SECTION A DYNAMICS Question 1 (a) What is the difference between a forced vibration and a free or natural vibration? [2 marks] (b) Describe an experiment to measure the effects of an out of balance rotating mass, e.g. an unbalanced road wheel and tyre on vibration. Is this a forced or natural vibration? (c) The front suspension of an automobile consists of an upright and two unequal wishbones. The upright is 250 mm, the lower wishbone 250mm and the upper wishbone 200 mm long. Draw a diagram of the suspension system at the instant when the upright is exactly vertical and the wishbones exactly horizontal. If the angle between the lower wishbone and the horizontal is changing at 0.5 deg/s angular velocity and 0.5 deg/s/s angular acceleration, calculate the instantaneous velocities and accelerations of the pin joint linking the upright and the upper wishbone. [15 marks] Question 2 (a) What are Inertial Forces and how do they constrain the design of mechanisms? How can the rpm limit of an Internal Combustion engine be increased? [10 marks] (b) A piston-and-cylinder mechanism is connected to a crankshaft. The crank is 50mm long, the connecting rod 250 mm long and the piston has a mass of 150g. If the engine speed is ω rad/sec and the crankshaft torque T Nm, calculate:- i) Maximum inertial force between the piston and connecting rod ii) Maximum force in the connecting rod [7 marks] Page 1 of 5
Question 3 (a) Explain why automobile suspensions are under damped. Why is the suspension a compromise between peak overshoot and setting time? (b) Sketch the dynamic response of a second-order system to a step input. Define the peak overshoot and settling time clearly.. (c) A 4-wheel road vehicle has a mass of 2000kg. Calculate suitable values for suspension spring stiffness and damping coefficient for each wheel. Explain any assumptions you make. Page 2 of 5
SECTION B - MICROPROCESSORS Question 4 (a) An 8 bit microprocessor has 16 wires on the address bus. i) Assuming the reboot address is 0000Hex, draw a memory map for 8k ROM and 2k RAM. ii) Design an address decoding circuit for your memory map. [7 marks] (b) The RAM is to be expanded to a total of 16k. Calculate a new memory map and design a new address decoding circuit. (Note that you may assume the original RAM is replaced with a single, larger chip ). Question 5 (a) What is a Software gearbox? [5 marks] (b) Draw a block diagram of a software gearbox used in either an aircraft fly-by-wire system or an automobile engine management system. (c) Explain the advantages and disadvantages of a software gearbox, compared with purely mechanical systems. Question 6 (a) Explain how four strain gauges, a seismic mass and a cantilever beam can be used to measure accelerations. How could a PC be used to capture the data? (b) How could a PC be used to control four LEDs from four switches? (c) What is a microcontroller? How are they programmed? Page 3 of 5
SECTION C - CONTROL Question 7 (a) Explain the difference between Nyquist and Bode diagrams. What are they used for? Which axis is calibrated in db and why? (b) Draw a block diagram of a PID controller used for a central heating system. Explain how the PID concept improves both steady state and step response. How does the system zero change the system stability? [8 Marks] (c) Given that the heating system is first order with G(s) = 10/(s+3), find the overall system poles and zeoes. Question 8 A steel rolling mill uses an electric motor to control the distance between two large rolls. The pair of rolls will reduce the thickness of the hot steel passing between them. A gauge is used to measure the thickness of the steel and a summing junction calculates an error signal, which is amplified and used to power the electric motor. The time taken for the steel to move from the rolls to the thickness gauge causes a time delay of T seconds in the feed back loop. If the steel travels at 1m/s calculate the maximum distance between the rolls and the measuring gauge, given the open loop transfer function is : G(s)H(s) = 100e -st /(s(s+4)) Hint:- Assume e -st ( 1-sT ), for small T. [25 marks] Page 4 of 5
Question 9 Draw a simple block diagram of the suspension system for a two-wheel motorcycle. You should include two springs, two shock absorbers, two unsprung masses (representing the wheels etc ) and two tyres with stiffness and damping. (a) How many degrees of freedom does the simplified suspension system have? [1 mark] (b) Derive the equations of motion as a set of simultaneous differential equations, but do not attempt to solve them. (c) Define some suitable state-space variables and rewrite the equations of motion in terms of your chosen state-space variables. (d) Define system inputs and outputs and rewrite your equations of motion in matrix form. Question 10 An aircraft autopilot can maintain an aircraft in straight and level flight. (a) How many degrees of freedom must the autopilot control? [2 marks] (b) (c) How many control surfaces can the autopilot adjust? Define some suitable state-space variables. [5 marks] (d) Write down the general form of the state space equations, as matrices. Do not forget to include feedback in your answers. Examiner: Dr R.C. Edney External examiners: Professor M. Imregun Professor D.I.A. Poll Page 5 of 5