Bending Stress RS Khurmi

Ω1 – ω2 = 2% ω = 0.02 ω and coefficient of fluctuation of speed, CS = 1 2ω − ω ω = 0.02 Let I = Mass moment of inertia of the flywheel in kg-m2. We know that maximum fluctuation of energy (ΔE), 12 230 = I.ω2.CS = I (31.42)2 0.02 = 19.74 I ∴ I = 12 230 / 19.74 = 619.5 kg-m2 Ans. 22.7 Stresses in a Flywheel Rim A flywheel, as shown in Fig. 22.9, consists of a rim at which the major portion of the mass or weight of flywheel is concentrated, a boss or hub for fixing the flywheel on to the shaft and a number of arms for supporting the rim on the hub.

The following types of stresses are induced in the rim of a flywheel: 1. Adjprog l220. Tensile stress due to centrifugal force, 2.

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Tensile bending stress caused by the restraint of the arms, and 3. The shrinkage stresses due to unequal rate of cooling of casting. These stresses may be very high but there is no easy method of de- termining. This stress is taken care of by a factor of safety. We shall now discuss the first two types of stresses as follows: 1. Tensile stress due to the centrifugal force The tensile stress in the rim due to the centrifugal force, assuming that the rim is unstrained by the arms, is determined in a similar way as a thin cylinder subjected to internal pressure. Let b = Width of rim, t = Thickness of rim, Flywheel „„„„„ 789 A = Cross-sectional area of rim = b × t, D = Mean diameter of flywheel R = Mean radius of flywheel, ρ = Density of flywheel material, ω = Angular speed of flywheel, v = Linear velocity of flywheel, and σt = Tensile or hoop stress.

Consider a small element of the rim as shown shaded in Fig. Let it subtends an angle δθ at the centre of the flywheel.

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