History of Evolution, Progress and Application of Safe Diagram for Tuned and Mistuned Systems

Concept of Safe diagram was introduced 30 years ago (Singh and Schiffer, 1982) for the analysis of the vibration characteristics of packeted bladed disc for steam turbines. A detailed description of Safe diagram for steam turbine blades was presented 25 years ago in the 17 th Turbo Symposium (Singh et. el, 1988). Since that time it has found application in the design and failure analysis of many turbo machineries e.g. steam turbines, centrifugal compressor, axial compressor, expanders etc. The theory was justified using the argument of natural modes of vibration containing single harmonics and alternating forcing represented by pure sine wave around 360 degrees applied to bladed disk. This case is referred as tuned system. It was also explained that packeted bladed disc is a mistuned system where geometrical symmetry is broken deliberately by breaking the shroud in many places. This is a normal practice which provides blade packets design. This is known as deliberate geometrical mistuning. This mistuning gave rise to frequency of certain modes being split in two different modes which otherwise existed in duplicate. Natural modes of this type construction exhibited impurity i.e. it contained many harmonics in place of just one as it occurs in a tuned case. As a result, this phenomenon gives rise to different system response for each split mode. Throughout the years that have passed, Safe diagram has been used for any mistuned systemrandom, known or deliberate. Many co-workers and friends have asked me to write the history of the evolution and of the first application of this concept and its application in more general case. This paper describes application of Safe diagram for general case of tuned system and mistuned system.