vehicle dynamics manual. very helpful for bachelor in automobile engineering students.

1. Vehicle Dynamics

2. Dynamics:
The study of things in motion
the branch of mechanics concerned with the
motion of bodies under the action of forces.

3. Vehicle dynamics
•The study of vehicles in motion and forces
associated with the motion
• Vehicle dynamics is a part of engineering based on classical
mechanics,
• but it may also involve
• physics, electrical engineering, chemistry, communications,
psychology etc.

4. History of Vehicle Dynamics
• 1769 - French military engineer, Nicholas Joseph Cugnot (1725-1804), built a three-wheeled, steam-driven
vehicle for pulling artillery pieces.
• 1784- a steam-powered vehicle by the Scottish engineer, James Watt (1736-1819),
• 1802 - Richard Trevithick (1771-1833), an Englishman, developed a steam coach that traveled from Cornwall
to London.
• 1886 - The first practical automobiles powered by gasoline engines by Karl Benz (1844-1929) and Gottlieb
Daimler ( 1834-1900)
• Rene Panhard, Emile Levassor, Armand Peugeot, Frank and Charles Duryea, Henry Ford, and Ransom Olds
• 1908 the automotive industry established in the United States with Henry Ford manufacturing the Model T
and the General Motors Corporation being founded.
• European companies like Daimler, Opel, Renault, Benz, and Peugeot

5. Why vehicle Dynamics study is required
• Safety- high speed manoeuvring, braking and cornering
• Comfort- occupant feels
• Vehicle designed considering the dynamics are safer, more
comfortable and fun to drive.
• Long life of vehicle system

6. Systems critical to vehicle dynamics
• Tires:
A considerable portion of the vehicle dynamics is focused
• Steering system
Control wheel geometry and movement
• Suspension system
isolate the occupant compartment from the disturbance from the
road.
• Braking system
• Frame / body

7. Dynamics are considered according to the use
of the vehicle
• Ride : vehicle response to vibration and disturbances caused by the
road and other sources
• Handling : vehicle response to the driver’s input of steering and
manoeuvring maintaining the stability.
• For a Vehicle designer, Ride and Handing are generally conflicting

8. Degrees of Freedom
The number of independent parameters that define its configuration in
terms of location or motion.
Movement along X direction
Movement along Y direction
Movement along Z direction
Rotation about X axis
Rotation about Y axis
Rotation about Z axis

9. Centre of gravity
• Point where the mass of body is concentrated
• Location of centre of gravity is the single most important parameter
which governs the overall dynamics
• Fore and alt location of centre of gravity determines the weight
distribution
• Height of CG determines how the vehicle behaves in turns and lateral
bumps

10. Vehicle Axis System
• right-hand orthogonal coordinate system
• Required to form the frame of reference for the analysis of motion
• x – Forward of the vehicle
• y - Lateral out the right side of the vehicle
• z - Downward with respect to the vehice
• p - Roll velocity about the x axis
• q - Pitch velocity about the y axis
• r - Yaw velocity about the z axis

11. Earth Fixed co-ordinate system and Euler
angles
• Vehicle attitude and path the vehicles takes during a maneuver are
defined with respect to a fixed coordinate system outside the vehicle.

12. Concept of sprung and un-sprung mass
• The portion of the vehicle supported by the spring is called sprung
mass - body
• The portion of the vehicle including tyres and suspension not
supported by the spring is called un-sprung mass
• Spring determines how the vibration are transferred and damped
from road to the body
• Un-sprung mass is desired to be low as possible

13. Newtons first law of motion
• An object will stay in rest or uniform motion unless acted upon by an
unbalanced force.
• Object at rest or uniform motion = Balanced force
The resistance of object to change the state of rest or motion is called
intertia.

14. Second law of motion
• Object at equilibrium will not accelerate.
• Acceleration = unbalanced forces
• F = mass x acceleration
• Net force = vector sum of all the forces acting
• For rotational
Torque = I x α
• I- moment of inertia
• α- Angular acceleration

15. Newton’s third law of motion
• Every action has equal and opposite reaction
• A body at equilibrium is possible due to the reaction force.

16. Forces on wheels
• Longitudinal Force (Fx)/ Tractive Force
• Lateral Force (Fy)-
• Normal Force (Fz)
• Overturning Moment (Mx)
• Rolling Resistance Moment (My)
• Aligning Moment (Mz) Slip Angle (a)
• Camber Angle (g)-

17. External Forces acting on a vehicle
• Aerodynamic Drag : Body force impinged by the air
• Road Disturbances : irregulates of road and tyre contact
• Cornering forces : reaction forces while taking turn
• Major sources of the resistance
• Aerodynamic =
• Rolling
• Gradient

18. Equation of motion of a vehicle
• Traction forces - driving resistance
• the rolling resistance of the front and rear tires Fr),
• the aerodynamic drag (Fw)
• grade climbing resistance (Fg)
• acceleration resistance (Fa)

19. Internal loads
Static :
Weight of the vehicle acts in the downwards direction at CG
Wheel reactions
Accelerating: Force at the tire pact moves vehicle with D’Alembert’s
force
Deaccelerating : brakes pads contact the disc
Cruising: Aerodynamics and rolling resistance
Cornering : Centrifugal force and reaction at wheels

20. Transmission Efficiency
• Transmission: reduce the speed and increase the torque
• new fuel-efficient, turbocharged, downsized engines with fewer cylinders and to diesel engines with higher
torque fluctuation

21. Tractive Forces on Driving Wheel
• Surface adhesion and the hysteresis mechanism.
• Sliding frictional force: tyre and road surface rub each other
• Adhesive force : Intermolecular bonds between tyre and road surface

22. Traction Characteristics
• Under acceleration and braking, additional slip is observed
• acceleration and braking forces are generated by producing
a differential between the tire rolling speed and its speed of travel.
• r = Tire effective rolling radius
• w = Wheel angular velocity
• V = Forward velocity

23. Braking vs Longitudinal Slip
• Longitudinal stiffness tends to be low when the tire is new and has full tread depth, increasing as
the tire wears.

24. Peak coefficient and slide coefficient versus
load
• On a dry road, when the slip approaches approximately 15-20 percent, the friction force will reach a
maximum (typically in the range of 70 to 90 percent of the load) as most tread elements are worked most
effectively without significant slip.
• On wet roads the peak friction force will typically be in the range of 25 to 50 percent of the vertical load.
• On ice-covered roads the peak friction will be only 10 to 15 percent of the vertical load and will be reached at
only a few percent slip.

25. Tractive forces according to the tire road grip
• Longitudinal traction required for braking and stopping distance
• Peak coefficient - limit for braking when the wheels do not lock up.
• Sliding coefficient – braking contribution from locked wheels

26. Response under different road condition
• The performance of tires on wet surfaces depends on the surface texture, water depth, tread pattern, tread
depth, tread material, and operating mode of the tire.
Tyre Tread is given to facilitate the flow of water preventing the
hydroplaning
Tread types- ribbed, siped and smooth

27. Tread Design on peak and sliding coefficient
friction

28. Hydroplaning
• The lift component of the hydrodynamic force is equal to the vertical load acting on the tire.
• Fh = ρf ×A×V2

29. Normal reaction of the road
• Vertical dynamics- ride and road holding
• The axles and associated wheel move as rigid bodies and impose excitation forces on the sprung mass.
• input -excitations and output- vibrations
• Transmissibility – gain – ratio of output to input- ratio of response amplitude to excitation amplitude
• ratio may be one of forces, displacements, velocities or accelerations

30. Quarter car model
• An Isolated Quarter Car Model
• Ks = Suspension stiffness
• Kt = Tire stiffness
• Ride Rate
• In the absence of damping, the bounce natural frequency
• M = Sprung mass
• W = M g = Weight of the sprung mass
• g = Acceleration of gravity

31. Quarter car model
• When damping is present, the resonance occurs
• good ride the suspension damping ratio on modem passenger cars usually falls between 0.2 and 0.4
• With a damping ratio of 0.2, the damped natural frequency is 98% of the undamped natural frequency, and =
at 0.4 damping, the ratio is about 92%.
• The ratio of W/K represents the static deflection of the suspension due to the weight of the vehicle.