Machine Design, Mechanisms, Vibrations and Manufacturing — Practice

Question 1

Find the degrees of freedom of a planar four-bar linkage.

Accepted Answer

F = 3(4 - 1) - 2(4) = 1.

Question 2

By what factor does the life of a ball bearing change if the load doubles?

Accepted Answer

Life falls to one-eighth, since L10 is proportional to (C/P)^3.

Question 3

A tool lasts 60 min at 100 m/min with n = 0.25. Find its life at 120 m/min.

Accepted Answer

T = 60 x (100/120)^4 = 28.9 min.

Question 4

Annual demand is 1200 units, ordering cost Rs 50 and holding cost Rs 6 per unit per year. Find the EOQ.

Accepted Answer

EOQ = root(2 x 1200 x 50/6) = root(20000) = 141 units.

Question 5

A mass of 4 kg is on a spring of stiffness 400 N/m. Find the natural frequency.

Accepted Answer

omega n = root(400/4) = 10 rad/s, about 1.59 Hz.

Question 6

A component has Se = 200 MPa and Sy = 400 MPa, with sigma a = 80 and sigma m = 100 MPa. Find the factor of safety by Soderberg.

Accepted Answer

1/FoS = 80/200 + 100/400 = 0.4 + 0.25 = 0.65, so FoS = 1.54.

Question 7

Chip thickness ratio is 0.5 and the rake angle is 10 degrees. Find the shear angle.

Accepted Answer

tan(phi) = 0.5 cos10/(1 - 0.5 sin10) = 0.4924/0.9132 = 0.539, so phi is about 28.3 degrees.

Question 8

State Chvorinov's rule and a consequence for riser design.

Accepted Answer

Solidification time is proportional to (V/A)^2, so the riser needs a larger volume-to-area ratio than the casting so that it freezes last.

Practice — Machine Design, Mechanisms, Vibrations and Manufacturing