Vehicle Dynamics CEE 320. Winter 2006 CEE 320 Steve Muench

Transcription

1 Vehicle Dynamics Steve Muench

2 Outline 1. Resistance a. Aerodynamic b. Rolling c. Grade. Tractive Effort 3. Acceleration 4. Braking Force 5. Stopping Sight Distance (SSD)

3 Main Concepts Resistance Tractive effort Vehicle acceleration Braking Stopping distance F ma + R + R + a rl R g

4 Resistance Resistance is defined as the force impeding vehicle motion 1. What is this force?. Aerodynamic resistance 3. Rolling resistance 4. Grade resistance F ma + R + R + a rl R g

5 Aerodynamic Resistance R a Composed of: 1. Turbulent air flow around vehicle body (85%). Friction of air over vehicle body (1%) 3. Vehicle component resistance, from radiators and air vents (3%) from National Research Council Canada R P a R a ρ ρ C C D D 1 hp 550 A V f A V f ft lb sec 3

6 Rolling Resistance R rl Composed primarily of 1. Resistance from tire deformation ( 90%). Tire penetration and surface compression ( 4%) 3. Tire slippage and air circulation around wheel ( 6%) 4. Wide range of factors affect total rolling resistance 5. Simplifying approximation: R rl f rl W P R f rl rl ft lb 1 hp 550 sec WV f rl V

7 Grade Resistance R g R g W sinθ For small angles, R g W tanθ g sinθ g tanθ g G R g WG tan g θ g R g θ g W θ g

8 Available Tractive Effort The minimum of: 1. Force generated by the engine, F e. Maximum value that is a function of the vehicle s weight distribution and road-tire interaction, F max Available tractive effort min (, F ) F e max

9 Tractive Effort Relationships

10 Engine-Generated Tractive Effort Force F e M e ε 0 η r d F e Engine generated tractive effort reaching wheels (lb) M e Engine torque (ft-lb) ε 0 Gear reduction ratio η d Driveline efficiency r Wheel radius (ft) Power ( ft lb) ft lb torque engine rpm hp 550 π sec 550 sec 60 min

11 Vehicle Speed vs. Engine Speed ( 1 i) πrne V ε 0 V velocity (ft/s) r wheel radius (ft) n e crankshaft rps i driveline slippage ε 0 gear reduction ratio

12 Typical Torque-Power Curves

13 Maximum Tractive Effort Front Wheel Drive Vehicle F max µ W ( l + f h) r 1+ L µ h L rl Rear Wheel Drive Vehicle What about 4WD? F max ( l f h) f µ W L µ h 1 L rl

14 Diagram R a ma h h θg R rlf F bf W f l f W R rlr l r W r F br L θ g

15 Vehicle Acceleration Governing Equation F R γ m ma Mass Factor (accounts for inertia of vehicle s rotating parts) γ ε m 0

16 Example A 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead stop as fast as possible. What s the maximum acceleration it can achieve before spinning its wheels? µ 0.40 (wet, bad pavement) 1989 Ford 5.0L Mustang Convertible Torque 300 rpm Curb Weight 3640 Weight Distribution Front 57% Rear 43% Wheelbase in Tire Size P5/60R15 Gear Reduction Ratio 3.8 Driveline efficiency 90% Center of Gravity 0 inches high

17 Braking Force Front axle F bf max µ W l [ + h( µ + f )] r L rl Rear axle F br max µ W l [ h( µ + f )] f L rl

18 Braking Force Ratio BFR l l r f + h h ( µ + f ) rl ( µ + f ) rear rl front Efficiency η b gmax µ

19 Braking Distance Theoretical ignoring air resistance S g ( γ ) b V1 V ( η µ + f ± sinθ ) b rl g Practical Perception d V 1 g V a g ± G For grade 0 d V V a 1 Total d p V1t p d d + s d p

20 Stopping Sight Distance (SSD) Worst-case conditions Poor driver skills Low braking efficiency Wet pavement Perception-reaction time.5 seconds Equation V1 SSD + V1t r a g ± G g

21 Stopping Sight Distance (SSD) from ASSHTO A Policy on Geometric Design of Highways and Streets, 001 Note: this table assumes level grade (G 0)

22 SSD Quick and Dirty 1. Acceleration due to gravity, g 3. ft/sec. There are 1.47 ft/sec per mph 3. Assume G 0 (flat grade) d ( a g ± G) ( 1.47 V ) ( 0) V1 V V V V g d 1.47 V1 t 1. 47Vt p p ( ) a p V d a s Vt p V V 1 in mph a deceleration, 11. ft/s in US customary units t p Conservative perception / reaction time.5 seconds

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24 Primary References Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (005). Principles of Highway Engineering and Traffic Analysis, Third Edition). Chapter American Association of State Highway and Transportation Officals (AASHTO). (001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.