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Cork Institute of Technology
Bachelor of Engineering in Mechanical Engineering- Award
(EMECH_7_Y3)
Summer 2008
Mechanics of Machines
(Time: 3 Hours)
Instructions Answer FOUR questions. All questions carry equal marks.
Examiners: Mr. A. Bateman Dr. P. Delassus Dr. F. S. Murphy
Q1. (a) Show that for a flat belt experiencing the centrifugal effect:
T 1 − mv^2
T 2 − mv
2 =^ e
μθ
where m = mass per unit length of the belt material and v = belt velocity. (10 marks)
(b) A belt transmits 20 horsepower from a pulley 0.9 m diameter, which runs at 300 rev/min. The angle of embrace of the belt and pulley is 160° and the coefficient of friction between belt and pulley is 0.25. The belt is 6.4 mm thick and has a density of 1107. kg/m^3. Determine the minimum belt width for a maximum belt stress of 2 MPa. (15 marks) (1 horsepower = 746 watts)
Q2. A motor vehicle has a mass of 1400 kg. The wheel radius is 0.3 m. The vehicle is equipped with four disc brakes, each comprising a circular disc attached to the wheel axle, upon which friction pads press from both sides at a mean radius of 0.11 m as shown in Figure (Question 2). The ‘active’ pad is actuated by a pressure cylinder of diameter 20
mm. The maximum pressure in the cylinder is 80 MPa. The friction coefficient between disc and pads is 0.1.
Figure (Question 2)
Assume equal effective braking on all four wheels and that the wheels do not skid. The vehicle is traveling at 30 m/s on a straight level road. Average wind resistance is 650 N. (a) Calculate the least distance in which the vehicle can be brought to rest. (15 marks) (b) Calculate the least distance in which the vehicle can be brought to rest when travelling down a hill of 1 in 10, the other conditions remaining the same. (10 marks)
Q3. (a) A helical spring is attached at one end to a rigid support and has a mass M at its free end. The free end of the spring is connected to a dashpot so that, as the mass vibrates vertically, the resistance of the fluid in the dashpot opposes the motion of the mass. With regard to this spring mass system, describe with sketches the three cases of (i) over- damping (ii) critical-damping (iii) under-damping. (10 mark (b) A spring-mass-damper system has a stiffness k = 56 kN/m and mass m = 40kg. The actual damping provided is 20 percent of critical. Determine the value of the logarithmic decrement. (15 marks)
Determine (a) The speed of G. (10 marks) (b) The torque on F. (10 marks) (c) The torque on G. (5 marks)
Q5. The drive shaft on an outboard motor rotates at speeds up to 5000 rev/min. It is supported by a spline in the crankshaft at the upper end and a bearing at the lower end, as shown in the Figure (Question 5).
Figure (Question 5)
The drive shaft is 13 mm diameter and 559 mm (22 inches) between supports. The maximum shaft deflection is given by δ = 0.0054 wl
4 EI where w is the weight per unit length of the shaft. The density of the shaft material is 7751 kg/m^3. The modulus of elasticity (E) for the shaft material is 207 GPa. (a) Determine the power developed by the engine if the allowable shear stress for the shaft is 83 MPa. (10 marks) (b) Check that the critical speed of the shaft is above 5000 rev/min. (15 marks)
Q6. A conical clutch is to have a mean diameter of 387 mm and a semi-vertex angle of 15°. It is to transmit 29.8 kW at 700 rev/min under a spring load of 2670 N. The maximum torque transmitted is to be 1.5 times the mean torque. The length of the conical surface is 76 mm. (a) Determine the coefficient of friction required at the contact surfaces. (10 marks) (b) Determine the maximum pressure on the linings. (10 marks) (c) Derive any formula used. (5 marks)
