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Transcript
Land Wind Racer Design RideWy University of Wyoming College of Engineering and Applied Sciences EPSCoR Undergraduate Research Day April 21, 2012 1 RideWy Team Mechanical Engineering • Austin Rykhus – Frame Design and construction • Lee Mitchell – Brake Design Energy Systems Engineering • Nick James –Stability and Steering Design • Shyla Allen – Sail Design Sponsors • Z4 Energy • Georgia Gayle • Kevin Luke Advisors • Dr. Naughton • Dr. Garnich • Mr. Morton 2 Celebration of Wind Race Rules • • • • • • Wind powered 3 to 84 wheels, 5” or larger All human crew, or as close as possible Equipped with braking & steering Assume liability for themselves & crew No commercial vehicles 3 Celebration of Wind Race Rules • Carry 1 person over course • Height < 13.5 ft • No chewing tobacco if the wind >15 knots (to avoid splashing the spectators) • Points deducted for: Celebration of Wind • • • • • Destroying spectators Biting Kicking Striking Gouging Race Day April 28, 2012 Rawlins, Wyoming • BRIBES will be taken into consideration 4 Land Wind Racer Design 5 Overview • • • • • • • Design Specifications Lessons Learned Design Approach Modeling Compliance Testing Alterations Finished Product 6 Design Specifications • Z4 Specifications • ≤ 80 lbf weight • 4 ft x 6 ft footprint • “WIN the RACE” • RideWy Specifications • 13 mph average tailwind • 40 mph maximum tailwind • 1.2 minimum FOS 7 Lessons Learned User Interface • • • • • Rider capabilities Steering Braking Sail Rigging Sitting position Frame • Weight and transport • Sail design Head Clearance 8 Design Approach • 3 vs. 4 wheels • 3 wheel inverted tricycle design • Lightweight, stable, and simple • Sail • Spinnaker sail – tailwind application • Braking – front vs. rear • Dual front brakes – majority of brake force • Steering • Rear steering – simplicity 9 Modeling – The Sail • Created from a pressure gradient – Bernoulli’s Principle • 1 2 L = ρ𝑉𝐴 2 AS CL 1 2 D = ρ𝑉𝐴 2 AS CD Variable Definition VS Velocity of Racer VT Wind Velocity VA Apparent Wind • Minimum β angle = More advantageous V VST • Total Propulsion Force: • VA Implemented in other modeling • V VT S β VS/VT =3 𝐹𝑇 = 0.00119 × 𝐶𝑇 × AS × 𝑉𝐴 2 • 𝐶𝑇 = 𝐶𝐿 2 + 𝐶𝐷 2 • β = 65 °, 𝑉𝑇 = 10 mph – Propulsion Force = 25 lbf 10 Modeling – The Sail • Dynamic Modeling • Solution relative to time (t) , distance (s), and velocity (v) • Differential Equations with MATLab Variables: • 𝑌1 = 𝑠 • 𝑌2 = 𝑣 Derivatives: • 𝐹1 = • 𝐹2 = 𝑑𝑠 = 𝑣 = 𝑌2 𝑑𝑡 𝑑𝑣 𝐹 = 𝑎 = 𝑑𝑡 𝑚 Variable CT AS VA Definition Lift and Drag Coefficient Wind Velocity Apparent Wind Recall: 𝐹 = 0.00119 × 𝐶𝑇 × AS × 𝑉𝐴 2 • ½ mile, β = 65 °, 𝑉𝑇 = 7 mph, Time = 3 minutes • Maximum Velocity = 7 mph 11 Modeling – Braking System • Front disc brakes with foot pedal • Sum the horizontal forces about the racer’s front wheel 𝑀 = 𝐹𝑓 = 𝐹𝑛 µ • Sum the moments about the front axle for vertical forces 𝐹𝑓 𝑅𝑤ℎ𝑒𝑒𝑙 = (𝑚𝑟𝑖𝑑𝑒𝑟 𝑔)𝐿𝑟𝑖𝑑𝑒𝑟 + (𝑚𝑣 𝑔)𝐿𝑐𝑔 + (𝑚𝑣 𝑔)ℎ𝑐𝑔 + 𝐹𝑤𝑖𝑛𝑑 ℎ𝑤𝑖𝑛𝑑 Variable Ff Fn Fb M cg Definition Friction Force Normal force Brake Force Brake Moment Center of Gravity rb Brake Disc Radius hwind Height of Wind force µ Coefficient of Friction Cg M wind rb Fn,fw 12 Modeling – Braking System • Applied braking force 𝐹𝑓 𝑅𝑤ℎ𝑒𝑒𝑙 = 𝐼𝛼 + 𝐹𝑏 𝑟𝑏 ≈ 𝐹𝑏 𝑟𝑏 • Stopping distance • Sail dropped, not accelerating forward 𝑉𝑠2 𝑉𝑠2 𝑆𝐷 = = 𝐹 2𝑎 2(𝑚𝑏 ) 𝑣 • Racer velocity = 20 mph, µ = 0.65 • Fb = 98 lbf • SD = 7.5 ft Variable Ff Fb mv Definition Friction Force Brake Force Mass of Racer rb Brake Disc Radius I Moment of Inertia α Angular Acceleration Vs Velocity of Racer SD Stopping Distance μ Coefficient Of Friction 13 Modeling – Stability • Modeled using a worst case scenario • Side Stability Σ 𝑀𝑜𝑚𝑒𝑛𝑡𝑠 = 𝑚𝑔 𝐿 − 𝐿𝑐𝑔 sin 𝑡𝑎𝑛−1 𝑤 ℎ𝐹𝑡 𝑠𝑖𝑛 sin 𝜃𝑠 − 𝑡𝑎𝑛−1 2𝐿 𝑤 2𝐿 − • Frontal Stability Σ 𝑀𝑜𝑚𝑒𝑛𝑡𝑠 = 𝑚𝑔𝐿𝑐𝑔 − ℎ𝐹𝑡 𝑐𝑜𝑠𝜃𝑠 − 𝑅𝐹𝑊 𝐹𝑏 Variable LCG Fb Ft h Ѳs Definition Distance to center of gravity Brake force Driving force from sail Height of point force of sail Angle of Ft Cg 14 Modeling –Steering • Similar to bicycle steering • Steering torque arm (nT) effected by • Caster angle (Ѳc) • Wheel Radius (RRW) • Fork Offset (Of) 𝑛 𝑇 = 𝑅𝑅𝑊 𝑠𝑖𝑛𝜃𝑐 − 𝑂𝑓 15 Modeling – Steering • Centrifugal force (FC) balanced by • FY1, FY2 and FY3 at contact points 𝐹𝑦3 = 1 − 𝐿−𝐿𝑐𝑔 3𝐹𝑐 𝐿 4 Variable VT RT m Definition Tangential velocity Turning radius Total mass • Restoring Moment 𝑀𝑍 = (𝑅𝑅𝑊 𝑠𝑖𝑛𝜃𝑐 − 𝑂𝑓 ) 1 − • 𝐿−𝐿𝑐𝑔 3𝑚𝑉𝑇2 𝐿 4𝑅𝑇 Of = 1in and θc = 15° Velocity (mph) Turning Radius (ft) Restoring Torque (ft-lbf) 10 25 20 50 4.2 ± 0.6 11± 1.3 16 Modeling Lateral Wheel Forces • Front wheel camber • Reduce lateral loads • Total lateral load Variable FY2 NFW RFW θcam Definition Cornering force at front wheel Normal force at front wheel Front wheel radius Camber angle ∑𝐹𝐹𝑊 = 𝑁𝐹𝑊 cos 90 − 𝜃𝑐𝑎𝑚 − 𝐹𝑌2 cos𝜃𝑐𝑎𝑚 𝐹𝑌2 = 𝐿−𝐿𝑐𝑔 3𝑚𝑉𝑇2 𝐿 4𝑅𝑇 • Camber – 10° • Reduces lateral loads by 25% 17 Frame Analysis • Compare and Validate each model • Beam analysis • Finite Element Analysis in SolidWorks 18 T –Frame Analysis m1 m2 m3 Rider mass Mast mass Front axle mass Ry_1 Reaction force in the y-direction Ry-2 Reaction force in the y-direction W1 , W2 Frame distributed load X1 Distance to mass 1 X2 Distance to the mast M Moment about the mast in the ydirection Not accounting for the beam slope or deformation at this point 19 T –Frame Analysis • MATLAB T Design • m1=140 lbf • m2=13 lbf • M=Ft*5.7 ft • Ft=20 lbf • Diagrams • Shear • Moment • Results • σ’ =8300 psi • FOS=4.9 20 Frame Analysis • Stress analysis on frame using SolidWorks Simulation • FEA T Design • m1=140 lbf • m2=13 lbf • M=Ft*5.7 ft • Ft=20 lbf • Results • σ’ =7700 psi • FOS=5.4 • Beam Analysis and FEA was performed on the Delta Design 21 Comparing Frame Analysis • T – Frame • Weight: 28 lbf • 1.6-1.9 FOS • Delta Frame • Weight: 31 lbf • 1.8-2.0 FOS 22 Fabrication • Construction began February 22, 2012 • Components fabricated • Frame • Running gear • Wheels & brakes • Modified bike components • Sail – Club 420 modified 23 Compliance Testing Sail Testing • Sail mounted to support post • Sail force using force dynamometer • Results • Wind = 7.5 mph, 20 lbf Frame Testing • Frame fixed to ground • Forces applied & deflection recorded • Results • 150 lbf rider, 70 lbf wind – 0.05 inches • Linear behavior – elastic strain region • Theoretical results • 150 lbf rider, 70 lbf wind – 0.03 inches 24 Compliance Testing Brake Testing • 150 lbf rider • Force dynamometer pulled to measure brake resistance • Results • Modeled force = 98 lbf • • Tested force = 53 lbf Stopping Distance = 10.5 ft Tipping Testing • Rear wheel fixed, racer rotation about right front wheel • 150 lbf rider • Dynamometer pulled on mast until tipped Results – Side load • Modeled force = 35 lbf • Tested force = 32 lbf 25 Alterations Made After Testing • The foot rest and braking pedal • Ergonomic issues • Sail control • Add line guides to front axle • Steering geometry • Improve restoring force 26 Finished Product 27 Sponsors • Z4 Energy • Sponsorship & Funding • North Sails & Sail Newport • Spinnaker Sail • Mckims’s Upholstery • Seat Upholstery • Department of Family and Consumer Sciences • Dr. Sonya Meyer • Dr. Donna Brown • Sail Alterations • Moonbuggy Team • Wheels and Brakes 28 Special Thanks Faculty & Shop Technicians Dr. Erikson Mr. Allen Mr. Schilt Mr. Dauer Mr. Morton Dr. Naughton Dr. Garnich 29 Questions! 30