Resistance Forces on A Vehicle P M V SubbaraoProfessorMechanical Engineering DepartmentEstimation of Vehicle Demands.

Resistance Forces on A VehicleThe major components of the resisting forces to motion are comprised of :Acceleration forces (Faccel = ma & I forces)Aerodynamic loads (Faero) Gradeability requirements (Fgrade)Chassis losses (Froll resist ).

Force System Due to Rolling Resistance*

Road Conditions *

Rolling ResistanceComposed primarily of Resistance from tire deformation (90%)Tire penetration and surface compression ( 4%)Tire slippage and air circulation around wheel ( 6%)Wide range of factors affect total rolling resistanceThe 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 Resistancewhere:P= power (kW) Crr= coefficient of rolling resistanceM= mass (kg)V= velocity (KpH)

Typical Values of Coefficient of Rolling Resistance

Contact TypeCrrSteel wheel on rail 0.0002...0.0010Car tire on road 0.010...0.035Car tire energy safe 0.006...0.009Tube 22mm, 8 bar 0.002Race tyre 23 mm, 7 bar 0.003Touring 32 mm, 5 bar 0.005Tyre with leak protection 37 mm, 5 bar / 3 bar0.007 / 0.01

Effect of Road Condition on Crr*

Rolling Resistance And Drag Forces Versus Velocity

Grade ResistanceComposed of Gravitational force acting on the vehicleFor small angles, gmggFg

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

ResistanceVehicle SpeedSteady State Demand Curve

Vehicle Speed vs. Engine Speed

V=velocity , km/hrr=wheel radius, m Ncrank=crankshaft rpmi=driveline slippageGO=Overall gear reduction ratio

Typical Engine Torque-Power Curves @ SS

Steady State Demand Vs Available Effort*

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

Inertial Resistance*where:FIR = inertia resistance [N] meff-vehicle = Vehicle mass + Equivalent mass of rotating parts [kg]a = car acceleration [m/s2], (from 0 to 100 km/h in: 6 s (4.63 m/s2), 18 s (1.543 m/s2))mvehicle = Vehicle mass [kg]meq = Equivalent mass of rotating parts [kg]

*

= angular accelerationk = radius of gyrationEquivalent 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 WheelsTractive Effort demanded by a vehicle):

Available Vehicle Tractive Effort (TE):The minimum of:Force generated by the engine, FeMaximum value that is a function of the vehicles weight distribution and road-tire interaction, Fmax

Tractive Effort Relationships*

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

*Torque and HP always cross at 5252 RPM. Why? Look at the equation for HP