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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 3.51 Deleting tool paths 63
Figure 3.52 Cutting supporting part of lower part 1 64
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 3.70 Deleting tool paths 73
Figure 3.71 Cutting supporting part of lower part 1 74
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
Combining equation (2.14) it obtains
= =
= = = =
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
Combining equation (2.18) it obtains
( )
=
= + + + +
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
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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
Modulus of the cross sectional area
( ) ( )( )
( )
= = = + +
+ + + +
+ + +
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
Combining equation (2.33) it obtains
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=42r
I3
Modulus of the cross sectional area
= =
= + +
= + +
=
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
Combining equation (2.34) it obtains
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
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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
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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
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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
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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
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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
On the menu, selecting Tool paths Surface (set up Drive: A, Cad file: N,
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
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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
On the menu, selecting Tool paths Surface (set up Drive: A, Cad file: N,
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 =
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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
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Tool parameters
Stock to leave is 0
ToleranceMax step over
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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
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Lower part 1
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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
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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
Simulating the cutting process as shown in figure 3.38
Figure 3.38 The cutting process of 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
Simulating the cutting process as shown in figure 3.40
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.
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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
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Creating tool paths
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 = 0.1 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
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Tool parameters
Stock to leaveStep over
Tolerance
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Figure 3.43 Creating the tool paths for supporting parts of upper part 1
Simulating the cutting process as shown in figure 3.44
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
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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
Simulating the cutting process as shown in figure 3.47
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Cutting supporting parts
of upper part 2
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Figure 3.47 Cutting supporting parts of upper part2
Saving the file and naming the file as cutting upper part 2
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
Regen path as shown in figure 3.49
Figure 3.49 Regen path
Simulating the cutting process as shown in figure 3.50
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Figure 3.50 Cutting supporting part of lower part 2
Saving the file and naming the file as cutting upper 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
Figure 3.51 Deleting tool paths
Regen path as shown in figure 3.49
Simulating the cutting process as shown in figure 3.52
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Figure 3.52 Cutting supporting part of lower part 1
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
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Cutting supporting part
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(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
Simulating the cutting process as shown in figure 3.55
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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
Regen path as shown in figure 3.58
Figure 3.58 Regen path lower new part 2
Stimulating the cutting process as shown in figure 3.59
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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
Regen path as shown in figure 3.58
Simulating the cutting process as shown in figure 3.60
Figure 3.60 The cutting procession of upper new part1
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Upper new part1
Upper new part 2
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Creating tool paths as shown in figure 3.43
Simulating the cutting process as shown in figure 3.63
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
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(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
Simulating the cutting process as shown in figure 3.66
Figure 3.66 Cutting supporting part of upper new part2
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Cutting supporting part of
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Saving the file and naming the file as cutting upper new part 2
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
Regen path as shown in figure 3.68
Figure 3.68 Regen path
Simulating the cutting process as shown in figure 3.69
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Figure 3.69 Cutting supporting part of lower new part 2
Saving the file and naming the file as cutting upper 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
Figure 3.70 Deleting tool paths
Regen path as shown in figure 3.68
Simulating the cutting process as shown in figure 71
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Figure 3.71 Cutting supporting part of lower part 1
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)
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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.
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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
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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
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(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
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(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
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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
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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
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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
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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
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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
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Unsmooth
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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).
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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.
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5 mm
The work piece and supporting
base is glued by Cyanoacrylate
Adhesive
The upper surface
of work piece
The upper
surface of
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(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
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Location pins
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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.
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23. http :// www .fiddleheads .ca /writings /violin _ sizing .html
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http://www.lancastersymphony.org/Portals/1/docs/pdfs/instfea/strings/StringInstrument_violinhistory.pdfhttp://www.lancastersymphony.org/Portals/1/docs/pdfs/instfea/strings/StringInstrument_violinhistory.pdfhttp://www.ehow.com/about_4619382_violin-bows.htmlhttp://www.bartenwebworks.nl/andreasgrutter/bow-couch/bow-couch.htmlhttp://www.altmanbows.com/frog_making.htmlhttp://www.altmanbows.com/bow_making.htmlhttp://www.altmanbows.com/button_making.htmlhttp://www.madehow.com/Volume-2/Violin-Bow.htmlhttp://www.asinari.it/vionoeng.htmhttp://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://www.asinari.it/vionoeng.htmhttp://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://www.solarnavigator.net/music/instruments/violin.htmhttp://www.solarnavigator.net/music/instruments/violin.htmhttp://www.fiddleheads.ca/writings/violin_sizing.htmlhttp://www.lancastersymphony.org/Portals/1/docs/pdfs/instfea/strings/StringInstrument_violinhistory.pdfhttp://www.lancastersymphony.org/Portals/1/docs/pdfs/instfea/strings/StringInstrument_violinhistory.pdfhttp://www.ehow.com/about_4619382_violin-bows.htmlhttp://www.bartenwebworks.nl/andreasgrutter/bow-couch/bow-couch.htmlhttp://www.altmanbows.com/frog_making.htmlhttp://www.altmanbows.com/bow_making.htmlhttp://www.altmanbows.com/button_making.htmlhttp://www.madehow.com/Volume-2/Violin-Bow.htmlhttp://www.asinari.it/vionoeng.htmhttp://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://musiced.about.com/od/beginnersguide/a/vparts.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://www.asinari.it/vionoeng.htmhttp://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonata-allegro.com/2009/01/10/parts-an-introduction-to-violin-making/http://sonataTop Related