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DETERMINING THE COEFFICIENT OF THERMAL EXPANSION




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DETERMINING THE COEFFICIENT OF THERMAL EXPANSION OF PRINTED WIRING BOARD COMPONENTS by Tong Wa Chao TC 660H Plan II Honors Program The University of Texas at Austin May, 1998 DETERMINING THE COEFFICIENT OF THERMAL EXPANSION OF PRINTED WIRING BOARD COMPONENTS by Tong Wa Chao TC 660H Plan II Honors Program The University of Texas at Austin May, 1998 Kenneth M. Liechti, Ph.D. Department of Aerospace Engineering and Engineering Mechanics Supervising Professor Mark E. Mear, Ph.D. Department of Aerospace Engineering and Engineering Mechanics Second Reader 3.6 Data Reduction To calculate the coefficient of thermal expansion of the Printed Wiring Board, three groups of data were used: the probe calibration curve, the fused silica calibration curve, and the Printed Wiring Board expansion curve. The slope of the probe calibration curve, k (volts/milli-inch), provided the inverse of the resolution of the probe. The expansion, ∆L, from initial temperature To to temperature T was calculated as ∆L = (V-Vo)/k (3.1) where V = voltage output of the probe at temperature T Vo = voltage output of the probe at initial temperature To The voltage values of the probe were taken into consideration only at stabilized displacements and temperatures to ensure static and thermal equilibrium. The same temperatures and soak times were employed for both the fused silica calibration and the Printed Wiring Board experiment to guarantee proper correspondence. The ∆L’s measured from the fused silica experiment were subtracted from the ∆L’s measured from the Printed Wiring Board experiment. This subtraction removed the undesired expansion of the Invar frame and the probe drift from the overall expansion recorded in the Printed Wiring Board experiment, but had not yet taken into account of the small expansion of the fused silica. ∆LPWBcorrected = ∆LPWBuncorrected – ∆Lfused silica (3.2) Lastly, the coefficient of thermal expansion of the Printed Wiring Board material, approximated by (∆L/∆T)/Lo, was calculated by accounting for α fused silica, the average expansivity of the fused silica over the relevant temperature range (∆L/∆T)/Lo = (∆LPWBcorrected /∆T)/Lo + α fused silica (3.3) 11 where ∆LPWBcorrected /∆T = slope of the curve of calibrated expansion versus temperature change Lo = length of the specimen at initial temperature To Although the Eulerian definition of the coefficient of thermal expansion was (∆L/∆T)/L (where L = Lo + ∆L), (∆L/∆T)/Lo was used because ∆L was so small that it could be assumed that L ≈ Lo. A pictorial explanation of this calibration strategy is shown in Figure 10. 12 4.0 Discussion of Results In this section, results from the calibration of the probe, the calibration of the Invar frame, and the coefficient of thermal expansion experiment are discussed. A calibration curve of the capacitive displacement probe is shown in Figure 7. The calibration was performed at room temperature, and the displacement corresponded very linearly with the voltage over a range of 20 milli-inches as expected. The resolution, given by the inverse of the slope, was 1.91 milli-inches/volt on the day the Printed Wiring Board expansion experiment was performed. Figure 8 shows ...





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