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, I3, LIBRARY
unwell Michigan State
University

 

 

 

This is to certify that the
thesis entitled

ALTERNATIVE MATERIAL FOR WORM GEARS USED IN
WINDSHIELD WIPERS AND POWER WINDOWS

presented by

SARITA SRILAKSHMI MAHEEDHARA

has been accepted towards fulfillment
of the requirements for the

MASTER OF degree in MECHANICAL ENGINEERING
SCIENCE

G‘W

Major Professor’s Signature
(0 / 5 / 2003
I I

Date

 

 

 

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6/01 cJCIRC/DateDuepes-p. 1 5

ALTERNATIVE MATERIAL FOR WORM GEARS USED IN
WINDSHIELD WIPERS AND POWER WINDOWS

BY

Sarita Srilakshmi Maheedhara

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

2003

ABSTRACT

ALTERNATIVE MATERIAL FOR WORM GEARS USED IN
WINDSHIELD WIPERS AND POWER WINDOWS
By

Sarita Srilakshmi Maheedhara

Worm gears are used in windshield wipers and power windows of
automobiles. The project proposed by Automation Tooling Systems, McAllen,
Texas, was to eliminate several material problems resulting from the
production of these worm shafts, such as production bottleneck and excessive
scrap etc. from the original material, steel. A possible solution has been
explored in this work by characterizing material properties of a promising
candidate (glass reinforced acetal copolymer) that can replace steel in worm
gears. Finite element analysis of the worm thread under service loads has
been performed to make a preliminary estimate of the size of the new
composite part. The results strengthen the possibility of the material
replacement for the worm shaft without sacrificing part performance, whilst
reducing part weight leading to improved fuel economy, noise reduction and

manufacturing problems associated with the steel part.

This thesis is dedicated to my parents, Mr. Maheedhara Ramakrishna and Mrs.
Maheedhara Annapurna, my sister Ms. Maheedhara Mrudula Archana and my

husband, Mr.Upadhyayula Sreeharsha

iii

ACKNOWLEDGMENTS

I express my sincere appreciation to Dr.Farhang Pourboghrat and Dr.John
Lloyd for all the patience, support and guidance they provided throughout my
research. I would like to acknowledge the financial support from Automation
Tooling Systems (ATS, McAllen, Texas), which helped me complete my research

and graduate studies. '

I would like to acknowledge Mr. Mike Rich, Dr. Tom Mass and Mr. Bob
Jurek for their support in conducting the various experiments. I would also like to
thank Mr. Steve Houle (ATS), Mr. Kenneth Rettmann (Visteon), Mr. Sujan E. Bin
Wadud (TA Instruments), Mr. Frank Lach and Mr. Zan Smith (T icona) for their

generous resources and support.

I would like to thank my colleagues, Mr. Narasimhan, Mr. Ekbote and Mr.

Ramoharan for their support and patience.
I am thankful to my parents and sister for their endless love and support.

Most importantly, I would like to thank my husband, Sreeharsha for his immense

support, encouragement and patience.

iv

TABLE OF CONTENTS

LIST OF TABLES ........................................................................... vii

LIST OF FIGURES .......................................................................... ix

LIST OF SYMBOLS ......................................................................... xi

CHAPTER 1

INTRODUCTION ............................................................................... 1

CHAPTER 2

LITERATURE REVIEW ....................................................................... 7

CHAPTER 3

3.1 EXPERIMENTAL WORK ................................................................. 14
3.1.1. Injection Molding ................................................................... 14
3.1.2. Uniaxial tensile test ............................................................... 15
3.1.3. DMA Creep test ................................................................... 21

3.2 GEOMETRY OF THE WORM ......................................................... 28

3.3 DETERMINATION OF THE FORCE COMPONENTS ACTING ON THE

WORM ............................................................................................ 29

3.4 DETERMINATION OF VOLUME AND MASS OF MATERIAL ................ 33

CHAPTER 4

FINITE ELEMENT ANALYSIS .............................................................. 35
4.1. REDESIGN OF THE WORM WITH PLASTIC ................................ 36

4.2. MODEL DEFINITION ................................................................ 44

4.3 COST ANALYSIS ......................................................................... 58
CHAPTER 5

SUMMARY AND CONCLUSIONS ......................................................... 59
BIBLIOGRAPHY ................................................................................ 60

vi

LIST OF TABLES

Table 1.1. Mechanical Properties of Steel and Alternative Materials used
for Worm Gear .............................................................................. 3

Table 3.1.1. Temperatures set in various sections of the injection-molding

machine ........................................................................................ 14
Table 3.1.2. Mechanical properties of GC25A at different temperatures ........ 18
Table 3.1.3. Mechanical properties of M90 at different temperatures ............ 18
Table 3.1.4. TI'S results for glass reinforced composite ........................... 23
Table 3.1.5. Curve-fit for E(t) vs. time at various temperatures ................... 24
Table 3.1.6. A (T), B (T) at varying temperatures .................................... 24
Table 3.1.7. A (T), B (T) from curve-fitting ............................................. 25
Table 3.1.8 (a) E (T, t) from experiment and curve-fitting at 23°C .............. 25
Table 3.1.8 E (T, t) from experiment and curve-fitting (b) at 40°C (c) at 60°C

(d) at 80°C ....................................................................................... 26
Table 3.1.8 (9) E (T, t) from experiment and curve-fitting at 100°C ............... 27
Table 3.2.1. Geometry of the worm and worm gear[37] ............................. 29
Table 3.3.1. Operational characteristics of the worm and the gear [Ref] ......... 30
Table 4.1.1 (a) Calculated dimensions of the worm gear ............................ 40
Table 4.1.1 (b) Calculated dimensions of the worm gear (cont) ................... 41
Table 4.1.2 (a) Forces acting on the worm tooth ....................................... 42
Table 4.1.2 (b) Forces acting on the worm tooth (cont) ............................. 43
Table 4.2.1 No. of nodes and elements used in the FEA analysis ................ 44
Table 4.2.2. Assumed material properties at initial time, to ......................... 45

vii

Table 4.2.3 FEA results for 6025A at 23°C(a) at Initial time. to (b) after 5

years .............................................................................................. 49
Table 4.2.3 (o) FEA results for GCZSA at 23°C after 10 years ..................... 50
Table 4.2.4 (a) FEA results for GC25A at 105°C at initial time, to ................. 50

Table 4.2.4 FEA results for GC25A at 105°C (b) after 5 years (c) after 10

years ............................................................................................. 51
Table 4.2.5 FEA results for GC25A at -40°C at initial time, to ...................... 52
Table 4.2.6. FEA results for AISI 1144 Steel ........................................... 52
Table 4.3.1. Volume of Composite material required ................................. 57

viii

LIST OF FIGURES

Figure 1.1 Worm gear [I'IW Spiroid, Chicago, IL] ..................................... 4

Figure 1.2 Worm gears in garage door openers [5] ................................... 4

Figure 1.3 Wiper motor with worm gear [6] .............................................. 5

Figure 3.1.1 (a) stress vs. strain graph of filled acetal ................................ 15
Figure 3.1.1 (b) stress vs. strain graph of unfilled acetal ............................. 16
Figure 3.1.2 GCZSA after and before the uniaxial tensile test ...................... 17

Figure 3.1.3 (a) M90 before the test and at oyserd ....................................... 17
Figure 3.1.3 (b) M90 before the test and at on" ........................................ 17
Figure 3.1.4 Young’s modulus (Mpa) vs. Temp. (°C) ................................ 19

Figure 3.1.5 Poisson’s ratio vs. Temp. (°C) ............................................. 19
Figure 3.1.6 Ultimate tensile stress (Mpa) vs. Temp. (°C) ........................... 20
Figure 3.1.7 Yield stress (Mpa) vs. Temp. (°C) ........................................ 20
Figure 3.1.8 E (T) vs. time for 6025A at various temperatures ................... 27
Figure 3.2.1 (a) Worm gear details [36] ................................................. 28
Figure 3.2.1 (b) Worm Gear profile ....................................................... 28
Figure 3.3.1 Forces acting on the worm/worm gear pair ............................ 32
Figure 4.1.1 Line of action for worm-worm gear pair [37] ........................... 39
Figure 4.2.1 cm for Steel (axial pitch=1.92mm)—Left View ...................... 53
Figure 4.2.2 am for Steel (axial pitch=1.92mm)—Right View ..................... 53
Figure 4.2.3 Equivalent plastic strain for Steel (axial pitch=1.92mm) ............ 54

ix

Figure 4.2.4 om for GC25AO23C (axial pitch=1.92mm) ......................... 55
Figure 4.2.5.Equivalent plastic strain for GC25A@23C (axial pitch=1.92mm).. 55
Figure 4.2.6 am for GCZSAOZSC (axial pitch=2.25mm)—Left View ............ 56

Figure 4.2.7 om for GCZSA@23C (axial pitch=2.25mm)—Right View ......... 56

LIST OF SYMBOLS

0 stress
a, yield stress

Su , our, ultimate tensile strength

0k fatigue limit

,u Poisson’s ratio

a strain

5,, plastic strain

E Young’s modulus
p density

D. P Diametral pitch

xi

Chapter 1

INTRODUCTION

Gears are used for transmission of power and motion in many
applications. A worm gear set consists of a shaft with helical threads and a
wheel with teeth either parallel to the axis of rotation (spur gear) or at an angle
to the axis (helical gear). Worm gears are used when the rotary motion has to
be converted to linear motion and where large gear reduction ratios are
desired. An interesting property of worm gears is that although they can rotate
either way, there is only one allowable driving gear, the worm. That is, the
worm can turn the gear; the gear cannot turn the worm, owing to the geometry
of the worm. Worm gears are used in odometers, conveyor systems, Torsen
(Torque Sensing) differentials [1], and most notably in business machines like
printers/scanners/plotters where the crosshead travel is controlled by a worm
gear. Worm gears are also used to drive the windshield wipers and power

windows in automobiles.

Gears are made of metal, which makes parts that use gears heavy.
Weight reduction has become a primary issue in many industries. Limited
knowledge about the characteristics and behavior of plastics/composites,
which are light in weight and are promising candidates for replacing metals,
has led to extensive research in the plastics industry. The automotive
industry, in particular, is exploring this ‘switch-over’ to plastics because of its

many advantages.

Plastics are light in weight (which is important for fuel economy); they
absorb shock and vibrations, and also reduce operating noise. They require
little or no lubrication, and are corrosion resistant. Metals used in gears could
be over-designed, and outlast the machinery they are a part of, while plastics,
which are designed for the same purpose, would last for the appropriate

service life.

Plastics allow design flexibility and are easily finished. They can be
injection molded, thus eliminating the machining and finishing processes,
which reduces production time and costs. The advantages of plastics offer

promising future uses in many industries.

Plastics gears have some limitations. The load carrying capacity of
plastics is low when compared to that of metals. From the Table (1.1), it is
evident that plastics/composites are inferior in properties when compared to
metals (steel in this case). Tensile strength of steel is 584.7Mpa, while Celcon
M90 (at yield) is 66Mpa, which is 11% the strength of steel, whereas Celcon
GC25A (at break) is120Mpa, which is 20% the strength of steel. Their

behavior is largely dependent on working temperature, and they have a high
coefficient of thermal expansion (COTE). Steel has a COTE of16.6x10'° /K,

while that of Celcon M90 isl.2xlO"/K and Celcon 6025A: 0.3x 10“/K.

Table (1.1) Mechanical Properties of Steel and Alternative Materials Used for
Worm Gear

 

. Coeff. Of
. Tensnle
MatenaV thermal
Property fang)" expansion Author
9 (I K)

 

httpJ/www.efunda.com/materialslalloys/
Steel 584.7 16.6x10'° alloy_home/steels_properties.cfm

 

M90 66 1.2 x 10" Room

 

 

G025A 120 0.3 x10“ Ticona

 

 

 

 

 

Although there are a few disadvantages in switching to plastic gears, the
advantages outweigh the limitations. The following case study supports the
choice of material made in this project: “A wear-resistant acetal copolymer
allowed Whirlpool to produce a gear that lasts four times the normal machine
life of its World Washer. The robust and long-lasting Splutch (Splined Clutch)
Assembly can withstand 30Nm torque” [2]. Some companies (Maytag,
Whirlpool) have recognized the benefits of switching to plastics, and claim that
the plastic gears helped reduce part weight, as well as noise. They also claim

that these gears are highly durable. [3]

Different types of non-metallic gears are currently being manufactured
for various industrial purposes. 74% are spur gears, 15% helical, 5% worm,
4% bevel and the rest either epicyclic or internal gears. While the maximum
diameter of a cut gear is 1m (reference circle diameter), injection molded
gears saw a maximum of 200mm diameter. Approximately, 70% of the plastic

gears manufactured, are injection molded. The most commonly used plastic
3

for gears is nylon (43%), followed by acetal (34%). Nearly 50% of them

operate below a power of 10W and less than 10% at over 1kW. [4]

 

 

Figure 1.1 Worm gear [Courtesy of Figure 1.2 Worm gears in garage
lTW Spiroid, Chicago, IL] door openers [5]

 

 

 

 

 

The current project proposed by ATS McAllen, Texas, aims to eliminate
several problems resulting from the production of worm shafts used in
windshield wipers and power windows. These problems include production
bottlenecks and excessive scrap. The objective of this project was to find an
alternative material for the worm gear and wheel that can offer a service life of
at least 10 years and also satisfy the design constraints (within the limited
motor housing space). By finding suitable materials, the ultimate goals to
minimize operating noise level, and operating vibration, maintain reliability,

improve production output, and reduce manufacturing costs, will be met.

 

    

I
i

1

Figure 1.3 Wiper motor with worm gear [6]
1. Perrnanent-magnet DC motor, 2. Worm gear, 3. Shaft and

 

 

 

The first step involved identifying possible candidate materials, by
comparing their mechanical properties as published by the suppliers. Two
materials were selected and standard material tests, such as tensile test and
creep test, were conducted to compare the material characteristics and to

assess the suitability of these candidates for the specific application.

Finite element analysis was performed on the worm gear tooth, using
the material properties obtained from the tests conducted. Thus a
comparative study on the performance of the worm gear, using different
materials, was done. The results are based on two criteria; one based on the
properties obtained from experiments and the other was based on properties
published [7]. The size of the gear made from composite should be 4.25 times
the current size of the steel worm, to last for a year and 5 times the original
size would last for 10 years when operating at a temperature of 1050, based

on the first criterion, while those based on the latter one yields a size of 3.25
5

times the original size to last for a year and 3.5 times to last for 10 years

operating at 105C.

Chapter 2

LITERATURE REVIEW

An effort to study the various effects and the trade-off paid by switching
to plastic gears began as early as 1965. It has been cited in a European
patent [8] that man-made materials are better than metals for worm gears, as
their efficiency is relatively higher. Hooke, C.J et al (1993) [9] observed that
the life of the gear depends on the tooth wear and not on fatigue at low loads.
Several tests were conducted, and a conclusion reached that acetal has a
sharp rise in wear, which was associated with the maximum surface
temperature of the gear reaching the melting point of acetal, as the
transmitted torque increased, thus limiting the use of acetal gears to low
torque transmission. The efficiency of various combinations of plastic and
steel gears with varying torques and running speeds was reproduced by
Walton D et al (2002) [10]. The graphs showed that the efficiency of acetal
/ABS - steel gear pair ranges from around 92% at low loads and increases up
to 96% at the highest load and that the efficiency is speed-dependent and all
the material combinations showed similar response to change in running
speeds. It is seen that the acetal-steel pair is the better combination for any

speed.

The efficiency of dry running plastic gear pairs is expected to be high at
the start (near-static condition) and increase with increasing load (for some
plastics) as the coefficient of friction decreases. Walton et al. [10] showed the
efficiency of a pair of POM (acetal) gears over a range of loads and speeds
under lubricated conditions. Performance of nylon6.6 (driver) - acetal pair
(driven), which is a promising combination was discussed. It was
demonstrated through experiments on a worm gear made of polymer
composite, that the transmission efficiency increases when lubricated under
O/W (Oil-in water) emulsions. This is due to self-lubrication of the material and

also due to the formation of a water film [11].

It has been observed that the efficiency of the acetal gears is high and
almost similar at low speeds, irrespective of the load. Also, efficiency is
independent of the speed when it is more than 500rpm while it decreases by
up to 10% when it ranges between 0 and 500rpm, and efficiency increases
with increase in torque. Wear, which is a measure of loss of material, is
relatively low in acetal gears running at a low torque of 7N-m. Acetal gears
running at 1000rev/min and at low loads showed approximately linear wear
and were nearly stable for sometime, and after a certain period, wear
increased rapidly and failed due to plastic bending, which occurred due to
material softening. If this material were overloaded, it would result in

excessive wear and tooth breakage [12].

Assuming that the loss in efficiency is entirely due to friction, Walton D

et al. derived friction coefficients for POM-POM gears for a range of loads and
8

speeds. An important implication made here is that the maximum contact

stresses occur on the tooth flank surface when p is greater than 0.3. A

comparison of wear, wear rates and performance of acetal/acetal and

nylon/nylon gears was made.

Vilmos Simon (1996) [13] performed stress analysis in worm gears. He
demonstrated that considering multiple teeth for finite element analysis proves
to be expensive in terms of memory size and computational time, while the
difference in the displacements and stresses is relatively small. And hence, a
single worm thread was considered for the finite element analysis for this

project.

A conclusion was made in Simon ‘5 work that stresses in the worm
thread are strongly influenced by the number of worm threads, pitch diameter,
tooth height and worm thread thickness factor while other worm design
parameters have a moderate effect on the stresses. Hence, these parameters
have to be borne in mind while designing the plastic worm. It was concluded
that the performance of acetal is entirely dependent on wear and its life is
limited to 500 hours at 1000 rev/min at low loads, and high wear rates could
be explained as the result of surface temperature reaching the material

melting point when transmission torque is increased.

The bending stress on the 10DP. (Diametral Pitch) acetal gears should
be limited to 2000psi, at a speed of 500 ft/min when running under dry

conditions, for the gear to last for more than 107 cycles. It has been observed
9

that a gear with fine pitch lasts longer than a coarse one as the former will
heat up less. The gear life is affected by the operating speed, which directly
affects the heat generation rate in a gear-pair. Gear life increases with speed
when it is in the range of 600—1600ft/min. At higher speeds, heat generation

increases and lubrication does not improve. [14]

John W. Kelly [15] proved that PK (aliphatic polyketones) has better
properties in terms of creep rupture and impact resistance, when compared
with POM, while POM (being a non-ductile polymer) is more creep-resistant.
The gears used in windshield wipers and power windows experience stalled
conditions, a stage where the rotation stops and the teeth in mesh experience
instantaneous maximum load. Hence a study has to be made to measure the
“accumulative creep strain” for acetal for the total stalled and cycled time.
Approximate Notched Izod impact test (ASTM D-256) values for acetal at -

40°C and 23°C are 42.7 and 53.4 J/m respectively.

Paul Wyluda and Dan Wolf [16] conducted experiments and finite
element analysis on acetal spur gears and came to a conclusion that the
prediction of the behavior of acetal gears is a complex phenomenon and that
it can be assumed linear elastic only for low loads and deformation. It was
suggested that both experimentation and FEA should be conducted, and
performing just one of the two would limit our understanding about the

behavior of the plastic gear.

10

It has been ascertained that plastic gears can be used for power
transmission and also the load carrying capacity of these gears can be
increased by modifying the design (9.9. tooth profile modification, increasing
the module to a value greater than 2) [17]. Though, it was initially suggested
that nylon could be used for power transmission, later investigations proved
that a phenomenon called creep occurred in the nylon gear, which influenced

abrasion that occurs in these gears. [18]

Crippa G. and Davoli P., 1995 [19] concluded in their work that glass-
reinforced composite should not be used to mate with steel gears, because,
though they carry the advantage of improving the mechanical properties of the
material, they cause wear (depending on their orientation), which is not
acceptable in the industry. However, adding a lubricant could reduce this wear
problem. Carbon fibers allow high torque transmission with acceptable wear.
Further exploration is needed to compare the performance of carbon vs.
glass-reinforced composites. It was also mentioned that plastic gears could
see a torque of 20-45Nm for more than 10 million cycles, at a speed of

1500rpm and 3-7kW.

The material under consideration to replace steel worm was chosen as
acetal (after an extensive search in the literature) as this material is
considered to be the most popular of the structural plastics [20], [21]. It was
also proved [20] that stress concentrations increase fatigue life, which is
defined as the number of cycles of oscillation N before a specimen fractures

at a given stress or strain [22].
11

Several analyses on plastic gears were performed using finite element
methods [13, 16, 23]. An effort has been made in this paper to determine the
mechanical properties of the plastic/ composite using the standard tests
(ASTM D638, DMA, DSC) and these properties were used in the finite
element analysis of the worm thread, to determine the difference in the
material behavior under similar loading. While in most works [13, 24], the load
was assumed to act on the tip of the gear tooth and there is also evidence
that several teeth carry load at all times [25]; for simplification of the problem,

this paper looks at stresses when the load acts on the face of a single tooth.

A study of nylon gears for transmission of torque shows that they
cannot be used without lubrication and also thermal conductivity is uneven
throughout the gear, which results in the tooth breakage near the pitch point
[26]. Though a similar behavior was seen in acetal, gears made of acetal
seem to be a better choice for low torques, when wear has to be kept to a
minimum [12]. Hooke C. J et al, 1996 [27] examined various materials, among
which acetal and nylon existed and they concluded acetal gears were superior
in performance and would last longer, provided the contact stress and
maximum temperature do not exceed 50Mpa and 80°C respectively. If wear

rate of 10'5 pm /cycle is acceptable, then they can see a temperature of 150°C.

Significant crack formation was observed in case of nylon gears when they

reached a temperature of 80°C.

Acetal gears can be successfully used to operate windshield wipers

and power windows by modifying a few design parameters; for instance, the
12

uneven temperature distribution can be suppressed by using small modules,
increasing the number of teeth as well as the face width, this also helps in
increasing the load capacity. When the face width is increased, it should also
be provided with ringed grooves to take care of the heat accumulated in the
middle, due to the low thermal conductivity of the plastic [28]. An equation
was developed to calculate the load capacity of the plastic gear using the

bending stress at the pitch point (where most of the fractures occur) [24].

13

Chapter 3

3.1. Experimental Work

3.1 .1 . Injection-Molding

Celcon M90 and Celcon GC25A, which were kindly donated by Ticona
(supplier), were chosen as the possible materials to replace steel in the worm
gears. The former is a grade of acetal capolymer; while the latter is a grade of
25% glass filled acetal copolymer. The materials, which come in the form of
pellets, were injection molded into tensile bars following the procedure
mentioned in the data sheets. Table 3.1.1 shows the temperatures maintained
in the different sections of the injection-molding machine. The injection speed
was set to 12.7mm/sec (0.50in/sec) and 6.35mm/sec (0.25in/sec) for Celcon
M90 and Celcon 6025A respectively. The screw was set to 40rpm speed and
the fill pressure was set to a limit of 6.89Mpa (1000psi).

Table 3.1.1.Temperatures set in various sections of the injection-molding

 

 

 

 

 

 

machine
Set (°F) Actual (°F)
Nozzle 430 429
Zone 1 400 400
Zone 2 380 382
Zone 3 340 340

 

 

 

l4

 

3.1.2 Unlaxlal tensile test

Universal lnstron test machine was used to conduct uniaxial tensile
test on Celcon M90 and Celcon GCZSA to determine the material behavior at
different temperature levels. The temperatures at which the specimens were
tested are 1500, 23C, and -4OC. Longitudinal and transverse extensometers
were used when applicable. Maximum travel for the longitudinal gage was
10% (2.54mm extension) and for transverse gage was 2% (0.508mm). The
crosshead speed was maintained at 1mmlmin. Five specimens for the filled
material and five to ten for the unfilled were tested at each temperature. The
filled bars behaved predictably (Fig. 3.1.1 (a)), and a typical stress-strain

curve was obtained, while the unfilled bars did not break (Fig. 3.1.1(b)).

Figure 3.1.1 (a) stress vs. strain graph of filled acetal

 

GC25A9 23C

 

 

 

 

a

Q

E —GczsAozec
g — Seriesz

c7)

 

 

0 0.005 0.01 0.015 0.02
Long. strain

 

 

 

15

Figure 3.1.1 (b) stress vs. strain graph of unfilled acetal

 

M90023C

12

10 /
—M90023C
/ — 890932
4

 

 

 

 

 

 

 

 

Stress (Mpa)

 

 

 

 

 

0 0.001 0.002 0.000 0.004 0.005
Long. strain

 

 

 

The test could not be conducted up to failure using the extensometers
on the unfilled specimens. If the stress-strain curve was linear the same test
bar was used to determine the ultimate load and when this curve turned non-
linear, a different specimen was used to determine the peak load. Since the
unfilled specimen did not yield, nor break, the ultimate load was assumed at
the point on the curve where the peak load was constant. The specimens
were kept at room temperature and 50% relative humidity. When tested at
temperatures other than the room temperature, the specimens and the grips
were quenched to that temperature in an Applied Test Systems
Programmable oven for at least 60 minutes to allow the test specimens as
well as the grips to have a uniform temperature. The tests show that the

material behavior largely depends on the temperature.

16

 

Figure 3.1.2. GCZSA after and before the unixial tensile test

 

Figure 3.1.3. (a) M90 before the test and (b) M90 before the test and
at Oyiejd, at Cult

Table 3.1.2 Mechanical properties of 6025A at different temperatures

 

 

 

 

 

 

 

 

 

Ult. tensile Yield stress
Temp(C) E (Mpa) .U
stress(Mpa) (Mpa)
-40 10257.372 0.401 138.345 20.514
23 8816.213 0.472 94.926 17.632
150 4854.369 0.542 47.145 9.708

 

Table 3.1.3 Mechanical properties of M90 at different temperatures

 

 

 

 

 

 

 

 

 

Ult. tensile Yield stress
Temp(C) E (Mpa) .14
stress (Mpa) (Mpa)
-40 3588.22 0.374 83.001 7.176
23 2857.67 0.427 54.387 5.715
150 952.78 0.424 20.925 1 .905

 

From Tables 3.1.2 and 3.1.3, it is seen that the material properties change

with temperature. Tensile strength of the material has been defined as the

stress needed to break the sample [29]. While the tensile strength and

young’s modulus of both grades of Celcon decreased with increasing

temperature, Poisson’s ratio increased with an increase in temperature. Then,

the fatigue limit, 0k. which is generally assumed as 30-40% of the tensile

strength is also influenced by the temperature [30].

18

 

 

 

 

 

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1 v o r r 1 v '
~60 «10 -20 0 20 40 so 30 100 120
Temp (C)
Figure 3.1.4 Young’s Modulus (Mpa) vs. Temp. (°C)
nu vs temp
0.00
0.54
0.50 /
y
g —£%W’1T§ 40.42
:5 0.37
E 0.30 +GczsA
S +M90
(I)
'3 .__..‘___,______9,20_ m
Q.
010
.v , o‘m ' 1 v v Y
00 -40 -20 0 20 40 so 30 100 120
Temp ( C)

 

Figure 3.1.5 Poisson’s ratio vs. Temp. (°C)

19

 

 

ult tensile stress vs temp

 

+ M90
+ GC25A

 

 

 

ult tensile stress,MPa

 

-60 40 -20 0 20 40 so 00 100 120
Temp,C

 

 

 

Figure 3.1.6 Ultimate tensile stress (Mpa) vs. Temp. (°C)

 

yleld stress vs temp

 

 

 

 

 

 

 

 

a

D.

2.. 15 \

§ -e—M90
.3 1° _ +cczsA
g

.9

 

6040-20020406080100120
Temp,C

 

 

 

 

 

 

 

Figure 3.1.7 Yield stress (Mpa) vs. Temp. (°C)

20

Though the neat plastic Celcon M90 did not show a yield point during the
uniaxial tensile test, for the purpose of running a non-linear analysis, yield was

assumed at the same point where the glass-reinforced plastic yielded. Using
Considere criterion [€13 =0] and power-law hardening equation [a = k£"],
a

we obtain the relation n=€ to be the limiting strain at which uniform
elongation ends and necking begins under the uniaxial deformation.
Assuming that 0:0), at 5:0.002, n can be solved, iteratively, using the

In(ay )- In(s,,)
ln(0.002)+ ln(e)- In(n) '

 

formula: n =

It has been demonstrated [31] that the values of k and n, thus calculated give
more accurate results and hence values obtained from the above calculations
have been used in the non-linear finite element analysis. For different values

of 5p assumed, corresponding stress values were obtained using the power-

law relation.

3.1.3 DMA Creep test

Though some experts were skeptical about using Dynamic Mechanical
Analysis (DMA) for creep prediction of composites, it has been stated [32] that
the time temperature superposition is applicable to fiber-reinforced plastics,

though only for short-terrn creep.

The viscoelastic nature of polymers causes their deformation to
depend on time as well as temperature. The characteristic of viscoelasticity is

that the elastic modulus of the material decreases over a period of time for a

’71

~

constant load, due to molecular rearrangement within the polymer. Time-
temperature superposition principle states that this behavior of molecular
rearrangement at a particular temperature over a long period of time can be
conveniently predicted by conducting DMA such as creep, stress relaxation,

etc at elevated temperatures for a shorter period of time [33].

Stress relaxation experiment was conducted to determine the long-
term properties of the materials. This procedure involves applying stress on
the specimen to maintain constant strain (of value 1.0) at different
temperatures, and this stress is measured as a function of time. The stress
relaxation modulus is obtained by dividing time dependent stress by constant
strain (TA Instruments Rheology Advantage Manual, [34]. Once this data is
recorded, using time-temperature superposition principle (TT S), we obtain the
corresponding modulus (E (t)) value at the reference temperature, which is a
function of time. A specimen of rectangular cross-section of dimensions 5 x
12.4 x 1.23 (mm x mm x mm) was used for conducting the stress relaxation
experiment. It has been demonstrated that creep experiments exhibit
excellent repeatability (2.3%) [35]. Due to lack of experimental resources at
the appropriate time, the tests were conducted only on single specimens of
each material, at the TA Instruments head office, Delaware. The results
obtained from this experiment have been tabulated with select data points as

in Table 3.4 for glass-reinforced acetal.

22

Table 3.1.4 TTS results for glass reinforced composite

T .=23C T .=4OC

 

Data about the material behavior of the composite at 1000 after 10
years could not be obtained with this experiment; hence it was done by
extrapolation with the existing values. A graph was drawn for E (t) vs. time
over a period of 10 years at temperatures where data was recorded, and a
curve-fit to these graphs resulted in constants A (T) and B (T) (T able 3.1.5).
The general form of the curve-fit to each of the plots is of the form:

E(T,t) = A (T) Ln(t) + B (T). The variation of these constants with temperature
(Table 3.1.6) was plotted and fitting a polynomial to these curves gave a set of
equations for A (T) and B (T), which were then used to calculate the unknown
value of E at 1000. Now, plugging these values of constants into the general

form of the curve-fit yields E (T, t), i.e., E is obtained as a function of time and

23

temperature. Assuming a constant error in the value of E (T , t) between the
experimental and the curve-fit at 1000, values were extrapolated for the
experimental set-up (which was then incorporated in the finite element
model).

The procedure used to predict the material property of the composite
operating at 100C is depicted below:

Table 3.1.5 Curve-fit for E (t) vs. time at various temperatures

 

 

 

 

 

 

Temp. C Curve Fit for E (t) vs. time graph
23 y = -247.26Ln(x) -l- 4689.3
40 y = -213.2Ln(x) + 3812.9
60 y = -155.77Ln(x) + 2540.6
80 y = -97.476Ln(x) + 1603.9

100 y = -102.53Ln(x) + 1090.6

 

 

 

 

Table 3.1.6 A (T), B (T) at varying temperatures

 

 

 

 

 

 

Temp. C A (T) B (T)
23 -247.26 4689.3
40 -213.2 3812.9
60 -1 55.77 2540.6
80 -97.476 1 603.9
100 -102.53 1090.6

 

 

 

 

 

24

The polynomials obtained for A (T) and B (T) are:-
' A (T): y = -0.0009x3 + 0.148x2 - 4.7729x - 204.04

B (T): y = 0.007x3 - 1.0273x2 - 10.647x + 5401.2

Table 3.1.7 A (T), B (T) from curve-fitting

 

 

 

 

 

 

 

 

 

Temp. C A (T) B (T)
23 -246.475 4698.046
40 -215.756 3779.64
60 -152.014 2576.1
80 -99.472 1558.72
100 -101.33 1063.5

 

Table 3.1.8 E (T, t) from experiment and curve-fitting at (a) 230 (b) 400 (c)

600 (d) 800 (e) 1000

Table 3.1.8 (a)

 

 

 

 

 

 

 

 

 

 

Temp., C
23 time, yr E(T) experimental error%
1 4698.0463 4690 -0.17
2.5 4472.204 4462 -0.23
5 4301 .360 4304 0.06
7.5 4201 .423 4207 0.13
10 4130.517 4123 -0.18
Avg. -0.08

 

 

 

 

 

25

 

Table 3.1.8 (b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temp., C
40 time, yr E(T) experimental error%
1 3779640 3779 -0.02
2.5 3581.945 3596 0.39
5 3432.394 3438 0.16
7.5 3344.913 3369 0.71
10 3282.843 3394 3.28
Avg. 0.91
Table 3.1.8 ( 0)
Temp., C
60 time, yr E(T) experimental error%
1 2576.1 2502 -2.96
2.5 2436.811 2391 -1.92
5 2331.443 2290 -1.81
7.5 2269.807 2239 -1 .38
10 2226.075 2181 -2.07
Avg. -2.03
Table 3.1 .8 (d)
Temp., C
80 time, yr E(T) experimental error%
1 1558.720 1598 2.46
2.5 1467.575 1501 2.23
5 1398.626 1437 2.67
7.5 1358.294 1404 3.26
10 1329.677 1386 4.06
avg 2.93

 

 

 

 

 

26

 

 

 

Table 3.1.8 (6)

 

 

 

 

 

 

 

 

 

 

 

 

Temp., C
100 time, yr E(T) experimental error%
1 1063.5 1 1 42 6.87
2.5 970.652 1042.299 6.87
5 900.416 966.878 6.87
7.5 859.330 922.759 6.87
10 830.179 891.457 6.87

 

The numbers in experimental column for Temp.=100°C for time 2.5 to 10yrs

are estimated

 

E(T) vs. time

 

 

 

 

 

y = -247.26Ln(x) + 4689.3

 

E(t), Mpa

\ y = -213.2Ln(x)T§8T2

 

¥ v = -155.77Ln(x) + 2540.6

 

v = -97.476Ln[x] + 1603.9

 

 

.§§§§§§§§§

y = -102.53Ln(x) + 1090.6

 

 

 

fl

0.00 200 4.00 6.00 8.00 10.00 12.00 14.00

time, yrs

 

 

—GC@230
GCO40C
—GC@600
—GC@80C
——GC@100C
—Log. (GC@230)
—Log. (GC@40C)
—-Log. (GCOSOC)
—Log. (GCOBOC)

—Log.
[QCQ1M]

 

 

 

Figure 3.1.8. E (T) vs. time for GC25A at various temperatures

27

 

 

3.2 GEOMETRY OF THE WORM

The finite element model of the worm is based on the design data

provided by Visteon Wiper/Washer Engineering. The worm dimensions are as

 

stated in Table 3.5.
wow THIOAT An PRESSURE
Pom RADIUS mss ANGLE
out!
DEPTH
out!

.\ .
y ‘ Inn-101.6
W new A53: E W 255:!!!"
W
HEAD l CIRCULAR
imcxness "7°“

Figure 3.2.1 (a) Worm gear details [36]

 

 

 

 

 

Lead 2 3.84
Axiol Pitch = 1.92

/“’\ Leod Angle = 10.05
”““““1gWitttfi'“‘“

. D—J \ “1,! k
I] I] i, 1I it ii I :i "-
‘ i ; I I: I l ‘I
'l‘ 'l'.‘. [Iii Iii]

 

 

 

 

 

Figure 3.2.1 (0) Worm Gear profile

 

 

 

28

Table 3.2.1 Geometry of the worm and worm gear [37]

 

 

 

 

 

 

 

 

 

 

 

 

Worm gear Worm
Major diameter 628610.076 8465:0032
Root diameter 595610.076 5.00:0.05
Tooth form lnvolute lnvolute
Normal module 0.6025 0.6025
Axial lead 1084.2 3.845
Circular tooth thickness 1.1561003 073410.025
Pitch diameter 61.19 6.88
Lead angle, A _ 10.0540
Normal circular pitch 1.89 1.89
Axial pitch _ 1.92
Normal pressure angle, 14.50 1450
(D0

 

 

 

 

3.3 DETERMINATION OF THE FORCE COMPONENTS AC'I1NG ON THE
WORM

Fig.3.7 illustrates the force components (tangential, radial and axial)
that act on the worm and the worm gear for a windshield wiper. As the exact
mechanism for a windshield wiper is not clear, the forces have been assumed
to be operating on the power window for the analysis. The FE model has been
simplified by neglecting the friction force components. The force components

are derived using the following formulae [38]:

29

 

Load Data

Maximum Sliding Velocity, V. = 85.2001/sec = 167.721t/min

Coefficient of friction for V3=167.72 ft/min., f =0.05 [39] (this is approximately

equal to the value given in the design data, f = 0.046).

Rotational speed and torque characteristics of the worm and the gear,
considered for the force analysis, are given in Table 3.6.

Table 3.3.1 Operational characteristics of the worm and the gear.

 

 

 

 

(Driver) Worm (Driven) Worm gear
Rotational speed (rpm) 1950.0 39.0
Torque (N-m) 0.8643 34.0

 

 

 

Number of teeth on the worm gear, N, = 100
Number of teeth on the worm, N,, = 2 (the number of teeth on the worm is

equal to the number of starts)

Stall force (Tangential) on Worm Gear:

ZTg _ 2x34.0

— =1112.57N (Tangential force on the worm gear = axial
dg 0.06112

 

force on the worm, F3, = Fwa)

But, this force is the total force acting on two teeth (as the number of starts is
two, hence two teeth mesh at any point of time with two teeth of the mating
gear, thus the load is distributed between two teeth).

Axial force per worm tooth, F8, = Fwa = $221]! = 556.28N

30

 

Worm Tangential force:

21,, _ 2x0.8643

3 =251.25~
4w 6.38x10"

 

F wt =
(Axial force on the worm gear = tangential force on the worm, Fga = m)

Tangential force per worm tooth, Fga = er = 3.5% =125.63N

Radial force:

 

F _ Fg, -tan¢ _1112.56xtan(14.5)

_ .. = 292.21N
gr cos). cos(l 0.05)

(Radial force on the worm gear = Radial force on the worm, Fgr = w)

Radial force per worm tooth, F8, = Fw, -_- 2232i]! =146.1N

31

‘6 -
' ' ,3 f :: Worm Shaft

   

Bull Gear

Force Components
th= Fwa= 1112.56 N
Fm: Fwr = 292.2 N

Fga= FM =251.25 N

Fig.3.3.1 Forces acting on the worm/worm gear pair

32

3.4 DETERMINATION OF VOLUME AND MASS OF MATERIAL

The total volume of material required to produce a worm gear from
plastic/composite can be determined by calculating the volume of the cylinder
(cylinder formed from inner radius) and the volume of the helical thread. For
the case of steel, the material is machined to make the thread and hence the
total volume of material required would be equal to the volume of the outer
cylinder. The volume of the helical thread can be determined by considering
its cross-section as a trapezoid. The length of the helix can be determined
from the axial pitch and inner radius [40]. The relations can be framed as
below:

Length of threaded worm using steel = 35 mm

Total length of the steel shaft = 181.2 mm
Diameter (pitch) = 6.88 mm
Major Diameter = 8.465 mm
Minor Diameter = 5.0 mm

No. of threads =NW x (length of threaded worm/axial pitch)
For a double threaded worm, NW = 2

Density of steel, p, = 7.87 gn'I/crn3

Density of GC25A, ch = 1.58 gm/cm3

Price of steel per in3 = $ 0.471 = 0.00287cents/mm3

Price of GC25A per in3 = $ 0.053 = 0.000323cents/mm3
Volume of the steel material required = [(shaff - Iength)xm02]

= 10197.69 mma

Mass of steel required, M, = p, x 10197.69 mm3 = 0.0803Kg = 60.2egm

33

Price of one steel cylinder = 29.26 cents
Volume of plastic material used = volume of solid shaft + volume of helix

= (shaft length x c.s area of 9 ft) +(length of helix x c.s area of he ical thread)

(area of circle) (area of trapezoid)
= [(shaft -length)x 71702] + [(helix —length)x% - h -(a + 3)]

= 3557.85 mm3 + 1028.298 mm3

= 17064.2 mma

where, inner radius of the shaft = r,- = 5.0 mm

tooth height: h =1.32 mm
parallel sides of the trapezoid, a = 0.634 mm

b =1.34mm

34

Chapter 4

FINITE ELEMENT ANALYSIS

A finite element model of a shaft with a single worm thread was
developed using Unigraphics®. Hypermesh® was used to develop the mesh
and to assign the boundary conditions and material properties and solver
used was ABAQUS implicit code, V6.3 [41]. Tetra 4 elements were used for
analyzing the material response. Though it is suggested to avoid tetra
elements due to their inefficiency to provide converging solutions [41], it is a
common practice to use them in most industrial applications dealing with
complex geometries; therefore the tetra 4 has been used for this analysis.
Both ends of the shaft were fixed and the force components calculated in
Chapter 3 were applied to a portion of the face (where the arc length was
approximately equal to the face width of the gear, 4.6mm) Properties of three
different materials, steel, Celcon M90 and Celcon G025A shown in Table
4.2.2 were applied to the model. Material properties for the plastic and
composite were obtained from experiments conducted at different

temperatures, -400, 230, and 1050.

For the purpose of simplicity, following assumptions are made in the
finite element analysis: (i) materials are within the linear elastic range (ii)
materials are isotropic (iii) loads applied are static in nature. The composite

was also assumed as an isotropic material due to various reasons, foremost

35

being, for simplicity. Fiber orientation and distribution in an injection molded
component largely depends on the component geometry, molding conditions,
such as gating, pressure, temperature and holding time, matrix material,
polymer melt viscosity, characteristics of fiber, such as density, aspect ratio
and volume fraction [42]. By assuming that all these factors were chosen
carefully so that the fibers were randomly oriented, and hence an assumption

that it is isotropic is justified.

4.1. REDESIGN OF THE WORM WITH PLASTIC

The initial analysis was performed on the model with original worm
dimensions. As expected, the results went into the plastic region. Using the
following set of relations, (which slightly deviate from the worm design
standards); the dimensions of the model were gradually increased and
depending on the results, were modified until an optimum design was reached
which was well within elastic limits:

Relations used in designing a worml :

Pressure angle, On: 14.5

Axial pitch, px = 1 .92

No. of threads on the worm, NW = 2

Lead angle, A = 10.05°

Helix angle, B = (90- A) = (9010.05) = 79.95°

Lead, L = N... . px

Normal circular pitch, pn = px cos A

Diametral pitch, Pa = n/ pn = 1.66

 

' All units in mm
36

Circular pitch, Pc = p.Jcos [3 = 10.81

Pitch diameter, dw = L / 1T tan A

Addendum, a = (1 .0/ Pa )= (1 .0/1 .66) = 0.602
(these relations are meant for a spur gear)
Dedendum, b = (1 .25/ Pa) = (1 .25/1 .66) = 0.753
Whole depth, m =0.6866 px = 0.6866192 = 1.318
Working depth, hi. = 06366" p"

0.0, do = d.,-I-2a = 6.882 + 2(0.602) =8.08(~8.465)
I.D, d. = do -2hI = 8.08—2(1.318) = 5.36(~5.0)

Face width of gear, F9 = 0.67 d...

Tooth thickness, tw = 0.5 p)( . cos A

Dimensions required for the design:

1) Axial pitch, px

2) Major diameter, 0. D

3) Root diameter, ID

4) Angle between 2 teeth, 20).. [this is constant]

Tables 4.1.1 (a) and (0) describe the gear dimensions for different values of

axial pitch. Table 4.1.2 (a) and (b) show the different force components acting

on the gear tooth based on the force analysis described in Chapter 3.3. The

desired output torque being constant, the increase in the gear dimensions

results in smaller forces acting on it. Since, the load acts over an area, it has

to be applied as DLOAD, which is similar to pressure. The area over which

the force components act (area of contact, Figure 4.1.1 [37]) has been

approximately chosen. A curve over the tooth surface was developed in

37

Unigraphics®, such that the length of the arc is nearly equal to the face width
of the mating gear. It is assumed that the force components act on a single
face of the tooth at any given point in time. Elements with common faces exist
at the edge of the tooth and hence the elements that form this edge have not
been considered as the area where the forces act. Hence, the criterion for
selecting the area for applying the pressure was the actual area of contact,

and not the face width or the working depth.

38

CurentModdFWbc
mummcmmezsmc

 

 

THE WORM AND GEAR MESH AT THE POINTS ALONG THE LINE OF
ACTION. IN OUR WORM-GEAR DESIGN, WE HAVE TWO TEETH IN
CONTACT AND TRANSFERRING LOADS AT ANY GIVEN POINT IN
TIME. THE LINE OF ACTION INTERSECTS AT THE PITCH
DIAMETERS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

.. l . Y r 3
.o. 7’4 LINE OF ACTION \
mg) *3 \
'0‘ - h 'l-fi
\ ;

\ /

\v‘ \U
-.04 7° _...._._

, c

-.06
-.25 2 15 1 0 05 1 15 2

 

THE GEAR IS DRIVEN IN
THIS DIRECTION

 

 

 

 

THE WORM-GEAR MESH IS DESIGNED TO
ALLOW A CLEARANCE OR BACKLASH AND IS

NOT INTENDED TO HAVE TOOTH CONTACT.

 

 

 

Figure 4.1.1 Line of action for worm-worm gear pair [37]

39

Table 4.1.1 (a) Calculated dimensions of the worm gear

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Axial L p, Pd P, d... a b h.
Pnchrpx
1.92 3.84 1.691 1.662 10.634 6.897 0.602 0.752 1.316
2.4 4.6 2.363 1.329 13.542 6.621 0.752 0.940 1.646
2.66 5.76 2.636 1.106 16.250 10.345 0.903 1.126 1.977
3.072 6.144 3.025 1.039 17.334 11.035 0.963 1.204 2.109
3.166 6.336 3.119 1.007 17.675 11.360 0.993 1.241 2.175
3.264 6.526 3.214 0.977 16.417 11.725 1.023 1.279 2.241
3.36 6.72 3.306 0.950 16.959 12.070 1.053 1.316 2.307
3.456 6.912 3.403 0.923 19.500 12.414 1.063 1.354 2.373
3.552 7.104 3.497 0.696 20.042 12.759 1.113 1.392 2.439
3.646 7.296 3.592 0.675 20.564 13.104 1.143 1.429 2.505
3.744 7.466 3.667 0.652 21.125 13.449 1.173 1.467 2.571
3.64 7.66 3.761 0.631 21.667 13.794 1.204 1.504 2.637
4.32 8.64 4.254 0.739 24.376 15.516 1.654 1.692 2.966
4.6 9.6 4.726 0.665 27.064 17.242 1.504 1.661 3.296
5.26 10.56 5.199 0.604 29.792 16.966 1.655 2.069 3.625
5.76 11.52 5.672 0.554 32.501 20.691 1.605 2.257 3.955
6.24 12.46 6.144 0.511 35.209 22.415 1.956 2.445 4.264
6.72 13.44 6.617 0.475 37.917 24.139 2.106 2.633 4.614
7.2 14.4 7.090 0.443 40.626 25.663 2.257 2.621 4.944
7.66 15.36 7.562 0.415 43.334 27.567 2.407 3.009 5.273
6.16 16.32 6.035 0.391 46.043 29.312 2.556 3.197 5.603
6.64 17.26 6.507 0.369 46.751 31.036 2.706 3.365 5.932
9.12 16.24 6.960 0.350 51.459 32.760 2.656 3.573 6.262
9.6 19.2 9.453 0.332 54.166 34.464 3.009 3.761 6.591

 

40

 

Table 4.1.1 (0) Calculated dimensions of the worm gear (cont.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Axial do (I; Fo tW height pitch heworking Area of

pitch,p,, die of depth ”mam
gear

1.92 8.100 5.464 4.621 0.94 1.318 61.1 1 1.20 5.56
2.4 10.12 6.830 5.776 1.18 1.648 76.39 1.50 8.69
2.88 12.15 8.196 6.931 1.41 1.977 91.67 1.81 12.51
3.072 12.96 8.742 7.393 1.51 2.109 97.78 1.93 14.24
3.168 13.36 9.015 7.624 1.56 2.175 100.8 1.99 15.14
3.264 13.77 9.289 7.856 1.60 2.241 103.9 2.05 16.07
3.36 14.17 9.562 8.087 1.65 2.307 106.9 2.11 17.03
3.456 14.58 9.835 8.318 1.70 2.373 110.0 2.17 18.02
3.552 14.98 10.10 8.549 1.74 2.439 1 13.0 2.23 19.03
3.648 15.39 10.38 8.780 1.79 2.505 1 16.1 2.29 20.08
3.744 15.79 10.65 9.011 1.84 2.571 119.1 2.35 21.15
3.84 16.20 10.92 9.242 1.89 2.637 122.2 2.41 22.25
4.32 18.22 12.29 10.39 2.12 2.966 137.5 2.71 28.15
4.8 20.25 13.66 1 1.55 2.36 3.296 152.7 3.01 34.76
5.28 22.27 15.02 12.70 2.59 3.625 168.0 3.31 42.06
5.76 24.30 16.39 13.86 2.83 3.955 183.3 3.61 50.05
6.24 26.32 17.75 15.01 3.07 4.284 198.6 3.91 58.74
6.72 28.35 19.12 16.17 3.30 4.614 213.9 4.21 68.13
7.2 30.37 20.49 17.32 3.54 4.944 229.1 4.51 78.21
7.68 32.40 21.85 18.48 3.78 5.273 244.4 4.81 88.98
8.16 34.42 23.22 19.63 4.01 5.603 259.7 5.1 1 100.4
8.64 36.45 24.58 20.79 4.25 5.932 275.0 5.42 1 12.6
9.12 38.47 25.95 21 .94 4.49 6.262 290.3 5.72 125.4

9.6 40.50 27.31 23.104 4.726 6.591 305.58 6.02 139.03

 

 

 

 

 

 

 

 

 

41

 

Table 4.1.2 (a) Forces acting on the worm tooth

 

Torque,To

Torque,TW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

px (N-m) (N-m) Fx'(N) Fy'(N) Fz'(N)
1.92 34 0.8643 -250.635 -1 1 12.64 292.2343
2.4 34 0.8643 -200.508 -890.1 17 233.7874
2.88 34 0.8643 -167.090 -741 .764 194.8228
3.072 34 0.8643 -156.647 -695.404 182.6464
3.168 34 0.8643 -151.900 -674.331 177.1117
3.264 34 0.8643 -147.432 -654.498 171 .9025
3.36 34 0.8643 -143.220 -635.798 166.9910
3.456 34 0.8643 -139.242 -618.137 162.3524
3.552 34 0.8643 -135.478 -601 .431 157.9645
3.648 34 0.8643 -131 .913 -585.603 153.8075
3.744 34 0.8643 -128.531 -570.588 149.8637
3.84 34 0.8643 -125.317 656.323 146.1171
4.32 34 0.8643 -1 1 1.393 494.510 129.8819
4.8 34 0.8643 -1 00.254 445.059 1 16.8937
5.28 34 0.8643 -91 .1402 404.599 106.2670
5.76 34 0.8643 -83.5452 -370.882 97.41 14
6.24 34 0.8643 -77.1 187 -342.353 89.9182
6.72 34 0.8643 ~71 .6102 -317.899 83.4955
7.2 34 0.8643 -66.8362 -296.706 77.9291
7.68 34 0.8643 -62.6589 -278.1 61 73.0586
8.16 34 0.8643 -58.9731 -261.799 68.7610
8.64 34 0.8643 ~55.6968 ~247.255 64.9409
8.832 34 0.8643 -54.4860 -241 .879 63.5291
9.12 34 0.8643 -52.7654 -234.241 61.5230
9.6 34 0.8643 -50.1271 -222.529 58.4469

 

 

 

 

42

 

Table 4.1.2 (b) Forces acting on the worm tooth (cont.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

load per tooth DLOAD
px Fx (N) F" (N) Fz (N) P" P" Pz
1.92 -125.317 -556.323 146.1 171 -22.5338 -100.034 26.2738
2.4 -1 00.254 -445.059 1 16.8937 -1 1.5373 -51 .2175 13.4522
2.88 -83.5452 -370.882 97.41 14 -6.6767 -29.6398 7.7848
3.072 -78.3236 -347.702 91.3232 -5.5014 -24.4224 6.4145
3.1 68 -75.9502 -337.1 65 88.5558 -5.01 63 -22.2688 5.8489
3.264 -73.7164 -327.249 85.951 3 -4.5866 -20.361 1 5.3478
3.36 -71.6102 -317.899 83.4955 -4.2046 -18.6653 4.9024
3.456 -69.621 0 -309.068 81 .1762 -3.8638 -1 7.1 527 4.5051
3.552 -67.7394 -300.715 78.9822 -3.5589 -15.7991 4.1496
3.648 -65.9567 -292.801 76.9038 -3.2853 -14.5844 3.8306
3.744 -64.2656 -285.294 74.9319 -3.0390 -13.4910 3.5434
3.84 -62.6589 -278.1 61 73.0586 -2.81 67 -12.5043 3.2842
4.32 -55.6968 -247.255 64.9409 -1 .9783 -8.7822 2.3066
4.8 -50.1271 -222.529 58.4469 -1.4422 -6.4022 1.6815
5.28 -45.5701 -202.299 53.1335 -1.0835 -4.8101 1.2634
5.76 -41 .7726 -1 85.441 48.7057 -0.8346 -3.7050 0.9731
6.24 -38.5593 -171.176 44.9591 -0.6564 -2.9141 0.7654
6.72 -35.8051 -1 58.949 41 .7478 -0.5256 -2.3332 0.6128
7.2 -33.41 81 -148.353 38.9646 -0.4273 -1 .8969 0.4982
7.68 -31 .3295 -139.080 36.5293 -0.3521 -1 .5630 0.4105
8.16 -29.4865 -130.899 34.3805 -0.2935 -1 .3031 0.3423
8.64 -27.8484 -123.627 32.4705 -0.2473 -1 .0978 0.2883
8.832 -0.02724 -0.12094 0.031765 -0.00023 -0.00102 0.00027
9.12 -26.3827 -117.120 30.7615 -0.2103 -0.9334 0.2452
9.6 -25.0636 -1 1 1 .264 29.2234 -0.1803 -0.8003 0.2102

 

43

 

4.2. MODEL DEFINITION

A static analysis was performed on the simplified model of the worm. The
worm is “encastred” on both ends of the shaft. Initially a 2-d mesh (T ria3) was
developed on the surface of the model, which was then developed into a 3d

(0304 elements). Number of the nodes and elements used for different

models are in Table 4.2.1.

Table 4.2.1. No. of nodes and elements used in the FEA analysis

 

axial pitch,px

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(mm) p,/1.92 no. of nodes no. of elements
1.92 1 3132 12645
2.4 1.25 3654 15150
2.88 1 .5 18276 93270
3.072 1.6 8174 35109
3.36 1.75 6911 29571
3.84 2 6780 28949
4.32 2.25 9269 40478
4.8 2.5 6780 28949
5.28 2.75 1 1 758 51 793
5.76 3 9030 39528
6.24 3.25 13440 59655
6.72 3.5 12436 55879
7.2 3.75 13418 59062
7.68 4 10461 46230
8.16 4.25 9128 40152
8.64 4.5 9956 44270
8.832 4.6 13846 61319
9.12 4.75 13484 59376
9.6 5 10141 44684

 

Material properties (Table 4.2.2) and boundary conditions were assigned to

the model In Hypermesh® and solved using ABAOUS solver. Material

44

 

properties for unfilled polymer and glass reinforced composite at initial time, to,
were available from experiments while the common properties published for
AISI 1144 steel were considered. [43]. Material properties at the end of 5

years and 10 years were obtained as discussed in Chapter 3.1.3.

Table 4.2.2. Assumed material properties at initial time, to

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6025A
Temperature E, Mpa sigma u, sigma y, Mpa
(Celsius) Mpa
-40 10257.372 138.34 20.514
23 8816.213 94.926 17.632
105 4854.369 47.145 9.708
M90
E, Mpa sigma u, sigma y, Mpa
Mpa
-40 3588.220 83.001 7.176
23 2857.670 54.387 5.71 5
105 952.780 20.925 1 .905
Steel E, Mpa sigma u, sigma y, Mpa
Mpa
23 210000 584.7 346.8

 

 

 

 

 

Elasto-plastic analysis was performed on the model where
material properties were known from experiments, whereas, elastic analysis
was performed for the extrapolated values. In both cases, the size of the
model was increased until the maximum stress was either less than or equal
to the yield stress of the material. The results obtained (T able 4.2.3 (a), (b),
(c), 4.2.4 (a), (b), (c), 4.2.5were based on two criteria: 1) yield stress is 0.2%

of the tensile strength (from experiments conducted at MSU) of the material 2)

45

safe stress published elsewhere. [7]. The elasto-plastic analysis of the model
is defined in the input file as follows (the number of nodes and elements have
been reduced as they occupy great amount of space):

** ABAOUS Input Deck Generated by HyperMesh Version : 5.1
** Generated using HyperMesh-Abaqus Template Version : 5.1-1

it

** Template: ABAOUS/STANDARD 30

it

'NODE
1,1.497510028E-14, 35.0 , 4.2325
2, 0.0 , 33.99344002519 , 4.2325
3, 0.0 , 32.986880050381, 4.2325
4, 0.0 , 31.980320075572, 4.2325
5, 0.0 , 30.973760100763, 4.2325
6, 0.0 , 29967200125954, 4.2325

*ELEMENT,TYPE=03D4,ELSET=n1
4164, 2491, 1921, 2063, 1910
4165, 2001, 1877, 1878, 1921
4166, 2368, 916, 929, 2392
4167, 1223, 1781, 2229, 2131
4168, 2510, 750, 2455, 2511
4169, 2673, 1563, 1582, 1740
4170, 1584, 73, 1752, 72
*SOLID SECTION, ELSET=n1, MATERIAL=G025A
“HMCOLOR COMP 6 10
*NSET, NSET=nset1
53, 54, 55, 56, 57, 58, 59, 60,
61, 1531, 1532, 1533, 1534, 1535, 1536, 1537,
1538, 1558, 1559, 1560, 1561, 1562, 1578, 1579,
1588.
'ELSET, ELSET=elem1
4278, 4362, 4397, 4578, 4616, 4901, 5087, 5107,
5118, 5396, 5401, 5677, 5887, 5889, 5934, 5995,
5996, 6159, 6160, 6169, 6208, 6496, 6498, 6537,
6596, 6770, 6860, 8098, 8225, 9076
*MATERIAL, NAME=G025A
*DENSITY
1 .58005—09,23.0
*ELASTIC, TYPE = ISOTROPIC
8816.21 ,0.47 ,23.0
*PLASTIC, HARDENING=ISOTROPIC
17.63 ,0.0 ,23.0
20.679 0000654 .230
23.156 000137 ,23.0
27.158 000292 ,23.0
30.410 000455 ,23.0

46

33.1 99
38.936
43.599
47.596
51 .1 33
54.328
57.257
59.971
62.507
64.894
67.1 52
69.299
71 .348
73.309
75.1 93

,0.00623 ,23.0

,0.01058 ,23.0
,0.01 505 ,23.0
,0.01 96 ,23.0
,0.0242 ,23.0
,0.0288 ,23.0
,0.0335 ,23.0
,0.0382 ,23.0
,0.0429 ,23.0
,0.0476 ,23.0
,0.0524 ,23.0
.0.0571 ,23.0
,0.061 9 ,23.0
,0.0667 ,23.0
,0.0715 ,23.0

82.088 ,0.0907 ,23.0
'STEP, INC = 1000, NLGEOM

“HMNAME LOADCOL 4 Ioadcol

"HMCOLOR LOADCOL 4 15

*STATIC

0.1 ,1.0 , ,

*BOUNDARY
1963,ENCASTRE
1962,ENCASTRE
1961 ,ENCASTRE
1960,ENCASTRE
1959,ENCASTRE
1958,ENCASTRE
1957, ENCASTRE
1956,ENCASTRE
1955,ENCASTRE

*DLOAD, OP=MOD
9076, P3,26.27
6169, P3,26.27
5401, P3,26.27
6208, P1 ,26.27
9076, P3,-100.03
6169, P3,-100.03
5401, P3,-100.03
6208, P1 ,-100.03
9076, P3,-22.53
6169, P3,-22.53
5401, P3,-22.53
6208, P1 ,-22.53

*NODE FILE

U.

RF,

*EL FILE

S.

47

SP,

SINV,

E,

EP,

PE,

*NODE PRINT,FREOUENCY=
U.

*EL PRINT,FREOUENCY=
S.

SP,

MISES.

E.

SINV,

EP,

PE,

*END STEP

2

2

48

yield stress from current work—b oyr

FEA ANALYSIS RESULTS

yield stress from Clifford E. Adams [7]-> or;

ELASTO-PLASTIC ANALYSIS

Table 4.2.3 (a) FEA results for G025A at 230 at to

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0y] = 17.63 Oy2 =
6025A@230 Mp a 48.26 Mpa
. . axial pitch Von Mises . Equivalen
”misfit" p" increased stress,Mp D'sfzfizren t plastic
a strain
1.92 0% 82.090 3.0330 1 .7600
2.88 50% 48.700 0.0675 0.0210
3.072 60% 31 .980 0.030 0.005
3.84 100% 22.8600 0.0194 0.0013
4.32 125% 17.6600 0.0126 0.0000 7'13; E'
4.8 150% 10.9200 0.0090 0.0000
ELASTIC ANALYSIS (TTS) [after 5yrs]
Table 4.2.3 (0) FEA results for GC25A at 230 after 5yrs
TI'SG025A@230 0,1 = 8.608 Mpa 0,2 = 23.6 Mpa
. . axial pitch Von Mises Displacement
ax1al p'tCh’ p, (mm) increased by stress,Mpa (mm)
3.36 75% 39.2500 0.0438
3.84 100% 29.3400 0.0375
4.32 125% 17.7200 0.0257
4.8 150% 15.0300 0.0192
5.76 200% 10.460 0.01975
6.72 250% 5.315 0.01 168

 

 

 

 

49

 

 

ELASTIC ANALYSIS (TTS) [after 10yrs]

Table 4.2.3 (o) FEA results for G025A at 230 after 10yrs

 

 

 

 

 

 

 

 

 

 

 

 

TTSGC25A@23C 0,1: 8.246 Mpa 0,2: 22.6 Mpa
. . axial pitch Von Mises Displacement

aXial p'tCh’ p" (mm) increased by stress, Mpa (mm)
3.84 100% 29.3400 0.0392
2.4 125% 17.7200 0.0269
5.76 200% 10.460 0.02062
6.72 250% 5.315 0.01219

ELASTO-PLASTIC ANALYSIS

Table 4.2.4 (a) FEA results for G025A at 1050 at to

 

 

 

 

 

 

 

 

 

 

G025A@1050 0,1 = 9.71 Mpa or,» = 26.57
Mpa
axial pitch, px axial pitch Von Mises Displacemen Equivalent
(mm) increased by stress,Mpa t (mm) plastic
strain
1.92 0% - -
2.88 50% 33.080 0.149 0.047
3.072 60% 24.680 0.065 0.020
3.36 75% 21 .530 0.052 0.013
3.84 100% 17.810 0.041 0.007
4.32 125% 1 1 .780 0.019 0.00096
4.8 150% 9.485 0.013 0.000

 

 

 

 

 

50

 

 

ELASTIC ANALYSIS (TTS) [after 1er

Table 4.2.4 (b) FEA results for 0025A at 1050 after 5yrs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'I'I‘SGCZSAO1050 0,1 = 2.246 Mpa 0,2 = 6.15 Mpa
. . axial pitch Von Mises Displacement

ax1al p'tCh’ p, (mm) increased by stress,Mpa (mm)
3.84 1 00% 25.3700 0.1 1 78

5.76 200% 9.0210 0.0633

6.24 225% 5.2600 0.0412

6.72 250% 4.7860 0.0371

7.2 275% 3.7400 0.0338

8.16 325% 2.2020 0.0209

8.64 350% 1 .8370 0.0191

9.6 400% 1.5120 0.0159

ELASTIC ANALYSIS (TTS) [after 10yrs]
Table 4.2.4 (o) FEA results for 0025A at 1050 after 10yrs
TI'SG025AO1050 0,1: 1.78 Mpa 0,2 = 4.88 Mpa
. . axial pitch Von Mises Displacement

ax1al p'tCh’ p, (mm) increased by stress,Mpa (mm)
6.24 225% 5.259 5.2590
6.72 250% 4.787 0.0467
7.2 275% 3.74 0.0426
7.68 300% 3.1 17 0.0316
8.832 360% 1 .936 0.0265
9.12 375% 1 .888 0.0255

9.6 400% 1.512 0.0201

 

 

 

 

51

 

 

 

ELASTO-PLASTIC ANALYSIS

Table 4.2.5. FEA results for G025A at -40°C at to

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6050590 6,. = 20.51 Mpa 6,2 = 56.14 Mpa
axial pitch, axial pitch Von Mises Displacem qu:;‘;:::nt
p, (mm) increased by stress,Mpa ent (mm) p .
strain
1 .92 0% 134.400 1 .192 0.543
2.88 50% 58.760 0.059 0.017
3.84 100% 26.470 0.020 0.00103
ELASTO-PLASTIC ANALYSIS
Table 4.2.6. FEA results for AISI 1144 Steel
Steel 0,1: 346.8 Mpa [Ref: efunda.com]
axial pitch, px Von Mises Displacement 612,031?
(mm) stress,Mpa (mm) strain
1 .92 348.500 0.008 0.000 9.21 E-05

 

 

 

 

 

52

 

0110‘: ”TT—T_ ‘ ESSIEHJIW ' "‘eiénftidb

 

Figure 4.2.1. am, for Steel (axial pitch=1.92mm)—Left View

Viwport: 1 01in- REFMmmyaheLWSéufiii—

 

Figure 4.2.2 0max for Steel (axial pitch=1.92mm)—Right View

53

Vlewatzi 6117 hTonTénfiTeéufia/tfiiyiilaeijmTeVThfiToa: | ['—

 

Figure 4.2.3. Equivalent plastic strain for Steel (axial pitch=1.92mm)

54

OETififinfiTem 7’ 'fimjnafe‘éfrfiahefiflwfilei Tum

 

Figure 4.2.5.Equivalent plastic strain for G025A@230 at time, to (axial
pitch=1.92mm)

55

a’AV‘v, . '1 '1 v;
A'AV‘V‘ ’1'}? 'y‘ '
A747 0 l

«gag,
13.17":
‘5

'mfia’m‘t' "om: Mammsswicaajzsjm’ '

VHHHEAUD
s18.1] _ "

 

Figure 4.2.7. omoxfor G025A@230 after 10yrs(axla| pitch=2.25mm)—Right View

56

 

4.3. COST ANALYSIS

The lead required for lifting the window through some distance is constant;

hence the same travel is required for the redesigned composite gear. The

volume of the composite required (based on calculations shown in Chapter

3.4) would be as in Table 4.3.1.

Table 4.3.1 Volume of composite material required

 

Volume of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

axial . % . Volume of Total Mass of Price of
pitch "'1: 3:? {$2234 solid shaft Volurraie G025A acetal
(mm) pitch (mm3) (mm3) (mm ) (Kg) (dollars)
1.920 0% 1028.290 3557.853 4586.144 0.0072 0.014813
2.880 50% 231 4.437 9559.431 1 1 873.868 0.01876 0.038353
3.072 60% 2633.105 10876.508 13509.614 0.02134 0.043636
3.840 100% 41 16.813 16994.545 21 11 1 .358 0.03335 0.06819
4.320 125% 5208.666 21508.721 2671 7.387 0.04221 0.086297
6.240 225% 10867.805 44876.220 55744.025 0.08807 0.1 80053
6.720 250% 12603.010 52045.794 64648.804 0.10214 0.208816
7.200 275% 14468.971 59746.447 74215.418 0.1 1726 0.239716
8.1 60 325% 1 8583.525 76740.992 95324.51 8 0.15061 0.307898
9.600 400% 25722.616 106215.906 131938.521 0.20846 0.426161

 

57

 

Chapter 5

SUMMARY AND CONCLUSIONS

Based on the FEA analysis, the mass and cost estimate show that
switching to a composite (e.g., 6025A) would reduce weight as well as the
material cost. Besides, the machining cost for a steel part is considerably high
compared to plastic one. The cost of the machined blank would cost about
$0.20/part while the machining processes such as hobbing, deburring would
result in a cost of $1 Olpart. The plastic part would require less machining (if
necessary) and hence the material cost as well as machining cost is much
less compared to the steel part. Injection molding (which is generally done in
huge quantities, (250,000-500,000 parts) would cost $0.20/part and the
investment cost would be about $16K-$20K. These estimates would defer
among different manufacturers, but would still result in cheaper processing of

plastic parts compared to steel ones [44].

This project did not consider thermo-mechanical 'issues. Hence, work
regarding the thermal aspect should be considered. Future work could be
developed by assuming the composite as orthotropic and determining,
experimentally, the mechanical properties in different directions. Dynamic
modeling and contact analysis could be performed and based on the results

obtained; prototype testing of a worm could be conducted.

58

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59

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62