ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

Memorial University Faculty of Engineering and Applied ScienceENGI7945 Machine Dynamics Final ExamWinter'09 - Prof. G. RideoutThursday, April 16, 9:00-11:30 AM - Value 40%

Attempt all questions. Read all questions carefully.

Q1: 10 marks; Q2: 10 marks; Q3: 10 marks; Q4: 10 marks - Total 40______________________________________________________________________________________

1. Figure 1 below shows a plot of the load torque ("-TL") of a punching operation, which has been

approximated as a series of triangular areas. The load is periodic over a cycle of period 2 radians.Assume equal intervals of /4 rad in Figure 1, with triangle peaks in the middle of each interval.

The punch is to be driven by a motor spinning at 1750 rpm, but the punch mechanism crankshaft is torotate at 120 rpm. In an attempt to make the flywheel smaller, the flywheel is to be mounted on themotor shaft, from which power is transmitted to the punch crankshaft via a single gear pair as shown inFigure 2.

Figure 1 - Load torque magnitude

Figure 2 - Shaft arrangement

a) Determine the required motor power and torque (3 marks).

b) Determine the required flywheel inertia (in units of kg-m2) to achieve a speed fluctuation coefficient of0.05 for a mean punch speed of 120 rpm. (5 marks)

c) Find minimum and maximum flywheel speeds during the cycle. (2 marks)

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

2. The vehicle in Figure 3 below is traversing a curve with mean radius 100 m, at forward velocity v in thedirection shown. The vehicle mass is 1400 kg, and the centre of mass is 450 mm above the road. Thecar's track width (lateral distance between left and right tires) is 1.5 m, and the centre of mass ismidway between the left and right wheels.

Each wheel/tire has a moment of inertia about its spin axis of 1.6 kg-m2. Assume each wheel has thesame rotaitonal speed, and rolls without slipping. Each wheel has a mean diameter of 600 mm.

The car's engine is in the rear, and it is laterally mounted as shown in the cutaway drawing. The

engine's crankshaft has a moment of inertia of 0.85 kg-m2 about an axis parallel to the spin axis of thewheels. Assume the engine's crankshaft spins in the same direction as the wheels. The gear ratiobetween the engine and rear axle is 3:1, meaning that the engine speed is 3 times the wheels' angularvelocity.

a) Determine the total gyroscopic moment on the car due to the rotation of the wheels and the engine'scrankshaft, in terms of v. Does this moment reinforce, or does it counterbalance, the tendency of thecar to roll outward as it rounds the curve? (5 marks)

b) Assuming the road is flat, and assuming a negligible car body roll angle, determine the maximumspeed v with which the car can round the curve without the inside wheels lifting off the ground. (5 marks)(Hint: a free-body diagram of the car as viewed from the front may help.)

Figure 3 - Car rounding circular track

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

3. A Vee-twin engine with 90o crank separation is shown in Figure 4. Both cylinders make an angle of

45o with respect to the horizontal, and have crank length R, connecting rod length L, and reciprocatingmass m. The engine runs at constant speed .

a) Determine primary and secondary shaking force vectors. (5 marks)b) Your primary shaking force magnitude should be in the form

tqtpmRFSP sincos2

where the p's and q's are constants.

Rewrite FSP as a phased sinusoid using the following equivalence:

γθsinqpθsinqθcosp 22

where phase angle = tan-1(p/q). (2 marks)

c) Schematically sketch a means of balancing the primary shaking forces, indicating number of shafts,orientation, and size of unbalances.. (3 marks)

Figure 4 - Vee-twin with 90-degree crank throw

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

4. For the mechanism shown in Figure 5 below, formulate the inverse dynamic equations to predict inputtorque , and reaction forces and moments for a given motion of link 2. Assume loop analysis has beencompleted and all positions, velocities and accelerations are known. Assume no friction in the linearbearing, or between the pin and slot.

a) Draw free body diagrams of each link (5 marks) b) Write dynamic equations, identify unknowns, and write the equations in matrix vector form (5 marks).

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Vector Loop

Figure 5 - Mechanism and vector loop

ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

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ENGI7945 Machine Dynamics Final Exam, Winter 2009 Name:Student No.:

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