Lightweight design of 45000r/min spindle using full factorial design and extreme vertices design methods

Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.

Preliminary Study on the Low Energy Ion Beam Mediated Parameters with Fractional Factorial Design Method

[Objective] The aim was to explore the biological effect of low energy ion beam mediated parameters with fractional factorial design method. [Method] The twin-embryos seed of autotetraploid rice DER10-04-01 was taken as the receptor material,and the Elymus dahuricus Turcz. was used as materials to provide DNA to carry out the ion beam mediated experiment. And the fractional factorial design method was used to study the parameters of low enery N＋ ion beam mediated foreign genes into rice. [Result] The implantation energy,dose,DNA concentrations and immersion time of DNA showed significant biological effects on the normal growth and development of DER10-04-01,in which the biological effects of implantation dose and DNA concentrations were relatively obvious. [Conclusion] The implantation energy,dose,DNA concentrations and immersion time of DNA were major factors showing important effects on the experimental result in ion beam mediated foreign genetic materials.

Evaluation of significant manufacturing parameters in lost foam casting of thin-wall Al-Si-Cu alloy using full factorial design of experiment

Controlling process parameters of lost foam casting （LFC） enables this process to produce defect-free complex shape castings. An experimental investigation on lost foam casting of an A1-Si-Cu cast alloy was carried out. The effects of pouting temperature, slurry viscosity, vibration time and sand size on surface finish, shrinkage porosity and eutectic silicon spacing of thin-wall casting were investigated. A full two-level factorial design of experimental technique was used to identify the significant manufacturing factors affecting the properties of casting. Pouring temperature was found as the most significant factor affecting A1-Si-Cu lost foam casting quality. It was shown that flask vibration time interacted with pouring temperature influenced euteetic silicon spacing and porosity percentage significantly. The results also revealed that the surface quality of the samples cast in fine sand moulds at higher pouring temperatures was almost unchanged, while those cast in coarse sand moulds possessed lower surface qualities. Furthermore, variation in slurry viscosity showed no significant effect on the evaluated properties compared to other parameters.

Optimization of hydrothermal synthesis of H-ZSM-5 zeolite for dehydration of methanol to dimethyl ether using full factorial design

H-ZSM-5 zeolite was synthesized by hydrothermal method. The effects of different synthesis parameters, such as hydrothermal crystallization temperature （170-190 ℃） and Si/A1 molar ratio （100-150）, on the catalytic performance of the dehydration of methanol to dimethyl ether （DME） over the synthesized H-ZSM-5 zeolite were studied. The catalysts were characterized by N2 adsorption-desorption, XRD, NH3-TPD, TGA/DTA, and SEM techniques. The full factorial design of experiments was applied to the synthesis of H-ZSM-5 zeolite and the effects of synthesis conditions and their interaction on the yield of DME as the response variable were determined. Analysis of variance showed that two variables and their interaction significantly affected the response. According to the experimental results, the optimized catalyst prepared at 170℃ with the Si/A1 molar ratio of 100 showed the best catalytic performance among the tested H-ZSM-5 zeolite.

Systematic Analysis of Carbon Dioxide Activation of Waste Tire by Factorial Design

In this study, waste tire was used as raw material for the production of activated carbons through pyrolysis. ＇Fire char was first produced by carbomzation at 550℃ under nitrogen. A two tactortal design was used to optimize the production of activated carbon from tire char. The effects of several factors controlling the activation process, such as temperature （.830-930℃）, time （2-6h） and percentage ot carbon dioxide （70%-100%） were investigated. The production was described mathematically as a function of these three factors. First order modeling equations were developed for surface area, yield and mesopore volume. It was concluded that the yield, BET surface area and mesopore volume of activated carbon were most sensitive to activation temperature and time while percentage of carbon dioxide in the activation gas was a less significant factor.

Artificial Neural Network and Full Factorial Design Assisted AT-MRAM on Fe Oxides, Organic Materials, and Fe/Mn Oxides in Surficial Sediments

Artificial neural network（ANN） and full factorial design assisted atrazine（AT） multiple regression adsorption model（AT-MRAM） were developed to analyze the adsorption capability of the main components in the surficial sediments（SSs）. Artificial neural network was used to build a model（the determination coefficient square r2 is 0.9977） to describe the process of atrazine adsorption onto SSs, and then to predict responses of the full factorial design. Based on the results of the full factorial design, the interactions of the main components in SSs on AT adsorption were investigated through the analysis of variance（ANOVA）, F-test and t-test. The adsorption capability of the main components in SSs for AT was calculated via a multiple regression adsorption model（MRAM）. The results show that the greatest contribution to the adsorption of AT on a molar basis was attributed to Fe/Mn（–1.993 μmol/mol）. Organic materials（OMs） and Fe oxides in SSs are the important adsorption sites for AT, and the adsorption capabilities are 1.944 and 0.418 μmol/mol, respectively. The interaction among the non-residual components（Fe, Mn oxides and OMs） in SSs interferes in the adsorption of AT that shouldn’t be neglected, revealing the significant contribution of the interaction among non-residual components to controlling the behavior of AT in aquatic environments.

Methodology of factorial design deriving guidelines for simulation of growth curve and production of sugars by Spirulina (Arthrospira) maxima

It is practical, economic and sometimes essential to derive rules or conclusions by performing lesser runs of experiments. In this part, a methodology based on 2 f factorial design was brought up to derive guidelines to simulate growth curve and production of sugars by Spirulina (Arthrospira) maxima . The growth curve or accumulation process of sugars was idealized by sets of straight lines limited by phase transfers of growth or accumulation of sugars. Normal analyses of the critical values of the transfers were used to derive their linear relationships with the initial conditions of the experimental factors. These linear functions were called guidelines and were used to simulate the growth curve or accumulation of sugars. Generalization of the guideline technique was determined by the kinetic limitation of nutrient nitrogen or sulfur that was dependent upon their stoichiometric deficiency directly derived from their initial values in the medium. This method uses the initial conditions of culture and does not need measurements of concentrations of nitrate, sulfate and pigments during cultivation. It is a practical and useful alternative way to trace and predict approximately the growth curve and production of sugars by S. maxima .

Optimization of Biosurfactant Production from Glycerol by Pseudomonas Aeruginosa EQ 109 Using Factorial Design 2^3

One possible application for the excess of glycerol, which is an exceeding byproduct in biodiesel industry, was used as carbon and energy sources for bioproducts synthesis. This work aims to evaluate biosurfactant production from glycerol by Pseudomonas aeruginosa EQ 109 isolated from crude oil-contaminated soil. Factorial design 2^3 was utilized to optimize the amount of biosurfactant produced, by using pH （A）, initial biomass concentration （B）, and initial glycerol concentration （C） as independent factors. The experiments were carried out in flasks containing 100 mL of mineral medium. Biosurfactant production was monitored by increase of the emulsification of aviation kerosene （E24） and surface tension reduction （STr）. The results have shown that, at pH = 7.0, in order to increase E24, variables as B and C are the most influential, leading to a maximum value of E24 = 79%, as well as for an increase of GC （GCmax = 49%）. STR was the variable with the best correlation factor for the proposed linear model （R2=0.96） and its maximum value was 48%. Xfwas not significant to the model, although it was influenced by pH and C, with C = 40g/L （Xfmax = 4.56 g/L）.

Abrasive resistance of metastable V–Cr–Mn–Ni spheroidal carbide cast irons using the factorial design method

Full factorial design was used to evaluate the two-body abrasive resistance of 3wt%C–4wt%Mn–1.5wt%Ni spheroidal carbide cast irons with varying vanadium（5.0wt%–10.0wt%） and chromium（up to 9.0wt%） contents. The alloys were quenched at 920℃. The regression equation of wear rate as a function of V and Cr contents was proposed. This regression equation shows that the wear rate decreases with increasing V content because of the growth of spheroidal VC carbide amount. Cr influences the overall response in a complex manner both by reducing the wear rate owing to eutectic carbides（M7C3） and by increasing the wear rate though stabilizing austenite to deformation-induced martensite transformation. This transformation is recognized as an important factor in increasing the abrasive response of the alloys. By analyzing the regression equation, the optimal content ranges are found to be 7.5wt%–10.0wt% for V and 2.5wt%–4.5wt% for Cr, which corresponds to the alloys containing 9vol%–15vol% spheroidal VC carbides, 8vol%–16vol% M7C3, and a metastable austenite/martensite matrix. The wear resistance is 1.9–2.3 times that of the traditional 12wt% V–13wt% Mn spheroidal carbide cast iron.

Modeling of biodiesel production: Performance comparison of Box–Behnken, face central composite and full factorial design

The performances of the response surface methodology(RSM)in connection with the Box–Behnken,face central composite or full factorial design(BBD,FCCD or FFD,respectively)were compared for the use in modeling of the NaOH-catalyzed sunflower oil ethanolysis.The influence of temperature,catalyst loading,and ethanol-to-oil molar ratio(EOMR)on fatty acid ethyl esters(FAEE)content was evaluated.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables but BBD and FCCD realization involved less number of experiments,generating smaller costs,requiring less work and consuming shorter time than the corresponding FFD.All three designs resulted in the same optimal catalyst loading(1.25%of oil)and EOMR(12:1).The reduced two-factorinteraction(2 FI)models based on the BBD and FCCD defined a range of optimal reaction temperature(25℃–75℃)and 25℃,respectively while the same model based on the 33 FFD appointed 75℃.The predicted FAEE content of about 97%–98.0%was close to the experimentally obtained FAEE content of about 97.0%–97.6%under the optimal reaction conditions.Therefore,the simpler BBD or FCCD might successfully be applied for statistical modeling of biodiesel production processes instead of the more extensive,more laborious and more expensive FFD.

Synthesis of biodegradable Mg-Zn alloy by mechanical alloying: Statistical prediction of elastic modulus and mass loss using fractional factorial design

Biodegradable Mg-Zn alloy was synthesized using mechanical alloying where a statistical model was developed using fractional factorial design to predict elastic modulus and mass loss of the bulk alloy.The effects of mechanical alloying parameters(i.e.,milling time,milling speed,ball-to-powder mass ratio and Zn content)and their interactions were investigated involving 4 numerical factors with 2 replicates,thus 16 runs of two-level fractional factorial design.Results of analysis of variance(ANOVA),regression analysis and R2 test indicated good accuracy of the model.The statistical model determined that the elastic modulus of biodegradable Mg-Zn alloy was between 40.18 and 47.88 GPa,which was improved and resembled that of natural bone(30-57 GPa).Corrosion resistance(mass loss of pure Mg,33.74 mg)was enhanced with addition of 3%-10%Zn(between 9.32 and 15.38 mg).The most significant independent variable was Zn content,and only the interaction of milling time and ball-to-powder mass ratio was significant as P-value was less than 0.05.Interestingly,mechanical properties(represented by elastic modulus)and corrosion resistance(represented by mass loss)of biodegradable Mg-Zn alloy can be statistically predicted according to the developed models.

Factorial Experimental Design to Study the Effects of Layers and Fiber Content on Concrete Flexural Behavior

Experimentation has come a long in helping researchers achieve breakthroughs in their different scientific areas and engineering happens to be one of those areas with the most impact from experimental advancement. The need for valid experimental results free from biases and confounding conclusions has prompted the development of new experimental techniques that takes consideration of all applicable factor and combinations in providing answers on a research topic, and the Factorial Experimental design credited to Sir Ronald Fisher is one technique yielding highly valid results. This paper uses the factorial design of experiments to research the flexural impact of polyvinyl acetate fiber and layered concrete in construction. The experiment considered two levels of fiber contents and two levels of layers, and prepared samples with all combinations of the variable factors. The samples were tested after 7 days from casting for flexural strength and an advance statistical analysis was performed on the flexural responses of the samples using R-program. The results from the analyses revealed the significance of the variables to the flexural strength of the samples, as well as their interactions. The experiment concluded that based on the number of layers and fiber content used for the experiment, casting concrete in layers does have a significant negative effect on the flexural strength of concrete, and the failure pattern of concrete members under flexural load in evidently influenced by the material composition of the concrete, and that it can be evidently influenced by casting the concrete in layers.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

Mathematical Modeling of Carbon Content and Intercritical Annealing Temperature in DP Steels by Factorial Design Method

2k factorial design is employed to find the mathematical relation between the carbon content and intercritical annealing temperature （IAT） in order to predict the responses namely martensite volume fraction （MVF）, microhardness （H）, yield strength （YS）, ultimate tensile strength （UTS）, total elongation （TEL）, yield ratio （YR） and Charpy impact energy （CIE） in dual phase （DP） steels. Steels containing different carbon contents （0.085% C and 0.380% C） had been chosen for this purpose. The main advantages of factorial design are its easy implementation and the effective computation compared with the other optimization techniques, which were employed for predicting mentioned responses in the literature. To verify the proposed approach based on factorial design, experiments for verification were performed. The results of the verification experiments and the mathematical models are in accordance with each other and the literature.

Connection Among Some Optimal Criteria for Symmetrical Fractional Factorial Designs

A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and uniformity criterion are proposed for comparing and selecting fractions. In this paper, we indicate that these criteria agree quite well for symmetrical fraction factorial designs.

Construction of Split-Plot Designs with General Minimum Lower Order Confounding

Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.

Weldability of Ferritic Ductile Cast Iron Using Full Factorial Design of Experiment

The weldability of a ferritic ductile cast iron was investigated as a function of different consumables and welding conditions. A 23 full factorial experimental design was used to analyze the effect of factors and their interac- tions on ultimate tensile strength of weldments. The shielded metal arc welding （SMAW） process was used with two types of consumables （E7018 and ENi-CI） under eight different conditions using as-cast samples. The microstructur- al evolution and fracture mechanisms were investigated by optical microscopy and scanning electron microscopy （SEM）, respectively. The hardness, tensile and impact tests were also performed to determine the weld quality. Based on experiment design, preheat, consumable, cooling condition, preheat cooling and preheat-consumable inter- actions were significant factors. Preheat is the most effective factor and in the case of E7018, preheat and cooling conditions were the most sensible factors. It was found that buttering was the most appropriate welding method for ferritic ductile cast iron.

Factorial study of moxibustion in treatment of diarrhea-predominant irritable bowel syndrome

AIM: To identify an appropriate therapeutic regimen for using aconite cake-separated moxibustion to treat diarrhea-predominant irritable bowel syndrome (D-IBS).

CONSTRUCTION OF OPTIMAL BLOCKING SCHEMES FOR ROBUST PARAMETER DESIGNS

Robust parameter design （RPD） is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, we obtain the correspondence relation between fractional factorial RPDs and the blocking schemes for full factorial RPDs. In addition, we provide a construction of optimal blocking schemes that make all main effects and control-by-noise two-factor interactions estimable.

Modeling Experimental Design for Photo-Fenton Degradation of Methomyl

Modeling experimental design was used to study the main effects and the interaction effects between operational parameters in the photocatalytic degradation of pesticide methomyl. The important parameters which affect the removal efficiency of methomyl such as concentration of Fe(NO3)3, concentration of H2O2, initial concentration of the pesticide and pH. The parameters were coded as x1, x2, x3 and x4, consecutively, and were investigated at two levels (–1 and +1). The effects of individual variables and their interaction effects for dependent variables, namely, photocatalytic degradation efficiency (%) were determined. From the statistical analysis, the most effective parameters in the photocatalytic degradation efficiency were initial concentrations of the methomyl and Fe(NO3)3. The interaction between initial concentration of the pesticide and Fe(NO3)3 was the most influencing interaction. The optimum conditions that were obtained for the photocatalytic degradation of methomyl were: minimum quantity of contaminant: 6 × 10–5 mol.L–1, maximum quantity of Fe(NO3)3: 5 × 10–4 mol.L-1, initial pH of the solution: 3 and maximum quantity H2O2: 10–2 mol.L–1.