Inversion of the Modified Universal Slopes Equation for Real Time Monitoring of Fatigue Life Expenditure

A straight forward algorithm for inverting the Muralidharan-Manson Modified Universal Slopes Equation (MUSE) has been developed to convert stress or strain data taken in real time from components in operation. The relationship has been applied to the development of a Service Life Measurement System (SLMS) for real time monitoring of fatigue life of critical aircraft components. By matching the component material strain-range/life-cycles relationship to three points in the high-cycle regime and to two points in the low-cycle regime, a curve-fit equation is generated that states total number of life-cycles Nf as a function of strain range and five curve-fit parameters. Since one of the parameters in the high-cycle regime permits infinite cycles at finite strain range, the equation is applicable to both endurance limit and non-endurance limit materials. A match was obtained for all of the 47 alloys listed in the original Muralidharan-Manson ASME paper [1], to within 4% over a life-cycle range of 10 to 107 cycles. Since the inverse MUSE (iMUSE) equation is obtained from a fit to points taken from a curve, as opposed to an original equation, it also can be generated for any typical S-N fatigue plot derived empirically or analytically. To demonstrate the viability of the underlying algorithm, a SIMULINK® simulation of the algorithm, operating in conjunction with the Matsuishi-Endo rainflow data sorting algorithm [2] was implemented. Taking a prerecorded temporal stream of strain data as a simulated component in operation, the SLMS SIMULINK® simulation sorts the data in real time into max-min strain range cycles and then outputs a corresponding evolution of component remaining fatigue life as a function of time. This straight forward algorithm promises to substantially improve maintenance event scheduling tasks for vehicle owners who are required to schedule maintenance events on the basis of evidence of need.