Relative statistical evaluation of printed circuit boards mechanical characteristics technological non-uniformity

Аuthors

Krylov V. P.^*, Pronin T. Y.^*

State University named after Alexander and Nikolay Stoletovs, 87, Gorky str. Vladimir, 600000, Russia

*e-mail: pronin_t_y@list.ru

Abstract

A model of statistical factor analysis was applied for a batch of 12 samples of glass-epoxy double-sided and multilayer printed circuit boards (PCBs) to examine the engineering tolerance of the average values of elastic modulus and mechanical loss coefficient. Experimental estimates of the variations were obtained in the form of ratios of standard deviations of the technological and measuring errors.

Samples of various thickness with a shape of rectangular plates with 130 by 60 mm size were alternately secured in the fixture on a vibrating table by the four screws on the corners. Registration of frequency characteristics near the first resonance was performed with the IMV shaker i220 in the sinusoidal vibration mode within the frequency range of 5 ... 2000 Hz with a vibration acceleration of 2 g. In this frequency range the device has no natural resonances.

The measurement cycle consisted of two series of measurements of each sample, performed within one working day, with one-hour interval between each series. Three cycles were performed: before and after the heat treatment in a convective reflow oven, and after 6 months of storage at room temperature.

The numerical values of the mechanical characteristics were measured by solving inverse ill-posed problems using SolidWorks Simulation program. The calculated model of factor analysis assumes the random nature of technological and measuring errors, as well as a linear correlation between the series of measurements. The Pearson correlation coefficient uniquely determines the relative statistical evaluation of the technological error of the aforementioned mechanical characteristics of the PCBs within the batch.

The relative estimate of the elastic modulus variation equals to 14 and does not depend on the heat treatment and storage within the confidence interval of the sample value of the correlation coefficient. The corresponding estimate of the variation in the coefficient of mechanical loss, initially equal to 3, increases by more than 50% after the heat treatment and returns to its original values after storage.

Recommendations on the application of the results obtained while the vibration strength testing of electronic devices of the unmanned spacecraft are given.

Keywords:

printed circuit boards, mechanical characteristics, technological error, measurement error, statistical evaluation

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