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.