Frequency Analysis of a Cymbal Materials & Deformation and the - - PowerPoint PPT Presentation
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 The (original)
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?
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
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
B20, B12, B8, MS63, FX9 Differences
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 Poisson's Ratio
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 Poisson's Ratio
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 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
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
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’.
Very Simplistic Based on a 14-inch Meinl Crash Cymbal Meshing Problems Curvature Mesh Fixings
Modes of Frequency 1 – 5 Graph 1 - Frequency Appears to show consistent percentage change.
Modes of Frequency 1 – 5 Graph 2 - Frequency Appears to show consistent percentage change – close up.
80 85 90 95 100 105 1 2 3 4 Frequency (Hertz) 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
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?
1000 2000 3000 4000 5000 6000 7000 10 20 30 40 50 60 70 80 90 100 Frequency (Hertz) Frequency Mode - Test Number
Low Frequency – Why? Modes of Frequency Conclusions Drawn: Consistent, predictable graph pattern What does this mean?
Mode 1 Mode 5 Mode 50 Mode 100
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
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
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 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 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
Meshing Curvature Mesh Consistent with all other tests
Results List Resonant Frequencies Exported to Excel and results analysed and converted into an appropriate graph
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!
75.00 80.00 85.00 90.00 95.00 100.00 1 2 3 4 Frequency (Hertz) 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
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
1 2 3 4 5
B24 Alloy B6 Alloy B8 Alloy
Percentage Change (in comparison to B20 Alloy) (%) Alloy Variation
In-depth understanding of Solidworks Simulation Applications of Finite Element Analysis How to optimise design solutions based on results
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