MID-TERM EXAMINATION, IIT HYDERABAD

ME 5670 – Vehicle Dynamics Date: 27/02/2015

Maximum Marks – 30 Time duration: 2 hours

Instructions:

i) All questions are compulsory. ii) Only calculator is allowed in the examination room.

1. Answer the following Marks: (3+2+2+3¿=10

For a vehicle moving in the forward direction with a steering angle δ having all the wheels of Rw and ias the angular velocity of ith wheel, then do the following:

a) If (x, y) is the co-ordinate of vehicle CG then find the location of all the wheels in both the cases.

b) Considering no-slip and no side forces, compute velocity of all the wheels in terms of vehicle parameters and its velocities at CG of the vehicle.

c) Taking tri-wheel vehicle, obtain velocity of vehicle CG and yaw rate in terms of vehicle and wheels parameters.

d) Considering X, Y, and ψ as state variables in global co-ordinate, compute the governing equation in terms of vehicle and wheel parameters when CG is located at the center of rear axle such that b=0 and a= L=distance between the axles.

********* Good Luck************

2. Answer the following questions: Marks: (2+2+6¿=10

a) For a linear system given by x=ax+byy=cx+dy, state the stability condition.

b) Define wheel slip ratio and longitudinal tractive force. Discuss about the variation of longitudinal tractive force versus slip ratio.

c) For a vehicle of mass Mv which is moving along a straight line is subjected to wind drag and traction force at the tire. If Fw is the wheel viscous friction which acts opposite to the wheel rotation then obtain the state equations and subsequently the stability condition of the vehicle under forward motion.

3. Answer the following questions: Marks: (2+4+4¿=10

a) Draw the closed loop diagram and then the transfer function of a closed loop with output y and input r under the effect of external disturbance ud, when Gp, Gc and H are transfer function of plant, controller and sensors.

b) Assuming negligible external disturbance and talking ideal sensor with any loss, obtain the closed loop transfer function of spring-mass-damper system with PID controller when it is subjected to an external force F, where, M is the mass, k is the spring constant, c is the damping constant, Kp is the proportional gain, Kd is differential gain and Ki is integral gain, respectively.

c) For proportional controlled system, obtain the expression of Kp of the above system when the steady state is kept within 5% of the desired value.

********* Good Luck************

********* Good Luck************

********* Good Luck************

********* Good Luck************

********* Good Luck************

********* Good Luck************

********* Good Luck************