Determine the velocity ratios that can be achieved by the

Question

Question 1:

It is required to design and assemble a planetary gear box for the operation of a machine in a production plant. The only annular wheel available contains 60 teeth and it has a modulus of 1 mm. The operation of the machine requires two output shafts from the gear box.

When one output shaft is engaged, the other one is put to rest using clutches. The velocity ratios required by the two outputs are as follows.

i) Determine the velocity ratios that can be achieved by the gear box in terms of number of teeth in the sun wheel (ts).

ii) Determine which component (out of the sun wheel, planet carrier and annular wheel) has to be used as the input shaft to get the required velocity ratios. Explain the reasons for your selection.

iii) Calculate the possible values for the number of teeth in sun wheel. Obtain the values for number of teeth in planetary wheels for each case and conclude the only possible value for the number of teeth in the sun wheel.

iv) One output shaft of the gear box is coupled to a gear wheel with 20 teeth and Moment of Inertia of 1 kgm² . This wheel is meshed with another gear to get a velocity ratio of 1:4. This second gear has a Moment of Inertia of 5 kgm². Calculate the torque that should be exerted by the output shaft to obtain an angular acceleration of 6 rad/s².

Question 2:

A screw jack has a thread diameter of 30 mm and a 6 mm pitch. The handle used is 500 mm long. If the friction coefficient is 0.15;

i) Calculate the velocity ratio and force ratio when a load is lifted.

ii) Calculate the mechanical efficiency of the screw jack.

iii) It is suggested to design a screw thread to obtain maximum efficiency for the jack.

Calculate the helix angle which gives the maximum efficiency for the screw jack with the same friction coefficient. Discuss the drawbacks if this screw thread is to be used in a screw jack.

Question 3:

A turning moment diagram for a single cylinder four stroke engine is drawn. The scaled drawing indicates following areas around the mean torque line.
Exhaust stroke = 650 mm²
, Suction stroke = 400 mm²
, Compression stroke = 1500 mm²

i) Calculate the area of the diagram for the power stroke above the mean torque line.

ii) Each 1 mm² represents 3 J. If the engine rpm has to be maintained between 198 and 202, calculate the Moment of Inertia of the flywheel.

iii) If the mass of the flywheel is 24 kg calculate the radius of gyration.

Question 4:

i) Explain how Hooke's joints are used in automotive transmission systems specifically highlighting the use of two Hooke's joints in a single shaft.

ii) For any fixed angle between shafts, what is/are the rotation angle(s) which give(s) the maximum velocity ratio? Support your answer with a direct proof.

iii) On the same graph plot the fluctuation of the velocity ratio of a Hooke's joint when the angles between the shafts are 150, 300, 450and 600 and comment on the maximum and minimum speed fluctuation.

Question 5:

A constant acceleration cam has to be designed such that it gives a 20 mm rise to a flat foot follower within the motion of 700. This rise should contain equal acceleration and deceleration.

Then it should dwell for 600 and fall in the same manner. If the rotation speed of the cam is 60rev/min;

i) Calculate the constant acceleration of the rise.

ii) Clearly stating the steps followed, draw the cam profile if the base circle radius is 80 mm. (You may use manual methods or CAD software, but clearly indicate the construction lines. If CAD software is used, a properly generated drawing should be attached; screenshots are not accepted.)

Question 6:

An internal combustion engine drives a slider-crank mechanism which has a crank length of 50 mm and connecting rod length of 170 mm. The constant rotation speed of the crankshaft is 300 rev/min.

i) Derive equations for the velocity and acceleration of the slider (piston) assuming that the crank length is small compared to the connecting rod.

ii) Calculate the angular velocity and acceleration of the connecting rod when the rotation angle is 400 using relative motion vector diagrams.

iii) Draw the mechanism to a scale and use the instantaneous centre and Klein's construction and determine the quantities calculated in (ii). Compare your results and comment on them.

iv) The equivalent piston mass is 3 kg. Plot the variation of the primary force and secondary force with the rotation angle of the crank in the same graph. Comment on the significance of each of the forces.

Question 7:

The rotor blades of a helicopter have a moment of inertia of 40 kgm² about the vertical axis. These blades are brought to rest from its maximum angular velocity of 100 rev/min, at a constant angular acceleration in 15 seconds. In the meantime, the pilot gives it a constant angular acceleration around longitudinal axis starting from rest and until it reaches 2 rev/min in 15 seconds.

i) Plot the graphs of

a. Angular velocity of blades vs. time

b. Longitudinal angular velocity of the helicopter vs. time

ii) Obtain a graph for the gyroscopic torque applied on the helicopter vs. time and find its maximum value. In a clear sketch show the direction of rotation of the blades and helicopter and the direction of the gyroscopic torque. Explain the effect of this torque on the system.

Attachment:- dynamics-of-machines.pdf