Design Analysis of a 2011 Subaru WRX STI MECH 542 Final Project Kettering University Professor A. Mazzei Team Members: Jason Berger Jacob Kornas Jordan Nizza Overview . Vehicle History . Vehicle Specifications . Vehicle Architecture . Competency 1—Weight Distribution and Tire Patch Forces . Competency 2—Suspension . Competency 3—Steering Systems . Competency 4—Rollover . Competency 5—Tires Vehicle History First Generation: 1992-2000 Third Generation: 2008-2011 Second Generation: 2001-2007 Fourth Generation: 2012-2015 Vehicle History . The first generation Subaru Impreza WRX was introduced in Japan in 1992. In 1994, the Impreza WRX STI was released in Japan with an increased power rating, stronger suspension, and a stronger transmission compared to the WRX. In 1995 the Subaru Impreza wagon, badged as the Outback Sport, was introduced to the United States. For the 2000 model year, the Subaru Impreza was redesigned with a notably larger footprint. The Subaru Impreza WRX STI was introduced in the United States in 2004 with a power rating of 300 horsepower. In 2008, the Subaru Impreza was redesigned and the STI version was only available as a hatchback. In 2011, the STI was once again available as a sedan, boasting 305 horsepower produced by a 2.5L turbocharged 4-cylinder boxer engine. In 2012, the Subaru Impreza was redesigned with small body styling and interior changes. https://en.wikipedia.org/wiki/Subaru_Impreza http://jalopnik.com/a-brief-history-of-the-subaru-wrx-461608007 Manufacturer Specifications Dimensions and Weights Engine Drivetrain Overall Length 180.3" Turbocharged 2.5L boxer DOHC, 4-cylinder, 16 valves All wheel drive Overall Width 70.7" Bore 3.92" x 3.11" Electronic stability control Overall Height 57.9" Compression Ratio 8.2:1 Driver controlled center differential Wheelbase 103.3" Redline 6700 RPM Front and rear limited-slip differentials Track f/r 60.2"/60.6" Maximum Boost 14.7 psi Ground Clearance 5.9" Power 305 hp @ 6000 RPM 6-speed manual transmission 1st 3.636 Suspension Curb Weight 3,384 lbs 2nd 2.235 3rd 1.521 Wheels and Tires Forged aluminum alloy lower L-arms, 4th 1.137 Front inverted struts, cross member stiffener, 5th 0.971 Wheels (f and r) 18" x 8.5" stabilizer bar 6th 0.756 Tires (f and r) 245/40R18 Rear Double-wishbone, stabilizer bar Economy Steering Front Final Drive 3.900 Rear Final Drive 3.545 Transfer Gear 1.1 City 17 mpg Rack and pinion Highway 23 mpg Quick Ratio 15.0:1 Brakes Lock-to-Lock 2.8 turns Front and rear anti-lock brakes Turning Radius Disc Diameter f/r 13.0"/12.6" Curb-to-Curb 36.1' Calipers f/r 4 piston/2 piston Wall-to-Wall 38.7' http://www.cars101.com/subaru/impreza/wrxsti2011.html Vehicle Architecture: Overview Front MacPherson Turbocharged 2.5L, Strut Suspension 4-Cylinder, DOHC Boxer Engine 245/40R18 Tires AWD Drivetrain Rdyn,F = Rdyn,R = 322.6 mm Rear Multi-Link Suspension http://pressroom.subaru.pl/photo/2010m_wrxsti/ Vehicle Architecture: Front Strut Assembly Spring Rate : 58.0 N/mm Lower L-Arm Steering Tie Rod Steering Rack Assembly Stabilizer Bar 13” Brake Rotor with Front CV Shaft 4-Piston Caliper http://jp.autoblog.com/photos/2011-subaru-impreza-wrx-sti-first-drive-2/ http://eibach.com/m-america/en/eibach-news/subaru-wrx-sti-2015-plus-pro-kit http://perrinperformance.com/i-13324020-front-sway-bar-for-2008-14-sti-09-14-wrx.html http://pressroom.subaru.pl/photo/2010m_wrxsti/ Vehicle Architecture: Rear Strut Assembly Spring Rate : Stabilizer Bar 60.0 N/mm Lower Wishbone Upper Wishbone 12.6” Brake Rotor Rear CV Shaft Toe Control Arm with 2-Piston Caliper http://jp.autoblog.com/photos/2011-subaru-impreza-wrx-sti-first-drive-2/ http://eibach.com/m-america/en/eibach-news/subaru-wrx-sti-2015-plus-pro-kit http://pressroom.subaru.pl/photo/2010m_wrxsti/ Competency 1—Weight Distribution Objectives . Define vehicle coordinate system . Calculate vehicle system center of gravity . Calculate sprung system weight and center of gravity . Calculate unsprung system weight and center of gravity Competency 1—Weight Distribution . Vehicle dynamics depend directly on weight distribution . Weight distribution affects the yaw, roll, and pitch motions of a vehicle during corning, braking, and acceleration . The location of the center of gravity of the vehicle affects weight transfer during braking and acceleration and the cornering performance of a vehicle Coordinate System Vehicle ISO Coordinate System Z Y X Equations Vehicle Center of Gravity Height Weight Distribution ℎ푣,푡 = ℎ푣,0 + ∆ℎ푙표푎푑 푙푣,푅 퐹푣,퐹 푊퐷,퐹 = = 푙 퐹푣,푡 ℎ푣,0 = 푢푙ℎ푢푙 푙푣,퐹 퐹푣,푅 푊퐷,푅 = = Body Center of Gravity Height 푙 퐹푣,푡 퐹푣,푡ℎ푣,푡−퐹푈,퐹푟푑푦푛,퐹−퐹푈,푅푟푑푦푛,푅 ℎ퐵표 = 퐹퐵표 Sprung Weight 푚,퐹 표푟 푅퐹푣,푡,표푊퐷,퐹 표푟 푅 Vehicle Center of Gravity Lateral Position 퐹푢,퐹 표푟 푅 = 1 + 푚,퐹 표푟 푅 1 푏퐹 푏푅 푏푣 = 퐹푣,퐹퐿−퐹푣,퐹푅 + 퐹푣,푅퐿−퐹푣,푅푅 퐹푣,푡 2 2 Unsprung and Sprung Weight 푚,퐹 표푟 푅퐹푣,푡,표푊퐷,퐹 표푟 푅 Dynamic Tire Radius 퐹푢,퐹 표푟 푅 = 1 + 푚,퐹 표푟 푅 1 2 퐻 퐹 = 퐹 − 퐹 푟푑푦푛,퐹 표푟 푅 = 25.4푑퐹 표푟 푅 + 푊퐹 표푟 푅 − ∆푟퐹 표푟 푅 퐵표,퐹 표푟 푅 푣,푡 푊퐷,퐹 표푟 푅 푈,퐹 표푟 푅 2 100 푊 퐹 표푟 푅 퐹푢,퐹 표푟 푅 푚,퐹 표푟 푅 = 퐹퐵표,퐹 표푟 푅 Vehicle Weight Distribution Given Parameters: 2011 Subaru WRX STI Calculated Values Parameter Definition Symbol Value Unit Value Unit Parameter Definition Symbol Value Unit Value Unit Vehicle curb weight Fv,t,0 3384 lbf 15053 N Vehicle weight at front axle Fv,F 2158.3802 lbf 9600.9534 N Analysis Weight, Two people Fv,t 3781 lbf 16819 N Vehicle weight at rear axle Fv,R 1622.6198 lbf 7217.7726 N Test weight - 3451 lbf 15351 N Loction of vehicle CG from the front axle plane lv,F 44.3313 in. 1126.0149 mm Front left corner test weight Fv,FL 952 lbf 4235 N Location of the vehicle CG from the rear axle plane lv,R 58.9687 in. 1497.8051 mm Front right corner test weight F 1018 lb 4528 N v,FR f Front axle unsprung weight Fu,F 206.9735 lbf 920.6642 N Rear left corner test weight F 762 lb 3390 N v,RL f Rear axle unsprung weight Fu,R 178.3461 lbf 793.3230 N Rear right corner test weight F 719 lb 3198 N v,RR f Front body (sprung) weight FBo,F 1951.4066 lbf 8680.2892 N Vehicle wheelbase l 103.3 in. 2623.8 mm Rear body (sprung) weight FBo,R 1444.2737 lbf 6424.4495 N Vehicle front track width bF 60.2 in. 1529.1 mm Total vehicle body (sprung) weight FBo 3395.6803 lbf 15104.7387 N Vehicle rear track width bR 60.6 in. 1539.2 mm Unloaded vehicle CG height hv,0 20.8440 in. 529.4376 mm Height of unloaded vehicle hul 57.9 in. 1470.7 mm Loaded vehicle CG height hv,t 21.2377 in. 539.4376 mm Loaded vehicle change in height Δhload 0.39 in. 10 mm Front dynamic tire radius rdyn,F 12.7008 in. 322.6000 mm Front tire wheel Diameter dF 18 in. 457.2 mm Rear dynamic tire radius rdyn,R 12.7008 in. 322.6000 mm Front tire width WF 9.65 in. 245 mm Loaded body CG height hBo 22.2064 in. 564.0429 mm Front tire aspect ratio (H/W)F 40 - - - Lateral position of vehicle CG bv -0.1981 in. -5.0322 mm Front tire deflection ΔrF 0.16 in. 4 mm Loction of the body CG from the front axle plane lBo,F 43.9363 in. 1115.9809 mm Rear tire wheel Diameter dR 18 in. 457.2 mm Location of the body CG from the rear axle plane lBo,R 59.3637 in. 1507.8391 mm Rear tire width WR 9.65 in. 245 mm Rear tire aspect ratio (H/W)R 40 - - - Laboratory Measurements: Rear tire deflection ΔrR 0.16 in. 4 mm Front axle weight distribution iWD,F 0.57 - - - Test weight = 3451 lbf Rear axle weight distribution iWD,R 0.43 - - - FL Corner Weight = 952 lbf Front unsprung to sprung weight ratio i 0.12 - - - m,F FR Corner Weight = 1018 lbf Rear unsprung to sprung weight ratio im,R 0.14 - - - RL Corner Weight = 762 lbf Vehicle CG height coefficient iul 0.36 - - - RR Corner Weight = 719 lbf http://www.cars101.com/subaru/impreza/wrxsti2011.html Competency 1—Tire Patch Forces Objectives . Define vehicle system tire patch forces . Calculate braking tire patch forces . Calculate acceleration tire patch forces . Calculate cornering tire patch forces Competency 1—Tire Patch Forces . All forces acting on a vehicle, minus aerodynamic forces, act at the tire contact patch . The weight transfer during braking and acceleration depends on the location of the center of gravity of the vehicle and the vehicle wheelbase . For example, in a dragster, weight transfer is small because the relatively low center of gravity height and the long wheel base . Tire patch forces depend on the coefficient of friction between the tire and road Braking Equations Maximum Braking Coefficient of Static Friction 푣2 = 0.0334 푥,퐵 푠 Front Tire Patch Normal Forces Front Tire Patch Ideal Braking Forces 1 ℎ 1 ℎ 퐹 = 퐹 + 퐹 푣,푡 퐹 = 퐹 + 퐹 푣,푡 푧,푊,퐵,퐹 2 푣,푡 푊퐷,퐹 푣,푡 푥,퐵 푙 푥,푊,퐵,퐹 2 푣,푡 푊퐷,퐹 푣,푡 푥,퐵 푙 푥,퐵 Rear Tire Patch Normal Forces Rear Tire Patch Ideal Braking Forces 1 ℎ푣,푡 1 ℎ푣,푡 퐹 = 퐹 − 퐹 퐹푥,푊,퐵,푅 = 퐹푣,푡푊퐷,푅 − 퐹푣,푡푥,퐵 푥,퐵 푧,푊,퐵,푅 2 푣,푡 푊퐷,푅 푣,푡 푥,퐵 푙 2 푙 Acceleration Equations Maximum Drive Off Coefficient of Static Friction 푣2 = 0.0334 푥,퐴 푠 Front Tire Patch Normal Forces Front Tire Patch Drive Off Forces 1 ℎ푣,푡 1 ℎ 퐹 = 퐹 − 퐹 퐹 = 퐹 − 퐹 푣,푡 푥,푊,퐴,퐹 2 푣,푡 푊퐷,퐹 푣,푡 푥,퐴 푙 푥,퐴 푧,푊,퐴,퐹 2 푣,푡 푊퐷,퐹 푣,푡 푥,퐴 푙 Rear Tire Patch Normal Forces Rear Tire Patch Drive Off Forces 1 ℎ푣,푡 1 ℎ 퐹푥,푊,퐴,푅 = 퐹푣,푡푊퐷,푅 + 퐹푣,푡푥,퐴 푥,퐴 퐹 = 퐹 + 퐹 푣,푡 2 푙 푧,푊,퐴,푅 2 푣,푡 푊퐷,푅 푣,푡 푥,퐴 푙 Cornering Equations Front Outside Tire Patch Normal Force Rear Outside Tire Patch Normal Force 1 ℎ푣,퐹 1 ℎ푣,푅 퐹푧,푊,표,퐹 = 퐹푣,푡푊퐷,퐹 + 퐹푣,푡푊퐷,퐹푦,퐶 퐹푧,푊,표,푅 = 퐹푣,푡푊퐷,푅 + 퐹푣,푡푊퐷,푅푦,퐶 2 푏퐹 2 푏푅 Front Inside Tire Patch Normal Force Rear Inside Tire Patch Normal Force 1 ℎ푣,퐹 1 ℎ푣,푅 퐹푧,푊,,퐹 = 퐹푣,푡푊퐷,퐹 − 퐹푣,푡푊퐷,퐹푦,퐶 퐹푧,푊,,푅 = 퐹푣,푡푊퐷,푅 − 퐹푣,푡푊퐷,푅푦,퐶 2 푏퐹 2 푏푅 Front Outside Tire Patch Cornering Force Rear Outside Tire Patch Cornering Force 1 ℎ푣,퐹 1 ℎ푣,푅 퐹푦,푊,표,퐹