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Analysis of tensioner induced coupling in serpentine belt drive systems Ryan Neward

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ANALYSIS OF TENSIONER INDUCED COUPLING IN SERPENTINE BELT DRIVE SYSTEMS

By

RYANNEWARD

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

Approved by:

Stephen Boedo

Dr. Stephen Boedo

(Thesis Advisor)

Department of Mechanical Engineering

Agamemnon Crassidis

Dr. Agamemnon Crassidis Department of Mechanical Engineering

Kevi n Kochersberger

Dr. Kevin Kochersberger Department of Mechanical Engineering

Edward Hensel

Dr. Edward Hensel Department Head of Mechanical Engineering

DEPARTMENT OF MECHANICAL ENGINEERING ROCHESTER INSTITUTE OF TECHNOLOGY MAY 2006

ANAL YSIS OF TENSIONER INDUCED COUPLING IN SERPENTINE BELT DRIVE SYSTEMS

I, Ryan Neward, hereby grant permission to the Wallace Library of Rochester Institute of Technology to reproduce my thesis in whole or part. Any reproduction will not be for commercial use or profit.

Ryan Neward Ryan Neward May 2006

11

Acknowledgements

I

like to thank my

would

opportunity to support

faculty advisor Dr. him in

work with

have been

my thanks to my

critical to

my

a

field

greatly to the

My sincere

my

direction

of

interests. His

throughout my research

me

guidance and

I

and writing.

and

express

Dr. Kevin

my thesis. Their inputs have

review

the

contributed

results.

gratitude goes out

research and provided me

to my

Dr. Agamemnon Crassidis

committee members

strength of

so close

success

Kochersberger for taking the time to

Stephen Boedo for allowing

to

all

those

LMS CADSI

at

initially supported my

who

the opportunity to learn their software. Despite the change in

my research, the

motivation

for my

work was

the field. In addition, the skills I learned through working valuable

to my understanding

Zamora,

at

LMS CADSI, for

of belt

drive

all of his

systems.

I

derived from their interest in with

would

time and effort in

their

software were

especially like to thank Joe

helping me understand the

software.

My appreciation goes

out

to Dr. Robert Parker

His

correspondence and support of my work.

my

research.

I thank the Mechanical

Selleck, for

especially Mrs.

I

would

like to

(both financial

express

and

breaks from my

Finally, I their

would

and sister

research.

Erin, for it was her

help

I

support

extensive

appreciation

deserve

am glad

to be

that made

all

would

able

like to dedicate my thesis to

never

thanks;

as

to thank the

long

the

parents.

have

all

days

the

for his

of papers was

Department

to my

special

help this thesis would never have been

list

University

in my engineering

motivational) this thesis

In addition, my brother

Ohio State

Engineering

all of their

my deepest

at

faculty

and

invaluable in staff,

studies.

Without their

had

support

a chance of success.

they provided

special woman

a

few

in my

needed

life,

worth while.

people mentioned

completed as

above;

without

it is today.

in

Abstract

Serpentine belt drive and

long

life. These

a spring-loaded

alternator,

air

in

automobiles

belt,

systems are composed of a

conditioner,

in the

used

of

or power

As

pump.

steering

a result of this,

frequency and the mode

In particular,

assumptions used. motions of the

coupling is

belt

are coupled

often neglected

a

Serpentine belt drives

due to the

coupled motion as well as a solution

be

will

experimental

data. In addition,

ability natural

assessed.

of the coupled and

frequencies

and

the

experience

transient vibrations due to the different

about

the

create a mathematical system such as

of the model will

the

depend primarily

motion of the automatic

model

natural

on

the

Both

employing

decoupled

and mode shapes

Using

study

models

due to

a solution

rotational motion

solution results will

a parametric

belt tensioner. This

only longitudinal belt

and rotational motions.

this coupling

driven pulleys,

key assumption is whether transverse and rotational

by authors who

decouple the transverse

compactness

such accessories as

it is important to

The accuracy

shapes.

due to their

driving pulley,

may include

state motions and

steady

system.

pulleys

a

that allows the designer to extract information

model

effect

widely

tensioner. The driven

many different types parameters

systems are

will

be

be

to accurately

changes

in

response and

based

in

upon

only, the importance

of

compared against published

performed

to determine the

predict changes

in

system

system parameters.

iv

Contents

1 INTRODUCTION

1

1.1

SERPENTINE BELT DRIVES

1

1.2

LITERATURE REVIEW

4

1.3

THESIS OBJECTIVE

9

11

2 DECOUPLED FORMULATION

11

ROTATIONAL MOTION MODEL

2.1 2.1.1

Problem Formulation

11

2.1.2

Equilibrium Analysis

20

2.1.3

Vibration Analysis

21 TENSIONER SPANS

26

FIXED-FIXED SPANS

27

2.2

TRANSVERSE MOTION MODEL

2.3

TRANSVERSE MOTION MODEL

2.4

ALGORITHM FOR DECOUPLED SOLUTION

-

-

32

3 COUPLED FORMULATION PARTIALLY COUPLED MOTION MODEL

3.1

32 32

of Motion

3.1.1

Equations

3.1.2

Equilibrium Analysis

3.1.3

Discretization

of the

29

41

Belt Spans FIXED-FIXED SPANS

3.2

TRANSVERSE MOTION

3.3

ALGORITHM FOR COUPLED SOLUTION

-

44 51

52

4 CASE STUDIES

4.1

-

ANALYTICAL AND EXPERIMENTAL

CASE STUDY 1

-

ANALYTICAL

54 54

4.1.1

System Configuration

54

4.1.2

Decoupled Results

54

4.1.2.1

Equilibrium

4.1.2.2

Natural frequencies

4.1.3

54

and mode shapes

58

Coupled Results

62

4.1.3.1

Equilibrium

62

4.1.3.2

Natural frequencies

4.1.4 4.2

and mode shapes

Comparison CASE STUDY 2

62

62 ANALYTICAL

70

4.2.1

System Configuration

70

4.2.2

Decoupled Results

70

4.2.2.1

Equilibrium

4.2.2.2

Natural frequencies

4.2.3

Coupled

4.2.4

Comparison

and mode shapes

70

75

results

CASE STUDY 3

4.3

70

75

EXPERIMENTAL

82

4.3.1

System Configuration

82

4.3.2

Decoupled Results

84

4.3.2.1

Equilibrium

4.3.2.2

Natural frequencies

4.3.3

Coupled Results

84 and mode shapes

84

88

vi

4.3.4

Comparison

5 SUMMARY AND CONCLUSIONS

88

94

5.1

PROBLEM OBJECTIVES

94

5.2

THESIS CONTRIBUTIONS

94

5.3

PARAMETRIC STUDY

95

5.4

CONCLUSIONS

96

5.5

RECOMMENDATIONS FOR FUTURE WORK

97

APPENDIX A

98

APPENDIX B

100

APPENDIX C

102

APPENDIX D

104

APPENDIX E

106

REFERENCES

107

vn

List

of

Figures

Figure 1.1: Serpentine belt drive Figure 2.1: Prototypical

2

system

serpentine

belt drive

13

system

Figure 2.2: Tensioner assembly Figure 2.3: Tensioner assembly

Figure 2.4: Tensioner

15

17

angles

motion and angle

definition

28

analysis

31

Figure 2.5: Algorithm for the decoupled Figure 3.1: Serpentine belt drive Figure 3.2: Tensioner

model

33

span coordinates

35

Figure 3.3: Basis functions jum(