APPLICATION OF DESIGN OF EXPERIMENTS TO EVALUATION THE PROPAGATION SPEED OF Lcr WAVES Cleudiane Soares Santos, Aliandro Henrique Costa Santos, Paulo Pereira Júnior and Auteliano Antunes dos Santos Júnior 1
Objective Study the influence of the variables(temperature, stress applied in the bar and force applied to the probe), involved on performance assessment of the speed of wave propagation critically refracted longitudinal waves (Lcr waves), in a bar structural aluminum 7050, using the Minitab software. 2
Introduction Critically refracted longitudinal waves (Lcr) are obtained after theuseofmeanstorefractwavesparalleltothesurface. incident wave L α 1 α = α 1 = 25.7 β T = 30 β L = 90 transmitter Linking bar receiver acrylic aluminium β L L Lcr Wave acrylic shoes β T transverse T wave Schematic drawing of the generation of waves Lcr (acrylic/aluminium) 3
Introduction Every experiment involves a series of variables with varying degrees of importance to the process under study. The most efficient way to conduct an experiment using a scientific approach is called statistical design of experiments (DOE). Represents a set of experiments established on scientific and statistical criteria. 4
Methodology The approach used in this research was based on DOE techniques. First, we selected the variables that Influence of Lcr wave propagation speed. Next, was realized the experiment as planning matrix and the program developed in LabView software to generate a database, and finally, we used the software Minitab for the analysis of experiments. 1. Selected the variables that Influence of Lcr wave propagation speed 2. Realized the experiment as planning matrix defined 3. Developed program in LabView software to generate a database 4. Used the software Minitab for the analysis of experiments 5
Design of Experiments (DOE) Determination of the parameters of the experiment: Controllable factors and their levels. Factors Low (-1) Medium (0) High (+1) A: Temperature (ºC) 20 22,5 25 B: Stress (bar) 50 75 100 C: Force (N) 22,5 53,9 115,8 The factors that were not controlled during the experiment were kept constant for the reduction of experimental error. We used the same mark (Panametrics) for ultrasonic transducers usedinthiswork,withthesamefrequencyof5mhz. 6
Design of Experiments (DOE) A: Temperature Factor Selected Levels Low (-1) Medium (0) High (+1) A: Temperature (ºC) 20 22,5 25 Average 19,8 22,6 25,5 7
Design of Experiments (DOE) Applied stress at pump [bar] B: Stress Resultant force in the bar [N] (in value absolute) Stress in the center of the bar [MPa] (in value absolute) 50 28274,33 40,39 75 42411,46 60,59 100 56548,67 80,78 Traction device Hydraulic hand pump with digital manometer 8
Design of Experiments (DOE) C: Force Weights used to stabilize the force on the probe Block Mass [kg] Weight Force [N] Config. 1 Config. 2 Config. 3 1 2,3 22,57 x x x 2 2,3 22,57 x 3 3,2 31,40 x x 4 4,0 39,24 x Weight Force [N] 22,57 53,97 115,79 9
Assembly of the Experiments 1 8 6 5 2 4 7 System used to measure the travel time of wave Lcr 3 LEGEND: 1. Computer with data acquisition board A/D 2. Signal conditioner 3. Probe 4. Portable pulser/receiver 5. Traction device 6. Hydraulic cylinders 7. Hydraulic hand pump with digital manometer 8. Aluminium bar 7050 attached with thermocouple 10
Planning Matrix The experimental planning for this work was defined as a full factorial design 3 k = 3 3 (k is the number of factors control of the experiment), resulting in 27 trials, so the Planning Matrix has three levels and three factors. Each test was repeated five times (R1 to R5), totaling 135 results. The repetitions enable the use of hypothesis testing in statistical analysis, which is not the case, but also allow us to estimate the dispersion. 11
Planning Matrix Experiment Factors (order) A (ºC) B (bar) C (N) 1 (12) 22,5 50,0 115,8 2 (22) 25,0 75,0 22,6 3 (3) 20,0 50,0 115,8 4 (27) 25,0 100,0 115,8 5 (2) 20,0 50,0 53,9 6 (24) 25,0 75,0 115,8 7 (20) 25,0 50,0 53,9 8 (5) 20,0 75,0 53,9 9 (19) 25,0 50,0 22,6 10 (11) 22,5 50,0 53,9 11 (14) 22,5 75,0 53,9 12 (13) 22,5 75,0 22,6 13 (16) 22,5 100,0 22,6 14 (26) 25,0 100,0 53,9 15 (21) 25,0 50,0 115,8 16 (9) 20,0 100,0 115,8 17 (10) 22,5 50,0 22,6 18 (1) 20,0 50,0 22,6 19 (4) 20,0 75,0 22,6 20 (17) 22,5 100,0 53,9 21 (6) 20,0 75,0 115,8 22 (25) 25,0 100,0 22,6 23 (7) 20,0 100,0 22,6 24 (15) 22,5 75,0 115,8 25 (23) 25,0 75,0 53,9 26 (8) 20,0 100,0 53,9 27 (18) 22,5 100,0 115,8 12
Experiment (order) A B C R 1 (m/s) R 2 (m/s) R 3 (m/s) R 4 (m/s) R 5 (m/s) Average (m/s) Standard Deviation (adm) 1 (12) 0-1 +1 6247,0 6248,0 6247,8 6248,8 6248,3 6247,98 0,664831 2 (22) +1 0-1 6231,7 6231,9 6232,9 6231,4 6232,4 6232,06 0,594138 3 (3) -1-1 +1 6256,6 6257,1 6257,3 6256,1 6256,6 6256,74 0,472229 4 (27) +1 +1 +1 6227,9 6227,9 6228,9 6228,9 6227,9 6228,30 0,547723 5 (2) -1-1 0 6256,1 6255,1 6255,1 6255,1 6255,1 6255,30 0,447214 6 (24) +1 0 +1 6233,9 6234,4 6233,9 6233,7 6233,7 6233,92 0,286356 7 (20) +1-1 0 6237,9 6238,4 6238,2 6237,4 6237,9 6237,96 0,378153 8 (5) -1 0 0 6250,5 6250,3 6250,8 6250,0 6250,3 6250,38 0,294958 9 (19) +1-1 -1 6237,9 6237,9 6237,9 6237,9 6237,4 6237,80 0,223607 10 (11) 0-1 0 6246,7 6246,0 6246,7 6247,0 6246,2 6246,52 0,408656 11 (14) 0 0 0 6241,7 6241,7 6242,0 6242,7 6242,0 6242,02 0,408656 12 (13) 0 0-1 6242,5 6242,2 6242,2 6242,0 6241,5 6242,08 0,370135 13 (16) 0 +1-1 6235,9 6235,9 6236,2 6236,2 6236,7 6236,18 0,327109 14 (26) +1 +1 0 6226,4 6227,4 6227,4 6226,9 6227,9 6227,20 0,570088 15 (21) +1-1 +1 6238,9 6239,5 6239,5 6239,5 6239,2 6239,32 0,268328 16 (9) -1 +1 +1 6246,5 6245,7 6246,5 6246,7 6246,2 6246,32 0,389872 17 (10) 0-1 -1 6244,7 6246,0 6245,7 6245,7 6246,2 6245,66 0,577062 18 (1) -1-1 -1 6255,3 6255,3 6255,6 6256,1 6255,6 6255,58 0,327109 19 (4) -1 0-1 6250,0 6250,0 6250,8 6250,3 6251,0 6250,42 0,460435 20 (17) 0 +1 0 6235,9 6235,2 6236,2 6235,9 6235,9 6235,82 0,370135 21 (6) -1 0 +1 6251,0 6251,0 6251,8 6251,8 6251,3 6251,38 0,402492 22 (25) +1 +1-1 6226,2 6226,9 6226,9 6227,4 6227,4 6226,96 0,492950 23 (7) -1 +1 +1 6244,7 6244,5 6244,7 6244,7 6245,5 6244,82 0,389872 24 (15) 0 0-1 6242,0 6243,0 6243,0 6243,7 6243,0 6242,94 0,606630 25 (23) +1 0 0 6231,9 6232,0 6231,9 6231,8 6231,9 6231,90 0,070711 26 (8) -1 +1 0 6245,0 6245,2 6245,0 6245,5 6245,2 6245,18 0,204939 27 (18) 0 +1 +1 6237,2 6236,7 6237,2 6237,2 6237,2 6237,10 0,223607 Results of five repetitions for the propagation speed of waves 13
Analysis of the Results R Chart of R1;...; R5 2,0 UCL=2,082 1,5 Sample Range 1,0 _ R=0,985 0,5 0,0 LCL=0 3 6 9 12 15 Sample 18 21 24 27 14
Analysis of the Results (a) Percent (b) Frequency Normal Probability Plot of the Residuals 99 90 50 10 1-2 -1 0 1 2 Standardized Residual Histogram of the Residuals 4,8 3,6 2,4 1,2 0,0-2,0-1,5-1,0-0,5 0,0 0,5 1,0 1,5 Standardized Residual Residual Plots for speed (c) Standardized Residual (d) Standardized Residual Residuals Versus the Fitted Values 2 1 0-1 -2 6230 6240 6250 6260 Fitted Value Residuals Versus the Order of the Data 2 1 0-1 -2 2 4 6 8 10 12 14 16 18 20 22 24 26 Observation Order 15
Analysis of the Results Main Effects Plot (data means) for Speed 6250 Temperature Stress 6245 6240 Mean of Speed 6235 6250 20,0 22,5 Force 25,0 50 75 100 6245 6240 6235 22,5 53,9 115,8 16
Analysis of the Results Interaction Plot (data means) for speed 50 75 100 22,5 53,9 115,8 T emperature 6250 6240 Temperature 20,0 22,5 25,0 6230 Stress 6250 6240 Stress 50 75 100 6230 Force 17
Conclusions The temperature was the variable with the greatest influence on results. It was observed that the lower the temperature, the higher the values for speed, while the higher the temperature, the lower the values for speed. The test created and defined procedure allowed the evaluation of proposals by the analysis influences the behavior of the propagation speed, indicating that the proposed procedure can be used for this type of analysis. 18
Future Work Improve the LabView TM program developed to calculate the propagation speed waves and analyzing the results of the propagation speed of the Lcr waves through the test of influence and other variables at different levels for the variables already studied in this work. 19