In high speed turbomachinery, the discs which support the blades are highly loaded structural members. The kineticenergy in discs is considerable and whilst designed to avoidburst failure, if this occurs the surrounding structure is oftennot strong enough to contain the disc fragments, e.g,

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The primary loading faced by a turbomachinery disc is thatinduced by rotation. This includes centrifugal self-loading anda radial load at the periphery due to the centrifugal loading ofthe attached blades and such loading induces stresses in thedisc that are proportional to the square of the angular velocityω. Although, the detailed design of a disc might includeconsideration of a range of potential failure mechanisms like,for example, low cycle fatigue induced by thermal andmechanical cycling, the basic disc shape is governed by thebasic strength requirement to resist circumferential or hoopburst. Whilst hoop burst of a rotating disc is a phenomenoninvolving material plasticity and large displacements andstrains, a rather simple approach, based on a linear-elasticanalysis of an axisymmetric model of the disc, has been shownto provide sufficiently accurate predictions of the burst speedfor the purposes of initial design. The method is attributed toRobinson and is discussed on p50 of Chianese Stefano’s 2011Master’s thesis:
Robinson, E.: Bursting tests of steam-turbine disk wheels.Trans. ASME 66, page 373, 1944. & nafe.ms/2jSTNrBHoop burst involves the circumferential or hoop stress σhwhich varies over the generator plane of the disc. Robinson’smethod requires the area weighted average hoop stress (~σh ) tobe calculated for a given angular velocity ω. The angularvelocity to cause the disc to burst is given in terms of theultimate tensile strength, σUTS, of the material.

The reader is asked to use his/her finite element system to determine the angular velocity to cause the two discs ofFigure 1 to burst based on a UTS of 1000MPa. For this study, no radial loads due to blades are considered. For theparallel sided disc the theoretical solution based on the Lamé equations can be used for software verification – see forexample, Hearn, E.J., Mechanics of Materials, 3rd Edition, Butterworth-Heinemann, 2000. The second, tapered, disc hasno theoretical solution and solution verification will need to be used to ensure that the mean hoop stress calculated bythe axisymmetric finite element model has converged sufficiently.