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In some damping systems, a circular disk immersed in oil
Chapter 2, Problem 111P(choose chapter or problem)
Problem 111P
In some damping systems, a circular disk immersed in oil is used as a damper, as shown in Fig. P9-56. Show that the damping torque is proportional to angular speed in accordance with the relation Tdamping = C ω where C = 0,5πμ(l/a +1/b)R4 Assume linear velocity profiles on both sides of the disk and neglect the tip effects.
Questions & Answers
QUESTION:
Problem 111P
In some damping systems, a circular disk immersed in oil is used as a damper, as shown in Fig. P9-56. Show that the damping torque is proportional to angular speed in accordance with the relation Tdamping = C ω where C = 0,5πμ(l/a +1/b)R4 Assume linear velocity profiles on both sides of the disk and neglect the tip effects.
ANSWER:
Step 1
A circular disc is immersed in a damping oil. The velocity of the damping oil from the circular disk surface to the surface of the chamber of oil changes linearly. We have to prove that the relation between the damping torque and the angular velocity is given by
Where is given by