Resistance Forces on A Vehicle P M V Subbarao Professor Mechanical Engineering Department Estimation of Vehicle Demands ….

Resistance Forces on A Vehicle The major components of the resisting forces to motion are comprised of : Acceleration forces (F accel = ma & I  forces) Aerodynamic loads (F aero ) Gradeability requirements (F grade ) Chassis losses (F roll resist ).

Force System Due to Rolling Resistance 3

Road Conditions 5

Rolling Resistance 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 The magnitude of this force is Approximated as: Rolling resistance of a vehicle is proportional to the component of weight normal to the surface of travel

Standard Formula for Rolling Resistance where: P= power (kW) Crr= coefficient of rolling resistance M= mass (kg) V= velocity (KpH)

Contact Type C rr Steel wheel on rail Car tire on road Car tire energy safe Tube 22mm, 8 bar0.002 Race tyre 23 mm, 7 bar0.003 Touring 32 mm, 5 bar0.005 Tyre with leak protection 37 mm, 5 bar / 3 bar / 0.01 Typical Values of Coefficient of Rolling Resistance

Effect of Road Condition on C rr 9

Rolling Resistance And Drag Forces Versus Velocity

Grade Resistance Composed of –Gravitational force acting on the vehicle For small angles, θgθg mg θgθg Fg

Total Vehicular Resistance at Constant Velocity AR = air resistance [N] RR = rolling resistance [N] GR = gradient resistance [N] TR = total resistance [N]

Resistance Vehicle Speed Steady State Demand Curve

Vehicle Speed vs. Engine Speed V =velocity, km/hr r =wheel radius, m N crank =crankshaft rpm i =driveline slippage GOGO =Overall gear reduction ratio

Typical Engine Torque-Power SS

Steady State Demand Vs Available Effort 16

Inertial or Transient Forces Transient forces are primarily comprised of acceleration related forces where a change in velocity is required. These include: The rotational inertia requirements (F I  ) and the translational mass (F ma ). If rotational mass is added to a translating vehicle, it adds not only rotational inertia but also translational inertia.

Inertial Resistance 18 where: F IR = inertia resistance [N] m eff-vehicle = Vehicle mass + Equivalent mass of rotating parts [kg] a = car acceleration [m/s 2 ], (from 0 to 100 km/h in: 6 s (4.63 m/s 2 ), 18 s (1.543 m/s 2 )) m vehicle = Vehicle mass [kg] m eq = Equivalent mass of rotating parts [kg]

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 = angular accelerationk = radius of gyration Equivalent Mass of Rotating Parts Torque due to any rotating part (ex. Wheel) wheels and axles = 78% of total polar inertia propeller shaft = 1.5% Engine = 6% Flywheel and clutch =14.5%

Therefore the equivalent mass of all rotational parts including losses is represented as:

Required Torque & Power at Wheels Tractive Effort demanded by a vehicle):

Available Vehicle Tractive Effort (TE): 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, F max

Tractive Effort Relationships 24

MATLAB for Vehicle Torque Requirement

MATLAB Model for Transmission System

Requirements of Vehicle on Road & Engine Power

Urban Driving Cycle

Engine RPM during Urban Driving Cycle

Engine Fuel Consumption During Urban Driving Cycle