At6604 Vehicle Dynamics r 2013 Learing Material_pm Subramanian

1 AT 6604 VEHICLE DYNAMICS- P.M SUBRAMANIAN, ASST PROF,AUTOMOBILE ENGG DEPT


AT 2402 VEHICLE DYNAMICS

PART A (2 Marks)

UNIT I CONCEPT OF VIBRATION

1. Define Degree of freedom.

The dof of a mechanical system is equal to the minimum number of independent co ordinates required to define completely the positions of all parts of the system at any instant of time.

2. Define Multidegree of freedom.

A multi degree of freedom system is one for which 2 or 3 co-ordinates are required to define completely the positions of all parts of the system at any instant of time.

3. Explain about Free vibrations.

When there is no external force acts on the body after giving an initial displacement, the body is said to be under free or natural vibration.

4. Explain about Forced vibrations.

When the body vibrates under the influence of external force the body is said to be under forced vibration. The frequency of forced vibration is called forced frequency.

5. Explain about Damped vibrations.

When there is reduction in amplitude over every cycle of vibration, the motion is said to be damped vibration.

6. Sketch the model of an automobile.

7. What is meant by magnification factor?

The ratio of amplitude of steady state response to the static deflection under the action of force Fo. It is ratio between the maximum actual amplitude of the body and maximum actual amplitude of the road. It depends on frequency ratio and damping factor.


8. Define transmissibility. Give the expression to find the force transmitted to the ground?

The transmissibility ratio or transmissibility is defined as the ratio of the force transmitted to the foundation ‘Ft’ through elastic supports to the force transmitted to the foundation through rigid supports ‘Fo’ exciting force. For a vehicle, It is the ratio between the force transmitted to the body and force acting on the road.

9. Explain about vibration absorber.

Vibration absorber are based on the concept of attaching a secondary mass to a primary vibrating system such that the secondary mass dissipates the energy and thus reduce the amplitude of vibration of the primary system The additional spring mass system in a machine which control the amplitude of vibrations.

10. Define Damping Ratio.

The damping ratio for a system with viscous damping is the ratio of actual damping co-efficient to the critical damping co-efficient.

11. What are the sources of vibration of a vehicle?

Road roughness, Engine Unbalance, Whirling of Shafts, Cam forces.

12. Show the SAE Vehicle axis system


13. How vibration is a factor for human discomfort?

The human comfort depends on frequency and amplitude of vibration. Only maximum acceleration increases the frequency and amplitude of vibration motion which results in human discomfort. The criterion for comfort is jerk, rate of change of acceleration.

14. Explain critical speed.

The angular speed of rotating machinery at which excessive vibration is produced; at this speed the periodic disturbing force coincides with a mechanical resonance of the shaft and/or of the machinery or its supports. The speed of a rotating system that corresponds to a resonant frequency of a system.

15. Define Logarithmic decrement.

The natural logarithm of ratio of any two successive amplitudes of like sign in the decay of a single frequency oscillation.

16. Define Critical Damping applied to vehicle springing system.

Critical damping is the minimum amount of viscous damping that allows a displaced system to return to its initial position without oscillation.

17. What is meant by modeling and simulation?

Modeling means representing the problem in to physical prototype, mathematical form, or by computer programming. Solving the problem by using computer is known as simulation. Simulation helps to understand the physical phenomenon/ behavior of a system subjected to external forces.

18. Define pitching, rolling and yawing motion of a vehicle.

The angular moment about lateral, longitudinal and vertical axis is termed as pitching, rolling and yawing motion of a vehicle.

19. What is meant by eigen value problem?

Eigen value gives the natural frequency of given system of vibration. It helps to design a system for damping out the vibrations and to check for resonance. It can be used to optimize the design by reducing the amplitude of vibration.

20. Differentiate damped vibrations from undamped vibrations.

For a damped vibration there will be reduction in amplitude over every cycle of vibration. The vibrating body will come to rest after certain time. Undamped vibrations no reduction in amplitude over every cycle of vibration. he vibrating body will come to rest after a long time.

21. List the advantages of modeling and simulation studies.

Modeling helps in representing the problem in to physical prototype, mathematical form, or by computer programming. Simulation helps in solving the problem by using computer is known as. Simulation helps to understand the physical phenomenon/ behavior of a system subjected to external forces.


22. Why the vibration measurement is necessary in dynamic systems?

• To Avoid Resonance.

• To validate the theoretically computed values.

• For design and operation of active vibration isolation systems.

• To measure road roughness for designing vehicle suspension systems.

22. Enumerate the vibration measuring instruments commonly used.

• Displacement Transducers, Velocity Transducers,Acceleration Transducers

• Piezo Electric Accelerometers, Piezo Resistive Accelerometers, Servo Accelerometers

• Optical Transducers


UNIT II TIRES

1. Illustrate the forces and moments acting on tire.

The lateral force Fy is the force along the Y axis, the longitudinal force Fx is the force along the X axis and the normal or vertical force Fz is the force along the Z axis. The moment along the Z axes Mz is called the aligning moment. The moment along the X axes Mx is called the overturning moment and the moment along the Y axis My is called the rolling resistance moment.

2. Enumerate the types of tires. Radial Ply tire, Bias Ply tire, Belted Ply tire.

3. Differentiate between Bias Ply and Radial ply tires. In bias ply tires, the cords in the carcass have an angle (or bias) of approximately 40 degrees with respect to the circumference. The cords in adjacent plies run in opposite directions. A bias ply tire usually has 2 or more plies (up to 20 plies for heavy-load tires).A radial tire also has plies just like the bias-ply tire, but the cords in these plies are made of a softer material like polyester instead of nylon. The cords in the plies run perpendicular to the circumference of the tire. On the side walls of the tire, the direction of these cords is radial and hence the name "radial" tires.

4. What is purpose of belted radial ply tires? The radial ply tire is a belted tire and has one or more belts, in addition to plies. A belt is a steel mesh placed between the body and the tread. Each belt adds an additional layer in the tread area but leaves the sidewall area untouched.

5. Define slip angle and cornering force of a tyre. When a side force is applied to a tire rolling in a wheel plane, tire will move along a path at an angle α with the wheel plane. To balance the applied side force, a lateral force is developed at the contact patch. The angle α is the slip angle and the lateral force at tire ground contact patch is called cornering force. This occurs due to lateral elasticity of the tire.


6. Define Cornering Stiffness. The term cornering stiffness provides a common basis for comparing the cornering behavior of different tires. Cornering stiffness is defined as derivative of the cornering force Fyα with respect to slip angle. Cornering stiffness depends on inflation pressure, Normal Load, Tractive Effort( Braking effort) and Lateral Force. The vertical load on the tire strongly influences the cornering characteristics.

7. What is meant by Tractive Effort?

The force available at the contact between the rear wheel tyres and road is known as tractive effort. The ability of the rear wheels to transmit this effort without slipping is known as traction. Hence usable tractive effort will never exceed traction.

8. Define longitudinal slip

The difference between the actual longitudinal velocity at the axle of the wheel VX and the equivalent rotational velocity reff ωw of the tire is called longitudinal slip. Longitudinal slip is equal to reff ωw - VX.

9. What is meant by tire normal load?

The vertical force on a tire is called the tire normal load. The normal load on a tire comes from a portion of the weight of the vehicle. It is influenced by fore-aft location of the c.g., vehicle longitudinal acceleration, aerodynamic drag forces and grade of the road.

10. Explain longitudinal tire force and parameters influencing it. The longitudinal tire forces are friction forces from the ground that act on the tires. It depends on a) the slip ratio b) the normal load on the tire and c) the friction coefficient of the tire-road interface.

11. Write the mathematical equation used for Magic formulae tire model.

Y is the output variable: longitudinal force Fx or lateral force Fy or aligning moment Mz, X is the input variable: slip angle α or slip ratio σx

B stiffness factor, C shape factor, D peak value, E curvature factor

12. What is the need for Pacejka "Magic Formula" Tire model? If the longitudinal slip ratio is not small or if the road is slippery, then a Non linear tire model needs to be used to calculate the longitudinal tire force. Pacejka "Magic Formula" Tire model can be used to model tire forces in this case.

13. What is meant by longitudinal slip ratio?


14. What is meant by camber thrust? A wheel set at a camber angle produces "camber thrust," which is a lateral force generated in the direction of the lean. The magnitude of camber thrust is substantially less than the forces generated by slip angle (direction in which the tire is rolling). Bias ply tires produce significantly greater camber thrust than do radial tires.

15. What is meant by caster angle? Caster angle introduces a new element. The caster angle refers to the longitudinal inclination of the steering axis. It creates a self-centering force that is somewhat different from the one created by the lateral steering axis inclination.

16. What is the effect of castor? A positive caster is established when the steering axis meets the ground ahead of the center point of the contact patch (a point directly under the axle). Most passenger cars have a positive caster on the order of 0 to 5 degrees. A positive caster causes the wheel to trail behind the steering axis. When the vehicle is steered, the caster angle develops an opposing force that tends to steer the vehicle out of the turn.

17. Define static stiffness of tyre. It is the slope of the static load- deflection curves. For a given inflation pressure, the load –deflection characteristics for both radial and bias ply tires are more or less linear, except at relatively low values of load.

18. Explain why Radial ply tire is preferred over Bias ply tire. The radial ply tire has low sidewall stiffness and provides a smoother ride. The contact patch is also larger and more stable with radial tires, hence providing better handling. The power dissipation of the radial ply tire could be as low as 60% of that of the bias ply tire under similar conditions and the life of the radial ply tire could be as long as twice that of the equivalent bias-ply tire.

19. Define normalized traction force for the tire. FX, FY, and FZ are the longitudinal, lateral, and normal (vertical) forces acting on a tire. The normalized traction force for the tire, ρ is defined as

20. Define tire road-friction coefficient.

The tire road-friction coefficient µ on any given road surface is defined as the maximum value that normalized traction force ρ can achieve on that surface for any slip ratio value.

21. Enumerate the benefits of tire-road friction estimation. The control algorithms used in vehicle control systems can be modified to account for the external road conditions if the actual tire-road friction coefficient information is available in real time. Tire-road friction estimation makes road-adaptive for control systems. For example, In the case of vehicle stability control systems, the value of tire-road friction coefficient is needed for estimating the target value of yaw rate for the vehicle.


22. What is meant by Tire Vibration? Explain its types. The mechanisms of tire vibrations can be classified into three main groups. The first group is the whole tire vibrations which are caused by the road roughness and running deflection. These vibrations are important in the frequency band below 500 Hz. The second group is the tread block radial and tangential vibrations. The last group is the aerodynamic phenomena such as air pumping and treads groove resonances. The last two phenomena are important above 1000 Hz.


UNIT III VERTICAL DYNAMICS

1. What are the sources of vibration? Road roughness, Engine Unbalance, Whirling of Shafts, Cam forces.

2. What is meant by Active Suspension? Active suspension systems sense the forces being applied to the wheels and constantly adjust the mechanical connections between the chassis and wheel assemblies to keep the chassis level and/or optimally absorb the energy associated with the vertical motion of the wheels. Additionally, with the advent of increased computer control, various options of suspension travel and response can be adjusted by the driver while driving. It controls the vertical movement of the wheels relative to the chassis or vehicle body with an onboard system, rather than in passive suspensions where the movement is being determined entirely by the road

3. What is meant by Passive Suspension? The vertical movement of the wheels relative to the chassis or vehicle body is being determined entirely by the road. The chassis of the vehicle is attached to the axles or wheel assemblies through coil springs or leaf springs that help to protect the chassis from sudden vertical forces applied to the wheels (e.g. due to bumpy roads, pot holes). The shock absorbers help to dissipate the energy applied to the springs and damp the oscillations that would normally occur when a brief excitation is applied to a mass-spring system.

4. What is meant by Semi Active Suspension? Systems that are only able to adjust the viscous damping coefficient of the shock absorber and not the spring rate are generally referred to as "semi-active" suspension systems. A basic semi-active suspension uses an electrically controlled valve to adjust the flow of hydraulic fluid inside the shock absorber to change its dampening characteristics.

5. Sketch the Quarter car active suspension model of a passenger car.

6. Explain the use of LQR in Vehicle Dynamics.

Linear-quadratic regulator (LQR) is a feedback controller whose equations will govern the undesirable function of the system. T This means that the settings of a (regulating) controller governing either a machine or process (like an airplane or chemical reactor) are found by using a mathematical algorithm that minimizes a cost function with weighting factors supplied by a human (engineer). The "cost" (function) is often defined as a sum of the deviations of key measurements from their desired values. In effect this algorithm finds those controller settings that minimize the undesired deviations, like deviations from desired altitude or process temperature. Often the magnitude of the control action


itself is included in this sum so as to keep the energy expended by the control action itself limited.

7. Explain about H infinite control method. H-infinite methods are used in control theory to synthesize controllers achieving stabilization with guaranteed performance. In this method, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization.

8. Explain about merits and demerits of H infinite control method. H infinite control method techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels The disadvantages include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled. The resulting controller is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the usual performance measures used to evaluate controllers such as settling time, energy expended, etc. Also, non-linear constraints such as saturation are generally not well-handled.

9. What is meant by LQ problem? The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem.

10. Explain Mercedes-Benz Magic Body Control system. It is an active system not only monitors forces imposed upon the car’s suspension system, but also monitors the conditions of the road ahead. Two image sensors on the front of the car actively scan the road ahead and prepare the suspension ahead of time to compensate for sudden changes in the road surface height.

11. Describe Skyhook damping. If the damping were placed between the sprung mass and inertial ground, instead of being placed between the sprung mass and the road, the resonant peak in the ride quality transfer function would be damped without causing the slower roll off at high frequencies. Thus significant ride quality improvement at the sprung mass frequency could be obtained without any high frequency harshness. Such a damper placed between the sprung mass and inertial ground is called a "sky-hook" damper.

12. Explain about Air suspension system. Air suspension is a type of vehicle suspension powered by an electric or engine-driven air pump or compressor. This compressor pumps the air into a flexible bellows, usually made from textile-reinforced rubber. The air pressure inflates the bellows, and raises the chassis from the axle. The purpose of air suspension is to provide a smooth and constant ride quality. The air bellows are also termed as air bags or air spring.


13. Enumerate the merits and demerits of Air suspension system. Merits:

• The bellows pressure can be changed depending on the load carried on the vehicle, the distance between the road surface and the vehicle’s superstructure.

• Spring comfort remains almost unchanged across the whole of the loading range. Sensitive loads can thus be carried without being severely damaged.

• The stability of the steering system and the transfer of the braking forces are improved since all wheels always have good adhesion to the road surface.

• The pressure in the air bellows, depending on the load the vehicle carries, is ideal for use in controlling automatic load-sensitive braking.

• air suspension systems are an excellent basis for cost-effective loading and unloading of containers

Demerits:

• High Installation cost. In most vehicles, even luxury models it comes at an extra cost. Only very high-end cars and SUVs such as the Mercedes S-Class and the Range Rover include it as standard.

• High Maintenance cost. If air suspension fails, the car can tilt to one side while moving. The traditional steel springs are easier and cheaper to fix than air suspension.

• 14. Define Tire Deflection Transfer Function.

The variables Zs, Zu and Zr represent the vertical displacements from static equilibrium of the sprung mass, unsprung mass and the road respectively.

15. Define Rattle Space Transfer Function.

16. Define Acceleration Transfer Function.

The variables Zs, Zu and Zr represent the vertical displacements from static equilibrium of the sprung mass, unsprung mass and the road respectively.

17. What is meant by Ride quality? Ride quality in general can be quantified by the vertical acceleration of the passenger locations. The presence of a well-designed suspension provides isolation by reducing the vibratory forces transmitted from the axle to the vehicle body. This in turns reduces vehicle body acceleration.


18. What is meant by Road Holding ability? How it can be improved? The road holding performance of a vehicle can be characterized in terms of its cornering, braking and traction abilities. Improved cornering, braking and traction are obtained if the variations in normal tire loads are minimized. This is because the lateral and longitudinal forces generated by a tire depend directly on the normal tire load.

19. Enumerate the merits of Semi Active Suspension System. Semi-active systems consume significantly less power compared to fully active suspension systems. The power consumption in a semi-active system is only for purposes of changing the real-time dissipative force characteristics of the semi-active device. They cannot cause the suspension system to become unstable. This is due to the fact that they do not actively supply energy to the vibratory suspension system but only dissipate energy from it.

20. What is meant by Magneto Rheological (MR) damper?

Magneto Rheological (MR) damper is a semi-active dissipator which uses MR fluid. Magneto rheological (MR) fluids are materials that respond to an applied magnetic field with a change in rheological behavior by the development of a yield stress that monotonically increases with applied magnetic field. The dissipative force provided by the damper can be controlled by controlling the electromagnetic field.

21. Explain the effect of suspension stiffness and damping on vehicle vibrations? Decreasing suspension stiffness improves ride quality and road holding. However, it increases rattle space requirements. Increased suspension damping reduces resonant vibrations at the sprung mass frequency. However, it also results in increased high frequency harshness.

22. Explain the effect of tire stiffness on vehicle vibrations? Increased tire stiffness provides better road holding but leads to harsher ride at frequencies above the unsprung mass frequency.

23. Explain the usage of quarter car, Half car and Full Car models. The quarter car suspension model is used to study and design automotive suspension systems for optimizing response to road irregularities. The half car and /or full car models can be used to study the influence of cornering on vehicle roll and the influence of braking and longitudinal acceleration on vehicle pitch.


UNIT IV LONGITUDINAL DYNAMICS AND CONTROL

1. Enumerate the aerodynamic forces and moments acting on the vehicle.

The aerodynamic forces on a vehicle act at centre of pressure.

Px- Air drag in Longitudinal Direction

Py- Side Force or Cross Wind in Lateral Direction

Pz- Aerodynamic lift force in vertical direction.

Aerodynamic moments arises since these forces do not act at center of gravity.

Mx- Rolling Moment caused by force Py about X axis

My - Pitching Moment caused by force Pz about X axis

Mz- Yawing Moment caused by force Py about Z axis

2. A vehicle of total weight 50 KN is held at rest on a slope of 100.It has a wheel base of

2.25 m and its CG is 1.0 m in front of the rear axle and 1.5 m above the ground level.

Find the normal reaction at the wheel.

W= 50KN, Ø =10, b=2.25m, l=1 m, h- 1.5 m

Rr=W/b (((b-l)cos Ø)- (h sin Ø)), Rf =W/b((l cos Ø)+(hsin Ø))

3. What are the factors that influence rolling resistance?

The rolling resistance depends on the nature of road surface, type of tyre, weight of the

vehicle, speed of the vehicle.

4. Write the expression for the reactions at the front and rear wheels of a rear wheel drive vehicle.

Rf =Wl/b, Rr = W(1- (l/b)), W=wt of vehicle in N, b-wheel base m, l-distance of CG

from rear axle.

5. Explain the load distribution of a four wheeler on a level road.

Rf = Wl/b ,Rr= W(1-l/b)

6. Define Grade Resistance. The component of the weight of the vehicle parallel to the gradient on the slope on which it moves is termed as grade resistance.

7. Define draw bar pull. When the excess power is fully utilized for pulling extra load attached to the vehicle then maximum drawbar pull = Tractive effort – road Resistance

8. Define gradeability. The maximum percentage grade which a vehicle can negotiate with full rated condition is known as gradeability.

9. Write the expression for the vertical reactions of a three wheeled vehicle. Rf = Wl/b, Rr1 =W/2(1-(l/b)-(2c/a)) N, Rr2 =W/2 ((2c/a) - (l/b) +1))


10. Sketch the schematic diagram of Vehicle longitudinal dynamics.

11. Write the equation of motion for longitudinal dynamics.

Consider a bicycle type model (the difference between right and left tires is ignored)

shown in above Figure. Ignoring the road gradient and wind speed, the longitudinal

dynamics can be represented as:

where m is the total mass of the vehicle, ax is the longitudinal acceleration/deceleration,

Fxf and Fxr are the front and rear wheel traction/braking forces,

Rx = Rxf + Rxr = Croll mg is the rolling resistance force with Croll being the rolling

resistance coefficient, Da is the aerodynamic drag force constant and Vx is the

longitudinal velocity.

12. What is the function of ABS?

The basic objective of the ABS is to either hold or release the braking pressure on the

wheels if there is a danger of the wheels locking. At the same time, the ABS needs to re-

permit application of the brakes again once the danger of locking has been averted. The

ABS system could also hold or release the braking pressure in order to keep the slip ratio

at the wheel from exceeding an optimum value.

13. What is meant by Prediction and Prediction point slip?

The process of determining whether or not the wheel is going to lock is called prediction.

Prediction point slip is defined as the wheel slip at the instant the control unit predicts for

the first time in a brake cycle that the wheel is going to lock.

14. What is meant by Reselection and Reselection point slip?

The process of determining whether or not the danger of locking has been averted is

called reselection. Reselection point slip is defined as the wheel slip at the instant it is

predicted for the first time in a brake cycle that the danger of locking is averted.


15. State the limitations of ABS.

The wheel slip cannot be measured with inexpensive sensors on a passenger vehicle. The

measurements available to the ABS system are measurements of the individual wheel

speeds at the four wheels. The stopping distance can be increased if there is a malfunction

in its components.ABS is an expensive and delicate control system.

16. Explain the function of Traction control system (TCS).

Traction Control systems optimize grip and stability of the car on the road during

acceleration by measuring wheel rotation. It stops wheel spin by reducing engine power

or temporarily applying the brakes to that wheel, allowing the car to accelerate smoothly,

even on slippery surfaces.

17. Write the expression for the equivalent aerodynamic drag force on a vehicle.

Where ρ is the mass density of air, Cd is the aerodynamic drag coefficient, AF is the

frontal area of the vehicle, which is the projected area of the vehicle in the direction of

travel, Vx is the longitudinal vehicle velocity, and Vwind is the wind velocity

18. What is meant by effective tire radius?

The effective tire radius is the value of the radius which relates the rotational angular

velocity of the wheel to the linear longitudinal velocity of the wheel as it moves through

the contact patch of the tire with the ground.

19. What is the function of stability control system?

The main function of vehicle stability control systems is to prevent vehicles from

spinning and drifting out. The stability control system restores the yaw velocity of the

vehicle as much as possible to the nominal motion expected. It reduces the deviation of

the vehicle behavior from its normal behavior on dry roads and by preventing the vehicle

slip angle from becoming large.

20. Enumerate the three types of stability control systems developed for yaw control?

• Differential Braking systems

• Steer-by-Wire systems

• Active Torque Distribution systems

21. Explain the function of Differential Braking systems.

Differential Braking systems which utilize the ABS brake system on the vehicle to apply

differential braking between the right and left wheels to control yaw moment.


22. Explain the function of Steer-by-Wire systems.

Steer-by-Wire systems which modify the driver's steering angle input and add a

correction steering angle to the wheels.

23. Explain the function of Active Torque Distribution systems.

Active Torque Distribution systems which utilize active differentials and all wheel drive

technology to independently control the drive torque distributed to each wheel and thus

provide active control of both traction and yaw moment.

24. Write the relation between Engine revolutions N in rpm and Vehicle speed V in Km/hr

N/V = 2.65 G/r (G= gear ratio, r = radius of tyre in metre)

25. Write the equation to calculate the tractive effort of a vehicle in terms of engine torque,

over all gear ratio, wheel radius and transmission efficiency.

F = (Te X G X ήt)/r N, Te= Engine Torque, G = over all Gear Ratio, ήt = Transmission

Efficiency, r =wheel radius

UNIT V LATERAL DYNAMICS

1. Write down the expressions for limiting speed and overturning speed when the vehicle running on a banked track.

θθ

θθ

θµθ

θµθ

sincos2(

)cossin2(

)sin(cos

)cos(sin 2

0

2

ah

ahcgV

cgVS

−

+=

−

+=

Vs = Sliding (limiting) Velocity in m/s, Vo= Overturning Velocity in m/s c= Radius of curvature of path traced by CG of the vehicle in m. θ = Inclination of wheel axis to horizontal or angle of banked road. µ = Coefficient of Adhesion between tyre & Road, a= Wheel track in m

2. What is meant by steady state handling characteristics of a vehicle? Steady state handling characteristics is concerned with the directional behavior of a vehicle during a turn under non time varying conditions.

3. What is meant by under steer? A vehicle that is heavier at the front will tend to under steer. Under steer results when the slip angle of the front tires is greater than the slip angle of the rear tires. A greater steering angle is then required in order to maintain the turn. When the steering angle reaches full lock and the turn cannot be maintained, the vehicle drifts to the outside. In an under steer condition, the driver is attempting to negotiate a turn, but the vehicle mushes ahead refusing to cooperate. A vehicle that understeers is considered safer in the hands of the average driver.


4. What is meant by over steer? A vehicle that is heavier at the rear will oversteer. During oversteer, the slip angle of the rear tires is greater than the front. Consequently, the turn-rate increases on its own and the driver therefore reduces the steering angle to compensate. During severe oversteer, the steering angle may reach full lock in the opposite direction while the vehicle continues on into the turn. The vehicle is then said to "spin out."

5. Define the critical speed of an over steer vehicle. It is the speed of the over steer vehicle at which the steer angle required to negotiate any turn is zero.

6. List out the requirements of good suspension system.

• Stiffness/Displacement Bound

• Compatibility

• Min Wear

• Maintenance low

• Initial cost low

7. Define yaw velocity gain with respect to steady state cornering. It is a parameter used for comparing the steering response of road vehicles. It is defined as the ratio of the steady state yaw velocity to the steer angle. Yaw velocity of the vehicle

( ) under steady state conditions is the ratio of the forward speed V to the turning radius R. Yaw Velocity Gain is given by Gyaw

δf = Steer Angle required to negoitate a given curve.

8. Justify why understeer is preferred over oversteer vehicle.

For an over steer vehicle, the curvature response increases with forward speed. At a particular speed curvature response approaches infinity. From steering response point of view the oversteer vehicle has the most sensitive handling characteristics, while the understeer vehicle is least responsive.

9. What is meant by roll axis of a vehicle? The roll centre is an imaginary, but accurately defined, point on the centre-line of the car around which the car rolls on its suspensions. The roll centre can be high off the ground, low, or even underneath the ground (it's only imaginary). A line connecting the rear suspension roll centre with that of the front is called the roll axis. If the axis runs nose-down, the car tends to oversteer. If the axis runs nose-up, the car tends to understeer.

L= Wheel base in m, Kus = Under Steer Coefficient, Vcrit= Critical

Speed in m/s


10. Write down the expressions for reactions at wheels due to centrifugal force for a four wheeled vehicle while taking a turn. The inner, outer reactions for front and rear wheels are given below.

−==

==

b

l

a

h

C

V

g

WPP

b

l

a

h

C

V

g

WPP

ORIR

OFIF

12

2

W = Wt of vehicle in N, C= Radius of curvature of path traced by CG of the vehicle in m, a= Wheel track in m, b = Wheel base in m, h= h.t of CG of vehicle from ground in m. l= Distance of CG in front of rear axle in m, V = Linear speed of the vehicle in m/s.

11. Write down the expressions for reactions at wheels due to gyroscopic couple for a four

wheeled vehicle while taking a turn. The inner, outer reactions for front and rear wheels are given below.

)(2

)(

)(

2

2

2

FSORIROFIF

FSOROFO

FSIRIFI

IGIgarC

VQQQQ

IGIgarC

VQQQ

IGIgarC

VQQQ

±====

±=+=

±=+=

12. Give the expression for angle of tilt for the conventional suspension system.

The angle of tilt is given by 22

22

Kd

FhC

Kd

TC==θ

F= Side Force acts at CG of vehicle, h = ht of CG from bottom point where resultant passes acts, d=Spring Base, K = Spring Stiffness, C =Constant depend on relative stiffness of spring used in front and rear.

13. Justify why independent suspension system has lower angle of tilt compared to conventional suspension system. Roll axis of conventional suspension system is higher than the independent suspension sytem.The wheel track ‘a’ is greater than spring base ‘d’, so θ will be small in independent suspension system.

14. State the conditions of no tilt for independent suspension system. The side force must be shared equally between the wheels. Roll axis must coincide with CG, line of action of side forces must pass through the roll axis.

Is = Moment of Inertia of slow rotating parts in N-m2

IF = Moment of Inertia of fast rotating parts in N-m2

G= Over all Gear Ratio = ωf / ωs


15. Explain the relationship between slip angle and steer angle. Steer angle required to negotiate a curve is a function of turning radius (R) and slip angle

of front and rear tire. ( )rf andαα , L= Wheel Base

rffR

Lααδ −+=

16. Explain the significance of under steer coefficient.

Under Steer Coefficient Kus =r

r

f

f

C

W

C

W

αα

− ,

Kus= 0 Neutral Steer, Kus> 0 = UnderSteer Kus< 0 = Over Steer. Wf, Wr = Normal load on each of front wheels and each of rear wheels in N. Cαf, Cαr = Cornering Stiffness of each of front and rear tires.

17. Sketch the curvature responses of neutral steer, over steer and under steer vehicles at a fixed steer angle.

18. Define characteristic speed of a under steer vehicle. It is the speed at which the steer angle required to negotiate a turn is equal to 2L/R.

us

CharK

LgV = L= Wheel Base, Kus Under Steer Coefficient

19. What is meant by Slip Angle?

When a side force is applied to a tire, a lateral force is developed at the contact patch due to the lateral elasticity of the tire and the tire will move along a path at an angle with the wheel plane. The angle is termed as slip angle.

20. What is meant by cornering force? Explain its significance. When a side force is applied to a tire, a lateral force is developed at the contact patch due to the lateral elasticity of the tire. The lateral force developed at the tire ground contact patch is called cornering force when the camber angle of wheel is zero. The relationship between the cornering force and slip angle mainly influences the directional control and stability of road vehicles.


21. What is meant by self aligning torque? Explain its significance.

The cornering force in ground plane is not in collinear with side force and normally behind it giving rise to torque which align the wheel plane with the direction of motion. The torque is called as self aligning torque one of the primary restoring moments which help the steered tires return to the original position after negotiating a turn.

22. Enumerate the various tests used for determining steady state handling characteristics. (1) Constant Radius Test, (2) Constant Forward Speed Test, (3) Constant Steer Angle Test.

23. What is meant by Transient Response Characteristics?

Between the application of steering input and the attainment of steady-state motion, the vehicle is in a transient state. The behavior of the vehicle in this period is usually referred to as transient response characteristics. The optimum transient response of a vehicle is that which has the fastest response with a minimum of oscillation in the process of approaching the steady-state motion.

24. Explain the term directional stability. The directional stability of a vehicle refers to its ability to stabilize its direction of motion against disturbances. A vehicle is considered to be directionally stable if, following a disturbance, it returns to a steady-state regime within a finite time. A directionally unstable vehicle diverges more and more from the original path, even after the disturbance is removed. The disturbance may arise from crosswind, momentary forces acting on the tires from the road, slight movement of the steering wheel, and a variety of other causes

25. Define cornering compliance. The ratio of load to cornering stiffness /coefficient (front & rear) is termed as cornering compliance. The unit is Deg/g indicates the number of degrees of slip angle at an axle per g of lateral force imposed at that point.



REGULATION 2013

PART B (16 Marks)


1. Briefly discuss about Transmissibility of Engine Mounting and Vibration Absorber. 2. Explain the free vibration of an automobile/vehicle vibration with single degree of

freedom and derive the expression for logarithmic decrement. 3. Discuss in detail the free vibration of a vehicle with single degree of freedom and draw

the response characteristics with time for critical, over and underdamped cases. 4. An engine weighing 1785.4 N is to be supported on four helical springs. When the engine

speed is 900 r.p.m there is a primary vertical disturbing force of maximum valve 312 N due to unbalanced reciprocating weights.Assuming that the engine vibrates in the vertical direction with neither horizontal nor angular movement,find the stiffness of each spring in N/m of deflection to limit the maximum total periodic force on the foundation to 22.3N. What will be the amplitude of vibration of the engine when its speed is 600 r.p.m?

5. (a) Explain with suitable example the concept of vibration absorber. (b) Define and derive an expression to find the transmissibility. Also draw the frequency response diagram and explain its significance.

6. The front suspension of a motorcar is having an equivalent weight of 11281.5N carried on spring stiffness. 88292 N/m. calculate the frequency of vertical natural vibration with the dampers removed. If the dampers are adjusted to give total damping force 4415.5 N/m/S calculate the frequency of damped vibration an the ratio of the second down ward to the first down ward.

7. Sketch the curves of Amplitude ratio Vs frequency ratio and Transmissibility Vs frequency ratio for different values of damping ratio for a typical value. Explain the important facts.

8. Define and derive an expression to find the magnification factor. Also draw the frequency response diagram and explain its significance,

9. An Engine of mass 300Kg is found to experience undesirable vibrations at an operating speed of 6000 rpm. If the magnitude of the excitation force is 240N. Design vibration absorber for this system so that the maximum amplitude of the absorber mass does not exceed 3mm.

10. Sketch the curves of Amplitude ratio Vs frequency ratio and Transmissibility Vs frequency ratio for different values of damping ratio for a typical vehicle. Explain the important facts.

11. Explain the vehicle vibration with two degrees of freedom for forced vibration. 12. The springs of a motor vehicle carry a load of 11500 N and with equal springing front

and rear. The combined spring rate is 9000 N/m. Calculate the frequency of a vertical natural vibration with the dampers removed. If the dampers are adjusted to give a total damping force 4500N/m/sec, calculate the frequency of damped vibrations and ratio of the second downward movement to the first downward movement.

13. The springs of a motor vehicle carry a load of 12 KN and with equal springing front and rear. The combined spring rate is 90 KN/m. Calculate the frequency of a vertical natural vibration with the dampers removed. If the dampers are adjusted to give a total damping force 4400N/m/sec, calculate the frequency of damped vibrations and ratio of the second downward movement to the first downward movement.


14. A wheel with weight W attached to it through a spring is rolling along a wavy surface with a constant speed of 18.25 m/sec. The static deflection of the spring under the load W is 9.8 X10-2 m and the surface is given by y = Y cos 2πx/ l. where x = V, l = wavelength of the wavy surface =1.83 m and Y = 2.5 X10-2 m. Determine the amplitude of the forced vibration.

UNIT II TIRES

1. Explain the variation of longitudinal tire force with various slip angles in detail. 2. Explain the variation of lateral tire force with various slip angles in detail. 3. Explain how tire forces can be evaluated by using Magic Formula tire model with

suitable illustrations. 4. Describe how tire road friction can be estimated for both traction and braking. 5. (a) Illustrate the forces and moments acting on tire with tire axis system.

(b) Describe about the tire vibration with suitable sketches. 6. Explain the different types of tire structures and its uses with neat sketches. 7. Explain the experimental method of tire road friction estimation on different road

surfaces. 8. (a) Briefly explain the causes for occurrence of rolling resistance of tire and factors

influencing it. (b) Explain the cornering characteristics of tyre and their relationship.

9. Explain the effect of tread pattern and speed on the braking performance of tires on various wet surfaces.

10. (a)Describe the load -deflection characteristic of bias ply and radial ply tire in static condition. (b)Explain the three distinct types of tire vertical stiffness and its evaluation.


1. Explain in detail about Full, half and quarter car suspension models with neat sketches. 2. Explain the design methodology for passive suspension system using quarter car model. 3. Explain the control system design for active suspension system using LQR formulation

for quarter car model. 4. Briefly explain about the construction and working of air suspension system with neat

sketch. 5. Explain the design methodology for active suspension system using quarter car model. 6. Describe the influence of suspension parameters on sprung mass and unsprung mass

vibrations. 7. Briefly explain the design and development of semiactive control systems for automotive

suspensions. 8. Explain the design methodology for semi active suspension system using quarter car

model. 9. What is meant by semi active suspension? Explain the working principle of it.

Also enumerate the merits of semi active suspension. 10. Explain about LQR formulation for active suspension design. 11. What is meant by sky-hook damping? Explain the influence of sky hook damping in

modifying the performance of active and semi active suspensions. 12. Describe the design and configuration of H infinite controller used for quarter, half and

full car suspension model.



1. (a)Derive an equation for distribution of weight at front and rear wheels for a three

wheeled road vehicle. (b)Explain about load distribution of a four wheeled road vehicle with deriving the expression.

2. Explain the calculation of maximum acceleration, maximum tractive effort and reactions for different drive.

3. A motor car with wheel base 2.75 m with a CG 0.85 m above the ground and 1.15 m behind the front axle has a co-efficient of adhesion 0.6 between the tyre and ground. Calculate the maximum possible acceleration when the vehicle is (a) Driven on four wheels (b) Driven on the front wheels only (c) Driven on the rear wheels only.

4. Briefly explain the aerodynamic forces and moments acting on the vehicle with its sign convention. Write the equation of motion for the forces and moments.

5. (a) Explain the forces acting on tire with tire axis system. (b) What is meant by rolling resistance? Briefly explain how rolling resistance influence the performance of vehicle.

6. Explain the working of anti lock braking system with a schematic layout. Explain the various factors that influence the ABS control systems.

7. Describe the functioning of a yaw stability control system and explain in detail about any one of its types.

8. Explain how steer by wire system can be designed for vehicle stability control. 9. Explain the operational principle of traction control system with a neat sketch. 10. Explain the methodology adopted for prediction of vehicle performance in detail. 11. A vehicle weighs 21.24 KN including the four road wheels. Each of the wheels has a

rolling radius of 33 cm and a radius of gyration of 25.4 cm and weighs 244.6 N. The engine develops a torque of 325 Nm at 3500 rpm. The equivalent mass of moment of inertia of the parts rotating at engine speed is 0.733Kg m2.The transmission efficiency is 85% and the total reduction ratio of the driveline in the third gear is 4.28 to 1.The vehicle has a frontal area of 1.86 m2 and the aerodynamic drag coefficient is 0.38.The coefficient of rolling resistance is 0.02.Determine the acceleration of the vehicle on a level road under these conditions.

12. Derive the expression for the relationship between the tractive effort and longitudinal slip angles of the pneumatic tyres.


1. (a) Explain briefly vehicle suspension in fore and aft direction. (b) A passenger car has a weight of 20.105 KN and a wheel base of 3.2m.The weight distribution on the front axle is 53.5%.and that on the rear axle is 46.5% under static conditions. If the cornering stiffness of each of the front tyres is 38.92 KN/rad and that of rear tyres is 38.25 KN/rad, determine the steady state handling behavior of the vehicle.

2. What is roll axis? Discuss vehicle under the action of side forces. 3. Derive a suitable expression to calculate the under steer coefficient. With that expression,

compute the characteristics speed of an under steer vehicle. 4. (i) Write a note on camber and camber thrust.

(ii) Discuss the directional stability of Vehicle. 5. (i)Write a note on transient effect on cornering

(ii Discuss about the directional stability of vehicle.


6. Briefly explain the steady state handling characteristics of road vehicles. 7. Briefly explain the transient response characteristics of road vehicles. 8. Explain in detail (1) Under Steer (2) Over steer (3) neutral Steer applicable steady state

handling characteristics of a vehicle. 9. A passenger car weighs 20.02 KN and has a wheel base of 2.794 m. The centre of gravity

is 1.27 m behind the front axle. If a pair of radial ply tyres, each of which has a cornering stiffness of 45.88 Kn/rad, are installed in the front and apair of bias ply tires each of which has a cornering stiffness of 33.13 KN/rad, are installed in the rear, determine whether the vehicle is understeer or over steer. Calculate also the characteristic or critical speed of the vehicle.

10. What is meant by steady state cornering? Deduce an expression for the relationship among the steer angle of the front tyre, turning radius,wheel base, understeer coefficient and explain the terms understeer and over steer of the vehicle.

11. Write an expression for steer angle required to negotiate a given curve and explain the terms over steer, under steer and neutral steer.

12. (i) A passenger car has a weight of 20.105 KN and a wheel base of 3.2 m. The weight distribution on the front axle is 53.5% and that on the rear axle is 46.5% under static condition. Determine the steady state handling behavior of the vehicle: (i) If the cornering stiffness of each of the front tyres is 38.92 KN/rad and that of the rear tyre is 38.25KN/Rad (ii) If the front tyres are replaced by a pair of radial tyres each of which has a cornering stiffness of 47.82 KN/rad and the rear tyres remain unchanged. (ii) Describe with neat sketches about the static and rolling properties of pneumatic tyres.

13. A car of total weight 19620 N runs at 72 Kmph round a curve so that its C.G moves in a circle of 80 m radius with its wheel axes at an angle of 10 0 to the horizontal.The C.G of the car is 1m above the ground and is midway between the axles.The diameter of the wheel is 0.6m,the wheel track is 1m and each pair of axle weighs 1962 N with a radius of gyration of 0.25 m. Determine the normal reactions on each wheel taking in to account centrifugal and gyroscopic effects.

14. (a) Derive an expression for vertical reaction at front and rear wheel for four wheeled vehicle. (b) Obtain an expression for overturning speed of vehicle running on a banked track.

15. A vehicle of total weight 49.05 KN is held at rest on a slope of 100. It has a wheel base of 2.25 m and its centre of gravity is 1.0 m in front of the rear axle and 1.5 m above the ground level. Find

i. What are the normal reactions at the wheels? ii. Assuming that sliding does not occur first, what will be the angle of slope so that the

vehicle will overturn? iii. Assuming all the wheels are to be braked, what will be the angle of slope so that the

vehicle will begin to slide if the coefficient of adhesion between the tire and the ground is 0.35?

16. Derive the expression for the limiting speed and overturning speed of a vehicle running on a banked track.

17. Derive an expression to find the normal reactions at the front and rear wheels considering the stability of a vehicle on a slope of θ to the horizontal. Also discuss the limiting valve for θ, if it is increased gradually (i) either the vehicle is about to overturn (ii) The vehicle is about to slide down the slope.

18. A car of total weight 20 KN runs at 80 km/hr round a curve so that its C.G moves in a circle of 32 m radius with its wheel axes at an angle of 12 0 to the horizontal. The C.G of the car is 1m above the ground and is midway between the axles. The wheel track is 1.2


m. Determine the normal reactions on each wheel taking in to account the centrifugal effect.

19. Determine the load carried by wheels at the outer and inner sides and the max value of coefficient of adhesion if there is no side slipping when the vehicle weighing 17.795KN runs at 96KMPH round a circular path so that the C.G moves in a circle of 122 m with its wheel axes at angle of 120 to horizontal. Its C.G is 1.06 m above the ground level and wheel track is 1.3 m. Explain the forces or couple acting.

20. Discuss about Stability of a vehicle on a curved track with the appropriate equations. 21. Deduce an expression for Stability of a vehicle on a slope. 22. Deduce an expression for Stability of a vehicle on a banked road. 23. A vehicle of total weight 49050 N is held at rest on a slope of 10°. It has a wheel base

of 2.25 m and its centre of gravity is 1.0 m in front of the rear axle and 1.5 m above the ground level. Find(a) What are the normal reactions at the wheels?(b) Assuming that sliding does not occur first, what will be the angle of slope so that the vehicle will overturning.

24. Determine the load carried by wheels at the outer and inner sides and the maximum value of coefficient of adhesion if there is no side slipping when the vehicle weighing 17795 N runs at 96 km/h round a circular path so that the centre of gravity moves in a circuit of 122 m with its wheel axes at angle of 12° to the horizontal. Its centre of gravity is 1.06 m above the ground level and wheel track is 1.3 m.

25. Derive an expression for the limiting speed to slide outward and overturning speed of a vehicle along the banked track.

26. What are the forces acting on a four wheeled vehicle while taking a turn? Explain with neat figure.



REGULATION 2013

UNIVERSITY QUESTIONS


PART A

1) Define: Degree of Freedom (April 2012) 2) What is Damping ratio (or) Damping factor (Nov 2011) 3) Define: Damped natural frequency 4) Define: Transmissibility ratio (Nov 2012) 5) What do you mean by modeling and Simulation? (April 2012) (Nov 2011) 6) Define: Damped Vibration 7) What is Magnification factor (or) Dynamic Factor (April 2010) 8) Write about the Sources of Vibration? (Nov 2012) 9) What is Whirling (or) Whirling of Shafts (April 2009) 10) What is transmissibility ratio (or) isolation factor (April 2010) 11) What is resonance? (April 2009)

12) What is Critical damping and logarithmic decrement? (April 2013)

13) What do you mean by modeling and simulation? (Nov 2012) (April 2013) 14) An unknown mass ‘m’ is attached to one end of a spring of stiffness ‘k’ having natural frequency of 6 Hz. When 1 kg mass is added to the system, the natural frequency is lowered by 20%. Determine the value of ‘m’ and k of the system. (Nov 2012) 15) What are the various sources of vibration in a vehicle? (Nov 2013) 16) What do u understand by modeling and simulation. (Nov 2013) 17) How vibrations cause a human discomfort? (May 2014)

18) Draw the general coordinate system of a vehicle. (May 2014)

PART B

1) Discuss the concept of vibration absorber with a suitable expression and show mathematically how the system is completely absorbing the vibration? (Apr 2011) (Nov 2010) 2) What do you mean by Magnification factor? Derive a suitable expression for calculating the magnification factor for a single degree of freedom? (Apr 2012) 3) Derive the equation for free and forced vibration for two degree of freedom? (Apr 2010)(Nov 2011) 4) Derive the expression to calculate the Magnification factor when a single degree of freedom system is subjected to an external force. Also draw the Magnification factor vs frequency ratio. Mention your observation from the curve. (Nov 2012) 5) Derive the equation for free and forced vibration for single degree of freedom for i) Under damped conditions ii) Over damped conditions iii) Critically damped conditions (Apr 2011). 6) Compute the ratio between the maximum forces transmitted to the ground vs maximum force applied with respect to single degree of freedom system. Plot this ratio against frequency ratio and provide your observations. (Nov 2012) 7) a) Briefly explain about the derivation for transmissibility ratio of a vibration system?

b) Briefly explain about the Modelling and Simulation? (April 2010)


8) Describe briefly the free vibration of a vehicle with single degree of freedom. (April 2013) 9) Discuss the concept of vibration absorber with example. (Nov 2013) 10) Derive a suitable expression for magnification factor. Also draw the Magnification factor vs frequency ratio and mention its importance. (Nov 2013) 11) Derive a suitable expression for transmissibility ratio. Also draw the Magnification factor vs frequency ratio and mention its importance. (May 2014) 12) For the system shown in figure, compute the damping ratio, state whether the system is critically damped, under damped or over damped. Determine x(t) for the initial condition given. (May 2014)

13) The front suspension of a motor car is having an equivalent weight of 11.5KN carried on spring stiffness 90kN/m. Calculate the frequency of vertical natural vibration with dampers removed. If the dampers are adjusted to give total damping force 4.5KN/m/s. Calculate the frequency of damped vibration and the ratio of second downward to first downward movement. (Nov 2013) 13) A wheel with weight W attached to it through a spring is rolling along a wavy surface with a constant speed of V is 18.25m/s. The static deflection of the spring under the load W is 0.098m and the wavy surface is given by y=Ycos(2πV/l)t. Determine the amplitude of forced vibration if length of wavy surface is 1.83m and Y=0.025m. (May 2014)


UNIT II TIRES

PART A

1. Compare radial ply and bias ply tyre (Nov 2011) 2. Define cornering stiffness and cornering coefficient? (April 2010)

PART B

1.


PART A

1.

PART B

2.

The entire Unit II & Unit III portions are newly added for Regulation 2013

for AT 6604 Vehicle Dynamics - New portions are not available with

previous Regulations – So university questions are not available for the

units

Unit IV – only 30% of portion are available with previous Regulations – So

university questions are not available for the remaining 70%



PART A

1. Discuss the weight distribution of a three wheeler? (April 2012) (April 2010)

(Nov 2012) (Nov 2013)

2. Discuss the weight distribution of a four wheeler? (April 2010) (April 2013) 3. Define: Tractive effort and traction? (Nov 2012) 4. Define: Drawbar pull (April 2009) 5. Define the term Gradeability? (Nov 2011)

PART B

1. Derive the suitable expression to find out the reaction forces, Maximum tractive effort and maximum forward acceleration for (i) Four wheel drive (ii) Front wheel drive (iii) Rear wheel drive (April 2010) (April

2013) 2. A motor car with total weight of 40 KN and wheel base of 2.75m with CG of 0.85m

above the ground and 1.15m behind the front axle. If coefficient of adhesion is 0.6, Compute the maximum possible acceleration and the normal reactions when the vehicle is i) Driven on front wheels only ii) Driven on rear wheels only iii) Derive the formula used for the above. (Nov 2012)

3. Compute the reaction forces, maximum acceleration and tractive effort for vehicle driving on front wheel drive, rear wheel drive and all wheel drive. (Nov 2013)

4. Two cars similar in all aspects excepting the one has rear wheel drive and the other has front wheel drive. If the engine power does not limit the ability to climb grades, state which car can ascend steep grades. (May 2014).

5. Write short notes on: (April 2011) a) Factors affecting rolling resistance b) Vehicle suspension in fore and aft direction.



PART A

1. What is meant by ‘Limiting Angle’? (Nov 2012) 2. What is gyroscopic couple? (April 2009) 3. What is axis of precession? (Nov 2011) 4. What is meant by limiting and overturning speed? (Nov 2013) (May 2014)

5. What is meant by gyroscopic couple and state its effect in a vehicle. (May 2014) 6. Justify why under steer is preferred over oversteer vehicle. (April 2013) 7. Define slip angle and cornering force of a tyre. (April 2010) 8. Define static stiffness of tire. 9. What do you mean by overturning speed and sliding speed? (Nov 2011) 10. Define yaw velocity gain with respect to steady state cornering. (April 2013) 11. What is meant by steady state and transient state in cornering? (Nov 2013) 12. Define static stiffness, dynamic stiffness of tyre. (May 2014) 13. Define lateral acceleration gain with respect to steady state cornering. (May 2014)

PART B

1. a) Explain about the distribution of weight of a three wheeled vehicle? (Apr 2009) b) Explain about the distribution of weight of a four wheeled vehicle? (Apr 2009)

2. Illustrate the vehicle stability on a banked track? (Apr 2009) 3. Discuss the stability of the vehicle when negotiating a turn. (Nov 2012) 4. A car of total weight 20kN runs at 80 km/hr round a curve so that its C.G. moves in a

circle of 82m radius with its wheel axes at an angle of 12° to the horizontal. The C.G. of the car is 1 m above the ground and is midway between the axes. The wheel track is 1.2 m. Determine the normal reactions on each wheel taking into account the centrifugal effect. (April 2011)

5. A car of total weight 20 KN runs at 70 km/hr round a curve so that its C.G. moves in a circle of 80m radius with its wheel axes at an angle of 10° to the horizontal. The C.G. of the car is 1 m above the ground and is midway between the axes. The diameter of the wheels is 0.6 m, the wheel track is 1 m. Each wheel weighs 1800 N with radius of gyration of 0.25 m. Determine the normal reactions on each wheel taking into account the centrifugal effect and gyroscopic effect.(Nov 2010)

6. A car of total weight 20kN runs at 80 km/hr round a curve so that its C.G. moves in a circle of 82m radius with its wheel axes at an angle of 12° to the horizontal. The C.G. of the car is 1 m above the ground and is midway between the axes. The wheel track is 1.2 m. Determine the normal reactions on each wheel taking into account the centrifugal effect.(April 2011)

7. A car of total weight 19620 N runs at 72 km/hr round a curve so that its C.G. moves in a circle of 80m radius with its wheel axes at an angle of 10° to the horizontal. The C.G. of the car is 1 m above the ground and is midway between the axes. The wheel track is 1 m and the diameter of the wheels is 0.6 m and each pair of axle weighs 1962 N, and the radius of gyration is 0.25 m. Determine the normal reactions on each wheel taking into account the centrifugal and gyroscopic effect.(Nov 2011) (April 2013)

8. A motor car takes a bend of 30.5 m at a speed of 64 km/hr. Determine magnitude of the centrifugal and gyroscopic couples acting on the vehicle and state the effect that the road has on the road wheels. Assume that (i) Each road wheel has a moment of inertia of 19.62 N-m2 and effective road radius of 0.4 m (ii) The rotating parts of the engine and


transmission are equivalent to a flywheel weighing 637.65 N with a radius of gyration of 0.1m. The engine turns in a clockwise direction when viewed from the front. (iii) The back axle ratio is 4 to 1, the drive through the gear box being direct. The gyroscopic effects to the half shafts at the back axle are to be ignored. (iv) The car weighs 11281.5 N and its centre ofgravity is at 0.6 m above the road wheel. (Apr 2012)

9. Discuss the stability of vehicle on a slope and running on a curved track. (Nov 2013). 10. Discuss the effect of roll axis and side forces acting on the vehicle. (Nov 2012) 11. A passenger car weighs 20 kN and has a wheel base of 2.8m. The center of gravity is

1270 mm behind the front axle. If a pair of radial ply tyres, each of which has a cornering stiffness of 45.88 kN/rad, are installed in the front and a pair of bias ply tyres each of which has a conrnering stiffness of 33.13 kN/rad are installed in the rear. (i) Determine whether the vehicle is understeer (or) oversteer. Also calculate the critical speed of the vehicle as appropriate.(ii) What would happen to the steady state handling characteristics of the vehicle, if the front and rear tyres are interchanged.(iii) Derive the formula used. (Nov 2012)

12. Derive an expression to compute the steer angle required to negotiate the given curve under steady state condition. With that explain under steer, neutral steer and over steer. (Nov 2013)

13. Derive the suitable expression to calculate the under steer coefficient with that expression to compute the characteristics speed of an under steer vehicle. Describe briefly the free vibration of a vehicle with single degree of freedom.

14. Write short notes on: (April 2012) a) Yaw velocity gain b) Lateral acceleration gain c) Curvature response gain for over steer, neutral steer and under steer.

15. Explain in detail i) Under steer ii) Over steer and iii) neutral steer applicable to steady state handling characteristics of a vehicle (April 2010)

16. a) Explain in detail the directional stability of a vehicle. (Nov 2011) (April 2013) b) Write short notes on steady state cornering.




















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