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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

Case Study: consider a shaft-disc system, as shown in [Fig 2.87]. The shaft is given an angular
velocity ‘Ω’, about the ‘x-axis’. The shaft-disc system is a part of an assembly which precesses about
the ‘y-axis’. Assume the inertia of the disc-shaft system to be ’I’ about the axis of spin and the shaft
and disc to be rigid. The platform remains perfectly horizontal. Find the vertical bearing reactions.

[Fig 2.87: a rotating shaft disc system on a precising platform]

Solution: the loads considered are as follows:

1) Gyroscopic moment
2) Weight of the shaft (Mg) and that of the disc (mg)

Let us start by writing the FBD of the shaft, as shown in [Fig 2.88].

[Fig 2.88: FBD of the disc mass system without the gyro effect]

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 95 age 95
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