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Semester 2 Examinations 200 9 / 20 10
Exam Code(s) 1 BM, 1 BG, 1BN, 1BP, 1BEI, 1BEE, 1BSE, 1EG Exam(s) 1 st Engineering (Mechanical, Biomedical, Electronic, Electronic and Computer, Sports and Exercise, Engineering Innovation – Electronic, Energy Systems, Undenominated) Module Code(s) ME Module(s) Fundamentals of Mechanical Engineering Paper No. Repeat Paper External Examiner(s) Prof. Noel O’Dowd Internal Examiner(s) Prof. Sean Leen, Dr. Nathan Quinlan * Instructions: Answer Question 1 and 2 other questions. All questions carry equal marks. Duration 2 hours No. of Pages Department(s) Mechanical and Biomedical Engineering Course Co-ordinator(s) Dr. Nathan Quinlan Requirements: Statistical/ Log Tables yes Graph Paper yes Release to Library: yes
Question 1 is mandatory. 1 Answer the following questions about the design-build-test project you completed for this course. (a) Briefly describe your main contributions to your team’s analysis, design and development efforts. ( 8 ) (b) If you were to repeat this project, what would you do differently? In other words, what did you learn from the experience? (6) (c) Describe one example of how scientific and/or mathematical analysis played a part in your team’s design. (6)
3 An engine drives a winch through a gear train, as shown schematically in Figure Q 3. A cable wound on the winch is used to raise an object of mass 44 kg. The system is initially at rest. At time t = 1 s, shortly after the engine is started, the torque and speed are measured at the engine as 36 Nm and 80 rpm respectively. gear 2 (60 teeth) engine 4.4 kg gear 1 (18 teeth) Ø301 mm winch gear 2 (60 teeth) engine 44 kg gear 1 (18 teeth) Ø winch gear 2 (60 teeth) engine 4.4 kg gear 1 (18 teeth) Ø301 mm winch gear 2 (60 teeth) engine 44 kg gear 1 (18 teeth) Ø winch Figure Q3 Engine, gear train and winch. (a) Calculate the rotational speed of the winch and the torque on the winch at time t = 1 s. ( 6 ) (b) Calculate the linear speed and acceleration of the 44 - kg object at time t = 1 s. (6) (c) Some time later, the weight is observed to be rising at a steady speed (i.e. with zero acceleration) of 0.35 m/s. Calculate the speed of the engine and the torque on it in this condition. (8)
4 Figure Q4 shows a performance curve for a DC motor operating at constant voltage. The motor will be used to power a 800-kg vehicle with a gear ratio k (ratio of roadwheel speed to motor speed) of 1/4 and roadwheel diameter 430 mm. Throughout this question, neglect friction in all the vehicle’s internal mechanisms, and neglect aerodynamic effects. torque (Nm) speed (rpm) 0 1000 2000 3000 4000 5000 6000 100 80 60 40 20 0 torque (Nm) speed (rpm) 0 1000 2000 3000 4000 5000 6000 100 80 60 40 20 0 Figure Q4 Torque-speed characteristic of a DC motor operating at constant voltage. (a) Based on the shape of the curve in Figure Q4, derive an equation that gives motor torque as a function of rotational speed , maximum speed 0 and stall torque T 0. Hence derive a similar equation for power. ( 4 ) (b) Derive an equation for the equilibrium speed of the vehicle travelling up a slope at an angle to the horizontal, as a function of vehicle mass m , gear ratio k and roadwheel diameter d , as well as 0 and T 0. Sketch a graph of this function, showing speed as a function of gear ratio (with all other parameters constant). ( 6 ) (c) Calculate the roadwheel torque required to drive the vehicle at constant speed up a slope at an angle of 10 ° to the horizontal. (4) (d) Using the equation you derived in part (b) above, or otherwise, calculate the equilibrium speed of the vehicle when travelling up a slope at an angle of 10 ° to the horizontal. (6)
