A metal tank wheel in the shape of a disc of radius R is lightened by cutting out six identical through- holes in the shape of discs, whose axes are parallel to the wheel’s axis of rotation, and whose radii are all r. The holes’ centers are positioned at the vertices of a regular hexagon of side A, with the wheel’s axis passing through the center of the hexagon. By what percentage is the wheel’s moment of inertia decreased around its rotation axis, as a result of the cut outs, for r=R/5 and A=3R/5? Is the solution: 18.24% (using negative mass for cutouts and parallel axis theorem)?
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
Given question:
A metal tank wheel in the shape of a disc of radius R is lightened by cutting out six identical through- holes in the shape of discs, whose axes are parallel to the wheel’s axis of rotation, and whose radii are all r.
The holes’ centers are positioned at the vertices of a regular hexagon of side A, with the wheel’s axis passing through the center of the hexagon.
We have to find the percentage decrease in the wheel's moment of inertia around its rotation axis as a result of the cut outs.
Given r= R/5 and A = 3R/5
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