Margin Requirements and Input Level Formulation in Dynamic Testing of ECS

Abstract

Historical and current governmental standards and regulations for aerospace ECS dynamic testing are reviewed. It is found that the test margins ranging from +4.5 dB to +6.0 dB over MPE and triple MPE duration for qualification are reasonable, so does the intent of using these level/duration for lot acceptance and service life extension tests as a stress test in offsetting the streamlined test sample size, for enhanced reliability. These measures have been adopted in AIAA Standard S-113-2005 1 . Applications of four common statistical distributions are examined in detail. The shortcomings of the lognormal distribution and merits of log-uniform distribution are identified. Methods for reduction of input dynamic levels are explored and illustrated. These include wave attenuation, equivalent attenuation by mechanical joints and mass loading effects. Ample of reductions are feasible which in turn can reduce the overall test levels required. Improvements of current methodologies and corrections of many common error types are suggested and illustrated. Nomenclature A = Peak acceleration (sinusoidal), g ave = Average value of data points in a discrete data set cdf = Cumulative Distribution Function ECS = Energetic Components and Systems Log-Uniform = Distribution in which natural logarithmic value of the variable is uniform K.D.F. = Knock Down Factor, -dB mean Average value in a continuous distribution M = Margin factor over MPE for R/C = 99/90 in a discrete data set; Loading mass MPE = Maximum Predicted Environment N = Number of data points in a data set; or number of data sets not to be exceeded n sigma = Number of standard deviations in a continuous distribution n sigma, 99/90 = n sigma for cdf corresponding to R/C = 99/90 n sigma, 95/50 = n sigma for cdf corresponding to R/C = 95/50 n std = Number of standard deviations in a discrete data set n std, 99/90= n std corresponding to: ave + n std *std mean + n sigma, 99/90 *sigma n std, 95/50 = n std corresponding to: ave + n std *std mean + n sigma, 95/50 *sigma P = Probability of not-to-exceed a value defined by N data points per a distribution pdf = Probability Density Function PSD = Power Spectral Density, g 2 /Hz R/C = Reliability/Confidence, in percentages sigma = Standard deviation in a continuous distribution SRS = Shock Response Spectrum, g std = Standard deviation of data points in a discrete data set Uniform = Uniform distribution with permitted sigma excursion per Normal distribution