Using Taguchi's contribution ratio and Pareto diagram in identification of influential factors in experiments: Case studies

U ovom radu se razmatra upotreba Taguchi-jevog koeficijenta učešća kao i prilagođenog Pareto dijagrama u cilju određivanja veličine uticaja projektovanih faktora u statistički planiranim eksperimentima (tradicionalnim ili Taguchi-jevim) na izlazne veličine u cilju određivanja najbolje kombinacije projektovanih fakora na posmatrane eksperimentalne rezultate u cilju dobijanja optimalnih rešenja. U radu su prikazane dve studije slučaja kod kojih svaki sadrži dva ekstremna rezultata. Prvi primer se odnosi na ispitivanje jednog ulaznog eksperimenta, podeljenog na tri manja u cilju ispitivanja projektovanog realnog, trodimenzionallnog radnog prostora kranista. U ovom primeru kod projektovanog eksperimenta je mereno više izlaznih veličina. Drugi primer se odnosi na dva eksperimenta koja su postavljena na isti način ali sa različitim izlaznim veličinama. Eksperimenti se odnose na geometrijske deformacije dva različita dela razvodnika optičkih kablova koji su različitih dimenzija i izrađuju se od različitih materijala, ali istim procesom livenja plastike, pri čemu je pokazano da eksperimenti imaju različite izlazne veličine, takve da jedan daje rezultate koji su upotrebljivi u praksi, dok su rezultati drugog eksperimenta neupotrebljivi usled velike slučajne greške. Shodno tome rad daje smernice za korišćenje Taguchi-jevog koeficijenta učešća i Pareto dijagrama za efektivno određivanje uticajnih faktora i njihove veličine u oblasti planiranja eksperimenata.This paper considers the usage of Taguchi's contribution ratio as well as an adjusted Pareto diagram for determining the size of influential design factors in experimental design on output values in order to determine the best combination of input factors, as well as factors that can determine output. Two case studies that cover extreme examples are presented in that aim. The first case study examines one input workspace design distributed on tree experimental designs defining space coordinates. Every design has several output values that were measured. The second case study presents two experiments regarding injection of plastic molding process, with same input factors at parts which are different in material and dimensions with geometric deformations as output. It was shown that different experiments lead to different results, of which one is acceptable, while other is useless for further examinations. Accordingly, this paper gives guidelines how to use Taguchi's contribution ratio and Pareto diagram effectively in determination of influential factors in experiments

Sinergetski efekat aditiva na morfološka i mikromehanička svojstva bakarnih prevlaka na različitim podlogama

Tanki bakarni filmovi debljine 10 μm deponovani su na hladno-valjanim supstratima od bakra i mesinga procesom elektrohemijske depozicije iz laboratorijski napravljenog sulfatnog kupatila sa dodatkom različitih aditiva (hloridnih jona (Cl-) i polietilen glikola (PEG)). Ispitivan je uticaj aditiva i parametara depozicije na strukturna i mehanička svojstva bakarnih prevlaka. Prisustvo aditiva omogućilo je nastajanje glatkih i sjajnih depozita usled promene njihove mikrostrukture. Mikromehanička svojstva filmova bakra ispitivana su metodom mikroindentacije po Vikersu. Izmerena vrednost tvrdoće kompozitnog sistema Cu film – supstrat je složena funkcija tvrdoće supstrata i tvrdoće filma. Za određivanje tvrdoće filmova iz kompozitne mikrotvrdoće korišćeni su modeli Korsunskog i Šiko-Lezaža. Eksperimentalna ispitivanja su pokazala da se istovremenim dodatkom aditiva (PEG+Cl-) ostvaruje kvalitetnija mikrostruktura depozita koji usled toga imaju bolja mikromehanička svojstva.Најбољи рад младог аутора на секцији / The best work of a young author in the sectio

Influence of additive thiourea on composite and absolute hardness of electrodeposited copper films

Elektrodepozicijom (ED) pod različitim procesnim uslovima (gustina struje, koncentracija tiouree, debljina filma) formirani su kompozitni sistemi tankih filmova Cu na folijama Cu koje se koriste za izradu maski za kontaktno štampanje. U cilju određivanja mehaničkih svojstava ovako dobijenih kompozitnih sistema i posebno, uticaja aditiva tiouree na poboljšanje mehaničkih svojstava filmova, izvršena su merenja tvrdoće standardnim testovima mikroindentacije po Vikersu. Izmerena vrednost mikrotvrdoće kompozitnih sistema je složena funkcija mehaničkih svojstava (tvrdoće) supstrata i filma, i njihovog relativnog odnosa. Za određivanje apsolutne tvrdoće filmova Cu, odabran je i korišćen kompozitni model Korsunskog. Pokazano je da se dodatkom aditiva tiouree u elektrolit pri elektrodepoziciji, može uticati na mikrostrukturu i mehanička svojstva filma Cu u smislu poboljšanja tj. povećanja apsolutne tvrdoće filma.Electrodeposited (ED) under various process conditions (current density, the concentration of thiourea, film thickness) were formed composite systems Cu thin films on copper foils used for making masks for contact printing. In order to determine the mechanical properties of the obtained composite systems and, in particular, the impact of additives thiourea in improving the mechanical properties of films, hardness measurements were performed by standard tests Vickers microindentation. The measured hardness value of composite systems is a complex function of the mechanical properties (hardness) of the substrate and the film, and their relative relationships. To determine the absolute hardness of Cu films, composite model Korsunsky was chosen and used . It is shown that the additive thiourea in the electrolyte during electrodeposition, can affect the microstructure and mechanical properties of Cu by improving and increasing the absolute hardness of the film

Influence of the structure of multilayer thin Ni/Cu films on their mechanical properties and MEMS devices fabrication applications

Tehnikom elektrohemijske depozicije iz dva kupatila (DBT), dobijeni su višeslojni filmovi Ni i Cu naizmeničnim deponovanjem na polikristalni bakarni supstrat. Promena parametara kao što su ukupna debljina filma, debljina pojedinačnog sloja i odnos debljina pojedinačnih slojeva Ni i Cu u filmu, utiče na mehanička svojstva višeslojnih filmova i omogućava formiranje različitih struktura za njihovu primenu u MEMS-u. Tanki filmovi Ni i Cu sa debljinom slojeva od 75 nm do 5 μm pokazuju dobru međuslojnu adheziju. Smanjenjem debljine pojedinačnog sloja do 300 nm i povećanjem odnosa debljina slojeva Ni:Cu na 1:4, došlo se do višestrukog povećanja vrednosti Vikersove mikrotvrdoće u odnosu na jednoslojne metalne filmove. Filmovi sa debljinom slojeva većom od 5 mikrometara, nemaju dobru medjuslojnu adheziju i uočava se delaminacija slojeva. Sve strukture višeslojnih filmova Ni i Cu se mogu primeniti za izradu trodimenzionalnih MEMS struktura od nikla, metodom selektivnog nagrizanja sloja bakra u kiselom rastvoru tiouree (tehnikom „površinskog mikromašinstva“).Multilayer Ni/Cu films were alternately electrochemically deposited on polycrystalline Cu substrate by dual-bath technique. Change of the parameters such as total film thickness, sublayer thickness and sublayer thickness ratio influences the mechanical properties of the multilayer Ni/Cu films and gives the possibilities for different MEMS fabrication applications. Thin Ni and Cu films with sublayer thickness from 75 nm to 5 µm have good interlayer adhesion. Decreasing the sublayer thickness leads to increase in the composite microhardness value. Delamination of the layers is noticed for the sublayer thickness greater than 5 µm. Three-dimensional Ni microstructures can be fabricated using multilayer Ni/Cu film by selective etching of Cu layers in in acidic thiourea solution („surface micromachining“ technique)

Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus

Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral

Micromechanical properties of composite systems obtained with electrodeposition of thin Ni and Cu films on different substrates

Tanki filmovi Ni i Cu sitnozrne strukture su elektrohemijski istaloženi iz laboratorijski napravljenih sulfamatnih i sulfatnih elektrolita, respektivno. DC elektrohemijsko taloženje filmova Ni je izvedeno na monokristalnim Si pločicama orijentacija (100) i (111), dok je elektrohemijsko taloženje Cu filmova izvedeno na debelim elektrohemijski istaloženim filmovima Ni kao supstratima. U cilju ispitivanja uticaja mikrostrukture supstrata i tankih filmova Ni i Cu na mehanička svojstva ovih kompozitnih struktura, izvršeno je merenje Vikersove mikrotvrdoće sa različitim opterećenjima. Za svaki kompozitni sistem koji se sastoji od tankog filma na supstratu, postoji kritična dubina utiskivanja, kada izmerena tvrdoća ne predstavlja tvrdoću istaloženog filma, već takozvanu “kompozitnu tvrdoću”, zbog učešća supstrata koji doprinosi otporu plastičnoj deformaciji. Odabran je kompozitni model Šiko-Lezaža (C-L model), koji je primenjen na eksperimentalne rezultate u cilju određivanja apsolutne tvrdoće Ni i Cu filmova. Za pomenute kompozitne sisteme je izvršena analiza parametra deformacionog ojačavanja (t/d)m, kojim se može izraziti razlika u odgovoru kompozinih sistema na opterećenja.Thin Ni and Cu films with fine-grained structures have been electrodeposited from self-made sulphamate-based and sulphate-based electrolytes, respectively. DC electrodeposition of Ni films was performed on single crystal Si wafers with different orientations named (100) and (111), and electrodeposition of Cu films was performed on thick electrodeposited Ni films as the substrates. In order to investigate the influence of the microstructure of the substrates and of the Ni and Cu thin films on mechanical properties of these composite structures, Vickers microhardness testings for different loads was done. For any composite system of thin film on a substrate, there is a critical indentation depth, when a measured hardness value is not the hardness of the electrodeposited film, but the so-called “composite hardness”, because the substrate also participates in the plastic deformations. Composite hardness model of Chicot-Lesage was chosen and applied to the experimental data in oreder to determine the absolute film hardness. Analysis of work hardening parameter (t/d)m, that can express the difference in tendency of the composite hardness with the indentation load, was performed for the above-mentioned composite systems

Uticaj brzine očvršćavanja na mikrostrukturu i raspodelu primesa tokom očvršćavanja legure Al-Cu

In this paper investigation of the influence of solidification rate on the microstructure and distribution of solute during the solidification of Al-2.2%Cu by Vertical Bridgman method was performed. The experiments were carried out over a range of solidification rates from 1.45x10-6 m/s to 8.71x10-5 m/s under a protective nitrogen atmosphere. Within the range of investigated solidification rates the change of interface shape from planar-to-cellular has been observed. It was observed that the solidification rate at which the formation of cellular structures begins is significantly different from the calculated one due to convection. According to the distribution of the solute, the effective coefficient of distribution (ke) was calculated for each solidification rate. Dependence of ke on solidification rate has been presented

Mikromehanička svojstva kompozitnih sistema formiranih elektrohemijskim taloženjem filmova nikla i bakra na različitim podlogama

Fine-grained nickel and copper thin films were electrodeposited (ED) from self-made sulphamate and sulphate electrolytes, respectively, on different substrates. The substrates were single crystal silicon with two different orientations, namely (100) and (111) and bulk electrodeposited Ni films. Nickel films on Si substrate and ED Cu films on bulk ED Ni substrate can be thought as composite systems of 'soft film on hard substrate' type. The influence of the substrate layer and chosen plating conditions on mechanical properties of these composite structures were investigated by Vickers microhardness testing for different loads. Above a certain critical penetration depth, a measured hardness value is not the hardness of the electrodeposited film, but the so-called 'composite hardness', because the substrate also participates in the plastic deformations during the indentation process. Composite hardness models of Jonsson-Hogmark (J-H), Burnett-Rickerby (B-R) and Korsunsky (K) do not fit experimental data for this type of composite system well. Chicot-Lesage (C-L) model based on the model for reinforced composites can be applied to experimental data even for the thick coatings (50 mm). Model (C-L) for reinforced composites was chosen for all specimen and the film hardness was calculated, for each indentation diagonal. The values obtained for the film hardness HF are influenced by the applied load. In case of the system of ED Ni film on Si substrate, film hardness lines have descending character, but in case of the ED Cu film on bulk ED Ni substrate, the film hardness increases. The variations should be related to physical phenomena such as the indentation size effect, the cracking in the neighborhood of the indent, the elastic contribution of the substrate for the lowest loads, or the crushing of the film for the highest loads.Elektrohemijskim taloženjem (ET) tankih filmova Ni i Cu na različitim podlogama, monokristalnom silicijumu orijentacija (100) i (111) i masivnom elektrohemijski istaloženom filmu Ni, formirani su kompozitni sistemi tipa 'mekog filma na tvrdoj podlozi'. Sitnozrni talozi Ni i Cu su bili dobijeni iz dva različita elektrolita pod odabranim uslovima elektrolize, Ni iz sulfamatnog i Cu iz sulfatnog elektrolita.U cilju određivanja mehaničkih svojstava ovih kompozitnih sistema, i posebno, određivanja svojstava filmova u okviru sistema, izvršena su merenja mikrotvrdoće utiskivanjem po Vikersovoj metodi za različita opterećenja. Izmerena vrednost mikrotvrdoće opisuje kompozitni sistem u celini i naziva se 'kompozitnom mikrotvrdoćom'. Ona ne predstavlja apsolutnu tvrdoću elektrohemijski istaloženog filma zbog učešća podloge u plastičnoj deformaciji tokom utiskivanja. Model Šiko-Lezaža (Chicot-Lesage) se pokazao odgovarajućim za analizu apsolutne tvrdoće tankih filmova za kompozitne sisteme 'mek film na tvrdoj podlozi' i primenjen je na eksperimentalne rezultate

Use of sodium oxalate and calcium formate for chemical activation of high volume fly ash (HVFA) binders

This study investigates hydration mechanism of a high volume fly ash (HVFA) binder, comprising 70 wt.% of fly ash (FA), chemically activated by using sodium oxalate (Na2C2O4) and calcium formate (Ca(HCOO)2). Prior to the binder synthesis, mechanical activation of FA was employed. Effects of the activators on the properties of the HVFA binders were determined by measuring setting times and compressive strength of the binders. Heat of hydration, pore solution composition, bound water and portlandite content, mineral composition, and microstructure of HVFA binder pastes were analyzed in order to compare the hydration mechanisms of the HVFA binders activated with the selected activators. The obtained results indicated that using of the two different activators led to the enhancement of the properties of the HVFA binders, but it was achieved in two distinct ways. It was found that the use of Ca(HCOO)2 mitigated adverse effects of the high alkalinity of the pore solution of chemically activated HVFA binder on hydration process and strength development in the later period. Therefore, it was concluded that Ca(HCOO)2 was more suitable for chemical activation of HVFA binders, compared to Na2C2O4

Microhardness analysis of thin metallic multilayer composite films on copper substrates

Composite systems of alternately electrodeposited nanocrystalline Ni and Cu films on cold-rolled polycrystalline copper substrates were fabricated. Highly-densified parallel interfaces which can give rise to high strength of composites are obtained by depositing layers at a very narrow spacing. The hardness properties of the composite systems were characterized using Vickers microhardness testing with loads ranging from 1.96 N down to 0.049 N. Above a certain critical penetration depth, a measured hardness value is not the hardness of the electrodeposited film, but the so-called 'composite hardness', because the substrate also participates in the plastic deformations during the indentation process. Dependence of microhardness on layer thickness, Ni/Cu layer thickness ratio and total thickness of the film was investigated. Model of Korsunsky was applied to the experimental data in order to determine the composite film hardness. The microhardness increased with decreasing the layer thickness down to 30 nm and it is consistent with the Hall-Petch relation. Layer thickness and layer thickness ratio are the important parameters which are responsible for making decision of the total film thickness