1.A 400 day clock contains a torsional oscillator/resonator that takes 30 s to rotate between its two positions of maximum angular displacement. This resonator consists of a flywheel with a mass of 400 g and radius of gyration of 60 mm which is suspended from a steel wire with a nominal length, l, of 120 mm and which acts as a torsional spring. The mainspring that powers the clock provides a small amount of energy to the resonator during each cycle in order to maintain a constant amplitude of oscillation.
Torsional stiffness of a beam:
2nd moment of area of a circular solid bar:
a)Calculate the diameter of the suspension wire assuming that the modulus of rigidity, G, of steel is 80 GPa. [7 marks]
b)Neglecting the effects of friction elsewhere in the clock, and stating any other assumptions made, explain how you might estimate what the required total energy stored in the clock mainspring must be in order to ensure that there is sufficient power to run the clock for 400 days. [3 marks]
c)As the clock is very sensitive to external vibration it is to be suspended on springs to isolate it from any vibration of the shelf it is placed on. The total mass of the clock is 2 kg and the magnitude of the external vibration must be reduced by at least a factor of 5 at frequencies above 20 Hz. What is the maximum stiffness of the suspension springs? [8 marks]
Describe how the spring supported clock would respond to vibration of the shelf at frequencies varying between 0 and 20 Hz.
1.You are designing the crankshaft for a small single cylinder air compressor with a piston stroke of 50 mm.
a)The mass of the crankpin, which is 100 grams, is causing the crank to be out of balance. Assuming that the overall diameter of the crankshaft cannot be greater than 80 mm, calculate the minimum mass of additional material required to correct the imbalance in the crankshaft and state where it should be positioned. [5 marks]
b)The piston designer now tells you that it will weigh 100 grams, and will be connected to the crankpin by a connecting rod which has a length of 75 mm and weighs 120 grams. Calculate the primary and secondary reciprocating forces at the design speed of 6000 rpm. [5 marks]
c)Determine how the correction you previously calculated for the crank balance should be altered to take account of this new information in order to minimise the total out of balance forces within the system. [5 marks]
By considering both the gas pressure on the piston and the acceleration forces due to its reciprocating motion it is determined that the maximum compressive force the connecting rod must withstand is 1000 N. Describe the process you would apply in order to evaluate whether it could withstand this force, stating what further information would be required to complete this analysis.