Vehicle Dynamic Systems Final Portfolio

Transcription

1 Summer 2015 Professor Arnaldo Mazzei Vehicle Dynamic Systems Final Portfolio 1987 BMW 325is Kevin Sallee Cody Clarke Jiaqi Huang

2 Contents Vehicle History Vehicle Information Competency 1: Weight Distribution & Tire Patch Forces Competency 2: Acceleration Competency 3: Braking Competency 4: Ride Competency 5: Low-Speed Steering Competency 6: High-Speed Steering (Handling) *All Calculations done for Light Loading condition

3 Vehicle History - The BMW 3 Series BMW's sporty compact executive sedan

4 Vehicle History - The BMW 3 Series In continuous production since 1975, it has seen six generations: E21, E30, E36, E46, E90, and F30 E21 ('75-'82) E30 ('83-'91) E36 ('92-'99) E46 ('99-'05) E90 ('06-'11) F30 ('12-present)

5 Vehicle Comparison 1987 BMW 325is Base Price $27, Price $58,012 Engine/Power 2.5 I6 / 168 HP Weight/Distribution 53% / 47% 1987 Volvo 760 Turbo Base Price $28, Price $60,222 Engine/Power 2.3 I4 / 160 HP Weight/Distribution 56% / 44%

6 Vehicle History - The BMW 3 Series It has always used a semi-trailing arm rear suspension setup, which aids in the car's highly acclaimed handling characteristics

7 Other Vehicle Information Garage Measurements Weight: 2825 lbs Distribution: 53.5%/46.5% Rear Deflection/Weight: 1.0 Inch / 200 lbs Front Deflection/Weight: 0.75 Inch / 200 lbs

8 Weight Distribution & Tire Patch Forces OBJECTIVES: 1. Define vehicle coordinate system 2. Define weight distribution 3. Describe weight center location 4. Define the vehicle system tire patch forces 5. Calculate tire patch forces during acceleration

9 Vehicle iso coordinate system Calculations base on iso coordinate system X-axis-linear velocity Y-axis-lateral velocity Z-axis-yaw velocity

10 Weight distribution & Weight center location In a vehicle which relies on gravity in some way, weight distribution directly affects a variety of vehicle characteristics, including handling, acceleration, traction, and component life. For this reason weight distribution varies with the vehicle's intended usage. The height of the vehicle s center of gravity affects the vehicle s acceleration and braking based on the amount of weight transfer. Vehicles with lower centers of gravity are able to create larger cornering forces, since they hold lower rolling moments on the X-Axis.

11 Vehicle system tire patch forces Tire patch forces are the amount of force transmitted from the body to the tires, which ultimately is passed on to the road. The tire patch forces are a function of the weight distribution and the vehicle s acceleration in the X and Y Axis. Longitudinal tire patch forces provide acceleration and braking, while lateral tire patch forces are responsible for cornering.

12 Weight Distribution & Tire Patch Forces Weights Total Weight: 2825 lbs Curb Weight: 2823 lbs Corner Weights: LF - Front - RF Front / Rear = 53% / 47% LR - Rear - RR

13 Vehicle Specifications Wheelbase (l) Wheel Diameter, front inches 14 inches mm Tire Width, front Track, front 195 mm 55.4 inches Tire Sidewall Ratio, front mm 65 Track, rear Δr, rear 55.7 inches 4 mm mm Dynamic Radius, front (r dyn,f ) Height (H ul ) mm 54.3 inches Wheel Diameter, rear mm 14 inches Height (H V,0 ) Tire Width, rear inches 195 mm mm Tire Sidewall Ratio, rear Curb Weight (F v,t ) lbs Δr, rear N 4 mm Dynamic Radius, rear (r dyn,r ) mm Weight Distribution Front Rear 53% 47% Individual Wheel Weights (lbs) FL FR RL RR Δh load 10 mm inches

14 Weight Distribution Calculations Light Load (F v,t,2p ) 3153 lbs N Vehicle Center of Gravity - Curb Vehicle Center of Gravity - Light Load F v,f lb F v,r lb F v,f,2p lb F v,r,2p lb N N N N l v,f inches l v,r inches l v,f,2p inches l v,r,2p inches mm mm mm mm h v,t inches b v 0 inches h v,t, 2p inches mm 0 mm mm Body (Sprung) & Axle (Unsprung) Weight Body (Sprung) & Axle (Unsprung) Weight F U,f lb F U,r lb F U,f lb F U,r lb N N N N F Bo,f lb F Bo,r lb F Bo,f lb F Bo,r lb N N N N l Bo,f inches l Bo,r inches l Bo,f inches l Bo,r inches mm mm mm mm h Bo mm h Bo, r mm h Bo, 2p mm h Bo, r mm inches h Bo, f mm inches h Bo, f mm

15 Normal Force(N) Tire Patch Braking Normal Forces at 60 mph FRONT 1000 REAR Braking g's

16 Normal Force (N) Ideal Tire Patch Forces (X-Axis) at 60 MPH Front Rear Vehicle Brakeing g's

17 Acceleration Dynamics Customer Focus Quickly increase speed from stop Easily accelerate in traffic Easily move from stationary on a hill Accelerates Smoothly Easily accelerate when loaded Engineering Focus Time-to-Speed Time-to-Distance Passing distance Acceleration capacity Grade ability Drag coefficient Projected frontal area Power-to-Weight ratio

18 1987 BMW 325is Acceleration Dynamics Acceleration Limit, g x,a = μ x,w i wd,r f Ro K m u x,w ( h v,t l ) = 0.45g Drag Coefficient 0.39 Frontal Area (m) Acceleration Limit g Rotational Inertia Coefficient, K m 1.09 Incline, α 0degrees Rolling Resistance, coefficient N Gravitational Resistance 0N

19 1987 BMW 325is Acceleration Dynamics F_max Max Power Aero Drag Acceleration Capacity N kph m/s N g's 1st nd rd th th Max Torque Aero Drag Acceleration Capacity kph m/s N g's

20 Speed (kph) 1987 BMW 325is Acceleration Dynamics 240 Time-to-Speed Time (sec) Max Power Max Torque

21 Distance (m) 1987 BMW 325is Acceleration Dynamics Time-to-Distance Time (sec) Max Power Max Torque

22 1987 BMW 325is Acceleration - CarSim Full Throttle Acceleration

23 1987 BMW 325is Acceleration - CarSim Full Throttle Acceleration

24 Braking Dynamics Brake system reduces vehicle speed by converting kinetic energy (vehicle motion) to thermal energy that can be dissipated to the atmosphere Sub-systems: Brake transmission fluid Actuation Foundation brakes Electronic braking assists Parking brake

25 Braking Dynamics Customer Focus Confident/Comfortable Braking Short stopping distance Pedal feel Consistency Fast response No noise or vibrations Controlled Braking Ability to steer and decelerate in all conditions Low maintenance Long rotor/lining life Engineering Requirements Government Regulations Stopping distance Pedal feel Brake system response Brake balance & bias Thermal management Lift & dive performance Combined cornering & braking performance

26 1987 BMW 325is Brake System Vacuum assisted with anti-lock brake control Front: 10.2 x 0.9 inch vented discs Rear: 10.2 x 0.4 inch vented discs Front brake rotor and caliper

27 1987 BMW 325is Brake System System Braking ratio assumed to be 75/25 (front/rear) = 3 Ideal Braking Ratio Coefficient of friction, assumed for dry pavement, μ = 0.9 i IBR = i WD,f+μ ( h V,t ) l i WD,r μ( h V,t ) l = i IBR < i SBR Front Skid Limited

28 IDEAL BRAKING RATIO 1987 BMW 325is Brake System 3 IDEAL BRAKING RATIO FOR VARYING COEFFICIENTS OF FRICTION COEFFICIENT OF FRICTION, Μ

29 AXLE VERTICAL FORCES (N) 1987 BMW 325is Braking Dynamics AXLE VERTICAL FORCES DURING STEADY BRAKING FZ,B,f FZ,B,r BRAKING G'S

30 LONGITUDINAL BRAKING FORCE (N) 1987 BMW 325is Braking Dynamics LONGITUDINAL AXLE FORCES DURING STEADY BRAKING FX,B,f FX,B,r FX,B,V BRAKING G'S

31 Distance (m) Time (sec) 1987 BMW 325is Braking Dynamics STOPPING TIME & STOPPING DISTANCE AT VARIOUS SPEEDS Speed (kph) Distance (Max) Distance (Min) Time (Max) Time (Min)

32 1987 BMW 325is Braking- CarSim 100 kph - 0

33 1987 BMW 325is Braking- CarSim

34 Ride Dynamics Customer Focus: Smooth ride on bumpy roads No shake or vibration over bumpy roads Absence of road & wind noise Absence of vehicle noise (squeaks & rattles) Engineering Ride Metrics Front ride frequency Ride frequency ratio Vertical Damping Impact isolation Single bump disturbances Pitch (braking & drive-off) Pitch damping

35 1987 BMW 325is Suspension Front Suspension Independent, lower control arm with strut and anti-roll bar Rear Suspension Independent, semitrailing arm with coil springs and anti-roll bar

36 1987 BMW 325is Suspension Ride Rates, as measured in the Garage (K R/f = 2 K R/f ): Front: 200 lbs to compress 0.75 = lb/in = 46.7 N/mm K R,f = N/mm Rear: 200 lbs to compress 1.00 = 200 lb/in = 35.0 N/mm K R,r = 17.5 N/mm

37 1987 BMW 325is Ride Metrics Sprung Mass Frequencies: f Bo,f/r = 500K R,f/rg π 2 F Bo,f/r f Bo,f = N m/s2 mm π N = Hz f Bo,r = N m/s2 mm π N = Hz f Bo,r f Bo,f = Hz Hz =.926 This ratio should be approximately The error is due to poor Ride Rate measurement technique in the garage. Further Calculations estimate f Bo,r based on this ratio f Bo.r = Hz

38 1987 BMW 325is Ride Metrics Suspension Rates: K f/r = K T,f/rK R,f/r K T,f/r K R,f/r Unsprung Bounce Frequencies: f U,f/r = 1 2π 2000 K T,f or r +K f or r g F U,for r K_R,f N/mm K_R,r N/mm K_f N/mm K_r N/mm K_Sp,f N/mm K_Sp,r N/mm f_u,f Hz f_u,r Hz

39 1987 BMW 325is Ride Metrics Bounce & Pitch frequencies ω 2 n = α+γ ± α γ β r J 2 Bounce & Pitch K'_f N/mm K'_r N/mm a m b m α rad/sec 2 ω_n, rad/sec Hz γ rad/sec 2 ω_n, rad/sec Hz β rad/sec 2 Z/ϴ_ m Bounce Center nat freq 1 = Bounce Frequency Z/ϴ_ m Pitch Center nat freq 2 = Pitch Frequency

40 Low Speed Steering Definition low speed steering is concerned with parking maneuvers and fundamental steering axis geometry. Vehicle system turning at low speeds Lock to lock turns of steering wheel Ability to return to vehicle system path Objective Define Ackermann steering geometry Calculate the steering deviation Calculate the percent Ackermann Calculate the curb-tocurb turning circle Compose an overview of low speed steering

41 Ackermann Steering Geometry Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radius.

42 Calculations i =45 b f = mm r r =10mm l= mm i s =15.9 F = o - A,O Where cotan( A,O ) = cotan( i + b f 2r r ), A,O =27.56 i s = H m =15.9 where H =180*DN ltl =702 l Steering Deviation F = o - A,O = =15.74 Percent Ackermann PA=100( i+ o i A,O )=9.74% Curb-to-curb turning circle D TC,CB = 1 l + r 500 sin r + A,O ( 0.1 F )+(10 3 Bf MAX )=9.76 m Hence, m =44.15 m = i+ o 2, o=43.3

43 Low Speed Steering Performance Steering Deviation, F Degree Percent Ackermann,PA 9.74 % Curb-to-curb turning circle 9.76 m Inside angle, i Degree Outside front road wheel steering angle, A,O Degree steering ratio, is Mean road wheel steer angle m Degree outside road angle o Degree Turns, lock to lock 3.90 Steering wheel displacement H Degree wheel base mm rr 10 mm Tire width 195 mm Δr 4 mm

44 High Speed Steering (Handling) Customer Focus Handling characteristics allow for fast cornering Good handling and stability at highway speeds Good handling in all weather conditions Maneuvers in and out of traffic with ease Responsive to steering wheel inputs Handling provides a good feel of the road Engineering Focus Maximum lateral acceleration Lateral acceleration response time Yaw velocity damping Understeer gradient Roll gradient Steering sensitivity Steering sensitivity ratio Roll damping On-center steering performance

45 High Speed Steering (Handling) Lateral acceleration, F Y,V = F V,t g y Understeer Gradient, USG = i WD,fF V,t i WD,r F V,t 2C α,r = δ 180 m π ( l Rv ) g y 2C α,f Where C α = tire cornering stiffness in N/deg Vehicle Roll Gradient, RG V = F Bo(h Bo h Ro,B ) K φ,v Where K φ,v = Chassis System Roll Stiffness

46 1987 BMW 325is Handling g_c (g_y) 0.81g RG_V,r 3.1deg/g h_ro,r 0.11m h_bo,r m R_v 1800inches RG_V,f 3.1deg/g h_ro,f 0.08m h_bo,f m F_Bo,r N b_r m δ_h 106.5degrees F_Bo,f N b_f m δ_m degrees φ_bo,r degrees φ_bo,f degrees M_roll,r Nm M_roll,f Nm K_φ,r Nm/deg K_φ,f Nm/deg K_φ,r,t Nm/deg K_φ,f,t Nm/deg K_s,φ,r Nm/deg K_s,φ,f Nm/deg Understeer Gradient (USG) deg/g_y

47 1987 BMW 325is Handling - CarSim Double-Lane-Change Maneuver

48 1987 BMW 325is Handling - CarSim Double-Lane-Change Maneuver