STUDY ON THE DEVELOPMENT ANGELA DE’ON - Library - Home

102 Pages·2006·0.86 MB·English

STUDY ON THE DEVELOPMENT
OF AXIAL STRESSES IN WOUND ROLLS

By
ANGELA DE’ON WELCH
Bachelor of Science in Mechanical Engineering
Oklahoma State University
Stillwater, OK
2006

Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 2006
STUDY ON THE DEVELOPMENT
OF AXIAL STRESSES IN WOUND ROLLS

Thesis Approved:

J. K. Good
Thesis Adviser
D. E. Fisher

C. E. Price

A. Gordon Emslie
Dean of the Graduate College
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TABLE OF CONTENTS

Chapter Page

I. INTRODUCTION TO STRESSES IN WOUND ROLLS.........................................1

II. BACKGROUND INFORMATION..........................................................................6

One-Dimensional Winding Models.........................................................................7
Two-Dimensional Winding Models......................................................................13

III. DISCUSSION ON TWO-DIMENSIONAL WINDING MODEL AND
APPLICATION TO THE POLYESTER WEB TO BE TESTED…………………...16

Material Properties.................................................................................................18
Model Outputs.......................................................................................................25

IV.EXPERIMENTAL PROCEDURE.........................................................................35

V. EXPERIMENTAL RESULTS................................................................................46

VI.COMPARISON OF MODEL AND EXPERIMENTAL RESULTS.....................56

VII.CONCLUSIONS...................................................................................................77

Conclusions............................................................................................................78
Future Work...........................................................................................................81

REFERENCES............................................................................................................83

APPENDIX..................................................................................................................86

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LIST OF TABLES

Table Page

Table 1: Material Properties.........................................................................................19

Table 2: Statistical Results for MD Strains in 6 inch Wide PET.................................48

Table 3: Statistical Results for CMD Strains in 6 inch Wide PET..............................49

Table 4: Statistical Results for MD Strains in 24 inch Wide PET...............................52

Table 5: Statistical Results for CMD Strains in 24 inch Wide PET............................53
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LIST OF FIGURES

Figure Page

Figure 1: Circumferential Corrugations.........................................................................2

Figure 2: Experimental Area of High Speed Web Line.................................................5

Figure 3: Changing Radial Stress with Changing ν and Constant ν and ν ...........20
θz θr zr

Figure 4: Changing Tangential Stress with Changing ν and Constant ν and ν ....21
θz θr zr

Figure 5: Changing Axial Stress with Changing ν and Constant ν and ν .............22
θz θr zr

Figure 6: Radial Stress Through 6 inch Web...............................................................26

Figure 7: Tangential Stress Through 6 inch Web........................................................27

Figure 8: Axial Stress Through 6 inch Web................................................................28

Figure 9: Radial Stress Through 24 inch Web.............................................................29

Figure 10: Tangential Stress Through 24 inch Web....................................................30

Figure 11: Axial Stress Through 24 inch Web............................................................31

Figure 12: Radial Stress in Wound Roll of PET..........................................................32

Figure 13: Tangential Stress in Wound Roll of PET...................................................33

Figure 14: Axial Stress in Wound Roll of PET...........................................................34

Figure 15: Rosette Strain Gage....................................................................................35

Figure 16: Single Element Strain Gage.......................................................................36

Figure 17: Strain Gage Attachment.............................................................................37

Figure 18: Wide-Range Strain Indicator (Model 3800)...............................................38

Figure 19: Placement of Strain Gage on Wound Roll.................................................39
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Figure 20: Collection of Experimental Strain Data.....................................................40

Figure 21: Measurement of Pile Height.......................................................................41

Figure 22: MD Strains in 6 inch Wide PET.................................................................47

Figure 23: CMD Strains in 6 inch Wide PET..............................................................49

Figure 24: MD Strains in 24 inch Wide PET...............................................................51

Figure 25: CMD Strain in 24 inch Wide PET..............................................................53

Figure 26: MD Strain Comparison..............................................................................54

Figure 27: CMD Strain Comparison............................................................................55

Figure 28: Bending Strain Diagram.............................................................................59

Figure 29: MD Strain for 6 inch Wide Web................................................................61

Figure 30: CMD Strain for 6 inch Wide Web..............................................................62

Figure 31: MD Strain for 24 inch Wide Web..............................................................63

Figure 32: CMD Strain for 24 inch Wide Web............................................................64

Figure 33: Depth of Gage in Wound Roll Example Plot.............................................65

Figure 34: MD Strain for 6 inch Wide Web for Comparison with Experimental Results
................................................................................................................................66

Figure 35: CMD Strain for 6 inch Wide Web for Comparison with Experimental Results
................................................................................................................................67

Figure 36: MD Strain for 24 inch Wide Web for Comparison with Experimental Results
................................................................................................................................67

Figure 37: CMD Strain for 24 inch Wide Web for Comparison with Experimental Results
................................................................................................................................68

Figure 38: Theoretical and Experimental MD Strains for 6 inch Wide Web..............69

Figure 39: Theoretical and Experimental CMD Strains for 6 inch Wide Web...........70

Figure 40: Theoretical and Experimental MD Strains for 24 inch Wide Web............71

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Figure 41: Theoretical and Experimental CMD Strains for 24 inch Wide Web.........72

Figure 42: Theoretical and Average Experimental Comparison of MD Strains for 6 inch
Wide Web..............................................................................................................73

Figure 43: Theoretical and Average Experimental Comparison of CMD Strains for 6 inch
Wide Web..............................................................................................................74

Figure 44: Theoretical and Average Experimental Comparison of MD Strains for 24 inch
Wide Web..............................................................................................................75

Figure 45: Theoretical and Average Experimental Comparison of CMD Strains for 24
inch Wide Web......................................................................................................76

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LIST OF SYMBOLS AND ABBREVIATIONS

PET Polyester Film
WHRC Web Handling Research Center
HSWL High Speed Web Line
MD Machine Direction
CMD Cross Machine Direction
pli pounds per linear inch
fpm feet per minute
E Radial Young’s modulus
r
E Tangential Young’s modulus
θ
σ Radial stress
r
σ Tangential stress
θ
σ Axial stress
z
ε Radial strain
r
ε Tangential strain
θ
ε Axial strain
z
r Radius
d Diameter
ν Poisson’s ratio of stress in θ-direction to strain in r-direction
rθ
ν Poisson’s ratio of stress in r-direction to strain in θ-direction
θr
ν Poisson’s ratio of stress in r-direction to strain in z-direction
zr
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ν Poisson’s ratio of stress in z-direction to strain in θ-direction
θz
P Normal pressure
K Material constant
1
K Material constant
2
δ Level of interference
ij
u, u Nodal points
i j
T Web tension
w
t Web thickness
w Web width
α Reinforcement factor
R Outer radius of core
outer
G Shear modulus
rz
Y Distance of neutral axis
R Radius of curvature
ε (r) Tangential strain at certain radius, r
θ
ε (r) Axial strain at certain radius, r
z
ε (gage) Tangential strain at gage’s radius
θ
ε (gage) Axial strain at gage’s radius
z
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CHAPTER I

INTRODUCTION TO STRESSES IN WOUND ROLLS

Web materials are very common in manufacturing environments today and will
continue to be in the future. A web is defined as a material whose length is much greater
than its width and whose width is much greater than its thickness. Webs can be made of
just about anything. Several common categories of web materials include paper, plastic
films, metal foils and laminates. Hundreds of thousands of products are made from these
webs and webs encompass many of the products used in daily life. In manufacturing
environments, wound rolls of web material are often the most economical and practical
solution for material storage and transportation.
Unfortunately, this is not without several problems. Just the act of winding the
web can cause damage of several kinds to the web. This damage has been the topic of
numerous research studies. The quality of the wound roll depends on the stresses which
exist in it. While these in-roll stresses determine the structural integrity of the roll, they
can also impart damage onto the roll. If these stresses are allowed to go uncontrolled, the
results are tearing and buckling along with many other defects in the wound material.
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