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) Problem Deformation How does it effect the sound? How can it be prevented? What role do materials play? Why does it happen?

Is this a 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

The (new) 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 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 B20, B12, B8, MS63, FX9 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 Differences 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

The Materials Zinc Copper Aluminium D 7130 7150 D 8930 8940 D 2670 2730 P 0.65 1 P 1.3 3 P 0.755 1.223 YM 90 107 YM 112 148 YM 69 72 PR 0.25 0.33 PR 0.34 0.35 PR 0.32 0.36 How I came up with the tS 90 200 tS 100 400 tS 55 61 material statistics EL 75 166 EL 30 350 EL 24 26 Shear 35 45 Shear 45 52 Shear 25 27 CES EduPack Manganese Tin D 7350 7500 D 7280 7310 P 0.85 1 P 3.354 4.403 YM 187 199 YM 41 45 PR 0.23 0.25 PR 0.325 0.335 tS 630 780 tS 11 18 EL 225 255 EL 7 15 Shear 74 82 Shear 14 18

B20, B12, B8 Alloys B20, B12, B8 Good bridge between B20 Number represents tin and B8 – averaged Percentage between the two. Lowest percentage of Slightly more expensive tin – hard to Bronze Alloys manufacture. “Powerful sounding characteristics” – Meinl. Traditional Material Much more durable Has a much more Cost ‘lively’ sound than Soft Material – Easy to the other Bronze manufacture and mould. Material Properties alloys. ‘Dark’ sound, and ‘smooth’ Sound Properties to strike. Most commonly used alloy.

MS63 FX9 Alloys MS63 FX9 MS63 - number representing copper percentage MS63 Brass Cheaper student ranges of cymbals Cheaper – Student Range “Positive sound characteristics... It offers the best possible sound qualities at an affordable price” FX9 Cheap to Manufacture Unique, Lively, Bright sound FX9 is a much more modern cymbal alloy that has only recently been adopted – invented by Meinl. Silver in appearance It has a very ‘bright’ and ‘lively’ sound Derived from Meinl’s Cymbal “Cymbals made from FX9 alloy offer new, fresh and lively sounds with Catalogue and Hugo a distinctive timbre” – Meinl. Pinksterboer’s ‘Cymbal Book’. FX9 is a durable alloy – more so than the majority of other cymbal alloys

The Model Very Simplistic Based on a 14-inch Meinl Crash Cymbal Meshing Problems Curvature Mesh Fixings

Testing the Materials Modes of Frequency 1 – 5 Graph 1 - Frequency Appears to show consistent percentage change.

Testing the Materials 105 100 Modes of Frequency 1 – 5 Frequency (Hertz) 95 Graph 2 - Frequency Appears to show consistent 90 percentage change – close up. 85 80 1 2 3 4 Frequency Mode - Test Number B20 Alloy B12 Alloy B8 Alloy MS63 Alloy FX9 Alloy

Why is this important? 10.00 Freq. Mode B12 B8 MS63 FX9 9.16 1 2.32 3.45 3.83 9.68 9.00 The effect the change of 2 2.32 3.44 3.84 9.69 3 2.39 3.54 3.02 8.66 frequency has 8.00 4 2.39 3.55 2.97 8.60 Average (%) 2.35 3.50 3.41 9.16 7.00 2.35 – 9.16% change 6.00 The difference in frequency 5.00 between the notes B7 (3951Hz) and C8 (4186Hz) is 4.00 3.50 3.41 just 235Hz, which is only a 3.00 5.9% increase 2.35 2.00 1.00 0.00 B12 B8 MS63 FX9

Testing the Materials 7000 Low Frequency – Why? 6000 Graph 3 – 100 Modes of 5000 Frequency Frequency (Hertz) 4000 Conclusions Drawn: Consistent, predictable graph 3000 pattern 2000 What does this mean? 1000 0 0 10 20 30 40 50 60 70 80 90 100 Frequency Mode - Test Number

Testing the Materials Mode 1 Mode 50 Low Frequency – Why? Modes of Frequency Conclusions Drawn: B20 Consistent, predictable graph pattern Mode 100 Mode 5 What does this mean?

What does all this mean? 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

Designing a Cymbal Alloy Manipulation Based on Material Properties Property Unit Minimum Maximum Average B24 Alloy Density GPa 8534.0 8548.8 8541.4 Properties should include: Manipulation Based on Price GBP/kg 1.8 3.3 2.6 Youngs Modulus kg/m³ 95.0 123.3 109.1 Frequency of Sound Smooth feel when struck Poisson's Ratio - 0.3 0.3 0.3 Tensile Strength MPa 78.6 308.3 193.5 Very Dark, low sound – low frequency Elastic Limit MPa 24.5 269.6 147.0 Run through FEA process Shear Stress MPa 37.6 43.8 40.7 B6 Alloy Density GPa 8831.0 8842.2 8836.6 B24 Alloy 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 B6 Alloy Tensile Strength MPa 94.7 377.1 235.9 Elastic Limit MPa 28.6 329.9 179.3 Properties should include: Shear Stress MPa 43.1 50.0 46.6 Alloy properties generated by Bright, lively sound – High Frequency simply modifying the excel Durable document to match my specifications

Designing a Cymbal Alloy 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 – The Results 100.00 5 Results Percentage Change (in comparison to B20 Alloy) 4 3 B24 displays a reduction in 95.00 2 frequency by an average of 1 (%) 3.4% Frequency (Hertz) 0 90.00 B24 Alloy B6 Alloy B8 Alloy -1 B6 displays an increase in -2 85.00 frequency by an average of -3 3.7% -4 Alloy Variation 80.00 Tests 1 - 5 - Frequency (Hertz) Success! 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 75.00 B20 Alloy 81.41 82.47 93.49 95.21 193.77 1 2 3 4 B8 Alloy 84.21 85.31 96.80 98.59 200.43 Frequency Mode Percentage Change (%) (to B20) Average B24 Alloy -2.74 -2.73 -4.31 -4.44 -3.014 -3.44692 B20 Alloy B8 Alloy B24 Alloy B6 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

What have I learnt? In-depth understanding of Solidworks Simulation Applications of Finite Element Analysis How to optimise design solutions based on results Abstract Cymbals - Rachel Gidluck

What would I change? 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

Questions