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Vehicle Dynamics and Motion
• DYNAMICS OF VEHICLES,
• here assumed to be ground veh ic les
Vehicle dynamics refers to the dynamics of vehicles, here assumed to be ground vehicles. Vehicle dynamics is a part of engineering primarily based on classical mechanics.
Operational Definition
Predicting Vehicle System Mechanical Dynamic Behavior and Performance during Drive Off, Braking, Ride, and Steering maneuvers
Definitions
ISO 15037-1:2006 Road vehicles -- Vehicle dynamics test methods – General conditions for passenger cars
ISO 15037-1:2006 specifies the general conditions that apply when vehicle dynamics properties are determined according to ISO test methods.In particular, it specifies general conditions for:•variables,•measuring equipment and data processing,•environment (test track and wind velocity),•test vehicle preparation (tuning and loading),•initial driving, and•test reports (general data and test conditions).
• Resistance
• Tractive effort
• Vehicle acceleration
• Braking
• Stopping distance
Outline
Driving Dynamics:• Straight line tracking • Maneuverability• Self Steer Behaviors• ( Relationship) slip
angle between the front an rear tires.
• Oscillatory
VEHICLE DYNAMICS -- VEHICLES IN MOTION 3 MODULES
Power
•Engine ; Gearbox ; Axles
Chassis
•Suspension ; Tires ; Steering
Body
•Aerodynamics Resistance
Vehicle Point of Interest -- Mathematical SystemSafety , Comfort and Economics
Vehicle Driver
RoadDisturbed AirAround the vehicle
Response
Input(Driver)
Mathematical Model
Output (Response
s)
Mathematical Model for a VehicleVehicle Behavior
Mass Forces Moments of inertiaStiffness Damping Friction Longitudinal , Lateral and Vertical dynamics
Vehicle Free Body Diagram System Of coordinates (ISO)
Longitudinal Dynamics
Forces – Newton’s Law and Momentums (distances) Rolling Resistance – no only frictional resistant of the tire.Property of the rubber and visco - elasticity
For example, a rubber tire will have higher rolling resistance on a paved road than a steel railroad wheel on a steel rail. Also, sand on the ground will give more rolling resistance than concrete.
σ
ε
Tire contact pressure = Inflation pressure
Hyster
esis
Fr
Coefficient of rolling resistance
Pulse tread forces and Resistance force
Lateral Dynamics Rolling Resistance Contact patch of tire – pressure distribution of the contact
• Elastomer material
• Loss of energy
• Pulse forces
• Moment
Reaction forceLoad compression
Pulse forceUn-Load
compression
Rolling Resistance
Energy Consumption
Rolling Resistance [ Fr ]
Rolling Resistance
Force: Frr = fr W
Traction Resistance Force: Ft ∑ F = m a
m a = Ftr + Ftf – Fr – Fa – w sin θ -Fd
Assumption -- h = ha = hd L = L1 + L2
Nf ( L) + w sin θ (h) + Fa (h) + m g (h) – w cos θ (L2) = 0
∑Momentum = 0
Solving for Nr and Nf
- h/L [ Ft – fr W ]
h/L [ Ft – fr W ]
Available Tractive Effort
The minimum of:
1. Force generated by the engine, Fe
2. Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax
max,mineffort tractiveAvailable FFe
Traction Force Calculation [ Ft ]
Engine
Tire
Force
Ft F max on Front Wheel Drive Vehicle
F max on Rear Wheel Drive Vehicle
F f = ( μ ) Nf
F r = ( μ ) Nr
Substituting on Previous Equations of (Nf)
Ff ( L2 + fr h) /L /[ 1 + μ h/L] Substituting on Previous Equations of (Nr)
Fr ( L1 - fr h) /L /[ 1 - μ h/L]
Composed of:1. Turbulent air flow around vehicle body (85%)
2. Friction of air over vehicle body (12%)
3. Vehicle component resistance, from radiators and air vents (3%)
Aerodynamic Resistance Ra
2
2VACR fDa
3
2VACP fDRa
sec5501
lbfthp
Power is in ft-lb/sec
Rolling Resistance Rrl
Composed primarily of
1. Resistance from tire deformation (90%)
2. 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:
WfR rlrl
WVfP rlrlR
147101.0
Vfrl
Rolling resistance coefficient
Composed of Gravitational force acting on the vehicle
Grade Resistance Rg
Engine-Generated Tractive Effort
Vehicle Speed vs. Engine Speed
Typical Torque-Power Curves
Torque and HP always cross at 5252 RPM. Why? Look at the equation for HP
Maximum Tractive Effort
Vehicle Acceleration
Braking Force
• Front axle
• Rear axle
L
fhlWF rlrbf
max
L
fhlWF rlfbr
max
Braking Distance
braking efficiency x coefficient of road adhesion γb = 1.04 usually
Stopping Sight Distance (SSD)
SSD – Quick and Dirty
Example # 1 Center of GravityThe curb weights of a Continental 4 doors sedan without passengers or cargo are 2,313 lb on the front axle and 1,322 lb. The wheelbase is 109 inches. Determine the fore/aft position of the center of gravity for the vehicle.
Formula: static loads on level ground:
Solving for b : b = L Wrs / W = 109” 1322-lb/(2313+ 1322)-lb= 39.64” aft of the front axle.
Example # 2 Load on grade
• A Taurus GL sedan with 3.0L engine accelerates from a standing start up a 6% grade at an acceleration of 6 ft/sec^2. Find the total load distribution on the axles at this condition.
So: c = 66.85 ; b = 39.15 and 6% grade = 3.433 degree angle Wf = W( c cos θ – ax/g h –h sen θ ) / L Wf = [3246 ( 66.85 (.998) – 6/32.2( 20) – 20 (0.599) ]/ 106 = 1892.2-lbWr = = W( b cos θ + ax/g h + h sen θ ) / L = 1,347.3-lb
Adding = 3,239.5-lb = 3,246 cos (3.43)
Example # 3 Braking DynamicsA Doge Viper (1705 kg [ 3759 lb]) traveling at 80 mph (35.76 m/s) stopped with the maximum sustained deceleration (.65 g @ SAE vol. 2 Section 25) . Determine (a) the force required to bring the car to a stop (b) average power absorbed by the brakes © and weight distribution. ( WB = 2.45-m ; h = .51-m 49/51)
(a) Force required to bring the car to a stop [ Fb ]Fb = Mass x Acceleration = 1705 ( .65) 9.81 = 10.87 KN (b) The average power Pavg
Pavg = Force x Velocity = Fb x V avg
Pavg = 10.87 ( 35.76)/2 = 194 kw
Static weight distribution : and
These equations are Combine to Determine the Dynamic weight on. the front and rear wheels during Braking.
References
• Automotive Engineering Fundamentals, Richard Stone and Jeffrey Ball (2004) SAE International Warrendale, Pa.
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition). Chapter 2
• American Association of State Highway and Transportation Officals (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.
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