Dr. B Dayal

Dr. B Dayal

VEHICLE DYNAMICSStudy of dynamic behaviour of a vehicle on road surface is termed as vehicle dynamics.The dynamic behaviour is determined by the forces on the vehicle from tyres, gravity and aerodynamics.The vehicle and its components are studied to determine what forces will be produced by each of these sources at a particular maneuver condition.How the vehicle will respond to these forces.Vehicle dynamics is basically interaction of:DriverVehicleRoadLoadEnvironment

COMPONENTS OF VEHICLE DYNAMICSComponents, attributes or aspects of vehicle dynamics include:Automobile layoutElectronic stability control (ESC)SteeringSuspensionTraction control system (TCS)

ATTRIBUTES OF VEHICLE DYNAMICSAerodynamic specificSome attributes or aspects of vehicle dynamics are purely aerodynamic. These include:Automobile drag coefficient Automotive aerodynamics Center of pressure Downforce Ground effect in cars Geometry specificSome attributes or aspects of vehicle dynamics are purely geometric. These include:Ackermann steering geometry Camber angle Caster angle

ATTRIBUTES OF VEHICLE DYNAMICSRide height Roll center Scrub radius Steering ratio Toe Wheelbase Mass specificSome attributes or aspects of vehicle dynamics are purely due to mass and its distribution. These include:

ATTRIBUTES OF VEHICLE DYNAMICSCenter of mass Moment of inertia Roll moment Sprung mass Unsprung mass Weight distribution Motion specificSome attributes or aspects of vehicle dynamics are purely dynamic. These include:Body flex Body roll

ATTRIBUTES OF VEHICLE DYNAMICSBump Steer Directional stability Critical speed Noise, vibration, and harshness Pitch Ride quality Roll Speed wobble Understeer, oversteer, lift-off oversteer, and fishtailing Weight transfer and load transfer Yaw

ATTRIBUTES OF VEHICLE DYNAMICSTire specificSome attributes or aspects of vehicle dynamics can be attributed directly to the tires. These include:Camber thrust Circle of forces Contact patch Cornering force Ground pressure Pneumatic trail Radial Force Variation Relaxation length

ATTRIBUTES OF VEHICLE DYNAMICSRolling resistance Self aligning torque Slip angle Slip (vehicle dynamics) Steering ratio Tire load sensitivity Roadway specificSome attributes or aspects of vehicle dynamics can be attributed directly to the roads on which they travel. These include:Banked turn, cross slope, drainage gradient, and cant or super-elevation

ATTRIBUTES OF VEHICLE DYNAMICSRoad slipperiness and Split friction Surface roughness, International Roughness Index, Profilograph, Texture Driving techniquesDriving techniques which relate to, or improve the stability of vehicle dynamics include:Cadence braking Threshold braking Double declutching Drifting (motorsport) Handbrake turn Heel-and-Toe Left-foot braking Opposite lock Scandinavian flick

VEHICLE DYNAMICS MODELSThe dynamic behavior of vehicles can be analysed in several different ways.Can be as straightforward as a simple spring mass system, through a three-degree of freedom (DoF) Using a multibody system simulation package such as MSC ADAMS or Modelica.Commercial packages such as CarSimOften simulated with advanced controller designs provided as software in the loop (SIL) with controller design software such as Simulink, or with physical hardware in the loop (HIL).

FUNDAMENTAL APPROACH TO MODELLINGA motor vehicle is made up of many components within its exterior envelope. For elementary analysis all components move together. For example in braking. Thus, it can be represented as a one lumped mass located at its center of gravity, with appropriate mass and inertia properties.For ride analysis it is often necessary to treat the wheels as separate lumped masses.For single mass representation, the vehicle is treated as a mass concentrated at its CG. The point mass at the CG, with appropriate moment of inertia, is dynamically equivalent to the vehicle itself for all motions.

SAE VEHICLE AXIS SYSTEM

COORDINATE SYSTEMSVehicle fixed coordinate system.On board, the vehicle motions are defined with referance to a right hand orthogonal coordinate system, which originates at the CG and travels with the vehicle.X forward and on the longitudinal plane of symmetryY - Lateral out the right side of the vehicleZ downward with respect to the vehicleP roll velocity about the x axisQ pitch velocity about the y axis.r yaw velocity about the z axis.Earth fixed coordinate systemvehicle attitude and trajectory through the course of a maneuver are defined with respect to a right hand orthogonal system fixed on earth. It is normally selected to coincide with the vehicle fixed coordinate system at the point where the maneuver is started.

COORDINATE SYSTEMSEarth fixed coordinate system.X forward travelY travel to the rightZ vertical travel (positive downward) heading angle (angle between x and X in the ground plane) side slip angle (angle between x axis and the vehicle velocity vector) course angle (the angle between the vehicles velocity vector and X axis)

FUNDAMENTAL APPROACH TO MODELINGEuler angles. Euler angles are determined by a sequence of three angular relations.beginning at the earth fixed system, the axis system is first rotated in yaw, then in pitch and then in roll to line up with the vehicle fixed coordinate system. The three angles obtained are euler angles.Newtons second law.Translational systems. The sum of the external forces acting on a body in a given direction is equal to the product of its mass and the acceleration in that direction.Fx = M . AxRotational system. The sum of the torques acting on a body about a given axis is equal to the product of its rotational moment of inertia and the rotational acceleration about that axis. Tx = Ixx . x

DYNAMIC AXLE LOADSW = Weight of the vehIf the vehicle is accelerating along the road, an equivalent inertial force known as d Alembert force = W/g.ax acting at the center of gravity opposite to the direction of the acceleration.Wf and Wr = tyre force normal to the road.Fxf and Fxr = tractive forceRxf and Rxr = rolling resistance acting in the ground planeDA = aerodynamic force acting at a point at height haRhz and Rhx are vertical and longitudinal forces acting at the hitch point when the vehicle is towing a trailer.Taking the moments about A:WfL + Daha + Waxh/g + Rhxhh + Rhzdh + Wh sin Wccos = 0An up hill altitude corresponds to +ve angle and downhill altitude ve angle.

ARBITRARY FORCES ACTING ON A VEHICLE

DYNAMIC AXLE LOADSTaking the moments about A:WfL + DAha + Waxh/g + Rhxhh + Rhzdh + Wh sin Wccos = 0An up hill altitude corresponds to +ve angle and downhill altitude ve angle.Similarly taking the moment about B:WrL Daha - Waxh/g Rhxhh - Rhz (dh +L) - Wh sin Wbcos = 0Therefore axle load expression becomes:Wf = (Wccos - DAha - Waxh/g Rhxhh Rhzdh - Wh sin )/LWr = (Wbcos +DAha +Waxh/g +Rhxhh +Rhz (dh +L) + Whsin )/LStatic loads on level groundWhen the vehicle is on level ground and static, equation becomes:Wfs = Wc / LWrs = Wb / L

DYNAMIC AXLE LOADSLow speed accelerationDA = 0 and assuming no trailer hitch forces, the loads on the axles are:Wf = W(c/L - axh/gL) = Wfs Waxh/glWr = W(b/L + axh/gL) = Wrs + Waxh/gLThus when the vehocle accelerates, load is transferred from the front axle to the rear axle in proportion to the acceleration (normalized by g) and the ratio of the CG height to the wheel base.Loads on gradesGrade is defined as the rise over the run. The common grades on interstate highways are limited to 4%. On primary and secondary roads 12 to 14%. ThusCos 1and sin Thus axle loads as influenced by the grades will be:Wf = W(c/L h/L) = Wfs Wh/LWr = W(b / L + h/L) = Wrs + Wh/L

Example problems1. The curb weight of a continental 4 door sedan without passengers or cargo are 2313 kg on the front axle and 1322 on the rear. The wheel base 2800 mm. determine the fore / aft position of the CG of the vehicle.2. A taurus GL sedan with 3.0 L engine accelerates from a standing start up a 6% grade at an acceleration of 1.83 m / sec2. find the load distribution on the axles at this condition.3. You are planning to buy a new mini van to pull your boat trailer out to those long weekends at the lake. Although you like the new front wheel drive (FWD) vans available, you are not sure a FWD will be able to pull the boat up out of the water on some of the steep access ramps you must use.(a) derive the expression for the maximum grade it can climb without wheel slippage (traction limited gradeability) for this vehicle combination in a FWD, RWD and 4WD power train. Assume the longitudinal acceleration is 0, neglect rolling resistance, assume boat is clear of water and no buoyancy forces

on it, ignore any change in hitch height and use the small angle approximations.Calculate the maximum gradeability for these combinations on a ramp with a coefficient of friction of 0.3, given the following information on the vehicle.Van properties: front axle weight = 3400 kg; rear axle weight = 2550kg; CG height = 625 mm; hitch height = 356 mm; hitch rear over hang = 584 mm; wheel base = 3000 mm

Combined boat / trailer properties: axle weight = 2688 kg; hitch load = 560 kg; wheel base = 2750 mm; CG height = 875 mm.

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