Vehicle Dynamics

Vehicle Dynamics Dr. Tahsean Ali Albadry Najaf Technical CollegeReferences*M.Khuvakh, Motor Vehicle Engine, MIR Publications

*Hamilton H. Mobie, Mechanisms and Dynamics Machinery, John Willey & Sons *P. W. Kett, Motor Vehicle Science, part2, Chapman& Hall Crank Gear Mechanism

DefinitionsCrank Gear :- Is a group of mechanical parts which convert the thermal energy into mechanical energy , it is consist of piston and its accessories , connecting rod , and crank shaft

Piston Travel:- is the distance which piston traveled from the TDC due to crank angle Central crank gear :- The crank gear in which the axis of the cylinder intersects that of the crank shaft.

Offset Crank Gear

The crank gear in which the axis of the cylinder was shifted with an offset (e) from the center of the crank shaft.

Harmonic MotionWhen the distance, velocity, and acceleration, of any particle change its magnitude periodically from zero to maximum to zero, this motion called harmonic motionDynamic & Kinematic calculationIt is important to make two kind of calculation:-1- Dynamic Calculations :- Which used the magnitude and the nature of the change in the gas forces of gas pressure .2- Kinematic Calculations :- The aim of it to determine the travel, velocity, and acceleration of piston, 8Crank mechanism notations

angle of crank travel counted from the cylinder axis in the direction of clockwise crank shaft rotation, =0 at TDC, =180 at BDC. angle between the connecting rod and the cylinder axis. angular velocity of crank shaft rotation. S =2R = piston stroke. R = crank radius. L = connecting rod length. = R/L ratio of crank radius to connecting rod length ( = 0.25 0.3).Calculation of piston travel( xp)

L+R

Piston Velocity EquationThe Piston Mean Velocity Piston AccelerationOffset Crank GearAn offset crank gear is one in which the cylinder axis dose not intersect the crankshaft but is displaced with respect to it by the distance e. The crank gear is additionally characterized by the magnitude of the relative offset K= e/R (which usually ranges between 0.05 and 0.15) The parameters of offset crank gearThe travel, velocity, and acceleration diagramsPiston Travel diagram Piston Velocity Diagram 21 Piston Acceleration Diagram Problems1- Calculate the piston travel, velocity, and acceleration for an engine with R= 50 mm and lrod=170 mm using the equation and graphical representation and compare the results (take 45o increment ,N= 3000 r.p.m).

2- An engine having =0.25 rotates at 3000 r.p.m, the connecting rod length is 140 mm. Determine the piston velocity and acceleration at a) TDC. b) When engine crank lies at 30o from TDC. c) At BDC.

3- Show how the ratio of crank radius to the connecting rod length affects the piston velocity( take the engine data in the problem (1) and three values of ) plot the result. Force Acting on A Crank Gear To determine the loads on engine bearing we must analyze all the forces acting a crank gear.The forces divided into three categories:- 1- The forces of gas pressure in the cylinder (Fg).2- The forces of inertia of the moving parts, that forces divided in turn into two forces, the inertia of reciprocating parts (Fi) and the rotating parts(FR).3- the friction forces (Ff) 24GAS PRESSURE FORCESINDICATOR DIAGRAM The plot of the engine cycle on P-V coordinates is often called indicator diagramPRESSUREVOLUMETDCBDCFgpistoncylinderFgpistoncylinderFgFgINERTIA FORCESTo determine the inertia forces we must estimate the masses of moving parts.The moving parts divided into three groups:-1- Reciprocating parts (Piston, Rings, Piston pin )2- Rotating parts (crank shaft)3- Complex plan parallel motion (connecting rod group )REDUCED SYSTEMThe crank gear is a complicated group of different members.These members moved in a different shapes to perform the final function. To determine the forces acts the crank gear we must reduces these members to two groups one of them have a linear motion, and the other is rotates around a fixed axis.The new shape called the reduced system. REDUCED SYSTEMReciprocating partsReciprocating parts include the following parts:-PistonRingsPiston pin

The piston mass to be lumped on the axis of piston pin axis it designated by (mP) mp32ROTATING PARTSThe mass of crank shaft This mass reduced to the crank radius (R) and designated by (mcr ).The mass of crank pin and balance mass (web) was lumped on the axis of crank pin, and designated (mcp).33REDUCING THE CRANK SHAFTwebmcpmcrR+cgRCOMPLEX PLAN PARALLEL MOTION (CONNECTING ROD)The connecting rod reduced into two masses:-

1- The mass lumped on the piston pin axis(mrodpp) 2- The mass lumped on the crank pin axis(mrodcp) cgmzmyzyCALCULATING THE MASSES OF UNSYMETRICAL BODY my = mmz = mREDUCING THE CONNECTING ROD MASSLrodLrodppLrodcpCg mrodmrodppmrodcpmCont.

The conditions of reduced system 3- A constant moment of inertia with respect to the center of gravity:- mi=mp+mrodppLrodRBAmR=mcr+mrodcpIn the above REDUCED SYSTEMthere are only two forcesAnalyzing the forces of the crank gearmiBAmRFiFgFiFgFRFgForces of gas pressure and forces of inertia of the reciprocating and rotating masses acting in a crank gearYXFgFiFgFiFgFRFgFR2- The centrifugal force of rotating masses of crank gear:- FR = - mR R 2 FR is always directed along the crank radius.It is constant in magnitude.It is applied at center B of crank pin.It is rotates together with the crank and not being balanced.It is transmitted to the engine supports through the shaft bearing and the crank case.It is resolved into two components:-

FRx = - mRR2 sinFRy = - mRR2 cos

FRyFRxFREngine torque calculationThe initial force acting on the piston is:- F = Fg + Fi F can resolved into two component

1- The lateral force perpendicular to the cylinder axis. Q=F tanPiston pin mpKFQKFKTorqueKNFtFQNFtQM tiltFtFtQQFtRhTHE TORQUE TILTING MOMENTENGINE BALANCEEngine BalancingAn engine is said to be balanced if forces constant in magnitude and direction are transmitted to its supports during stable operation conditions.The cases of unbalance:-1- The periodic change of the inertia force(Fi)2- the variation of total torque T along the operation of multi cylinder engine.

61THE RECIPROCATING ENGINE CAN NEVER BE BALANCED CMPLETELY.62STATIC AND DYNAMIC BALANCEThe forces of inertia of the rotating elements of an engine crank gear are balanced so arranging the crank or counterweights to insure the following two conditions :-1- The center of gravity of the reduced system of the shaft should be on the axis of rotation.That is the (( STATIC BALANCE )) 631-the The sum of the moments of the centrifugal forces of inertia of the revolving masses should equal zero with respect to any point of shaft axis.That is the (( dynamic balance ))64Single Crank Shaft The sum of the centrifugal forces developed by two counterweights should be equal and opposite in direction to the centrifugal force (FR ).65FRFBFBRcgmBrRR2mBRmR =mcr + mcw66Calculation of counterweight massDouble crank shaft baFRFBFBFRRr MR =MB MR =FR * a MB =FB * bMulti Crank Symmetrical ShaftsMultiple cylinder engine usually balanced with out using counterweight.

In the Multi Crank unsymmetrical crank shaft dynamic balance is possible only using counterweight. THE END