Nguyen Danh Tuyen Thesis

8/3/2019 Nguyen Danh Tuyen Thesis

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ABSTRACT

Normally, violin bows are produced by craftsman, and they still have some

disadvantages, such as unstable qualities, high prices, low production...etc. Therefore,the purpose of this thesis is to present a new method of producing violin bows to

overcome these limitations. Especially, according to this method, to produce violin

bows, we needed a 4-axis CNC machine. However, there isnt any 4-axis CNC machine

but only a 3-axis one in my school. So a new solution will be presented to deal with this

obstacle: Using a 3-axis CNC machine to produce a violin bow of which quality is still

accepted. Furthermore, a new cross section of the bow stick is also introduced in this

thesis.

In the new CAD/CAM method, CAD is applied to draw the violin bow. Then CAM

is applied to create NC codes that are imported into CNC machine to produce the bow

stick. Thanks to the method, bow sticks are almost produced automatically, as well as

have stable qualities, high production. Furthermore the expense of producing violin

bows are reduced, and their prices are lower. In addition, in this thesis by researching a

cross sectional area of the violin bows, the new ones are created that are lighter,

comfortable, and strong enough.

Keyword: Violin bow, CAD, CAM, CNC, bending stress

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ACKNOWLEDGEMENT

To be able to be successful in completing my master thesis, first of all, Id like to

thank my advisors, associate professor Ming Jong Wang and associate professor Hsin-Te Liao very much. My teachers always took care me of my thesis process and gave

me a lot of valuable suggestions as well as orientation while I was working on my

thesis. In addition, they not only taught me valuable knowledge to fulfill my thesis but

also taught me a lot of other important skills, such as a good working attitude, specially,

modern research method in scienceetc.

I heartily like to thank our school, Ming-hsin University of Science and Technology

(MUST ) as well as the Taiwanese government that granted me a full scholarship for my

master program. It helped me to have a chance to receive advanced technologies in the

world and very impressive management methods. Staying here for about 2 years, truly

speaking, the Taiwanese taught me a lot of valuable things to become a better citizen,

for example behaving with people and manners in public places.

I also would like to thank the staff like Miss Kitty, Mrs Katty, Mrs Chen, in

mechanical engineering department , who are very enthusiastic to help anything we

needed, as well as my Taiwanese and Vietnamese classmates who helped me so much

when I studied at MUST.

In the end, from the bottom of my heard, I would like to express my gratitude and

appreciation to my English teacher Frank Varela and my family for their supports and

encouragements.

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3.1.2Creating the bow stick 39

3.1.3Making button 43

3.1.4Fitting all parts 46

3.1.5The material of the violin bow 47

3.2Creating NC codes 47

3.2.1Creating NC codes for the traditional bow stick 47

56

56

3.2.2Creating NC codes for the new bow stick 64

68

3.2.3Exporting to NC codes 74

3.3Introduction to the CNC machine Vcenter-65 77

3.4Producing the bow sticks 78

CHAPER 4 RESULTS AND DISCUSSIONS 85

CHAPER 5 CONCLUSIONS AND FUTURE WORK 92

5.1Conclusions 92

5.2Future work 92

REFERENCES 93

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TABLE OF FIGURES

Figure 1.1 The violin bow 2

Figure 2.1 Different shapes of cross section of sticks 5

Figure 2.2 Forces applied to the violin bow stick 5

Figure 2.3 Shifting the coordinate system 6

Figure 2.4 Circular cross section 6

Figure 2.5 Elliptical cross section 7

Figure 2.6 (a) Eight divisions of octagon; (b) Dimensions and symbols of octagon 8

Figure 2.7 (a) Four divisions of octagon; (b) Dimensions and symbols of area A1 9

Figure 2.8 (a) Four divisions of decagon; (b) Three divisions of area A1 12Figure 2.9 (a) Dimensions and symbols of division A5; (b) Dimensions and symbols of

division A1 13

Figure 2.10 (a) Division of new cross section; (b) dimensions and symbols of new cross

section 16

Figure 2.11 Measuring the dimensions of the traditional violin bow 22

Figure 2.12 Dimension near the bottom 22

Figure 2.13 Dimensions of the bow stick 23

Figure 2.14 Dimensions of head 24

Figure 2.15 Creating the new holder part 24

Figure 2.16 Extruding the part with pad 25

Figure 2.17 Creating datum coordinate system 25

Figure 2.18 Creating Spline 26

Figure 2.19 Creating head 28

Figure 2.20 (a) The completed traditional bow stick; (b) The dimensions of traditional

bow stick 29

Figure 2.21 Creating the new holder part 32

Figure 2. 22 Creating datum coordinate systems 33

Figure 2.23 Creating cross sections of bow stick 34

Figure 2.24 Creating new main bows tick 35

Figure 2.25 (a) The completed new bow stick; (b) Dimensions of new bow stick 36

Figure 3.1 Ferrule & Ebony frog blank 37

Figure 3.2 Chiseling and planning the frog 37

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Figure 3.3 Assembling the silver liner and eyelet 38

Figure 3.4 Creating silver ring 38

Figure 3.5 Making the silver ring rounded 39

Figure 3.6 Gluing pearl eye and silver ring 39

Figure 3.7 Planning and measuring the stick 39

Figure 3.8 Heating the violin bow stick 40

Figure 3.9 Bending violin bow stick 40

Figure 3.10 Gluing ivory and ebony liner of tip 41

Figure 3.11 Shaping and refining the tip 41

Figure 3.12 Chiseling the mortise 41

Figure 3.13 Drilling hole 42

Figure 3.14 Forming the nipple 42

Figure 3.15 Planning the stick 42

Figure 3.16 Fitting frog to stick 43

Figure 3.17 Making silver ring 43

Figure 3.18 Making the body of button 44

Figure 3.19 Gluing the silver ring to the body 44

Figure 3.20 Creating the collar 44

Figure 3. 21 Drilling the hole for fitting the screw 45

Figure 3.22 Fitting the screw to the button 45

Figure 3.23 Fitting another silver ring 45

Figure 3.24 Lathing the hole 46

Figure 3.25 Filing the button into octagon shape 46

Figure 3.26 Creating NC codes 47

Figure 3.27 Dividing the bow stick 48

Figure 3.28 Opening file IGES 49

Figure 3.29 Rotating all entities of part1 50

Figure 3.30 Creating contours of lower part 1 50

Figure 3.31 Roughing lower part 1 51

Figure 3.32 Semi finishing lower part 1 52

Figure 3.33 Finishing lower part 1 53

Figure 3.34 Simulating the cutting process of lower part1 54

Figure 3.35 Creating contours of lower part 2 55

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Figure 3.36 The cutting process of lower part2 55

Figure 3.37 Regen path of lower part2 56

Figure 3.38 The cutting process of upper part2 56

Figure 3.39 Regen path lower part 1 57

Figure 3.40 The cutting process of upper part1 57

Figure 3.41 Opening the file upper part 1 58

Figure 3.43 Creating the tool paths for supporting parts of upper part 1 60

Figure 3.44 The cutting process of supporting parts of upper part 1 60

Figure 3.45 Opening the file upper part 2 60

Figure 3.46 (a) Deleting old contours and tool paths; (b) Creating new contours 61

Figure 3.47 Cutting supporting parts of upper part2 62

Figure 3.48 Deleting tool paths 62

Figure 3.49 Regen path 62

Figure 3.50 Cutting supporting part of lower part 2 63



Figure 3.53 Dividing new violin bow 65

Figure 3.54 Creating contours of lower new part1 65

Figure 3.55 Simulating the cutting process of lower new part1 66

Figure 3.56 The contours of lower new part 2 66

Figure 3.57 The cutting process of lower new part2 67

Figure 3.58 Regen path lower new part 2 67

Figure 3.59 The cutting process of upper new part2 68

Figure 3.60 The cutting procession of upper new part1 68

Figure 3.61 The file upper new part 1 69

Figure 3.62 (a) Deleting tool paths of new part; (b) New contours of new part 1 69

Figure 3.63 Cutting supporting part of upper new part 1 70

Figure 3.64 The file upper new part 2 70

Figure 3.65 (a) Deleting old contours and tool paths of upper new part2; (b) New

contours of upper new part 2 71

Figure 3.66 Cutting supporting part of upper new part2 71

Figure 3.67 Deleting tool paths of upper new part 2 72

Figure 3.68 Regen path 72

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Figure 3.69 Cutting supporting part of lower new part 2 73



Figure 3.72 Creating NC codes 75

Figure 3.73 Adjusting the NC program 76

Figure 3.74 The completed file of NC codes 77

Figure 3.75 CNC machine Vcenter-65 78

Figure 3.76 Starting machine 79

Figure 3.77 Returning machine zero points 80

Figure 3.78 Drilling holes 80

Figure 3.79 The dimensions of holes on the base 81

Figure 3.80 The dimensions of holes on the work piece 81

Figure 3.81 Putting location pins on the base 82

Figure 3.82 Positions of pins while producing the lower part1 82

Figure 3.83 Positions of pins in the under part2 83

Figure 3.84 Positions of pins in the upper part2 83

Figure 3.85 Positions of pins in the upper part1 83

Figure 3.86 Selecting a stock origin 83

Figure 3.87 Inputting NC codes 84

Figure 3.88 Starting the program 84

Figure 4.1 Traditional bow stick 85

Figure 4.2 New bow stick 85

Figure 4.3 The unsmooth part of bow stick 86

Figure 4.4 Mesh surface 86

Figure 4.7 The normal wooden supporting base 89

Figure 4.8 The new supporting base and location pins 89

Figure 4.9 Tolerance when selecting stock origin twice 90

Figure 4.10 Important surfaces of work piece 90

Figure 4.11 The broken cutting tool 91

LIST OF TABLE

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NOMENCLATURE

A Cross sectional area

c The distance from neutral axis to oustermost point of a cross section

dCi Diameter of cross section i ( i 1,13= ) of traditional bow stick

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dNi Diameter of cross section i ( i 1,13= ) of new bow stick

F Area of some cross sections

h Height of violin bow head

I Moment of inertia of cross section about neutral axis

k Large width of violin bow head

IX The moment of inertia of the cross section about X axis

Ix The moment of inertia of the cross section about x axis

li The distance from the end of holder part to the section i

M Bending moment

m The distance that x axis shift to X axis

n The length of holder part

P Applied force from the index finger of player

q Small width of violin bow head

R Outer radius of new cross section

R1 Reaction force at tip from hair of bow

R2 Reaction force at the bottom from the thumb of right hand

r Radius

rc The radius of circular cross section

rN The radius of new cross section

S Modulus of the cross sectional area

S( ALO) Area of triangle ALOS( BLO) Area of triangle BLO

x Neutral axis

y The distance from neutral axis

z The length of violin bow head

b Bending stress

axm The maximum bending stress

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axCm The maximum bending stress of circular cross section

axNm The maximum bending stress of new cross section

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CHAPTER 1 INTRODUCTION

Scientifically speaking, it is very beneficial to listen to classical music. Such as it

helps human reduce stress, improve IQ (Intelligent quotient), even it can help enhance

animal products, sales at store, as well as decrease the crime rate. Instruments that

belong to classical music include bowed strings (violin, viola), woodwind (flute, oboe,

Clarinet, Bassoon), brass instruments (trumpet, French horn, Trombone, Tuba),

keyboard instruments (Plucked, Struck: piano, celesta, Aerated: organ, Electronic:

electronic organ, synthesizer) and guitar family. Among them, the woodwind

instruments play the most important role in a symphony orchestra or classical music [1].

And the violin plays the most important role in these instruments. Therefore we can see

that the violin bow has a extremely significant role in classical music.

The violin is a string instrument. It has a human shape and a human voice,

especially appropriate for the country of its modern origin. It is believed that the violin

originated from Italy in the early 1500s [2].The modern violin became established, in

the 19th century. It had been invented by Francois Tourte. Its weight, length, and

balance allowed the player to produce power and brilliance in the higher ranges. It was

Louis Spohrs invention of the chin rest around 1820 that made it possible for the player

to hold the violin comfortably and play in the standing positions. Spohrs chin rest also

resulted in the significant advancement of playing technique and allowed the violin

repertories to reach its very high level. The advent of the shoulder rest (no known date)

was also an important contribution to the ease of playing. With the origin of violin

bows, scholars have varying answers about them. Stringed instruments were around

possibly thousands of years before bows came along. They were played by plucking.

Bowing may trace back to 10th century Islamic civilizations. Scholars believe that

bowing began in the nomadic horse-riding cultures of Central Asia. By 1000 A.D., the

spread of Islam contributed to the use of bowed instruments in China, India, Java, North

Africa, the Near East, the Balkans and Europe. Since bows are made from horse hair, it

makes sense that bowed instruments would originate in horse-riding cultures [3].

A violin bow as shown in figure1.1, also is referred to as a fiddlestick, is as essential

as the instrument itself. Without the bow, a violin cannot produce music. Each

component of the violin bow serves a specific purpose, enabling the bow to glide across

the strings and create the vibrations that are the sounds of a violin. To evaluate the

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quality of a violin bow, demand many factors. However we can judge it according to the

following aspects: Sound (strong core, a lot of high overtones, a strong middle range),

volume (loud, low, focused, not so focused, good carrying power, no carrying power),

weight (heavy, light, balance (good, heavy at the tip, heavy at the frog), string contact

(even over the hole bow, not good at the tip, in the middle, at the frog), bounce (good

over the hole bow, regular, good only in one point, irregular), stability (is stable along

the whole stick, breaks out to the side in the middle, at the frog), stiffness (good, stiff at

the frog, middle, tip, weak at the frog , middle, tip), aesthetics (nice tip, frog, beautiful

wood, mother of pearl, gold , silver, nickel mounted), feeling (is comfortable in your

hands, not comfortable) [4].

Figure 1.1 The violin bow

However, almost all violin bows are hand-made, so their quality is very difficult to

be controlled, or in other words, each violin bow maker with different skill will create

the very different quality of violin bows. Even if, the quality of the violin bow that are

made by only one person also varies. Because the violin maker sometimes doesnt

concentrate on his work, so he will create some mistakes of violin bows. Furthermore,

because they are hand-made, so their prices are very high and unstable, for instance,

there is violin bows with hundreds of US dollars, but there are also violin bows with

thousands of US dollars or more. In addition, production of violin bows that are created

by hand is quite low, as well as there is very few people can produce violin bows, since

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it is very difficult to learn by oneself to produce them, and should be taught by a violin

bow maker.

In the past, it was very few people that could play musical instruments of classical

music, because they are usually musical instrument of high class people, for example

royal or very rich people. With the development of economics, as well as human life,

therefore, there are more and more people who want to learn and play them, particularly

the violin, at present. However, there is a large barrier with them, not only it is difficult

to play but also costly. Hence, it will be very beneficial, if there is a new method to

produce a violin or a bow that reduces the human labor, the design time, its price, and

its quality is guaranteed. The stick of violin bow plays a very critical role of its quality,

so we only focus on manufacturing the stick of violin bow with material of wood in this

thesis. From the above points, CAD/CAM techniques are used to produce a real violin

bow stick.

The design method for violin bow stick is founded on theories of mechanics and

strength of materials. The stick of violin bow is defined as a beam approximately. The

stick is supported by strings and right hand of player respectively, and bent by the index

finger of players right hand. From the purpose of selecting the violin bow that has a

stick with the smallest bending stress when bearing the same load. The bending stress is

in inverse proportion to the moment of inertia of the cross section. And the modulus of

the cross sectional area is in proportion to moment of inertia of cross section. Therefore,

the cross section of stick with the lager S is preferred. In this thesis, the formulas for the

moment of inertia of different cross sections were derived to find the one with the

largest S and the cross section with the largest S will the best selection for bow stick

design.

The 4-axis CNC machine is required to produce violin bow sticks. However, there

are only 3-axis CNC machines in our school. And the maximum operating length of

these machines is shorter than the bow stick. A new production technique is developed

to overcome above problems. All new ideas of bow design and production are from my

advisor associate professor Ming- Jong Wang.

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CHAPTER 2DESIGN OF THE BOW STICKS

2.1 The classification of violin bows

Violin bows are classified according to their materials. At present, there are fourmain kinds of violin bows that are presented as the following:

The tropical hardwood violin bow is usually made from Brazilwood or another

common tropical wood. These bows are inexpensive and readily available, making them

a common bow choice for beginning violin players.

The Pernambuco violin bow is heavier and more durable than Brazilwood, but can

also be more expensive due to the fact that the wood is a disappearing natural resource.

Pernambuco is an elastic wood that is extremely responsive to the touch. The wood is

supple and easy on the hands, and produces a richer and fuller sound. Experienced

players will choose this bow over a Brazilwood model.

In addition, there are two other kinds of violin bows: Cacbon fiber and Fiber glass

that are not as good as two above kinds because these materials are not as flexible as the

tropical wood and Pernambuco wood. They are also a common choice for a beginning

violin player.

2.2 The new idea of bow stick design

From the purpose of selecting the violin bow that has a stick with the smallest

bending stress when bearing the same load. In equation (2.1) and (2.3), the bending

stress is in inverse proportion to the moment of inertia of cross section. And the

modulus of the cross sectional area is in proportion to moment of inertia of cross

section. Therefore, the cross section of stick with lager S is preferred. In this thesis, the

formulas for the moment of inertia of different cross sections, such as circle, ellipse,

octagon, decagonetc as shown in figure 2.1 were derived to find the one with larger

S.

(a) Circle (b) Ellipse (c) Octagon (d) Decagon (e) New shape

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Figure 2.1 Different shapes of cross section of sticks

2.2.1 The bending stresses of bow stick

Assume the bow stick as a simple supported beam as shown in figure 2.2

R1 R2

Stick of violin bow P

Figure 2.2 Forces applied to the violin bow stick

The bending stress in this beam

=bM y

I (2.1)

The moment of inertia2= I y dA (2.2)

The maximum bending stress ax

= =mM c M

I S

Where =I

S

c(2.3)

The formula of moment of inertia, during shifting axis

Assuming a cross section has an area of F, a moment of inertia about neutral axis x

of Ix. If the coordinate system oxy shift to the coordinate system OXY which axis x

shifts a distance of m as shown in figure 2.3. Let IX is the moment of inertia about axis

X. It will obtain the formula as shown in formula (2.4) [5]

= + 2X xI I F m (2.4)

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dF

x

X

yY

O

o

m

F

Figure 2.3 Shifting the coordinate system

To compare the maximum bending stresses of cross sections, in their formulas, it

should have common parameters, such as radius, diameter, areaetc. In this thesis, to

be easy to compare the maximum bending stress and the masses of violin bows which

have sticks with different cross sections, the areas of cross sections are selected as a

common parameter. Or other hand, the areas of cross sections are equal.

2.2.2 The maximum bending stress of circular cross section

r

Figure 2.4 Circular cross section

The formulas of area and moment of inertia of circular cross section are basic ones

and available in many books, so it isnt necessary to present how to make them. All

formulas are derived from reference [6].

As shown in figure 2.4:

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Cross sectional area A= r2 =A

r

(2.5)

Moment of inertia =4

rI4

Modulus of the cross sectional area = = = =4 3I I r 1 r

Sc r 4 r 4

Combining equation (2.5) it obtains 3 / 2S 0.141A (2.6)

The maximum bending stress = = =max 3 3M 4 4M

MS r r

(2.7)

= max 3 / 2

M M

S 0.141A (2.8)

2.2.3 The maximum bending tress of elliptical cross section

The formulas of area and moment of inertia of elliptical cross section are basic ones

and available in many reference books, so it isnt necessary to present how to make

them. All formulas are derived from reference [6].

b

a

Figure 2.5 Elliptical cross section

In figure 2.5

Cross sectional area: = A a b

Ifb=0.6a then = =A

A a 0.6 a a0.6

(2.9)

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Moment of inertia:

=3b a

I4

Modulus of the cross sectional area:

= = = = =

3 2 3I I b a 1 0.6a a 0.6 aS c a 4 a 4 4

Combining equation (2.9) it obtains

3 / 2S 0.182A (2.10)

The maximum bending stress: = max 3 / 2M M

S 0.182A (2.11)

2.2.4 The maximum bending stress of octagonal cross section

As shown in figure 2.6(a), the cross sectional area

A = AA1+AA2+AA3+AA4+AA5+AA60+AA7+AA8

= AA1+AA1+AA1+AA1+AA1+AA1+AA1+AA1

= 8AA1 (2.12)

A B

O

L

AA1

AA2

AA3

AA4AA5

AA6

AA7

AA8

d

45

22.5

(a) (b)

Figure 2.6 (a) Eight divisions of octagon; (b) Dimensions and symbols of octagon

As shown in figure 2.6(b)

AA1 =S( ALO)+S( BLO)=S( BLO)+S( BLO)

=2S( BLO) (2.13)

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= =

= =

=

00

00

360AOB 45

8

45LOB 22.5

2

dOL2

= = 0d

LB OL.tan LOB tan 22.52

(2.14)

= = = 2

0 01 1 d d d S( BLO ) LB OL tan 22.5 tan 22.52 2 2 2 8

(2.15)

From equations (2.12), (2.13) and (2.15) it obtains:

Cross sectional area: = =

20 2 0d

A 8 2 ( tan 22.5 ) 2 d tan 22.58

Therefore =0

Ad

2tan22.5(2.16)

A1A2

A3 A4

O

BL

EN

M F

22.5

45

d

d

A

(a) (b)

Figure 2.7 (a) Four divisions of octagon; (b) Dimensions and symbols of area A1

As shown in figure 2.7(a)

Moment of inertia

( ) ( ) 2 2 2 2I= y dA= y d A1+A2+A3+A4 = y d A1+A1+A1+A1 =4 y dA1 (2.17)

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Let From equation (2.17) 2I1= y dA1 I=4I1 (2.18)As shown in figure 2.7 (a) and (b) I1=I( BNE) +I(NEFM) +I(MOLB )

(2.19)

As shown in figure 2.7 (b) = =BE AB 2LB


= =

= = = =

0 0

0 0

d BE 2 tan( 22.5 ) d tan( 22.5 )

2

2 NB NE MF BE sin(45 ) d tan( 22.5 )

2

= = =

= =

= =

0

0

dMN FE LB tan( 22.5 )

2

dOM LB tan( 22.5 )2

dMB OL

2

Calculating I( BNE)

Applying equation (2.4) it obtains

= + +

= + +

= + +

3

2

42 2

4

002

0 0 2

NE NB 1 NBI( BNE ) NE NB ( MN )36 2 3

NE 1 NBNE ( MN )

36 2 3

2 2d tan(22.5 ) d tan( 22.5 )2 1 2 d 2d tan( 22.5 ) ( tan( 22.5 ) )36 2 2 2 3

( ) = + +

40 21 1 2d tan( 22.5 ) (1 )16 9 3

(2.20)

CalculatingI(NEFM)

= =

=

3

3

0 0

MF MN I( NEFM )

3

1 2 dd tan( 22.5 ) tan( 22.5 )

3 2 2

= 4 0 42 d tan ( 22 .5 )48

(2.21)

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CalculatingI(MOLB)

=

3

OM OLI( MOLB )

3

= =4

0 3 01 d d d tan( 22.5 ) ( ) tan( 22.5 )3 2 2 48

(2.22)

From equations (2.19), (2.20), (2.21), (2.22), it obtains

( ) ( )

( )

+ + +

= + + + +

44

0 4 0 0 3 0 2

04

4 0 4 0 2

I1=I( BNE) +I(NEFM) +I(MOLB)

d 1 1 2= tan( 22.5 ) d 1 tan( 22.5 ) tan( 22.5 ) d tan( 22.5 ) (1 )

48 48 16 3

tan( 22.5 ) 2 1 1 2d tan( 22.5 ) tan( 22.5 ) (1 )

48 48 16 9 3


( )

=

= + + + +

04

4 0 4 0 2

I 4I1

tan( 22.5 ) 2 1 1 24d tan( 22.5 ) tan( 22.5 ) (1 )

48 48 16 9 3

Modulus of the cross sectional area

( )

( )

04

4 0 4 0 2

04

3 0 4 0 2

I I tan(22.5 ) 2 1 1 2 2S= = =4d + tan(22.5 ) + tan(22.5 ) +(1+ )

c (d/2) 48 48 16 9 3 d

tan(22.5 ) 2 1 1 2=8d + tan(22.5 ) + tan(22.5 ) +(1+ )

48 48 16 9 3

Combining (Eq2.16)

3 / 2S 0.01A (2.23)

The maximum bending stress

= max 3 / 2M M

S 0.01A (2.24)

2.2.5 The maximum bending tress of decagonal cross section

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A1A2

A3 A4

A6

A5

A7

36r

O

P

M

(a) (b)

Figure 2.8 (a) Four divisions of decagon; (b) Three divisions of area A1

From figure 2.8 (a)

Cross sectional area A.

A = A1+A2+A3+A4 = A1+A1+A1+A1

= 4A1 (2.25)

Because the decagon is regular, so = =0

0360MOP 36 10

Therefore from figure 2.8(b)

= + + = + +1

A1 A5 A6 A7 A5 A5 A52

= = = = 0 2 05 5 1 5 1 5

A1 A5 OP OM sin( AOB ) r r sin36 r sin36 2 2 2 2 2 4

Combining equation (2.25) it obtains = 2 0A 5r sin36

Therefore = 0

Ar

5 sin36 (2.26)

From figure 2.8 (a)

Moment of inertia about neutral axis

( )

( )

2 2

2 2

I = y dA= y d A1+A2+A3+A4

= y d A1+A1+A1+A1 =4 y dA1

Let = 2I1= y dA1 I 4I1 (2.27)

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72

O I K

QF

PL

M

367

2

O

P

M

3

6

E

r

G

(a) (b)

Figure 2.9 (a) Dimensions and symbols of division A5; (b) Dimensions and symbols ofdivision A1

From figure 2.8(a) and figure 2.9(b), it obtains

I1=I(OIPL)+I(IKQF)+I( QFP)+I( PLM)

From figure 2.9(a)

= =

= =

0 0

0

ME OM cos72 r cos72

MP 2ME 2r cos72

From figure 2.10(b)

0PQ=MP=2r cos72

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( )

0 0 0

0

0 0 0

0 2

0 2 0 2

0

0 0

0 0

0 0

LP=OI=MPsin72 =2r cos72 sin72

= r sin144

LM=MPcos72 =2r cos72 cos72

= 2r (cos72 )

OL=IP=OM -LM

= r-2r (cos72 ) =r 1-2 (sin18 )

= r cos36

FQ=IK=PQ sin36 =MP sin36

=2r cos72 sin36

FP=PQ cos36 =2r cos72 co

=

0

0

s36

GQ MP IF=KQ= =r cos72

2 2

( )

( )

= =

=

33

0 0

34 0 0

OI OL 1 I( OIPL ) r sin144 r cos 36

3 3

1r sin144 cos36

3

( )

( )

= =

=

33

0 0 0

44

0 0

IK IF 1 I( IKQF ) 2r cos72 sin36 r cos72

3 32 r

sin36 cos723

Applying equation (2.4) it obtains

= + +

= +

+ +

= +

23

0 0 0 0 3

20 00 0 0 0 0

4 40 0 3 0 4 0 0

FQ FP 1 FP I( QFP ) FP FQ IF

36 2 3

2r cos72 sin36 ( 2r cos72 cos 36 )

36

1 2r cos72 cos 36 2r cos72 cos 36 2r cos72 sin36 r cos72

2 3

4r rsin36 (cos 36 ) (cos72 ) cos72 sin144

9 2( )

+

20

20 2 cos36 cos72 1

3

( ) = + +

20

34 0 0 0 3 0 04 1 2 cos 36

r cos72 sin36 (cos 36 ) cos72 sin144 19 2 3

14


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( )

= + +

= +

+ +

= + +

=

23

30 0 2

20 2

0 0 2 0

24 0 2

0 0 6 4 0 0 2 0

4

LP LM 1 LM I( PLM ) LP LM OL

36 2 3

r sin144 2r (cos72 )

361 2r (cos72 )

r sin144 2r (cos72 ) r cos362 3

2r 2(cos72 ) sin144 (cos72 ) r sin144 (cos72 ) cos36

9 3

r sin144 + +

20 2

0 0 2 0 4 02 2(cos72 )(cos72 ) (cos72 ) cos36 9 3

Therefore

( ) ( )

( )

= + +

+ + + +

+ + +

43 4

4 0 0 0 0

20

34 0 0 0 3 0 0

4 0 0 2 0 4 0

I1=I(OIPL)+I(IKQF)+I( QFP)+I( PLM)

1 2 rr sin144 cos 36 sin36 cos72

3 3

4 1 2 cos 36 r cos72 sin36 (cos 36 ) cos72 sin144 1

9 2 3

2 2(cosr sin144 (cos72 ) (cos72 ) cos 36

9

20 2

72 )

3

Combining equation (2.27), it obtains

Moment of inertia

( ) ( )( )

( )

=

= + +

+ + + +

+ + +

3 44 0 0 0

20

34 0 0 0 3 0 0

20 2

4 0 0 2 0 4 0

I 4I1

4r sin144 cos 36 2 cos72

3

4 1 2 cos 36 4r cos72 sin36 (cos 36 ) cos72 sin144 1

9 2 3

2 2(cos72 )

4r sin144 (cos72 ) (cos72 ) cos 36 9 3


( ) ( )( )

( )

= = = + +

+ + + +

+ + +

3 43 0 0 0

20

33 0 0 0 3 0 0

20 2

3 0 0 2 0 4 0

I I 4S r sin144 cos 36 2 cos72

c r 3

4 1 2 cos 36 4r cos72 sin36 (cos 36 ) cos72 sin144 1

9 2 3

2 2(cos72 )4r sin144 (cos72 ) (cos72 ) cos 36

9 3

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Combining equation (2.26), it obtains:

3 / 2S 0.137 A (2.28)

The maximum bending stress:

= max 3 / 2M MS 0.137 A (2.29)

2.2.6 The maximum bending stress of new cross section

O1 O2

I

KM

R

r

H

A5

O1

AA1AA4

AA3 AA2

A2 A3 A4

(a) (b)Figure 2.10 (a) Division of new cross section; (b) dimensions and symbols of new cross

section

In figure 2.10(a)

Cross sectional area

A = AA1+AA2+AA3+AA4 = AA1+AA1+AA1+AA1

= 4AA1 (2.30)

The area of arc O2IM

2

2

2 2

A2+A3+A4= R

2

1 1A3+A4= KI KO2= RsinRcos

2 2

1= R sin 2

4

A2=A2+A3+A4-(A3+A4)

1= R - R sin 22 4

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2R

A2= (2-sin2)4

The area of arc O1IH

cos sin

sin

( )

sin

( sin )

area of cirle ( )

( ( sin ) ( sin )

2

2

2 2

2

2 22

A2 A3 A5 r 2

1 1A2 A5 O1K KI r r

2 2

1r 2

4

A3 A2 A3 A5 A2 A5

1r r 2

2 4

r

2 24

1AA1 A2 A3

4

1 r R1r 2 2 2 2

4 4 4

+ + =

+ = =

=

= + + +

=

=

= +

=

2 2r RAA1 ( 2 sin 2 ) ( 2 sin 2 )

4 4 = + (2.31)

Combining equations (2.30), (2.31), it obtains

= + 2 2A r ( 2 sin 2 ) R ( 2 sin 2 ) (2.32)

In figure 2.11(b)

= =

= =

KI O1I sin r sin

KI IO2 sin R sin

Therefore = r sin R sin

If = = 045 then =r R (2.33)

Combining equation (2.32), it obtains

Cross sectional area A=2r2 =A

r2

(2.34)

In figure 2.10(a)

Moment of inertia

( )

( )

2 2

2 2

I y dA y AA1 AA2 AA3 AA4

y AA1 AA1 AA1 AA1 4 y dAA1

= = + + +

= + + + =

Let 2I1 y dAA1=

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I 4I1= (2.35)

In figure 2.10(b), it obtains

I1= I(1/4 circle area )- I(A2)- I(A3) (2.36)

Calculating I(A2)In figure 2.10(b)

I(A2) = I(arcO2IM) I( IKO2) (2.37)

[ ]

[ ]

Where : '

,

=

=

=

2I(arcO2IM) y dAy = r' sin ' ; 0,

dA= r'dr'd ' ; r' 0 R

( )

=

=

=

=

=

R

2

0 0

R23

0 0

R

3

0 0

R4

00

4

I(arcO2IM) ( r' sin ') r' dr' d '

( r' ) dr' sin ' d '

( 1 cos 2 ')( r' ) dr' d '

2

sin 2 ' ( ' )

(r') 2

4 2

sin2( )R 2

4 2

=

41 sin 2R

8 2

(2.38)

=

3

KO2 KII( IK02)

12

= =3 4 3R cos ( R sin ) R cos (sin )

12 12

(2.39)

From equations (2.37), (2.38), (2.39),it obtains:

=

4 341 sin 2 R cos (sin )

I( A2 ) R8 2 12

(2.40)

Calculating I(A3)

In figure 2.10(b)

I(A3) = I(arcO1IH) I( IKO1) (2.41)

= 2I(arcO1IH) y dA

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[ ]

[ ]

Where =: y = r' sin ' ; ' 0,

dA= r'dr'd ' ; r'= 0,r

( )

=

=

=

=

=

r

2

0 0

r23

0 0

r

3

0 0

r4

00

4

I(arcO1IH) ( r' sin ') r' dr' d '

( r' ) dr' sin ' d '

( 1 cos 2 ')( r' ) dr' d '

2

sin 2 ' ( ' )

(r') 2

4 2

sin2( )r 2

4 2

=

41 sin 2r8 2

(2.42)

=

3

O1K KI I( IKO1)

12

= =

3 4 3r cos ( r sin ) r cos (sin )

12 12

(2.43)

Combining equations (2.41), (2.42), (2.43),it obtains:

=

4 341 sin 2 r cos (sin )I( A3 ) r

8 2 12

(2.44)

=4 41 r r

I(1/4 circle _ area ) =4 4 16

(2.45)

Combining equations (2.36), (2.40), (2.44), (2.45), it obtains:

=

4 3 4 3

4 4 41 1 sin 2 R cos (sin ) 1 sin 2 r cos (sin )I1 r R r 16 8 2 12 8 2 12

Combining equation (2.35), it obtains the moment of inertia

=

= + +

4 3 4 34 4 4

3 34 4

1 1 sin 2 R cos (sin ) 1 sin2 r cos (sin ) I r R r

4 2 2 3 2 2 3

sin 2 cos (sin ) sin 2 cos (sin )r R

4 2 4 3 2 4 3


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=42r

I3


= =

= + +

= + +

=

3 34 4

3 4 33

3

I IS c r

sin 2 cos (sin ) sin 2 cos (sin ) 1r R

4 2 4 3 2 2 3 r

sin 2 cos (sin ) R sin 2 cos (sin )r

4 2 4 3 r 2 2 3

2r

3


3 / 2S 0.236 A (2.46)

The maximum bending stress:

= = =max 3 3M 3 3M

MS 2r 2r

(2.47)

= max 3 / 2M M

S 0.236 A

(2.48)

2.2.7 Selecting the cross section of bow stick to design and produce

From equations (2.6), (2.8), (2.10), (2.11), (2.23), (2.24), (2.28), (2.29), (2.46), (2.48)

It obtains the table 2.1

Table 2.1: Value S and max

20

Circle Ellipse Octagon decagon New shape

S 3 / 20.141A 3 / 20.182A 3 / 20.01A 3 / 20.137A 3 / 20.236 A

max 3 / 2M

0.141A3 / 2

M

0.182A3 / 2

M

0.01A3 / 2

M

0.137A3 / 2

M

0.236 A


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From the table 2.1, the cross section of new shape or new cross section has the

largest modulus of cross sectional area or the smallest bending stress. It is realizes that

every bow stick thas has the same of cross section area has the same amount of volume

and mass because every stick has the same length. And any cross section of sticks with

less stress can save more material of wood. In other words, the cross section of stick

with less stress can be lighter. It is easier for the player to hold and control the bow.

From the above points, the bow stick with new cross section will be selected to design

and produce.

2.3 Design of traditional bow stick

To design the traditional violin bow stick, its dimensions should be know. To get

them, it takes the real traditional bow stick as a referential one and measures its

dimensions from which, it obtains data to design the traditional bow stick by UG

software

2.3.1 Measuring the dimensions of the real traditional bow stick

The traditional bow stick is measured by a caliper as shown in figure 2.1. The

traditional violin bow is divided into three parts as shown in figure 2.12, 2.13, and 2.14

to measure. All steps of measure as presented in the following

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Figure 2.11 Measuring the dimensions of the traditional violin bow

The holder part as shown in figure 2.12 has an octagonal cross section with length

n= 63(mm) and inscribed diameter d=8(mm).

Figure 2.12 Dimension near the bottom

Measuring the bow stick as shown in figure 2.13

The stick of the traditional bow stick has a circular cross section of which diameter is

variable. Therefore, it should be divided into 13 segments to measure. Let dCi is

diameter of the cross section at segment i ( i 1,13= ), and li is the distance from bottom to

segment i. The result as shown in table 2.2

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Figure 2.13 Dimensions of the bow stick

Table 2.2: The dimensions of real violin bow stick

i 1 2 3 4 5 6 7

il (mm) 134 184 234 284 334 384 434

dCi (mm) 8.42 8.42 8.4 8.35 8.3 8.24 8.1

i 8 9 10 11 12 13

(mm)il 484 534 584 634 684 714

dCi (mm) 7.66 7.16 6.7 6.3 5.8 5.5

Measuring the head as shown in figure 2.14

The head has a height h=19.1(mm), length z= 21.55(mm), width k=9.8, q=4.3

23

lidci


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Figure 2.14 Dimensions of head

2.3.2 Drawing the traditional bow stick

Form the dimensions of traditional bow. It obtains the data to draw the traditionalone by UG software. All main steps of designing the traditional bow as presented in

the following:

Creating a holder part as shown in figure 2.15, its dimensions: length n= 63(mm)

and inscribed diameter d=8.42(mm).

(a) Drawing an octagon (b) Extruding the octagon

Figure 2.15 Creating the new holder part

Extruding the part that will be assembled with pad, with diameter d= 8mm, length

l=71mm as shown in figure 2.16

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Figure 2.16 Extruding the part with pad

Creating the main bow stick: At the beginning creating Spline, after that using

command revolve to make it

To create Spline , it should make a new datum coordinate system as shown in figure

2.17

Figure 2.17 Creating datum coordinate system

Creating the Spline: The Spline is drawn according the data derived from the (table

2.2), after that command revolve is used to create the violin bow stick as shown in

figure 2.18

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Figure 2.18 Creating Spline

Creating head: Its very complicated to draw the head of violin bow. So it should

use many different commands, such as extrude, subtract, edge blend, face blend, fillet.

Its dimensions were shown as in figure 2.14. The order of creating the head as presented

in the following steps in figure 2.19

(a) Drawing the boundary of head (b) Extruding the boundary

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(b)

Figure 2.20 (a) The completed traditional bow stick; (b) The dimensions of traditional

bow stick

2.4 Design of new bow stick

To design the new bow stick, it is necessary to know its dimensions. They are

almost referred from the dimensions of real bow stick that has a cicular cross section.

However, the dimensions of the main bow stick will be calculated from the stick of

real one.

2.4.1 Calculating the dimensions of new bow stick

The dimensions of new bow stick are based on the dimensions of real traditional

violin bow. However, the dimensions of new main stick will be calculated from the

dimensions of main stick of real one.

Dimension of a holder part: The holder part has an octagonal cross section with

length m= 63(mm) and inscribed diameter d=8.9(mm) as shown in figure 2.12

Dimensions of the main stick:

The purpose of this thesis is to create a new bow stick that is lighter than the

traditional one and still guarantees enough strength.It is realized that the mass of bow

tick is proportional to its cross section area. Therefore, to get the new bow that is

lighter than the traditional one, the cross section area of new bow stick should be

smaller than traditional ones.

It is assumed that the new and traditional bow stick have the same of material and

are applied the same of forces. Let the maximum stress of the material is max , the

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maximum bending stress of traditional bow stick is maxC . To guarantee the enough

strength of traditional bow stick, it should be

maxmax =C

n

(2.49)

Where n is the factor of safety ( 1n ).

Let maximum bending tress of new bow stick is maxN . To guarantee the enough

strength of new bow stick, it also should be maxmax =Nk

(2.50)

Where k is the factor of safety ( 1k )

To guarantee that the strength of new and traditional bow stick is the same, n should be

equal k or n=k. Therefore, combining equations (2.49) and (2.50), it obtains

max max=C N . In other hand, the maximum bending stress of new and traditional bow

stick should be equal. According to equations (2.7), and (2.47)

The maximum bending stress of traditional bow stick that has a circular cross

section

Cmax 3

C

4M

r

=

The maximum bending stress of new bow stick

Nmax 3

N

3M

2 r =

Because Cmax Nmax 3 3C N

4M 3M, therefore

r 2 r = =

1/3 1/3

N C N C C3 3r r d d 1.056d8 8 = =

N Cd 1.056d (2.51)

It is assumed that the length of new and traditional violin bow stick are equal, so from

the equation (2.51), it obtains that at the same l i , Ni Cid 1.056d (2.52)

Therefore, from values dCi of table 2.2, it obtain values of dNi as shown in table 2.3

For an example: in table 2.2, with i=1, 1 C1l 134 mm, d 8.42 mm= = from equation

(2.52), it obtains that

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At l1=134, the diameter of new cross section i N1d 1.056 8.42 8.89= =

Similarly, it obtains the values of dNi

Table 2.3: The dimensions of new violin bow stick

i 1 2 3 4 5 6 7

il (mm) 134 184 234 284 334 384 434

Nid (mm) 8.89 8.89 8.87 8.82 8.76 8.70 8.55

i 8 9 10 11 12 13

li(mm) 484 534 584 634 684 714

Nid (mm) 8.09 7.56 7.08 6.3 5.8 5.5

According above calculation:

At i = 1 , l1=134 (mm)

Diameter of circular cross section dC1= 8.35 (mm) (Because the traditional violin bow

stick has a circular cross section)

Diameter of new cross section dN1 = 8.89 (mm)

According to equations (2.7), and (2.34) , it obtains

The area of circular cross section2 2

2 11 1

8.423.14 55.65

4 4

2CC C

dA r mm = = =

The area of new cross section2 2

2 11 1

8.892 2 2 39.51

4 4= = = = 2NN N

dA r mm

It is realized that AC1 = 55.65>39.51=AN1

Therefore, it can conclude that

At i=1, l1=134 (mm), the cross section of new and traditional bow stick have the

same of maximum bending stress. However the area of new cross section is smaller than

the traditional ones.

Similarly, it can obtains that

At the same of li the cross section of new and traditional bow stick have the same

of maximum bending stress. However the area of new cross section is smaller than the

traditional ones.

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(a) Creating a datum coordinate system

(b) All coordinate systems

Figure 2. 22 Creating datum coordinate systems

Creating cross sections of bow stick, to avoid stress concentration, it should fill

sharp edges by radius 1 (mm) as shown in figure 2.23

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(b) The completed the main bow stick

Figure 2.24 Creating new main bows tick

Creating the new bow head: all dimensions of the new and traditional bow head are

equal. Therefore, all steps of creating new bow head are similar to the steps of creating

the head of traditional bow stick as shown in figure 2.19

In the end, it obtains the completed new bow stick and its dimensions as shown in

figure 2.25

(a)

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(b)

Figure 2.25 (a) The completed new bow stick; (b) Dimensions of new bow stick

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CHAPER 3MANUFACTURING THE BOW STICKS

3.1 Producing the violin by the traditional method

Making a violin bow is a delicate and critical process. It is just as important as

making the real violin, since bows are often made to promote optimal sound with

certain instruments. As with all instrument-making efforts, a good amount of

experience, strong attention to detail and patience will help to create a quality product

that plays well and lasts for many years.

3.1.1 Making the frog

Creating ebony frog blank: The two parts of the ferrule have been welded by silver,

then, they have been roughly fitted onto an ebony frog blank as shown in figure 3.1

.

Figure 3.1 Ferrule & Ebony frog blank

Figure 3.2 Chiseling and planning the frog

37

Chanel


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Figure 3.5 Making the silver ring rounded

Gluing the pearl eye and silver ring into their respective recesses in the frog, they

are then filed flush with the surface of the ebony as shown in figure 3.6 [7].

Figure 3.6 Gluing pearl eye and silver ring

3.1.2 Creating the bow stick

Measuring the dimensions of the stick by template as shown in figure 3.7, It is a

traditional tool of the trade, and is very fast and accurate to use. Each one of the

notches is 1/2 millimeter wider than the one that precedes it.

Figure 3.7 Planning and measuring the stick

39

Template


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Heating a bow stick in the flame of an alcohol lamp, a short section is heated at the

same time. The stick is heated slowly, allowing the heat to penetrate to the core. The

wood is heated almost to the scorching point. As the wood gets hot it becomes more

flexible as shown in figure 3.8.

Figure 3.8 Heating the violin bow stick

Bending the bow stick as shown in figure 3.9, the two chalk lines indicate the area

that has just been heated. As the wood cools, it will hold the curve shape. When this

section of the stick is cool, I'll move on down the stick to heat and bend the next

section. The curve, or camber, is judged only by eye. The amount and shape of the

curve will have a significant effect on the playing qualities of the finished bow.

Figure 3.9 Bending violin bow stick

Gluing the mastodon ivory and ebony liner on the roughly shaped tip, the string

holds the ivory and ebony in place until the glue dries as shown in figure 3.10

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Figure 3.10 Gluing ivory and ebony liner of tip

Shaping the tip with a knife and refining the shape of the tip with a file as shown in

figure 3.11

Figure 3.11 Shaping and refining the tip

Chiseling the mortise in the stick for the adjusting screw as shown in figure 3.12

Figure 3.12 Chiseling the mortise

Making the hole for the adjusting screw by mill machine as shown in figure 3.13

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`

Figure 3.13 Drilling hole

Forming the nipple on the end of stick by special drill as shown in figure 3.14

Figure 3.14 Forming the nipple

Planning the stick to fit the frog as shown in figure 3.15

Figure 3.15 Planning the stick

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Fitting stick to frog as shown in figure 3.16 [8]

Figure 3.16 Fitting frog to stick

3.1.3 Making button

Making the silver ring as shown in figure 3.17, the button ring begins as a flat piece

of metal, silver or gold that is bent into a short round tube. The two ends of the piece of

metal are welded by a small snippet of silver or gold. After two ends are jointed, the

joint of these ends will be filed and it will disappear.

After the ring is welded, it is pounded on a tapered mandrel in order to make it

perfectly round, and of the proper diameter.

Figure 3.17 Making silver ring

Lathering the body of button as shown in figure 3.18

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Drilling the hole for the screw into the ebony as shown in figure 3.21

Figure 3. 21 Drilling the hole for fitting the screw

Driving the screw into the button as shown in figure 3.22

Figure 3.22 Fitting the screw to the button

Lathing a head of button body to glue another silver ring as shown in figure 3.23

Figure 3.23 Fitting another silver ring

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Lathing the hole for the end of button for the pearl eye as shown in figure 3.24

Figure 3.24 Lathing the hole

Filing the button into octagon shape as shown in figure 3.25, stopping occasionally

to take measurements [9].

Figure 3.25 Filing the button into octagon shape

3.1.4 Fitting all parts

Fitting the button to the frog to get the finished violin bow, To increase the strength

of the violin bow, stick is fitted two parts: wrapping and pad

Roughing the stick refers to the process of carving and planning the stick to its

approximate finished dimensions, after that using the special planes to fashion the stick

into its characteristic octagonal shape. Then, using a direct heat device such as a spirit

lamp or gas burner, the stick is heated slowly until it becomes flexible enough to bend.

When ready, the stick is bent into an approximate or rough curve. When cooled, the

stick is set aside, and the work on the frog begins.

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3.1.5 The material of the violin bow

The making of the bow begins with the selection and rough cutting of the correct

woods and raw materials. Pernambuco wood is the accepted type of wood from which

the stick of the bow is fashioned. Pernambuco wood grows only in the Amazon delta

region in a Brazilian state of the same name. Actually there are several sub-species of

this wood, many of which are completely extinct, and others which are rapidly nearing

extinction. After harvesting, the logs are sawn into planks, and then into "blanks" which

are cut into the rough outline resembling the stick and its tip. Besides, there are some

other materials that can make the bow, such as Cacbon fiber, fiber glass. The ebony for

the frog is split from log cross sections into small wedges which resemble the finished

outside dimensions [10].

3.2 Creating NC codes

The steps of creating NC codes are shown in figure 3.26. After finish drawing the

bow stick by Ug software, exporting to a file.IGES, after that, Software Mastercam is

used to open the file.IGES and creates tool paths, then export to NC codes.

Figure 3.26 Creating NC codes

Because the length of bow stick is too long (735.6mm), so the bow stick cant be

produced directly, during conditions of our school. However, there is a solution to deal

with the problem that is the violin bow stick divided is into 2 parts to produce step by

step.

3.2.1 Creating NC codes for the traditional bow stick

Dividing the traditional bow stick into 2 parts as shown in figure 3.27

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(a) The full length of bow stick

(b) Part1

(c) Part2

Figure 3.27 Dividing the bow stick

Open file IGES by software Mastercam (milling), on the menu, selecting file

converters IGES file.IGES as shown in figure 3.29

48

These parts only have a function of supporting violin bow, when it is produced


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Figure 3.28 Opening file IGES

Creating NC codes for the lower part1

Rotating 900 all entities, on the menu, selecting Xform Rotate All

Entities Done

To be easy to manufacture by CNC machine, so it should rotate all entities of bow

stick 900 as shown in figure 3.29

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Figure 3.29 Rotating all entities of part1

Creating contours of objects, on the menu selecting Create Rectangle

When using the command pocket, it should make contours around the bow stick. All

dimension of contours as shown in figure 3.30

Figure 3.30 Creating contours of lower part 1

Roughing

On the menu, selecting Tool paths Surface (set up Drive: A, Cad file: N,

check: N, contain Y) Rough Pocket.

Some important parameters: tool name is sphere mill, tool diameter = 2 mm, stock

to leave = 0.5 mm, spindle speed = 3500rpm, feed rate = 700 mm/minute, plunge rate =

200 mm/minute, react rate = 1000 mm/minute, total tolerance = 0.1 mm, max step down

= 1.5 mm, step over = 1mm as shown in figure 3.31

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Figure 3.31 Roughing lower part 1

Semi finishing


check: N, contain N) Finish Parallel

Some important parameters: tool name is sphere mill, tool diameter = 2 mm, stock

to leave = 0.25 mm, spindle speed = 5000rpm, feed rate = 700 mm/minute, plunge rate

51

Create new tool

Diameter

Tool parameters

Step over

Max step down


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= 200 mm/minute, react rate = 1000 mm/minute, total tolerance = 0.05 mm, max step

over = 0.5 mm as shown in figure 3.32

Figure 3.32 Semi finishing lower part 1

Finishing


check: N, contain N) Finish Parallel

Some important parameters: Tool name is sphere mill, tool diameter = 2 mm, stock

to leave = 0 mm, spindle speed = 5000rpm, feed rate = 700 mm/minute, plunge rate =

52

Parameters of cutting tool

Tolerance

Max step over

Stock to leave


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200 mm/minute, react rate = 1000 mm/minute, total tolerance = 0.01 mm, max step over

= 0.1 mm as shown in figure 3.33

Figure 3.33 Finishing lower part 1

53

Tool parameters

Stock to leave is 0

ToleranceMax step over


65/105

Simulating the cutting process

On the menu, selecting Tool paths Operations Verify as shown in figure 3.34

After finish creating tool paths, it should know how CNC machine will work, so

command verify is used to simulate tool paths.

Figure 3.34 Simulating the cutting process of lower part1

Saving the file and naming the file as under part 1, on the menu, selecting file

save file name

Creating NC codes for the lower part 2

54

Lower part 1


66/105

Almost steps in this part are similar to the part of creating NC codes for the lower

part 1

Opening file IGES by software Mastercam (milling) as shown in figure 3.28

Rotating 900 all entities as shown in figure3.29

Creating contours of objects as shown in figure 3.35

Figure 3.35 Creating contours of lower part 2

Roughing as shown in figure 3.31

Semi finishing as shown in figure 3.32

Finishing as shown in figure 3.33

Simulating the cutting process as shown in figure 3.36

Figure 3.36 The cutting process of lower part2

55

Lower part2


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Saving the file and naming the file as lower part 2

Creating NC codes for the upper part 2

In this part, it doesnt need to do steps of creating tool paths as the part of creating

NC codes for the lower part2. It only needs to do some following steps

Rotating 180 lower part2 as shown in figure 3.29

Regen path, because the lower part2 was rotated, so the tool paths are mistaken.

Therefore, it has to be fixed as shown in figure 3.37

Figure 3.37 Regen path of lower part2


Figure 3.38 The cutting process of upper part2

56

Upper part2


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Saving file and naming the file as upper part 2

Creating NC codes for the upper part1

It is similar to the part of creating NC codes for the upper part2.

Rotating 180 lower part1 as shown in figure 3.29

Regen path as shown in figure 3.39

Figure 3.39 Regen path lower part 1


Figure 3.40 The cutting process of upper part1

Saving the file and naming the file as upper part 1

After finishing manufacturing the above parts, it needs to cut supporting parts to get

the completed bow stick.

57

Upper part1


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Creating NC codes for cutting supporting parts Upper part 1

Opening the file upper part 1 as shown in figure 3.41

Figure 3.41 Opening the file upper part 1

Deleting old contours and tool paths, creating new contours to get the geometry

as shown in figure 3.42

(a)

(b)

Figure 3.42(a) Deleting tool paths of upper part 1; (b) Creating new contours of

upper part

58


70/105

Creating tool paths


check: N, contain Y) Rough Pocket.

Some important parameters: Tool name is sphere mill, tool diameter = 2 mm, stock

to leave = 0.1 mm, spindle speed = 5000rpm, feed rate = 700 mm/minute, plunge rate =

200 mm/minute, react rate = 1000 mm/minute, total tolerance = 0.01 mm, max step

down = 0.5 mm, step over = 0.6mm as shown in figure 3.43

59

Tool parameters

Stock to leaveStep over

Tolerance


71/105

Figure 3.43 Creating the tool paths for supporting parts of upper part 1


Figure 3.44 The cutting process of supporting parts of upper part 1

Saving the file and naming the file as cutting upper part 1

Upper part 2

Opening the file upper part 2 as shown in figure 3.45

Figure 3.45 Opening the file upper part 2

60

Cutting supporting parts of upper part1


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Deleting old contours and tool paths, creating new contours to get the geometry as

shown in figure 3.46

(a)

(b)

Figure 3.46 (a) Deleting old contours and tool paths; (b) Creating new contours

Selecting tool paths as shown in figure 3.43


61

Cutting supporting parts

of upper part 2


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Figure 3.47 Cutting supporting parts of upper part2


Lower part 2

It doesnt need to do steps of creating tool paths as the part of cutting supporting

part of upper part2. It only needs to do some following steps

Rotating 180 upper part 2 as shown in figure 3.29

Deleting tool paths (only keeping the supporting part of bow head) as shown in

figure 3.48

Figure 3.48 Deleting tool paths


Figure 3.49 Regen path


62


74/105

Figure 3.50 Cutting supporting part of lower part 2


Lower part 1

It is similar to the part of cutting supporting part of lower part 2

Rotating 180 upper part as shown in figure 3.29

Deleting tool paths (only keeping the supporting part of holder) as shown in figure

3.51




63

Cutting supporting partof lower part 2


75/105


3.2.2 Creating NC codes for the new bow stick

All steps in this part are similar to part 3.2.1. Therefore, in this part, it only presents

figures that are different from pictures in part 3.21.

Dividing the new bow stick into 2 parts as shown in figure 3.53

(a) The full length of new bow stick

(b) New part1

64

These parts only have a function of supporting violin bow, when it is produced

Cutting supporting part

of lower part 1


76/105

(c) New part2

Figure 3.53 Dividing new violin bow

Opening file IGES by software Master cam (milling) as shown in figure 3.28

Creating NC codes for the lower new part1

Rotating 900 all entities as shown in figure 3.29

Creating contours of objects as shown in figure 3.54

Figure 3.54 Creating contours of lower new part1

Roughing as shown in figure 3.31

Semi Finishing as shown in figure 3.32

Finishing as shown in figure 3.33


65


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78/105

Figure 3.57 The cutting process of lower new part2

Saving the file and naming the file as lower new part 2

Creating NC codes for the upper new part 2

Open lower new part2

Rotating 180 lower new part2 as shown in figure 3.29


Figure 3.58 Regen path lower new part 2

Stimulating the cutting process as shown in figure 3.59

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Lower new part 2


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Figure 3.59 The cutting process of upper new part2

Saving the file and naming the file as upper new part 2

Creating NC codes for the upper part1

Open file lower new part1

Rotating 180 lower new part1 as shown in figure 3.29



Figure 3.60 The cutting procession of upper new part1

68

Upper new part1

Upper new part 2


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81/105

Creating tool paths as shown in figure 3.43


Figure 3.63 Cutting supporting part of upper new part 1

Saving the file and naming the file as cutting upper new part 1

Upper part 2

Opening the file upper new part 2 as shown in figure 3.64

Figure 3.64 The file upper new part 2

Deleting old contours and tool paths, creating new contours to get the geometry as

shown in figure 3.65

70

Cutting supporting part of upper new part 1


82/105

(a)

(b)

Figure 3.65 (a) Deleting old contours and tool paths of upper new part2; (b) New

contours of upper new part 2

Selecting tool paths as shown in figure 3.43


Figure 3.66 Cutting supporting part of upper new part2

71

Cutting supporting part of

upper new part2


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Under new part 2

Open upper new part 2

Rotating 180 upper new part 2 as shown in figure 3.29

Deleting tool paths (only keeping the supporting part of head) as shown in figure

3.67

Figure 3.67 Deleting tool paths of upper new part 2


Figure 3.68 Regen path


72


84/105

Figure 3.69 Cutting supporting part of lower new part 2


Under part 1

Open upper new part1

Rotating 180 upper new part 1 as shown in figure 3.29

Deleting tool paths (only keeping the supporting part of holder) as show in figure

3.70



Simulating the cutting process as shown in figure 71

73

Cutting supporting partof low new part 2


85/105


3.2.3 Exporting to NC codes

After finishing creating tool paths, NC codes are created as shown in figure 3.72, on

the menu, selecting tool paths operations post save NC file.

It is similar to all cases (traditional and new violin bow stick)

74

Cutting supporting partof lower part 1


86/105

Figure 3.72 Creating NC codes

Normally, after exporting to the NC codes by Mastercam software, it cant use them

to import to the CNC machine. It should adjust them a little bit as shown in figure 3.73.

There are some common NC codes as presented in the following

A0 is the command for the CNC machine with over 3 axes (the tool rotate 0 degree

about X axis). Because our CNC machine is 3-axis one, so we should delete A0 in the

program.

T1M6 is Changing to cutting tool No1 automatically, we only use 1 cutting tool, so

we dont need to change cutting tool automatically. Therefore we delete T1M6.

Every word in the round bracket () doesnt work in the CNC machine, so we delete

it.

75


87/105


88/105

G90 is Absolute Positioning

M00 is Program stop

M01 is optional program stop

M02 is Program end

M03 is Spindle on clockwise

M04 is Spindle on counter clockwise

M05 is Spindle stop

M06 is Tool change

M30 is program end, reset to start [3]

In the end, it obtains the completed file of NC codes as shown in figure 3.74

Figure 3.74 The completed file of NC codes

3.3 Introduction to the CNC machine Vcenter-65

77
http://www.cncezpro.com/g90m.cfmhttp://www.cncezpro.com/g90m.cfm


89/105

Figure 3.75 CNC machine Vcenter-65

Some important parameters of the CNC machine Vcenter-65 as shown in table 3.1

Table 3.1 The specification of CNC machine V center-65

X axis travel 650mm

Y axis travel 410mm

Z axis travel 510mm

Rapid feed rateX/Y: 18000mm/min

Z: 120000mm/min

Spindle speed 60-6000 rpm

Max load 300kg

Max tool diameter 76mm

Max tool length 300mm

Max tool weight 6kg

Power requirement 15.6KVA

Net weight 4500kg

Max machine height 2600mm

NC controller Fanuc O-M

3.4 Producing the bow sticks

It is the same of producing traditional and new bow stick by the CNC machine. Bow sticks

are produced by the CNC machine V center -65.

The work piece has the material of wood and dimensions: 800x45x20 mm

All steps of implementation are introduced as the following:

Starting machine as shown in figure 3.76

78


90/105

(a) Turning on power (b) Turning on system

(c) Switching on machine (d) Turning on machine

Figure 3.76 Starting machine

Returning machine zero points as shown in figure 3.77

(a) Returning Zero points (b) Pressing buton X, Y, Z

79


91/105

(c) Machine at Zero points

Figure 3.77 Returning machine zero points

Drilling holes at the work piece and base for location as shown in figure 3.78. These

holes have a function of locating the workpiece with the base and machine. When the

work piece has to be moved to produce different parts. Thank to these holes, the

accuracy of product ( bow stick) is guaranteed.

( a) Drilling holes on the workpiece ( b) Drilling holes on the base

Figure 3.78 Drilling holes

The dimensions of holes on the base as show in figure 3.79

80


92/105

900

262.5125125125

35

15.5

66

15

20

4

Figure 3.79 The dimensions of holes on the base

The dimensions of holes on the work piece as shown in figure 3.80

800

125250250

35

45

20

4

5

Figure 3.80 The dimensions of holes on the work piece

Putting 3 location pins into holes of the base. The dimensions of location pins:

height 45mm, diameter d=4 mm as shown in figure 3.81

81


93/105

Figure 3.81 Putting location pins on the base

Assembling the work piece on the base as shown in figure 3.82

workpieceBase

location of pin

Figure 3.82 Positions of pins while producing the lower part1

Positions of pins while producing the lower part 2 as shown in figure 3.83, upper part

2 as shown in figure 3.84, upper part 1 as shown in figure 3.85

82


94/105

Workpiece Base

position of pin

Figure 3.83 Positions of pins in the under part2

Workpiece Base

position of pin

Figure 3.84 Positions of pins in the upper part2

workpieceBase

location of pin

Figure 3.85 Positions of pins in the upper part1

Selecting a stock origin as shown in figure 3.86

Figure 3.86 Selecting a stock origin

83


95/105

Inputting NC codes as shown in figure 3.87

(a) Starting the program (b) Selecting the file of NC codes

(c) Inputing NC codes to CNC machine

Figure 3.87 Inputting NC codes

Starting the program as shown in figure 3.88

Figure 3.88 Starting the program

84


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97/105

Figure 4.3 The unsmooth part of bow stick

While carrying out this thesis, it was faced with a lot of problems and got a lot of

valuable knowledge when these problems were resolved, such as some following

typical examples:

With design section, the most difficult barrier is that to create new bow stick with

different sections. A good solution introduced is command Mesh Surface. With this

command, to be easy to mesh surfaces together, it should create datum coordinate

systems as shown in figure 4.4

Figure 4.4 Mesh surface

86

Unsmooth

part


98/105

Because the CNC machine V center-65 only can operate the products with the

maximum length of 650 mm. Meanwhile the length of bow stick is 735.6 mm, so it

should be divided into 2 small parts (part1 and part2) to produce step by step. At the

beginning, the supporting parts for the violin bow stick werent designed, so after finish

producing the lower part1 and lower part2, the upper part 2 was produced. However the

bow stick was very weak, so there was inaccuracy as shown in figure 4.5. After that, it

had to change the design that creates supporting parts for it as shown in figure 3.27 and

figure 3.53.

Figure 4.5The bow stick is produced without supporting parts

With the section of creating NC codes, there are so many parameters that need to set

up in Mastercam software. So, to get the reasonable parameters, such as spindle speed,

feed rate, react rate, tolerance, max stepetc. They should be tested many times. After

testing, it got some important notices of Mastercam in this thesis, for instance a surplus

stock or stock to leave of previous operation has to be greater than a surplus stock of

after operation. If not, the tool sometimes doesnt cut the work piece. (in this thesis,

stock to leave of roughing is 0.5 mm, semi finishing is 0.25mm, finishing is 0 mm. it is

realized that 0.5 > 0.25 > 0). The max tolerance is 0.01 mm. because our CNC machine

operates with the maximum accuracy of 0.01 mm, during current conditions in our

school. According to the design, it needs 4-axis CNC machine. However, there isnt any

4-axis CNC machine but only a 3-axis one (Vcemter-65) in my school. Therefore, it

should create NC codes for the CNC machine that produces the bow stick according to

2 sides (upper and under) separately. The cutting depth of the tool or flute as shown in

figure 4.6 is quite short (5mm), therefore supporting parts have to be cut twice (upper

side and under side).

87


99/105

Figure 4.6The cutting tool

With the production section, it is an extremely difficult one, as well as takes time.

The fixture plays a very important role in this section. To get a good fixture, the bow

sticks were produced many times by CNC machine. After each time of producing, it

also took a very good lesson as introduced in following typical examples: At the

beginning the work piece was put on the normal supporting base that is made of wood.

The work piece and the base were glued by Cyanoacrylate Adhesvie. After finishing

the lower side of violin bow stick and releasing it from the base, there were some

problems: It was very difficult to release work piece from the base, and the surface of

the base was broken as shown in figure 4.7(b), so it was not accurate any more, when

the CNC machine manufactures the upper side of bow stick. Because the surface of

base was broken, so its upper surface was not flat, and the upper surface of work piece

was not flat as shown in figure 4.7(a). Therefore it was not accurate any more, when the

upper side of bow stick is produced.

88

5 mm

The work piece and supporting

base is glued by Cyanoacrylate

Adhesive

The upper surface

of work piece

The upper

surface of

basse


100/105

(a) Gluing the workpiece to the base

(a) The broken surface

Figure 4.7 The normal wooden supporting base

Therefore, it had to replace the base by the new one and Cyanoacrylate Adhesvie by 3

location pins as shown in figure 4.8. However the new supporting base is pretty

expensive, and can only be used a few times.

Figure 4.8 The new supporting base and location pins

Selecting the stock origin also plays a very important role. It is easy to get an error

when selecting it not accurately. To be more accurate, we should select origin once. In

89

New supporting base

Location pins


101/105


102/105

Figure 4.11 The broken cutting tool

Because, the real traditional bow stick was measured by a Caliper, so the result

wasnt highly exact. If it is possible with conditions of our school, it should measure

the real traditional bow stick by a measuring machine.

To redure production time, the cutting tool with larger diameter ( greater than 2mm,

such as 6 mm) should be used while roughing the work piece.

91


103/105


104/105

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Nguyen Danh Tuyen Thesis