this, they often use break-by-wire a form of

electronically controlled braking technology.

A high-voltage (i.e., 36- or 42-volt) ISG is employed in full hybrids to start the ICE. It spins the

engine more than 900 rpm, whereas conventional 12-volt starter motors spin the engine at

approximately 250 rpm [9]. Thus the full hybrid vehicle is able to have an instantaneous start. In

full hybrids the ISG is placed in the position of the flywheel and can have its motion decoupled

Literature Review 10

from the engine [9]. The ISG device also allows full hybrids to have engine start-stop, also called

an idle-stop ability. The idle-stop function refers to when the engine shuts down as soon as a

vehicle stops from its ICE driving mode, which saves on the fuel it normally burns while idling

[8]. The vehicle returns to the engine driving mode of operation by way of the ISGs start-up of

the crankshaft, which restarts the engine in less than 300 milliseconds [9]. In summary, at

standstill the tachometer of the engine drops to 0 rpm since the engine has ceased; the engine is

started only when needed, which is often several seconds after acceleration has begun. The

engine start-stop feature is achieved by way of an electronic control system that shuts off the ICE

when it is not needed to assist in driving the wheels or to produce electricity for recharging the

batteries. The start-stop feature by itself is estimated to produce a ten percent fuel gain in hybrids

over conventional vehicles, particularly in urban driving conditions [9]. Since the ICE is

required to provide only the average horsepower used by the vehicle, the engine is downsized in

comparison to a conventional automobile that obtains all its power from an ICE. Frequently in

full hybrids the ICE uses an alternative operating strategy such as the Atkinson Cycle, which has

a higher efficiency while having a lower power output. Examples of full hybrids include the

Ford Escape and the Toyota Prius [9].

2.2.1.2 Power Hybrids

Akin to the full hybrid, the ISG of the power hybrid enables the same features: electric launch,

regenerative braking and engine idle-stop. The distinguishing characteristic from full hybrids is

the ICE is not downsized to meet only the average power demand [9]. Thus the engine of a

power hybrid is large and produces a high amount of horsepower compared to the former.

Overall a power hybrid has the assist of a full size ICE and therefore has more torque and a


greater acceleration performance than a full hybrid or a conventional vehicle with the same size

ICE [9]. The Lexus RX400h unit is an example of a power hybrid [9].

2.2.1.3 Mild Hybrids

In the hybrid types discussed thus far, the ISG is positioned between the engine and transmission

to provide traction for the wheels and for regenerative braking. Often times the armature or rotor

of the electric motor-generator, which is the ISG, replaces the engine flywheel in full and power

hybrids [9]. In the case of the mild hybrid the ISG is not decoupled from the ICE and hence it is

not able to drive the wheels apart from the engine. It remains that the ISG shares the same shaft

with the ICE. In this environment the electric launch feature does not exist since the ISG does

not turn the wheels independently of the engine; and energy cannot be generated and consumed

at the same time. However the ISG of the mild hybrid allows for the remaining features of the

full hybrid: regenerative braking and engine idle-stop; including the fact that the engine is

downsized to meet only the average demand for horsepower. Mild hybrid vehicles include the

GMC Sierra pickup and 2003 to 2005 Honda Civic models [9].

2.2.1.4 Micro Hybrids

Micro hybrid is the category of hybrids that can contain a B-ISG transmission and is also closest

to modern conventional vehicles. This class normally features a gas or diesel ICE [9]. The

conventional automobile is modified by installing an ISG unit on the mechanical drive in place

of, or in addition to, the starter motor. The starter motor, typically 12-volts, is removed only in

the case that the ISG device passes cold start testing, which is also dependent on the engine size

[10]. Various mechanical drives that may be employed include: chain, gear or belt drives, or a


clutch/gear arrangement. The majority of literature pertaining to mechanical driven ISG

applications does not pursue clutch/gear arrangements since it is associated with greater costs

and increased speed issues. Findings by Henry et al. [11] show that the belt drive, in

comparison to chain and gear drives, has a decreased cost (especially if the ISG is mounted

directly to the accessory drive), has no need for lubrication, has less restriction in the packaging

environment and produces very low noise. Also, mounting the ISG unit on a separate belt from

that linking the accessory pulleys is undesirable since applying the ISG directly to the accessory

belt drive requires less engine, transmission or vehicle modifications.

As with full, power and mild hybrids the presence of the ISG allows for the start-stop feature.

The automobiles electronic control unit (ECU) is calibrated, or engine control circuitry (a

separate ECU) is added to the conventional car in order to shut down the engine when the

vehicle is stopped [12]. The control system also controls the charge cycle of the ISG [9]. This

entails that it dictates the field current by way of a microprocessor to allow the system to defer

battery charge cycles until the vehicle is decelerating [13]. This produces electricity to recharge

the battery primarily during deceleration and braking. The B-ISG transmission of a micro hybrid

and its various components are discussed in the subsequent section. Examples of micro hybrid

vehicles are the PSA Groups Citroen C2 and C3 [14], Fords Fiesta [14] and BMWs Mini

Cooper D and various others of BMWs European models [15].


Figure 2.1. Hybrid Functions

Source: Dr. Daniel Kok, FFA, July 2004, modified [16].

Figure 2.1 shows that the higher the voltage available to the ISG unit, the more hybrid functions

it is capable of performing. It is noted that B-ISG transmissions, of the micro-hybrid class, may

also exceed the typical functions of micro-hybrids. For instance Fords HyTrans van (developed

in partnership with Ricardo UK Ltd., Valeo SA, Gates Corporation and the UK Department for

Transport) uses a B-ISG system and a 42-volt battery. The van is diesel-powered and has

characteristics of a mild hybrid such as cold cranks and engine assists [17].

2.2.2 B-ISG: Structure, Location and Function

2.2.2.1 Structure and Location

The ISG is composed of an electrical machine, normally of the inductive type, which includes a

stator (stationary part of the ISG) and a rotor (non-stationary part of the ISG); and a converter,

comprising of a regulator, a modulator, switches and filters. There are various configurations to

integrate the ISG unit into an automobile power train. One configuration situates the ISG

directly on the crankshaft in the place of the present flywheel [11]. This set-up is more compact

however it results in a longer power train, which becomes a potential concern for transverse-


mounted engines [18]. An alternative set-up is to have a side-mounted ISG. This term is used to

describe the configuration of mounting the electrical device on the side of the mechanical drive

[18]. As mentioned in Section 2.2.1.4, a belt drive is used as the mechanical drive for the thesis

research, hence the ISG is belt-mounted, and the transmission becomes a belt-driven ISG system.

In this arrangement, the ISG replaces the alternator [13], and in some cases the starter motor may

be removed. This design allows for the functions of the ISG system mentioned in the description

of the ISG role in micro-hybrids [9]. The side-mounted ISG, specifically the belt-mounted ISG,

is more evolutionary to the conventional car since it allows for a more traditional under-hood

layout [11].

2.2.2.2 Functionalities

The primary duty of the ISG in a micro hybrid, specifically in a B-ISG setting, is to bring the

engine from rest to normal operating speeds within a time span ranging from 250 to 400 ms [3],

and in some high voltage settings to provide cold starting.

The cold starting operation of the ISG refers to starting the engine from its off mode rather than

idle mode, and/or when the engine is at a low temperature, for example -29 to -50 degrees

Celsius [2]. If the ISG is used for cold starting, the peak torque is determined by the torque

requirement for the cold starting operation of the target vehicle since it is greater than the

nominal torque. For this function, the machine has to provide a breakaway torque about 1.5 [to]

1.8 times the nominal cranking torque to overcome static torque and rotate the engine from 0 to

[between] 10 [and] 20rpm [2]. This remains to be a challenge for the ISG, as the 12-volt

architecture most commonly found in vehicles does not supply sufficient voltage [2]. The

introduction of the ISG machine and other electrical units in vehicles encourages a transition


from a 12-volt, or 14-volt, to a 42-volt electrical architecture [19]. The transition to 42-volt

architecture brings potential higher-voltage functionalities that come with an ISG system [20].

At present when the [ISG] machine cannot provide enough torque for initial cold engine

cranking, the conventional starter will [remain] in the system and perform only for the initial

cranking while the stop-start function is taken over by the [ISG] machine [2]. The ISGs launch

assist torque, the torque required to bring the engine from idle speed to the speed at which it can

develop a higher torque output, is 2000 to 2500 rpm for most gas engines [3].

Delphis Energen 5 High Output 12-volt Belt-alternator-starter (or B-ISG) was implemented by

researchers on a 5.3 L, V-8 engine with an automatic transmission in a Chevrolet Silverado truck

[21]. The ISG was applied in a belt-mounted configuration and was used only for warm engine

re-starts. The results of Wezenbeek et al. [21] showed that the starting torque for a re-start by the

12-Volt ISG was 42 Nm. ISGs have also been used in 14V, 36V and 42V architectures [13].

2.3 Belt Drive Modeling

The modeling of a serpentine belt drive and tensioning mechanism has typically involved the

application of Newtonian equilibrium equations to rigid bodies in order to derive the equations of

motion for the system. There are two modes of motion in a serpentine belt drive: transverse

motion and rotational motion. The former can be viewed as the motion of the belt directed

normal to the direction of the belt/pulley contact plane, similar to the vibratory motion of a taut

string that is fixed at either end. However the study of the rotational motion in a belt drive is the

focus of the thesis research.


Much work on the mechanics of the belt drive was carried out by Firbank [22]. Firbanks

models helped to understand belt performance and the influence of driving and driven pulleys on

the tension member. The first description of a serpentine belt drive for automotive use was in

1979 by Cassidy et al. [23], and since this time there has been an increasing body of knowledge

on the mathematical modeling of serpentine belt drives. Ulsoy et al. [24] presented a design

methodology to improve the dynamic performance of instability mechanisms for belt tensioner

systems. The mathematical model developed by Ulsoy et al. [24] coupled the equations of

motion that were obtained through: a dynamic equilibrium of moments about a pivot point, the

equations of motion for the transverse vibration of the belt, and the equations of motion for the

belt tension variations appearing in the transverse vibrations. This, along with the boundary and

initial conditions, were used to describe the vibration and stability of the coupled belt-tensioner

system. Their system also considered the geometry of the belt drive and tensioner motion.

Hereafter, Beikmann et al. [25] predicted the belt drive vibration for a system composed of a

driving pulley, driven pulley and a dynamic tensioner. The authors coupled the linear equations

of transverse motion for the respective belt spans, with the equations of motion for pulleys and a

tensioner. This was used to form the free response of the system and evaluate its response

through a closed-form solution of the systems natural frequencies and mode shapes.

A complex modal analysis of a serpentine belt drive system was carried out by Kraver et al. [26]

to determine the effect of damping on rotational vibration mode solutions. The equations of

motion developed for a multi-pulley flat belt system with viscous damping, and elastic


properties, including the presence of a rotary tensioner, were manipulated to carry out the modal

analysis.

Beikmann et al. [27] also derived a nonlinear model to predict the operating state of a belt-

tensioner system by way of nonlinear numerical methods and an approximated linear closed-

form method. The authors used this strategy to develop a single design parameter, referred to as

a tensioner constant, to measure the effectiveness of the tensioning mechanism in relation to its

operating state from a reference state. The authors considered the steady state tensions in belt

spans as a result of accessory loads, belt drive geometry and tensioner properties.

Zhang and Zu [28] conducted a modal analysis for the response of a linear serpentine belt drive

system. A non-iterative approach was used to explicitly form the equations for the systems

natural frequencies. An exact closed-form expression for the dynamic response of the system,

using eigenfunction expansion, was derived with the system under steady-state conditions and

subject to harmonic excitation.

The work conducted by Balaji and Mockensturm [29] considered a front-end accessory drive

(FEAD) with a decoupler or isolator attached to a pulley. The rotational response for the FEAD

was found analytically by considering the system to be piecewise linear about the equilibrium

angular deflections. The effect of their nonlinear terms was considered through numerical

integration of the derived equations of motion by way of the iterative method fourth order

Runge-Kutta. The authors in this case considered the longitudinal (i.e. rotational) vibration of

the belt spans only.


The first to carry out the analysis of a serpentine belt drive system containing a two-pulley

tensioner was Nouri in 2005 [30]. Nouri found the closed-form analytical solution of a

serpentine belt drive with a two-pulley tensioner for the case of sinusoidal excitation. He

employed Runge Kutta method as well, to solve the equations of motion, to find the response of

the system under a general input from the crankshaft. The authors work also included the

optimization of the tensioner design in order to minimize belt span vibrations due to crankshaft

excitation. Furthermore the author applied active control techniques to the tensioner in a belt

drive system.

The works discussed have made significant contributions to the research and development into

tensioner systems for serpentine belt drives. These lead into the requirements for the structure,

function and location of tensioner systems particularly for B-ISG transmissions.

2.4 Tensioners for B-ISG System

2.4.1 Tensioners: Structure, Function and Location

Literature shows that the improvement of a serpentine belt life in a B-ISG system centers on the

tensioning mechanism redesign. This mechanism as shown by researchers, including

Wezenbeek et al. [21] and Henry et al. [11], is crucial in establishing the least tension in the belt

(above a zero value) in order to guard against failure by way of slip due to slack spans in the belt

and oscillations during engine re-start. It is noted by Firbank [22] that the mechanics of a belt-

drive is based on the idea that belt behaviour is governed by the elastic extension or contraction

of the belt arising from tension variations [22], these variations may be compensated for by an

adjustable tensioner.


The two types of tensioners are passive and active tensioners. The former permits an applied

initial tension and then acts as an idler, and normally employs mechanical power and can include

passive hydraulic actuation. This type is cheaper than the latter and easier to package. The latter

type is capable of continually adjusting the belt tension since it permits a lower static tension.

Active tensioners typically employ electric or magnetic-electric actuation and/or a combination

of active and passive actuators, such as electrical actuation of a hydraulic force.

Conventional belt tensioners comprise of a single tensioner arm that is fitted with a sole idler

pulley to engage a serpentine belt [31]. A radial bearing is used to rotatably connect the idler

pulley to the tensioner arm [31]. The tensioner arm is mounted on a pivot pin that is wrapped by

a bushing, and is free to rotate [31]. The pin covered by the bushing is fixed to the engine

housing [31]. A rotary spring is wrapped about the bearing pin and bushing to provide a pre-

tension force to the belt via the tensioner arm and idler pulley, thus taking up the slack due to the

changes in belt length [31]. When the belt undergoes stretch under a load the spring drives the

tensioner arm and idler pulley further into the belt [31]. Belt tension changes under the modes of

operation, which can include when the crankshaft (or driving pulley) abruptly decelerates from a

steady-state condition, and auxiliary components continue to rotate still in their own inherent

inertia and thus become the primary drivers [31]. These fluctuations in belt tension lead to belt

flutter or skip, and slip that may damage other components present in the belt drive [31].

Locating the tensioner on the slack side of the belt is intended to lower the initial static tension

[11]. In conventional vehicles the engine always drives the alternator, so the tensioner is located

in the belt span that links the crankshaft and alternator pulleys. In a B-ISG setting, the slack span


of the belt alternates between the driving mode of the ISG and the driving mode of the crankshaft

[32]. Research by Henry et al. [11], and also the summary of prior art for tensioners in Table

2.1, show that placing the idler/tensioner pulley in the slack span in the case that the ISG is

driving instead of in the slack span when the crankshaft is driving, allows for easier packaging

and for the least static tension. Designs shown in Table 2.1, place the tensioner/idler pulley in the

same span as Henry et al. [11], or in both the slack and taut spans if using a double

tensioner/idler configuration.

2.4.2 Systematic Review of Tensioner Designs for a B-ISG System

The proposals for belt tensioner devices to manage the issue of high peaks in belt tension, for B-

ISG settings, are largely in patent records, as the re-design of a tensioner has been primarily a

concern of automotive makers thus far. A systematic review of the patent literature has been

conducted in order to identify, evaluate and collate relevant tensioning mechanism designs

applicable to a B-ISG setting. Its research objective is to influence the selection of a tensioner

configuration for the thesis study.

The predefined search strategy used by the researcher has been to consider patents dating only

post-2000, as many patents dating earlier are referred to in later patents, as they are developed on

in most cases by the original inventor (e.g., an INA Schaeffler KG patent published in 2000 may

refer to its own earlier patent presented in 1999). Patents dating pre-2000 that do not have any

successor were also considered. The inclusion and exclusion criteria and rationales that were

used to assess potential patents are as follows:

Inclusion of,


tensioner designs with two arms and/or two pivots and/or two pulleys;

mechanical tensioners (i.e., exclusion of magnetic, or electrical actuators or any

combination of active actuators) in order to minimize cost;

tension devices that are an independent structure apart from the ISG structure, in order to

reduce the required modification to the accessory belt drive of a conventional automobile;

and

advanced designs that have not been further developed upon in a subsequent patent by the

inventor or an outside party.

Table 2.1 provides a collation of the results for the systematic review based on the selection

criteria. Illustrations of the collated patent designs may be seen in Appendix A. It is noted that

the patent literature pertaining to these designs in most cases provides minimal numerical data

for belt tensions achieved by the tensioning mechanism. In most cases, only claims concerning

the outcome in belt performance achievable by the said tension device is stated in the patent.

Table 2.1 Passive Dual Tensioner Designs from Patent Literature

Bayerische

Motoren Werke

AG

Patents: EP1420192-A2, DE10253450-A1 [33]

Design Approach:

2 tensioner pulleys (idlers) and 2 tension arms are mounted outside the periphery of the belt drive; these form tiltable clamping arms around a common axis of rotation

A torsion spring is used at bearing bushings to mount tension arms at ISG shaft

Each tension arm cooperates with torsion spring mechanism to rotate through a damping device in order to apply appropriate pressure to taut and slack spans of the belt in

different modes of operation

Bosch GMBH Patent: WO0026532 et. al. [34]

Design Approach:

2 tension pulleys: each one is mounted on the return and load spans of the driven and driving pulley respectively

Idlers (tension pulleys) each connect to a spring, which is attached on one end to a fixed point


Idlers motions are independent of each other, and correspond to the tautness or slackness in their respective spans,

Or alternatively, a spring connects the idler pulleys, and one of the two idlers is fixed at its axis of rotation

Daimler Chrysler

AG

Patents: DE10324268-A1 [35]

Design Approach:

2 idlers are given a working force by a self-aligning bearing

Bearing supports auxiliary unit (ISG) and is arranged concentrically with the axle auxiliary unit pulley

Dayco Products

LLC

Patents: US6942589-B2 et. al. [36]

Design Approach:

2 tension arms are each rotatably coupled to an idler pulley

One idler pulley is on the tight belt span, while the other idler pulley is on the slack belt span

Tension arms maintain constant angle between one another

One arm forms a positive differential angle with the belt and the remaining arm forms a negative differential angle with the belt

Idler pulleys are on opposite sides of the ISG pulley

Gates Corporation Patents: US20060249118-A1, WO2003038309-A [37]

Design Approach:

A tensioner pulley contacts the belt at the slack span during start-up (ISG-driving mode)

A tensioner is asymmetrically biased in direction tending to cause power transmission belt to be under tension

McVicar et al.

(Firm: General

Motors Corp.)

Patent: US20060287146-A1 [38]

Design Approach:

2 tension pulleys and carrier arms with a central pivot are mounted to the engine

One tension arm and pulley moderately biases one side of belt run to take up slack during engine start-up, while other tension arm and pulley holds appropriate bias against

taut span of belt

A hydraulic strut is connected to one arm to provide moderate bias to belt during normal engine operation and velocity sensitive resistance to increasing belt forces during engine

start-up

INA Schaeffler

KG et. al.

Patents: DE10044645-A1 [39], DE10159073-A1 [40], EP1723350-A1 et. al. [41],

DE10359641-A1 et. al. [42], EP1738093-A1 et. al. [43], DE102004012395-A1 [44],

WO2006108461-A1 et. al. [45]*

Design Approach:

2 tension arms and 2 pulleys approach o Mutually independent tensioning arms are supported for rotation in the same

plane of the housing part

o Idler pulley corresponding to each tensioning arm engages with different sections of belt

o When high tension span alternates with slack span of belt drive, one tension arm will increase pressure on current slack span of belt and the other will

decrease pressure accordingly on taut span;

o Or when the span under highest tension changes, one tensioner arm moves out of the belt drive periphery to a dead center due to a resulting force from the taut

span of the ISG starting mode

o Deflection of the taut span acts on associated pulley to apply a counter-moment to the other idler pulley on the slack span


o The 2 lever arms are of different lengths and each have an idler pulley of different diameters and different wrap angles of belt (see DE10045143-A1 et.

al.)

1 tensioner arm and 2 pulleys approach o 2 idler pulleys are pinned to a beam arranged on a clamping arm that is tiltably

linked to the beam o The ISG machine is supported by a shock absorber o During ISG start-up, one idler pulley is induced to a dead center position while

it pulls the remaining idler pulley into a clamping position until force

equilibrium takes place

o A shock absorber is laid out such that its supporting spring action provides necessary preloading at the idler pulley in the direction of the taut span during

ISG start-up mode

Litens Automotive

Group Ltd.

Patents: US6506137-B2 et. al. [46]

Design Approach:

2 tension pulleys on opposite sides of the ISG pulley engage the belt

They are positioned such that their applied forces result in opposing directed moments with respect to the tension devices axis of pivot

The pivot axis varies relative to the force applied to each tension pulley

Diameters of the tensioner pulleys are approximately equal, and belt wrap angles of the tensioner pulleys are approximately equal

A limited swivel angle for the tensioner arms work cycle is permitted

Mitsubishi Jidosha

Eng KK,

Mitsubishi Motor

Corp.

Patents: JP2005083514-A [47]

Design Approach:

2 tensioners are used

1 tensioner is held on the slack span of the driving pulley in a locked condition and a second tensioner is held on the slack side of the starting (driven) pulley in a free condition

Nissan Patents: JP3565040-B2 et. al. [48]

Design Approach:

A single tensioner is on the slack span once ISG pulley is in start-up mode

The tension device is comprised of a oil pressure tensioner and a half ratchet mechanism (a plunger which performs retreat actuation according to the energizing force of the oil

pressure, spring and load received from the ISG)

The tensioner is equipped with a relief valve to keep a predetermined load lower than the maximum load added by the ISG device

NTN Corp. Patent: JP2006189073-A [49]

Design Approach:

An automatic tensioner is equipped with a hydraulic damper mechanism comprised of: a screw bolt using saw-screwed teeth and a cylinder nut, a return spring and a spring seat

in a pressure chamber (within the screw bolt), a rod seat (that is fitted to the lower end of

the cylinder nut), a spring support (arranged on varying diameter stepped recessed

sections of the rod seat) and a check valve with an opening/closing passage

The cylinder and screw bolt act as the rigidity buffer under excessive loads during ISG start-up mode of operation

Valeo Equipment

Electriques

Moteur

Patents: EP1658432, WO2005015007 [50]

Design Approach:

The invention relates to a system or a starter (10) in which a pulley (80) is rotationally mounted on a section (22) of a shaft which axially extends inside a pulley (80) and


forwards, at least partially outside a support element (200) and is characterized in that

the free front end (23) of said shaft section (22) is carried by an arm (206) connected to

the support element (200).**

*The author notes that published patents and patent applications may retain patent numbers for multiple patent

offices (i.e. European Patent Office, German Patent Office, etc.). In such cases the published patent number, or in

the absence of such a number, the published patent application number, has been specified. However published

patent documents in the above cases also served as the document (i.e. identical) to the published patent if available.

**Quoted from patent abstract as machine translation is poor.

2.5 Summary

The research on tensioner designs from the patent literature demonstrates a lack of quantifiable

data for the performance of a twin tensioner particularly suited to a B-ISG system. The review of

the literature for the modeling theory of serpentine belt drives and design of tensioners shows

few belt drive models that are specific to a B-ISG setting. Hence, the literature review supports

the thesis objective of modeling a B-ISG tensioner, specifically one that has a passive twin

tensioner configuration, and as well measuring the tensioners performance. The survey of

hybrid classes reveals that the micro-hybrid class is the only class employing a closely

conventional belt transmission, and hence its B-ISG transmission is applicable for tensioner

investigation. The patent designs for tensioners contribute to the development of the tensioner

design to be studied in the following chapter.

25

CHAPTER 3: MODELING OF B-ISG SYSTEM

3.1 Overview

The derivation of a theoretical model for a B-ISG system uses real life data to explore the

conceptual system under realistic conditions. The literature and prior art of tensioner designs

leads the researcher to make the following modeling contributions: a proposed design for a

passive two-pulley tensioner, computation of geometric attributes for a B-ISG system with the

proposed tensioner, and derivation of the systems equations of motion (EOM) under dynamic

and static states, as well as deriving the EOM for the B-ISG system with only a passive single-

pulley tensioner for comparison. The principles of dynamic equilibrium are applied to the

conceptual system to derive the EOM.

3.2 B-ISG Tensioner Design

The proposed design for a passive two pulley tensioner configures two tensioners about a single

fixed pivot point in the interior space of a serpentine belt drive. One end of each tensioner arm

coincides with the centre point of a tensioner pulley, and this point marks the axis of rotation of

the pulley. The other end of each arm is pivoted about a point so that the arms share the same

axis of rotation. This conceptual design henceforth is called a Twin Tensioner. Figure 3.1 shows

a schematic for the proposed design.

Modeling of B-ISG 26

Figure 3.1 Schematic of the Twin Tensioner

The tensioner pulley coordinates are described by (Xi,Yi), their radii by, Ri, their arm lengths, Lti,

and their angles, ti. The rotation of the arms is resisted by stiffness, kt, of a coil spring acting

between the two arms, and spring stiffness, kti, acting between each arm and the pivot point. The

motion of each arm is dampened by dampers and, akin to the springs, a damper acts between the

two arms, ct, and a damper, cti, acts between each arm and the pivot point. The result is a

tensioning mechanism with four degrees of freedom (DOF) that includes independent rotations

of the two pulleys and two arms.

The following section relates the geometry of the rigid bodies in a B-ISG system equipped with a

Twin Tensioner to their respective motions.


3.3 Geometric Model of a B-ISG System with a Twin Tensioner

The B-ISG system with the Twin Tensioner is shown in Figure 3.2. The geometry of the drive

provides the lengths of the belt spans and angles of wrap for the belt and pulley contact surfaces.

These variables are crucial to resolve the components of forces and moment arms acting on each

rigid body in the system and are used in the derivation of the EOM in section 3.4. Zhen Mus

geometric modeling approach [51], used in the development of the software, FEAD, was applied

to the Twin Tensioner system to compute the systems unique geometric attributes.

Figure 3.2 B-ISG Serpentine Belt Drive with Twin Tensioner

It is noted that in Figure 3.1 and Figure 3.2, showing the schematic of the Twin Tensioner and

the overall system respectively, that for the purpose of the geometric computations the forward

direction follows the convention of the numbering order, counterclockwise. The numbering

order is in reverse to the actual direction of the belt motion, which is in the clockwise direction in

this study. The fourth pulley is identified as an ISG unit pulley. However the properties used

for the ISG pulleys geometry, inertia, stiffness and damping is modeled as a conventional


alternator pulley. This pulley is conceptualized as an ISG when it is modeled as the driving

pulley, at which point the requirements of the ISG are solved for, and its non-inertia attributes

are not needed to be ascribed.

Figure 3.3 shows the geometric attributes needed to resolve the wrap angle of the belt on each

pulley. Variables (Xi,Yi), and XYfi, XYbi, XYfbi, and XYbfi are the ith pulley centre coordinates and

its possible belt connection points respectively. Length, Lfi, is the length of the span connecting

the points, XYfi and XYf(i+1), or XYbi and XYb(i+1) on the ith and (i+1)th pulleys respectively.

Similarly Lbi, is the length of the span between, XYfbi and XYfb(i+1), or XYbfi and XYbf (i+1) on the

ith and (i+1)th pulleys respectively. Angles i, fi and bi represent the angle between a line

connecting the ith and (i+1)th pulley centres, and the angles of the belt connection spans with

lengths Lfi and Lbi respectively. Ri is the radius of the ith pulley.

Figure 3.3 Angles, Coordinates and Possible Belt Contact Points for the ith and i+1th Pulleys

[modified] [51].


The angle between the horizontal and the line connecting the ith and (i+1)th pulley centres, i, is

calculated using Zhens method [51]. This method uses the pulleys coordinates and a cosine

trigonometric relation.

i acos

Xi 1

Xi

Xi 1

Xi

2

Yi 1

Yi

2

Yi 1

Yi

if

(3.1a)

i 2 acos

Xi 1

Xi

Xi 1

Xi

2

Yi 1

Yi

2

Yi 1

Yi

if

(3.1b)

The lengths for connecting the possible belt spans are described by the variables Lfi and Lbi.

The centre point coordinates and the radii of the pulleys are related through the solution of

triangles which they form to define values of the possible belt span lengths:

Lfi

Xi 1

Xi

2

Yi 1

Yi

2

Ri 1

Ri

2

(3.2a)

Lbi

Xi 1

Xi

2

Yi 1

Yi

2

Ri 1

Ri

2

(3.2b)

The set of possible belt span lengths leads to the calculation of fi and bi, the angles between the

line connecting the ith and (i+1)th pulley centres and the possible contact point on the pulley

perimeter.


(3.3a)

(3.3b)

The array of possible belt connection points comes about from the use of the pulley centre

coordinates and their radii and the sine of the sum, or differences, of i and fi or bi. The angle,

i, is calculated in equations (3.1a) and (3.1b), and angles fi and bi are calculated in equations

(3.3a) and (3.3b). The formula to compute the array of points is shown in equations (3.4) and

(3.5) for the ith and (i+1)th pulleys. Equation (3.4) describes the forward belt connection point

on the ith pulley, which is in the span leading forward to the next (i+1)th pulley.

(3.4a)

(3.4b)

(3.4c)

(3.4d)

bi atan

Lbi

Ri

Ri 1


Equation (3.5) describes the backward belt connection point on the ith pulley. This point sits on

the ith pulley in the contacting belt span, which leads backward to connect with the (i-1)th

pulley.

(3.5a)

(3.5b)

(3.5c)

(3.5d)

The selection of the coordinates from the array of possible connection points requires a graphic

user interface allowing for the points to be chosen based on observation. This was achieved

using the MathCAD software package, as demonstrated in the MathCAD scripts found in

Appendix C. The belt connection points can be chosen so as to have a pulley on the interior or

exterior space of the serpentine belt drive. The method used in the thesis research was to plot the

array of points, in the MathCAD environment, with distinct symbols used for each pair of points

and to select the belt connection points accordingly. By observation of the selected point types,

the type of belt span connection is also chosen. Selected point and belt span types are shown in

Table 3.1.


Table 3.1 Selected Contact Point Types on the ith Pulley and Types for the ith Belt Span

Pulley Forward Contact

Point

Backwards Contact

Point

Belt Span

Connection

1. Crankshaft XYf,1 XYbf2,1 Lf1

2. Air Conditioning XYfb,2 XYf2,2 Lb2

3. Tensioner 1 XYbf,3 XYfb2,3 Lb3

4. Alternator/ISG XYfb,4 XYbf2,4 Lb4

5. Tensioner 2 XYbf,5 XYfb2,5 Lb5

The inscribed angles, ji, between the datum and the forward connection point on the ith pulley,

and ji, between the datum and its backward connection point, are found through solving the

angle of the arc along the pulley circumference between the datum and specified point. The

wrap angle, i, is found as the difference between the two inscribed angles for each connection

point on the pulley. The angle between each belt span and the horizontal, as well as the initial

angle of the tensioner arms are found using arctangent relations. Furthermore, the total length of

the belt is determined by the sum of the lengths of the belt spans.

3.4. Equations of Motion for a B-ISG System with a Twin Tensioner

3.4.1 Dynamic Model of the B-ISG System

3.4.1.1 Derivation of Equations of Motion

This section derives the inertia, damping, stiffness and torque matrices for the entire system.

Moment equilibrium equations are applied to each rigid body in the system, and net force

equations are applied to each belt span. From these two sets of equations the inertia, damping


and stiffness terms are grouped as factors against acceleration, velocity and displacement

coordinates respectively, and the torque matrix is resolved concurrently.

A system whose motion can be described by n independent coordinates is called an n-DOF

system. Consider the free body diagram of the Twin Tensioner in Figure 3.4, in which each

pulley of inertia Ii is supported on an arm of inertia Iti. It is assumed that the pulleys are

constrained to rotate about their respective central axes and the arms are free to rotate about their

respective pivot points, then at any time the position of each pulley can be described by a

rotational coordinate i(t), and a coordinate ti(t) can denote the rotation of each arm. Thus the

tensioner system comprises of four rigid bodies, where each is described by one coordinate, and

hence is a four-DOF system. It is important to note that each rigid body is treated as a point

mass. In addition, inertial rotation in the positive direction is consistent with the direction of belt

motion. The belt span tensions, Ti, and coupled radii, Ri, apply moments to the pulleys.

Figure 3.4 Twin Tensioner: Free Body Diagram of a Four-Degree of Freedom System


For the serpentine belt system considered in the thesis research there are seven rigid bodies, each

having a one-DOF of motion. The EOM for a seven-DOF system form second-order coupled

differential equations, meaning that each equation includes all of the general coordinates and

includes up to the second-order time derivatives of these coordinates. The EOM can be

obtained by applying DAlemberts principle that the sum of the moments taken about any point,

including the couples, equals to zero. Therefore, the inertial couple, the product of the inertia and

acceleration, is equated to the moment sum as shown in equation (3.5).

I = M (3.5)

The moment equilibrium equations for the Twin Tensioner in Figure 3.4, where the positive

direction is in the clockwise direction, are shown in equations (3.6) through to (3.10). The

numbering convention used for each rigid body corresponds to the labeled serpentine belt drive

system shown in Figure 3.2. Qi represents the required torque of the ith rigid body, ci is the

damping constant of the ith rigid body, ji is the angle of orientation for the ith belt span and

, and are the angular displacement, angular velocity and angular acceleration of the ith

tensioner arm. The initial angle of the ith tensioner arm is described by toi.

I3 3 = T3 R3 T2 R3 Q3 + c3 3 (3.6)

I5 5 = T4 R5 + T5 R5 Q5 + c5 5 (3.7)


It1 t1 = Tt1 Lt1 sin to 1 j4 + sin to 1 j5 kt t1 t2 kt1

t1 ct t1 t2 ct1 t1 (3.8)

It2 t2 = Tt2 Lt2 sin to 2 j2 + sin to 1 j3 kt t2 t1 kt2 t2

ct t2 t1 ct2 t2 (3.9)

t1 = t1 to 1 (3.10a)

t2 = t2 to 2 (3.10b)

The free body diagrams for the remaining rigid bodies, crankshaft pulley, air conditioner pulley

and ISG pulley are in the general form of Figure 3.5. The sum of the moments about the axes of

rotation, are taken for these structures in equations (3.11) through to (3.13).

Figure 3.5 Free Body Diagram for Non-Tensioner Pulleys


I1 1 = T5 R1 T1 R1 + Q1 c1 1 (3.11)

I2 2 = T1 R2 T2 R2 + Q2 c2 2 (3.12)

I4 4 = T3 R4 T4 R4 + Q4 c4 4 (3.13)

The relationship between belt tensions and rigid body displacements is in the general form of

equation (3.14), where and are damping and stiffness matrices due to the belt respectively,

with each factorized by a radial arm length. This relationship is described for each span in

equations (3.15) through to (3.20). The belt damping constant for the ith belt span is cib.

=

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DESIGN & ANALYSIS OF A TENSIONER FOR A BELT-DRIVEN