NAFEMS Benchmark Challenge - No 8
Calculation of the Hoop Burst Speed for Rotating Discs
Rotating discs are often, particularly in turbomachinery applications, highly stressed components containing significant kinetic energy which, if the disc bursts, has the potential to cause serious damage.
The design methodology for such discs is based upon an empirically derived formula that is based on the idea that discs burst when the average hoop stress reaches the ultimate tensile strength (UTS) of the material.
It is that case, because it can be shown theoretically, that parallel sided discs do become unstable when the average hoop stress reaches the yield stress. However, this theory does not extend to tapered discs or to the wide variety of disc geometries seen in industrial turbomachinery. It is also noted that the theory is based on the Tresca yield criterion which, whilst more conservative than the von Mises criterion, has long been known not to represent well the plastic behaviour of ductile metals - the von Mises criterion provides a far better representation of reality.
The approach adopted in industry for the design of arbitrarily shaped discs is to use the theoretical formula for the burst of parallel sided discs but to modify it by factoring down the UTS significantly and often to an extent that the 'failure' stress is then less than the yield stress. Whilst this approach might be safe, the degree of conservatism is not known and this should be of concern to engineers working in this field.
Angus Ramsay, the author of this challenge, worked in the Turbomachinery industry for some 10 years and was always concerned with the approach adopted because of the lack of any observable theoretical basis for it. This challenge was deliberately set in order to investigate further the theoretical basis for the formula used and it has been shown that it does indeed owe little to science and more to the propagation of folklore.
Project: Design against Burst of Rotating Discs.