frequency analysis of a cymbal - wordpress.com · 2013-03-03 · 5.00 6.00 7.00 8.00 9.00 10.00 b12...
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Frequency Analysis of a Cymbal Materials & Deformation and the effect it has on Frequency
Barnee Lloyd - 11828773 - DP238 - Finite Element Analysis - University of Brighton
School of Computing, Engineering and Mathematics
Deformation
How does it effect the sound?
How can it be prevented?
What role do materials play?
Why does it happen?
The (original) Problem
Does it matter?
Things I discovered through
research
The Cymbal Book by Hugo
Pinksterboer
Using bent cymbals
Buying bent cymbals
‘Interesting’ sounds
Companies that ‘fix’ broken
cymbals
Is this a problem?
Materials
How do Materials effect the
sound?
What is it about them that
changes the sound?
How can it be adjusted?
What are the advantages?
Lack of understanding of this
area in manufacture
The (new) Problem
B20, B12, B8, MS63, FX9
Differences
The Materials Property Unit Minimum Maximum Average Property Unit Minimum Maximum Average
B20 Alloy B8 Alloy Density GPa 8600.0 8614.0 8607.0 Density GPa 8798.0 8809.6 8803.8
Price GBP/kg 1.7 3.3 2.5 Price GBP/kg 1.5 3.1 2.3 Youngs Modulus kg/m³ 97.8 127.4 112.6 Youngs Modulus kg/m³ 106.3 139.8 123.0
Poisson's Ratio - 0.3 0.3 0.3 Poisson's Ratio - 0.3 0.3 0.3 Tensile Strength MPa 82.2 323.6 202.9 Tensile Strength MPa 92.9 369.4 231.2
Elastic Limit MPa 25.4 283.0 154.2 Elastic Limit MPa 28.2 323.2 175.7 Shear Stress MPa 38.8 45.2 42.0 Shear Stress MPa 42.5 49.3 45.9
B12 Alloy MS63 Alloy Density GPa 8732.0 8744.4 8738.2 Density GPa 8264.0 8277.7 8270.9
Price GBP/kg 1.5 3.2 2.4 Price GBP/kg 1.1 2.3 1.7 Youngs Modulus kg/m³ 103.5 135.6 119.6 Youngs Modulus kg/m³ 103.9 132.8 118.3
Poisson's Ratio - 0.3 0.3 0.3 Poisson's Ratio - 0.3 0.3 0.3 Tensile Strength MPa 89.3 354.2 221.7 Tensile Strength MPa 96.3 326.0 211.2
Elastic Limit MPa 27.2 309.8 168.5 Elastic Limit MPa 46.7 281.9 164.3 Shear Stress MPa 41.3 47.9 44.6 Shear Stress MPa 41.3 49.4 45.4
FX9 Alloy Density GPa 8360.4 8393.4 8376.9
Price GBP/kg 1.1 2.4 1.8 Youngs Modulus kg/m³ 119.5 148.7 134.1
Poisson's Ratio - 0.3 0.3 0.3 Tensile Strength MPa 177.6 423.6 300.6
Elastic Limit MPa 65.9 304.9 185.4 Shear Stress MPa 47.7 55.2 51.4
MS63 FX9 B8 B20 B12
How I came up with the
material statistics
CES EduPack
The Materials Zinc
D 7130 7150
P 0.65 1
YM 90 107
PR 0.25 0.33
tS 90 200
EL 75 166
Shear 35 45
Manganese
D 7350 7500
P 0.85 1
YM 187 199
PR 0.23 0.25
tS 630 780
EL 225 255
Shear 74 82
Aluminium
D 2670 2730
P 0.755 1.223
YM 69 72
PR 0.32 0.36
tS 55 61
EL 24 26
Shear 25 27
Copper
D 8930 8940
P 1.3 3
YM 112 148
PR 0.34 0.35
tS 100 400
EL 30 350
Shear 45 52
Tin
D 7280 7310
P 3.354 4.403
YM 41 45
PR 0.325 0.335
tS 11 18
EL 7 15
Shear 14 18
Lowest percentage of tin – hard to
manufacture.
Much more durable
Has a much more ‘lively’ sound than the other Bronze
alloys.
Soft Material – Easy to manufacture and mould.
‘Dark’ sound, and ‘smooth’ to strike.
Most commonly used alloy.
Good bridge between B20 and B8 – averaged between the two.
Slightly more expensive
“Powerful sounding characteristics” – Meinl.
B20, B12, B8
Number represents tin
Percentage
Bronze Alloys
Traditional Material
Cost
Material Properties
Sound Properties
B20, B12, B8 Alloys
FX9 is a much more modern cymbal alloy that has only recently been adopted – invented by Meinl.
It has a very ‘bright’ and ‘lively’ sound
“Cymbals made from FX9 alloy offer new, fresh and lively sounds with a distinctive timbre” – Meinl.
FX9 is a durable alloy – more so than the majority of other cymbal alloys
MS63 - number representing copper percentage
Cheaper student ranges of cymbals
“Positive sound characteristics... It offers the best possible sound qualities at an affordable price”
Cheap to Manufacture
MS63 FX9
MS63 Brass
Cheaper – Student Range
FX9
Unique, Lively, Bright sound
Silver in appearance
Derived from Meinl’s Cymbal
Catalogue and Hugo
Pinksterboer’s ‘Cymbal Book’.
MS63 FX9 Alloys
Very Simplistic
Based on a 14-inch
Meinl Crash Cymbal
Meshing Problems
Curvature Mesh
Fixings
The Model
Modes of Frequency
1 – 5
Graph 1 - Frequency
Appears to show consistent
percentage change.
Testing the Materials
Modes of Frequency
1 – 5
Graph 2 - Frequency
Appears to show consistent
percentage change – close
up.
Testing the Materials
80
85
90
95
100
105
1 2 3 4
Fre
qu
en
cy (
He
rtz)
Frequency Mode - Test Number
B20 Alloy B12 Alloy B8 Alloy MS63 Alloy FX9 Alloy
2.35
3.50 3.41
9.16
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
B12 B8 MS63 FX9
The effect the change of
frequency has
2.35 – 9.16% change
The difference in frequency
between the notes B7
(3951Hz) and C8 (4186Hz) is
just 235Hz, which is only a
5.9% increase
Why is this important? Freq. Mode B12 B8 MS63 FX9
1 2.32 3.45 3.83 9.68 2 2.32 3.44 3.84 9.69 3 2.39 3.54 3.02 8.66 4 2.39 3.55 2.97 8.60
Average (%) 2.35 3.50 3.41 9.16
Low Frequency – Why?
Graph 3 – 100 Modes of
Frequency
Conclusions Drawn:
Consistent, predictable graph
pattern
What does this mean?
Testing the Materials
0
1000
2000
3000
4000
5000
6000
7000
0 10 20 30 40 50 60 70 80 90 100
Fre
qu
en
cy (
He
rtz)
Frequency Mode - Test Number
Low Frequency – Why?
Modes of Frequency
Conclusions Drawn:
Consistent, predictable graph
pattern
What does this mean?
Testing the Materials Mode 1
Mode 5
Mode 50
Mode 100 B20
Easy method of predicting
cymbal properties
Helped to gauge by what % an
alloy should be changed by to
create the desired effect
Custom Cymbal Properties
Reduced testing time –
Enhanced Manufacturing
Capabilities
What does all this mean?
Properties should include:
Bright, lively sound – High Frequency
Durable
Properties should include:
Smooth feel when struck
Very Dark, low sound – low frequency
Manipulation Based on
Material Properties
Manipulation Based on
Frequency of Sound
Run through FEA process
B24 Alloy
B6 Alloy
Alloy properties generated by
simply modifying the excel
document to match my
specifications
Designing a Cymbal Alloy Property Unit Minimum Maximum Average
B24 Alloy
Density GPa 8534.0 8548.8 8541.4
Price GBP/kg 1.8 3.3 2.6
Youngs Modulus kg/m³ 95.0 123.3 109.1
Poisson's Ratio - 0.3 0.3 0.3
Tensile Strength MPa 78.6 308.3 193.5
Elastic Limit MPa 24.5 269.6 147.0
Shear Stress MPa 37.6 43.8 40.7
B6 Alloy
Density GPa 8831.0 8842.2 8836.6
Price GBP/kg 1.4 3.1 2.3
Youngs Modulus kg/m³ 107.7 141.8 124.8
Poisson's Ratio - 0.3 0.3 0.3
Tensile Strength MPa 94.7 377.1 235.9
Elastic Limit MPa 28.6 329.9 179.3
Shear Stress MPa 43.1 50.0 46.6
Importing Material properties
from calculated alloys – in
this case B24
Designing a Cymbal Alloy
Meshing
Curvature Mesh
Consistent with all other tests
Designing a Cymbal Alloy
Results
List Resonant Frequencies
Exported to Excel and results
analysed and converted into
an appropriate graph
Designing a Cymbal Alloy
Results
B24 displays a reduction in
frequency by an average of
3.4%
B6 displays an increase in
frequency by an average of
3.7%
Success!
Designing a Cymbal Alloy – The Results
75.00
80.00
85.00
90.00
95.00
100.00
1 2 3 4
Fre
qu
en
cy (
He
rtz)
Frequency Mode
B20 Alloy B8 Alloy B24 Alloy B6 Alloy
Tests 1 - 5 - Frequency (Hertz) Alloy 1 2 3 4 5 B24 Alloy 79.18 80.22 89.46 90.99 187.93 B6 Alloy 84.48 85.58 96.92 98.70 201.11 B20 Alloy 81.41 82.47 93.49 95.21 193.77 B8 Alloy 84.21 85.31 96.80 98.59 200.43
Percentage Change (%) (to B20) Average B24 Alloy -2.74 -2.73 -4.31 -4.44 -3.014 -3.44692 B6 Alloy 3.777 3.777 3.672 3.667 3.788 3.736243 B8 Alloy 3.447 3.445 3.542 3.547 3.4371 3.483473
-4
-3
-2
-1
0
1
2
3
4
5
B24 Alloy B6 Alloy B8 Alloy
Pe
rce
nta
ge C
han
ge (
in c
om
par
iso
n t
o B
20
Allo
y)
(%)
Alloy Variation
In-depth understanding of
Solidworks Simulation
Applications of Finite Element
Analysis
How to optimise design
solutions based on results
What have I learnt?
Abstract Cymbals - Rachel Gidluck
Would have liked to explored
the possibility of finding a
quicker method of predicting
cymbal properties based on
material in the form of a
more accessible equation –
without having to run it
through Solidworks
What would I change?
Questions