Final_Presentation_Example_group_8

Final_Presentation_Example_group_8 - BTW Lacrosse BTW...

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Unformatted text preview: BTW Lacrosse BTW Problem Definition and Purpose Problem The head is used in passing, catching, The and head to head checking Lacrosse heads crack Our purpose is to provide an improved Our way to carry, protect, and propel a lacrosse ball at a lighter weight lacrosse What’s out there now? What’s Customer Needs and Requirements Requirements Lightweight Flexible Rigid Thermal conductivity Electrical conductivity Crack resistance Scratch resistance Water resistance Easily dyed Recyclable Low cost Most important properties Most Modulus Toughness Improved Aesthetics Stress Concentrated Areas Density Cost to Manufacture The Head of the Class The Head of the Class Scoop: Flexible High Impact Resistance •Sidewalls: •Rigid •Overall Lightweight Our Contradiction and Our Goal Our The lacrosse head must be flexible so that The it will not break. However, it must also be rigid so that it will be functional as a lacrosse head. lacrosse To create a lightweight lacrosse stick head To to withstand high energy point impact collision both statically and dynamically without failing. without Broken Head Broken TRIZ Analysis TRIZ Strength vs. Weight of Stationary Strength Object Object T Make the design more simple than present present a By eliminating fancy designs we reduce stress By concentrations and points of failure. concentrations TRIZ Analysis TRIZ T Change from uniform to composite materials materials a By making the lacrosse head out of composite By or shape memory alloys, we can create head that is lighter, stronger, and more flexible than the competition. the Objective Objective We want to be able to maintain lightweight We while increasing the use life of the stick. while objective function to minimize is [m=ρπ abL] Constraint Constraint Cannot fail under loading either: Statically, Fmax = I σ f Ym L Dynamically, σ f2 = 6UmE Dynamically, 6U where Um= movo2 2 L(I/b2) L(I/b mo = mass of impacting object mass vo = velocity of object velocity Regulations Regulations The head shall be one piece, TRIANGULAR in concept. The inside width must continually increase from the center of the Ball Stop to the top of the head. Weight max. of 567 grams From the beginning of the sidewall, the height shall be 4.5 cm max.­3.2 cm min. Must be about 20 cm wide, 27 cm long, and no deeper than 6 cm Cross Sectional Area Cross “…a structure designed to withstand effectively structure an impact load should: an Have a large volume Be made of a material with a low elastic modulus and Be a high yield strength high Be shaped so that the stresses are distributed as Be evenly as possible throughout the structure” evenly • Beer, et al. Circular cross section is ideal for stress Circular distribution distribution Elliptical cross section for ball movement, low Elliptical elastic modulus and high yield strength elastic Variables Variables Fixed Free Circumference, or Circumference, Length= L Length= (L = 85 cm) Height= 2b (2b = 4.5 cm) Thickness= 2a A=π ab ab I=(π ab3)/4 (I/Ym) =(π ab2)/2 Performance Index Performance Static Loading Ashby Material Selection Ashby Ideal Materials Ideal Extreme Materials Extreme Performance Index Performance Dynamic Loading Stress Concentration Points Stress Why does the stick Why usually fail at eyelits? usually K1c=Yσ(πa)^(1/2) σmax= σ(1+2(a/b)) Since a=b for circular Since eyelet, eyelet, Then σmax=3 σapplied. Then =3 Finding the force… Finding F=ma m=1134g (maximum weight of an m=1134g opponent’s stick) opponent’s a=∆ v/s=50mph/0.05s=22.352m/s2 50mph is the near max shot velocity in girl’s 50mph lacrosse lacrosse 0.05s is the approximate contact time F=506.9 N Coupling Constant Coupling Ms/Md= (M1/M2)=(FL2)/(2bmovo2) CC=14.37 Material Selection Analysis Material Density, ρ (g/cm3) Modulus, E (GPa) Tensile S trength, s (GPa) Specific S tiffness, (E/ ρ) M1 (σ ) /ρ (static) 2 M2 (σ /ρE) (dynamic) M1/M2 Steel Aluminum Titanium 7.80 2.70 4.50 200.00 69.00 91.00 1.72 0.48 0.76 25.64 25.56 20.22 0.22 0.18 0.17 0.0019 0.0013 0.0014 116.0092807 142.8571429 120.0527704 AS4 AS4C AS4D T300 P100S IM4 IM6 IM7 IM7C IM8 Boron Kevlar 29 Kevlar 49 SCS 6 Nicalon Alumina S-2 Glass E-Glass Sapphire PV36/700 PV42/800 PV42/850 1.79 1.78 1.79 1.76 2.15 1.78 1.76 1.79 1.80 1.80 2.60 1.44 1.44 3.30 2.55 3.95 2.46 2.58 3.97 1.79 1.80 1.79 228.00 231.00 245.00 231.00 724.00 276.00 279.00 292.00 290.00 310.00 385.00 80.00 124.00 400.00 180.00 379.00 86.80 69.00 435.00 248.00 290.00 292.00 4.28 4.35 4.69 3.65 2.20 4.80 5.59 5.76 5.80 5.17 3.80 2.80 3.62 3.50 2.00 1.59 4.59 3.45 3.60 4.69 5.52 5.76 127.37 129.78 136.87 131.25 336.74 155.06 158.52 163.13 161.11 172.22 148.08 55.56 86.11 121.21 70.59 95.95 35.28 26.74 109.57 138.55 161.11 163.13 2.39 2.44 2.62 2.08 1.02 2.69 3.18 3.22 3.22 2.87 1.46 1.94 2.51 1.06 0.78 0.40 1.86 1.34 0.91 2.62 3.07 3.22 0.0448 0.0460 0.0502 0.0328 0.0031 0.0468 0.0636 0.0635 0.0644 0.0479 0.0144 0.0681 0.0734 0.0093 0.0087 0.0017 0.0985 0.0669 0.0075 0.0495 0.0584 0.0635 53.2959327 53.1400966 52.2165388 63.2183908 329.2405639 57.5479566 49.9194847 50.6944444 50.0345066 59.9497196 101.3424585 28.5714286 34.2446838 114.4164760 90.0000000 239.1167192 18.9312977 20.0000000 120.8333333 52.8784648 52.5362319 50.6944444 Epoxy Polyimide Copper Silicon Carbide 1.38 1.46 8.90 3.20 4.60 3.50 117.00 400.00 0.06 0.10 0.40 0.31 3.33 2.40 13.15 125.00 0.04 0.07 0.04 0.10 0.0005 0.0021 0.0002 0.0001 78.4982935 33.9805825 292.5000000 1290.3225806 And the winner is… And Material Density, ρ (g/cm3) Modulus, E (GPa) Tensile Strength, s (GPa) Specific Stiffness, (E/ ρ) M1 (σ /ρ ) (static) M2 (σ 2 /ρ E) (dynamic) M1/M2 Kevlar 29 1.44 80.00 2.80 55.56 1.94 0.0681 28.5714286 Kevlar 49 1.44 124.00 3.62 86.11 2.51 0.0734 34.2446838 S-2 Glass 2.46 86.80 4.59 35.28 1.86 0.0985 18.9312977 E-Glass 2.58 69.00 3.45 26.74 1.34 0.0669 20.0000000 Polyimide 1.46 3.50 0.10 2.40 0.07 0.0021 33.9805825 S-2 Glass / Polyimide Epoxy S-2 Now, solving for our mass… m = 2FL2ρ 2FL 3 bσ f ρ = 2.36* g/cm3 2.36* σ f = 4.59 GPa 4.59 m = 5.580 grams * In a 90/10 S-2 Glass / polyimide epoxy composite And our free variable.. And So, if m = ρπ abL So, ρ π abL Then our a = .0394 mm The thickness is 2a = .0787 mm The Increasing the thickness to 5 mm The $$$ The S-2 Glass is $13.23/kg, polyimide epoxy is S-2 $3.96/liter $3.96/liter So, the material cost for the 90/10 S-2 So, Glass-Polyimide epoxy head is $4.90 Glass-Polyimide Most of cost will be in manufacturing Conclusion Conclusion Therefore, we have a composite head Therefore, made of S-2 Glass fibers and a polyimide epoxy in a 90/ 10 distribution epoxy The total weight is 354.5 grams The (reasonable) (reasonable) The thickness, 2a, is 0.5 cm (reasonable) The height, 2b (fixed), is 4.5 cm The total material cost is about $4.90/head Marketing Marketing Assumptions $25000 initial outlay in equipment costs, 10 year life, $25000 no salvage no $60000 per annum in leasing costs $75 charged per head • • • $5 in materials $5 in shipping $65 in profit 50,000 current players with 10% growth 36% tax rate 15% desired ROR 15% Cost Analysis Cost % Mkt Pen 10 20 30 40 50 60 70 80 90 100 n 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1 7,950 12,850 33,650 54,450 75,250 96,050 116,850 137,650 158,450 179,250 2 16,130 65,321 114,514 163,706 212,898 262,090 311,282 360,474 409,666 458,858 3 49,374 136,770 224,166 311,562 398,958 486,353 573,749 661,145 748,541 835,937 4 94,515 232,756 370,997 509,237 647,478 785,718 923,959 1,062,200 1,200,440 1,338,681 5 155,044 360,371 565,699 771,027 976,354 1,181,682 1,387,009 1,592,337 1,797,665 2,002,992 6 235,412 528,650 821,888 1,115,126 1,408,364 1,701,602 1,994,840 2,288,078 2,581,316 2,874,554 7 341,294 749,089 1,156,883 1,564,678 1,972,473 2,380,267 2,788,062 3,195,856 3,603,651 4,011,446 8 479,918 1,036,311 1,592,705 2,149,098 2,705,492 3,261,885 3,818,279 4,374,672 4,931,066 5,487,459 9 660,478 1,408,902 2,157,326 2,905,751 3,654,175 4,402,600 5,151,024 5,899,448 6,647,873 7,396,297 10 894,663 1,890,465 2,886,268 3,882,070 4,877,872 5,873,674 6,869,476 7,865,279 8,861,081 9,856,883 Statistical Analysis Statistical Assume… F = 507N (our impact force) A = pi*ab = 0.0003534 m2 • a = .005 m (set to compensate for processing) • b = .0225 m (set) So our σ = F/A = 1.435 MPa So Standard Deviation of 459 MPa (10% of Standard given) given) Statistical Analysis Statistical And so we have z… z = (4.59 GPa – 1.435 MPa)/459 MPa z = 10 So with these assumptions failure So probability due to given conditions is less than 1 in 1000. less References References The University of Florida Women’s Lacrosse The Team Team http://www.uspto.gov http://www.brine.com http://www.stx.com http://www.deBeer.com http://www.warrior.com http://www.compositesone.com/basics.html Mechanics of Materials, 3rd Edition, Beer, et al. McGraw-Hill Company Inc., 2001, New York. McGraw-Hill Fatal Flaws?.... Fatal Or Questions? Performance Index Performance Top Section – Static Loading Performance Index Performance Top Section – Dynamic Loading Momentum Momentum Impact Mass: mo= 1140g (mass of an 1140g opponents stick) opponents Impact Velocity: vo= 22.352 m/s (high-end 22.352 shots are around 50mph) shots ...
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This note was uploaded on 06/10/2011 for the course EMA 7414 taught by Professor Mecholsky during the Spring '11 term at University of Florida.

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