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Design of Experiments and Taguchi Experimental Design. Professor Joe Greene CSU, Chico. Design of Experiments. Need for Experiments Factorial Experiments Two-Factor Factorial Experiments Statistical Analysis for Two-Factor Experiments Other Factorial Experiments

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## Design of Experiments and Taguchi Experimental Design

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**Design of Experiments and Taguchi Experimental Design**Professor Joe Greene CSU, Chico Taguchi**Design of Experiments**• Need for Experiments • Factorial Experiments • Two-Factor Factorial Experiments • Statistical Analysis for Two-Factor Experiments • Other Factorial Experiments • General Factorial Experiments • Randomized Complete Block Design • 2k Factorial Design • Taguchi Designs Taguchi**Need for Need for Experiments**• Need to establish cause and effect relationships • Home • Car repair- Trouble-shooting starting, noise, and braking problems • Home repair- Electrical and mechanical problems, cooking, etc. • Gardening and lawn maintenance- watering and pesticide use • School • Studying versus grades performance • Attendance versus grade performance • Industry • Maintenance and trouble-shooting of equipment • Effects of moisture, line rate, operators on productivity and quality • Trouble shooting production problems for incoming Materials • Trouble shooting production problems on Target values for performance or appearance Taguchi**Experimental Goals**• Statistical Accuracy • Proper selection of the responses to be measured • Determination the number of factors that affect a response • The interactions between the factors • The number of repetitions per run • The form of analysis to be completed • Cost • Minimize the cost • Reduce the number of experiments to the minimum • Study the main factors • Thoroughly understand the process under study • Choose the minimum number of experiments Taguchi**Factorial Experiments**• Study the effects of 2 or more factors with factorial experiments • Each factor and each combination of factors are studied • Example • Factor A has 2 levels (high, low) • Factor B has 2 levels (on, off) • Then the total number of experiments is 2x2=4, or • high-on, high-off, low-on, low-off • Experiments measure the difference of the response from one level of the factor (high for A) and another level (low for A). Taguchi**Factorial Experiments- Design**• Example • Factor A- 2 levels- A1, A2 • Factor B- 2 levels- B1, B2 • Measured values are • 10, 20 • 30, 40 • The effect Factor A has on the experiment is the average difference between the levels A= 30+40 - 10+20 = 20 2 2 B= 20+40 - 30+10 = 10 2 2 Conclusion Changes in Factor A causes more of an effect than B. Factor A is more significant than Factor B Taguchi**Factorial Experiments- Interaction**• Example- No Interactions Interactions Taguchi**Two-Factor Factorial Experiments**• Problem- Molding problems on Injection Molder has caused defects to sky rocket. The problems started when the PP resin was switched to a different supplier. Additionally, a new operator was added • Experiment design to determine the cause of the defect • Factor A- 2 levels: Resin 1= PP_old and Resin 2 PP_new • Factor B- 2 levels- Operator 1= Tom and Operator 2= Bob • Experiment run to see what is the cause- Operator or Resin Taguchi**Two-Factor Factorial Experiments**• Experimental Layout Taguchi**Significance of Difference**• Level Averages • Sum Differences from Table • Graph Results • Analysis of Variance • Statistical Measurement Method • Measures the total variability in the data measured by the Sum of Squares • Separate out the the differences caused by the individual factors • Calculates the differences caused by the error • Uses the F statistic to calculate the significance Taguchi**ANOVA Example**• Analysis of Variance Note: F Statistic determines significance. If F is greater than a specified value than the factor is significant. Taguchi**ANOVA Example Calculation**• Analysis of Variance SST= Sum (results)2 - y..2 N = (10)2 + (20)2 + (30)2 +…+(70)2 - (1280)2 8 SSResin = Sum (Resin y.)2 - y..2 n N SSOperator = Sum (Operator y.)2 - y..2 n N SSError= SST - SSResin - SSOperator Taguchi**Other Factorial Experiments**• General Factorial Experiments • Involves experiments with more than 2 factors • Requires many experiments to run • Randomized Complete Block Design • Special design of experiment that blocks out certain extraneous effects • Used to investigate the effects of one ore more factors when entire experiment cannot be run under homogeneous conditions • 2k Factorial Design • Special design for 2 levels and k factors Taguchi**Taguchi Experimental Design**• History of Dr. Genichi Taguchi • After WWII, the Japanese initiated a major effort to participate in the world market. • The first products were inexpensive, but of poor quality. • The Japanese government set up government agencies modeled after US companies (Bell Labs). One such company, Electrical Communication Laboratories of Japan (ECL), hired Dr. Taguchi to reduce the cost of experimentation. • Dr. Taguchi developed a series of experiments that resembled partial factorial designs and featured orthogonal (balanced) arrays. • The experimental method is called “The Taguchi Approach” Taguchi**Comparison: Taguchi vs. Conventional Experimental Design**• Traditional experimental designs were introduced by R.A. Fisher in 1920’s in England • Limitations of traditional design • Limited variety of layouts and difficult data analysis • Limited number of variables with many required repetitions • Passive approach to interactions. Difficulty in resolving them • F statistic only recognized as fully significant. Partial effects are not calculated • Taguchi has • Multiple layouts and designs and efficient data analysis • Minimum number of experiments • Active approach to interactions and calculates partial contribution Taguchi**Features of Taguchi**• Orthogonal Arrays • Efficient data collection • Separated effects from one another • Balanced, separable, or not mixed • Minimum number of experiments • Experimental Designs • Two Level- L8, L16, L32 have 8 experiments, 16 experiments, and 32 experiments, respectively • Three Level- L9, L27 have 9 experiments and 27 experiments. • Data Analysis- Software available • Level Averages • ANOVA Taguchi**Examples Taguchi**• Design of Experiment for thermoplastic composites • Objectives • What is the best combination of Twintex composites and GMT? • What are the optimum process conditions? • Paper for SAE Taguchi**Improving Performance of BMC Bumper Beams**DOE Study • Evaluate Effectiveness of Prepreg Technology to Selectively Increase Stiffness & Impact Performance • Find Optimum Combination of the 2 Materials • 4 Variables were Compared vs Static Load : • Prepreg Type • BMC Glass % • Weight Fraction of Prepreg • Tonnage of Press Taguchi**Improving Performance of BMC Bumper Beams**DOE Study • 3-Point Loading Test (ASTM D790), with FMVSS 581 Pendulum Impactor head • Typical mid-sized Vehicle Bumper was Used • Test loaded Beam at Centerline @ 51 mm/min • Load/Deflection Response Measured & Recorded • Test’s Measurable was Beam’s Static Load, Recorded at 25 mm of Deflection • Specific Load = Static Load/Beam Weight Taguchi**Static Test Setup with a Pendulum Face Moving at a Constant**Speed into a Rigidly Mounted Beam Taguchi**DOE Study**• TP-BMC Glass Weight Percentage: • 20%, • 30%, and • 40%. • .Weight percentage of prepreg: • 25%, • 50%, and • 75%. • .Press Tonnage (metric): • 450 t, • 675 t, and • 900 t. • .Prepreg type: • satin weave (1:1),: • twill weave (4:1), and • unidirectional (uni); Taguchi**DOE Study**Taguchi**Improving Performance of BMC Bumper Beams**DOE Study • Materials Processed on conventional BMC and GMT Equipment • BMC logs were extruded. Prepreg Plates Cut to Shape and heated in GMT oven • Projected Area of Part was 370 x 1520 mm, with Nominal Thickness of 8 mm • GMT & Prepreg added in Combinations of Fractions of Prepreg to Total Beam Weight • 3 Beams in each Combination Molded for Experiment Taguchi**Improving Performance of GMT Bumper Beams**DOE Study • Pre-preg Materials Placed & Indexed in Oven to exit at the Same Time as BMC log • Material Temperature 210-240C @ Oven Exit • Prepreg Heated at same Rate due to Similar Thermal Properties & Thickness • Materials Placed in Tool (Transfer Time 20-30 sec) and then compression molded Taguchi**Experimental Layout for the Taguchi L-9**Note: Equivalent Full Factorial Design would require 81 experiments : Number of Experiments = (levels)Factors = 34 = 81 experiments Taguchi**Improving Performance of BMC Bumper Beams**DOE Study • 27 Beams, 3 each of 9 Variants, plus 15 BMC-Only • Control Beams were BMC 20%, BMC 30%, and BMC 40%, • Experiment was not Randomized to Minimize Duration Taguchi Study Permits Interpolation of Results to Other Variants not Physically Manufactured or Tested Taguchi**Static Load for BMC and Prepreg**Experiment Number Taguchi**Mass of Beams for GMT/Prepreg**1 2 3 4 5 6 7 8 9 GMT GMT+ C-GMT30+ C-GMT40+ Experiment Number Taguchi**Mean Static Load vs. Beam Mass for BMC/Prepreg**Static Load versus Beam Mass for GMT/Prepreg Experiment Taguchi**Mean Specific Static Load for BMC/Prepreg**GMT GMT+ C-GMT30+ C-GMT40+ Experiment Number Taguchi**Level Averages for GMT/Prepreg**Taguchi**Analysis of Variance(ANOVA) ResultsSignificance Of Each**Variable 14985 19.68 28446 18.96 GMT Type 2 82651 41325 54.28 81128 54.08 9531 12.52 17539 11.69 Lay-Up 2 4622 2311 3.04 3100 2.07 e1 0 0 e2 18 13704 761 19795 13.20 Total 26 150007 5770 100 Taguchi**Optimum Levels of Each Variable as Determined from Level**Averages Graph Taguchi**Improving Performance of GMT Bumper Beams**Confirmation Run • Confirmation Run used same Process Settings • Used the GMT product with 30% Chopped Fiber & Each of the Prepreg Materials • 5 Beams with Each Prepreg Material were made, plus 5 Control Beams • Test Results confirmed C-GMT 30+ Product was Improved by Adding Prepreg Material Taguchi**Conclusions**• Comingled thermoplastic prepregs improve the stiffness properties of TP-BMC composites by 15% to 20%. • The static load of composite bumper beams increases with up to a maximum of 22% to 25% glass (by volume). • Comingled thermoplastic prepregs improve the static bumper performance of TP-BMC composites to a level superior to published results for standard GMT materials. • The significant material and processing parameters in this experiment are TP-BMC glass weight percentage, weight percentage prepreg, press tonnage, and prepreg type. • The optimum levels for maximum dimensionless static load are: • TP-BMC glass weight percentage = 30% • Weight percentage prepreg = 75% • Press tonnage (metric) = 900 t • Prepreg type = Satin Taguchi

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