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Niko Vujic
2025-09-07 00:20:34 +02:00
parent 18049aa01c
commit 7114ca772f
82 changed files with 3961 additions and 332 deletions
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62
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.aux
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radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.blg
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@@ -1,17 +1,17 @@
[0] Config.pm:308> INFO - This is Biber 2.20
[0] Config.pm:311> INFO - Logfile is 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.blg'
[49] biber:342> INFO - === Sun Aug 24, 2025, 17:44:24
[59] Biber.pm:420> INFO - Reading 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf'
[91] Biber.pm:994> INFO - Found 21 citekeys in bib section 0
[101] Biber.pm:4463> INFO - Processing section 0
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[217] bbl.pm:677> INFO - Writing 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl' with encoding 'UTF-8'
[221] bbl.pm:780> INFO - Output to ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl
[221] Biber.pm:131> WARN - Duplicate entry key: 'kuznetsov2018strengthPLA' in file 'literatura.bib', skipping ...
[221] Biber.pm:131> WARN - legacy year field '1963.' in entry 'bazjanacNauka1' is not an integer - this will probably not sort properly.
[221] Biber.pm:133> INFO - WARNINGS: 2
[43] biber:342> INFO - === Sat Sep 6, 2025, 21:08:47
[54] Biber.pm:420> INFO - Reading 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf'
[85] Biber.pm:994> INFO - Found 21 citekeys in bib section 0
[95] Biber.pm:4463> INFO - Processing section 0
[101] Biber.pm:4654> INFO - Looking for bibtex file 'literatura.bib' for section 0
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[199] Biber.pm:4283> INFO - Sorting list 'nty/global//global/global/global' of type 'entry' with template 'nty' and locale 'hr-HR'
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[214] bbl.pm:780> INFO - Output to ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl
[215] Biber.pm:131> WARN - Duplicate entry key: 'kuznetsov2018strengthPLA' in file 'literatura.bib', skipping ...
[215] Biber.pm:131> WARN - legacy year field '1963.' in entry 'bazjanacNauka1' is not an integer - this will probably not sort properly.
[215] Biber.pm:133> INFO - WARNINGS: 2

19
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.fdb_latexmk
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radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.fls
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\OT1/phv/m/n/12 Tijekom talo[]zenja slo-jeva, novi sloj ras-top-lje-nog fi-la-m
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@@ -24,6 +24,7 @@
\usepackage{listings}
\usepackage{xcolor}
\usepackage{pdflscape}
\usepackage{multirow} % dodaj u preambulu
\lstdefinestyle{python}{
language=Python,
@@ -454,23 +455,23 @@ Taguchijeva metoda je eksperimentalna metoda za analizu utjecaja više ulaznih p
\bigskip
\textbf{Osnovni pojmovi:}
\begin{itemize}
\item \textbf{Faktori (engl. factors):} Varijable koje se kontroliraju u eksperimentu. U ovom radu, to su npr. visina sloja, širina ekstruzije, postotak
ispune itd.
\item \textbf{Razine (engl. levels):} Odabrane vrijednosti koje pojedini faktor može poprimiti. Na primjer, visina sloja može imati 3
razine: 0.1\,mm, 0.2\,mm i 0.3\,mm.
\item \textbf{Faktori:} Varijable koje se kontroliraju u eksperimentu. U ovom radu, to su odabrani parametri ispisa
\item \textbf{Razine:} Odabrane vrijednosti koje pojedini faktor može poprimiti.
\item \textbf{Ortogonalna matrica:} Matrica koja omogućuje sustavno variranje faktora i njihovih razina tako da se s minimalnim brojem eksperimenata
obuhvati maksimalna količina informacija. Najčešće korištene su matrice tipa L9, L18, L27 itd., ovisno o broju faktora i razina.
obuhvati maksimalna količina informacija.
\item \textbf{Signal-šum omjer (S/N omjer):} Kvantitativna mjera kojom se procjenjuje kvaliteta odziva. Povezuje korisni signal (željeni odziv) s
neželjenim šumom (varijacijom). Za slučaj kada se želi maksimizirati odziv (npr. čvrstoća), koristi se S/N omjer za kriterij što je vrijednost viša, to je bolja:
neželjenim šumom (varijacijom). Za slučaj kada se želi maksimizirati odziv (u ovom slučaju čvrstoća), koristi se S/N omjer za kriterij što
je vrijednost viša, to je bolja:
\begin{equation}
\begin{equation}\label{eq:sn_ratio}
\text{S/N} = -10 \cdot \log_{10}\left( \frac{1}{n} \sum_{i=1}^{n} \frac{1}{y_i^2} \right)
\end{equation}
gdje je $y_i$ izmjerena vrijednost odziva u $i$-tom ponavljanju, a $n$ broj ponavljanja eksperimenta za danu kombinaciju parametara.\\
\end{itemize}
\textbf{Zašto se koristi u optimizaciji procesa:}
@@ -492,8 +493,14 @@ Njezine glavne prednosti su:
U ovom radu koristit će se Taguchijeva metoda kako bi se utvrdio utjecaj 5 faktora ispisa (visina sloja, širina ekstruzije, postotak ispune, orijentacija modela
i broj slojeva stijenke) na mehaničku čvrstoću ispitnih uzoraka izrađenih FDM tehnologijom. Za svaki eksperimentalni uzorak mjerit će se vlačna i smična čvrstoća,
a S/N omjer koristit će se za procjenu optimalne kombinacije parametara i njihove robusnosti.\\
Cilj nam je, dakle, pronaći razine faktora koje daju velik signal (visoke vrijednosti čvrstoće) i mali šum (stabilno, malo rasipanje), zato maksimiziramo S/N
omjer.\\
\end{flushleft}
\subsection{ANOVA analiza (analiza varijance)} \label{subsec:anova}
Analiza varijance (engl. \textit{Analysis of Variance} – ANOVA) je statistička metoda kojom se utvrđuje značajnost utjecaja pojedinih faktora na
@@ -624,9 +631,9 @@ kvalitetna raspodjela podataka, biti će odabrane tri visine sloja prema tablici
\hline
0.08mm & 20\% & 0.4mm \\
\hline
0.22mm & 55\% & 0.4mm \\
0.14mm & 55\% & 0.4mm \\
\hline
0.36mm & 90\% & 0.4mm \\
0.28mm & 90\% & 0.4mm \\
\hline
\end{tabular}
\end{table}
@@ -715,8 +722,8 @@ U Tablici~\ref{tab:sumarni_parametri} prikazan je sažetak svih ispitivanih para
\hline
\multirow{3}{*}{Visina sloja}
& 0.08\,mm \\
& 0.22\,mm \\
& 0.36\,mm \\
& 0.14\,mm \\
& 0.28\,mm \\
\hline
\multirow{3}{*}{Širina ekstruzije}
& 0.4\,mm \\
@@ -783,8 +790,8 @@ Kada znamo koje kombinacije su nam potrebne, možemo napraviti tablicu \ref{tab:
\hline
\multirow{3}{*}{Visina sloja}
& 0.08\,mm & \multirow{3}{*}{3} \\
& 0.22\,mm & \\
& 0.36\,mm & \\
& 0.14\,mm & \\
& 0.28\,mm & \\
\hline
\multirow{3}{*}{Širina ekstruzije}
& 0.4\,mm & \multirow{3}{*}{3} \\
@@ -828,21 +835,21 @@ kombinacije koje je potrebno ispitati.\\
1 & Orijentacija 1 & 0.08\,mm & 0.4\,mm & 20\% & 2 \\
2 & Orijentacija 1 & 0.08\,mm & 0.6\,mm & 55\% & 4 \\
3 & Orijentacija 1 & 0.08\,mm & 0.8\,mm & 85\% & 6 \\
4 & Orijentacija 1 & 0.22\,mm & 0.4\,mm & 55\% & 6 \\
5 & Orijentacija 1 & 0.22\,mm & 0.6\,mm & 85\% & 2 \\
6 & Orijentacija 1 & 0.22\,mm & 0.8\,mm & 20\% & 4 \\
7 & Orijentacija 1 & 0.36\,mm & 0.4\,mm & 85\% & 4 \\
8 & Orijentacija 1 & 0.36\,mm & 0.6\,mm & 20\% & 6 \\
9 & Orijentacija 1 & 0.36\,mm & 0.8\,mm & 55\% & 2 \\
4 & Orijentacija 1 & 0.14\,mm & 0.4\,mm & 55\% & 6 \\
5 & Orijentacija 1 & 0.14\,mm & 0.6\,mm & 85\% & 2 \\
6 & Orijentacija 1 & 0.14\,mm & 0.8\,mm & 20\% & 4 \\
7 & Orijentacija 1 & 0.28\,mm & 0.4\,mm & 85\% & 4 \\
8 & Orijentacija 1 & 0.28\,mm & 0.6\,mm & 20\% & 6 \\
9 & Orijentacija 1 & 0.28\,mm & 0.8\,mm & 55\% & 2 \\
10 & Orijentacija 2 & 0.08\,mm & 0.4\,mm & 85\% & 4 \\
11 & Orijentacija 2 & 0.08\,mm & 0.6\,mm & 20\% & 6 \\
12 & Orijentacija 2 & 0.08\,mm & 0.8\,mm & 55\% & 2 \\
13 & Orijentacija 2 & 0.22\,mm & 0.4\,mm & 20\% & 6 \\
14 & Orijentacija 2 & 0.22\,mm & 0.6\,mm & 55\% & 2 \\
15 & Orijentacija 2 & 0.22\,mm & 0.8\,mm & 85\% & 4 \\
16 & Orijentacija 2 & 0.36\,mm & 0.4\,mm & 55\% & 4 \\
17 & Orijentacija 2 & 0.36\,mm & 0.6\,mm & 85\% & 6 \\
18 & Orijentacija 2 & 0.36\,mm & 0.8\,mm & 20\% & 2 \\
13 & Orijentacija 2 & 0.14\,mm & 0.4\,mm & 20\% & 6 \\
14 & Orijentacija 2 & 0.14\,mm & 0.6\,mm & 55\% & 2 \\
15 & Orijentacija 2 & 0.14\,mm & 0.8\,mm & 85\% & 4 \\
16 & Orijentacija 2 & 0.28\,mm & 0.4\,mm & 55\% & 4 \\
17 & Orijentacija 2 & 0.28\,mm & 0.6\,mm & 85\% & 6 \\
18 & Orijentacija 2 & 0.28\,mm & 0.8\,mm & 20\% & 2 \\
\hline
\end{tabular}
}
@@ -867,8 +874,8 @@ parametri za smično ispitivanje.\\
\hline
\multirow{3}{*}{Visina sloja}
& 0.08\,mm & \multirow{3}{*}{3} \\
& 0.22\,mm & \\
& 0.36\,mm & \\
& 0.14\,mm & \\
& 0.28\,mm & \\
\hline
\multirow{3}{*}{Širina ekstruzije}
& 0.4\,mm & \multirow{3}{*}{3} \\
@@ -917,24 +924,24 @@ odgovara matrici L27 koja sadržava pet faktora po tri razine, te zahtjeva 27 ek
7 & Orijentacija 3 & 0.08\,mm & 0.8\,mm & 20\% & 4 \\
8 & Orijentacija 1 & 0.08\,mm & 0.8\,mm & 55\% & 6 \\
9 & Orijentacija 2 & 0.08\,mm & 0.8\,mm & 85\% & 2 \\
10 & Orijentacija 2 & 0.22\,mm & 0.4\,mm & 20\% & 6 \\
11 & Orijentacija 3 & 0.22\,mm & 0.4\,mm & 55\% & 2 \\
12 & Orijentacija 1 & 0.22\,mm & 0.4\,mm & 85\% & 4 \\
13 & Orijentacija 3 & 0.22\,mm & 0.6\,mm & 20\% & 4 \\
14 & Orijentacija 1 & 0.22\,mm & 0.6\,mm & 55\% & 6 \\
15 & Orijentacija 2 & 0.22\,mm & 0.6\,mm & 85\% & 2 \\
16 & Orijentacija 1 & 0.22\,mm & 0.8\,mm & 20\% & 2 \\
17 & Orijentacija 2 & 0.22\,mm & 0.8\,mm & 55\% & 4 \\
18 & Orijentacija 3 & 0.22\,mm & 0.8\,mm & 85\% & 6 \\
19 & Orijentacija 3 & 0.36\,mm & 0.4\,mm & 20\% & 4 \\
20 & Orijentacija 1 & 0.36\,mm & 0.4\,mm & 55\% & 6 \\
21 & Orijentacija 2 & 0.36\,mm & 0.4\,mm & 85\% & 2 \\
22 & Orijentacija 1 & 0.36\,mm & 0.6\,mm & 20\% & 4 \\
23 & Orijentacija 2 & 0.36\,mm & 0.6\,mm & 55\% & 6 \\
24 & Orijentacija 3 & 0.36\,mm & 0.6\,mm & 85\% & 2 \\
25 & Orijentacija 2 & 0.36\,mm & 0.8\,mm & 20\% & 2 \\
26 & Orijentacija 3 & 0.36\,mm & 0.8\,mm & 55\% & 4 \\
27 & Orijentacija 1 & 0.36\,mm & 0.8\,mm & 85\% & 6 \\
10 & Orijentacija 2 & 0.14\,mm & 0.4\,mm & 20\% & 6 \\
11 & Orijentacija 3 & 0.14\,mm & 0.4\,mm & 55\% & 2 \\
12 & Orijentacija 1 & 0.14\,mm & 0.4\,mm & 85\% & 4 \\
13 & Orijentacija 3 & 0.14\,mm & 0.6\,mm & 20\% & 4 \\
14 & Orijentacija 1 & 0.14\,mm & 0.6\,mm & 55\% & 6 \\
15 & Orijentacija 2 & 0.14\,mm & 0.6\,mm & 85\% & 2 \\
16 & Orijentacija 1 & 0.14\,mm & 0.8\,mm & 20\% & 2 \\
17 & Orijentacija 2 & 0.14\,mm & 0.8\,mm & 55\% & 4 \\
18 & Orijentacija 3 & 0.14\,mm & 0.8\,mm & 85\% & 6 \\
19 & Orijentacija 3 & 0.28\,mm & 0.4\,mm & 20\% & 4 \\
20 & Orijentacija 1 & 0.28\,mm & 0.4\,mm & 55\% & 6 \\
21 & Orijentacija 2 & 0.28\,mm & 0.4\,mm & 85\% & 2 \\
22 & Orijentacija 1 & 0.28\,mm & 0.6\,mm & 20\% & 4 \\
23 & Orijentacija 2 & 0.28\,mm & 0.6\,mm & 55\% & 6 \\
24 & Orijentacija 3 & 0.28\,mm & 0.6\,mm & 85\% & 2 \\
25 & Orijentacija 2 & 0.28\,mm & 0.8\,mm & 20\% & 2 \\
26 & Orijentacija 3 & 0.28\,mm & 0.8\,mm & 55\% & 4 \\
27 & Orijentacija 1 & 0.28\,mm & 0.8\,mm & 85\% & 6 \\
\hline
\end{tabular}
}
@@ -1248,7 +1255,6 @@ Za svaki ispitni uzorak zabilježeni su:
\item konfiguracija parametara definirana ortogonalnom matricom
\item vrijednosti sile
\item izračunata naprezanja
\item vrijednosti pomaka
\end{itemize}
Na taj način dobiven je skup podataka koji se dalje koristi u analizi prema Taguchijevoj metodi.
@@ -1339,38 +1345,251 @@ Izračun površina i geometrijskih momenata presjeka proveden je pomoću vlastit
\subsection{Obrada rezultata vlačnog ispitivanja}\label{subsec:obrada_rezultata_vlačnog_ispitivanja}
Primjenom Taguchijeve metode i izračuna signal-šum (S/N omjer) moguće je odrediti koji parametri ispisa imaju najveći utjecaj na čvrstoću uzoraka te identificirati
optimalne kombinacije parametara. Za svaki uzorak izmjerena je maksimalna sila $F_\text{max}$ pri lomu, te je izračunata vlačna čvrstoća prema izrazu:\\
\begin{equation}
\sigma = \frac{F_\text{max}}{A}
\end{equation}
gdje je $A$ površina poprečnog presjeka epruvete u zoni loma.\\
Nakon odrađenog vlačnog ispitivanja na kidalici, zabilježene su sile prikazane u tablici \ref{tab:rezultati_vlacni}. Svaki uzorak ispitivan je do loma, te je
zabilježena najveća sila u procesu ispitivanja. \\
\subsubsection{Signal-šum omjer rezultata vlačnog ispitivanja}\label{subsubsec:signal_sum_omjer_rezultata_vlacnog_ispitivanja}
Primjenom Taguchijeve metode i izračuna signal-šum (S/N omjer) moguće je odrediti koji parametri ispisa imaju najveći utjecaj na čvrstoću uzoraka te identificirati
optimalne kombinacije parametara. Za svaki uzorak, pomoću maksimalne sile $F_\text{m}$ pri lomu, te je izračunata vlačna čvrstoća prema izrazu:\\
\begin{equation}
\sigma = \frac{F_\text{m}}{A_{ekv}}
\end{equation}
gdje je $A_{ekv}$ površina ekvivalentnog poprečnog presjeka epruvete kada bi bila potpuno ispunjena.\\
Ekvivalentu površinu koristimo kako bi svi uzorci imali istu referencu za računanje naprezanja. Pošto je unutrašnjost ispitnog uzorka kompleksna, te površina
poprečnog presjeka nije konstanta, niti je jednostavnog oblika, koristeći program opisan u poglavlju \ref{subsec:racunalna_analiza_poprecnog_presjeka} kako bi se
odredila maksimalna površina poprečnog presjeka, te uzročno posljedično i naprezanje ($\sigma ''$) koje bi se pojavilo kada bi ispitni uzorak zbilja puknuo u presjeku
najvećom površinom (najgori slučaj koji nam po metodi "što više to bolje" daje najniži rezultat). Također je zabilježena i minimalna površina poprečnog presjeka
svakog ispitnog uzorka kako bi se mogao odrediti lokalni maksimum naprezanja ($\sigma '$) koji se pri zabilježenoj sili dogodio (opisano u daljnjoj analizi).
\begin{flushleft}
Za svaku eksperimentalnu kombinaciju iz ortogonalne matrice L18 (tablica \ref{tab:taguchi_l18_vlacni} izračunat je signal-šum (SNR) omjer prema izrazu
\ref{eq:sn_ratio}. Gdje je $y_i$ izmjerena vrijednost čvrstoće u $i$-tom ponavljanju, a $n$ broj ponavljanja. Budući da
je svaki ispitni uzorak (zbog ograničenih resursa) ispitivan samo jednom, izraz \ref{eq:sn_ratio} možemo pretvoriti u izraz \ref{eq:sn_ratio_vlak} (za
vlak).
Za svaki rezultat izračunat je S/N omjer (pripadajuč za taj slučaj) prema kriteriju što je vrijednost viša, to je bolja.\\
\end{flushleft}
\begin{equation}
\text{S/N} = -10 \cdot \log_{10}\left ( \frac{1}{\sigma^2}\right) = 20\cdot log_{10} \left (\sigma \right )
\label{eq:sn_ratio_vlak}
\end{equation}
\begin{table}[H]
\centering
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
Eksperiment & $A_{ekv}$ [mm$^2$] & $A_{min}$ [mm$^2$] & $A_{max}$ [mm$^2$] & $F_m$ [kN] & $\sigma$ [MPa] & $\sigma'$ & $\sigma''$ & SNR [dB] \\ \hline
1 & 100 & 44.493 & 44.493 & 0.778 & 7.78 & 17.4859 & 17.4859 & 17.8196 \\ \hline
2 & 100 & 87.819 & 87.819 & 3.299 & 32.99 & 37.5659 & 37.5659 & 30.3676 \\ \hline
3 & 100 & 100 & 100 & 0.794 & 7.94 & 7.9400 & 7.9400 & 17.9964 \\ \hline
4 & 100 & 87.6308 & 87.6308 & 2.792 & 27.92 & 31.8609 & 31.8609 & 28.9183 \\ \hline
5 & 100 & 91.5613 & 91.5613 & 2.468 & 24.68 & 26.9546 & 26.9546 & 27.8469 \\ \hline
6 & 100 & 93.9905 & 93.9905 & 2.871 & 28.71 & 30.5456 & 30.5456 & 29.1607 \\ \hline
7 & 100 & 92.7473 & 92.7473 & 2.423 & 24.23 & 26.1247 & 26.1247 & 27.6871 \\ \hline
8 & 100 & 96.3896 & 96.3896 & 1.891 & 18.91 & 19.6183 & 19.6183 & 25.5338 \\ \hline
9 & 100 & 79.2649 & 79.2649 & 2.431 & 24.31 & 30.6693 & 30.6693 & 27.7157 \\ \hline
10 & 100 & 35.669 & 71.34 & 3.398 & 33.98 & 95.2648 & 47.6311 & 30.6245 \\ \hline
11 & 100 & 36.045 & 72.09 & 3.218 & 32.18 & 89.2773 & 44.6386 & 30.1517 \\ \hline
12 & 100 & 26.908 & 53.817 & 2.768 & 27.68 & 102.869 & 51.4336 & 28.8433 \\ \hline
13 & 100 & 32.415 & 52.865 & 2.472 & 24.72 & 76.2610 & 46.7606 & 27.8610 \\ \hline
14 & 100 & 24.155 & 48.31 & 2.527 & 25.27 & 104.616 & 52.3080 & 28.0521 \\ \hline
15 & 100 & 42.804 & 85.607 & 3.647 & 36.47 & 85.2023 & 42.6017 & 31.2387 \\ \hline
16 & 100 & 26.909 & 53.817 & 2.491 & 24.91 & 92.5713 & 46.2865 & 27.9275 \\ \hline
17 & 100 & 44.555 & 89.111 & 4.111 & 41.11 & 92.2680 & 46.1335 & 32.2789 \\ \hline
18 & 100 & 15.895 & 31.79 & 2.263 & 22.63 & 142.372 & 71.1859 & 27.0937 \\ \hline
\end{tabular}
}
\caption{Rezultati vlačnog ispitivanja}
\label{tab:rezultati_vlacni}
\end{table}
\begin{flushleft}
Nakon što smo odredili sve vrijednosti za signal-šum omjere, moguće je onda odrediti srednji signal-šum za svaku od razina svakog faktora u tablici
\ref{tab:taguchi_l18_vlacni}, srednju čvrstoću svake razine svakog parametra, te finalno i razliku maksimalnog i minimalnog signal-šum omjera svake razine svakog
faktora. Sa tim podacima, možemo napraviti predikciju optimalne kombinacije signal-šum omjera. Svi navedeni podaci prikazani su u tablici \ref{tab:snr_vlak}.
\end{flushleft}
\begin{table}[H]
\centering
\scriptsize
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Faktor & Razina & Srednji SNR [dB] & Srednja čvrstoća [MPa] & $\Delta$ (SNR) & Optimalna kombinacija SNR \\ \hline
\multirow{2}{*}{Orijentacija}
& 1 & 25.8940 & 21.94 & \multirow{2}{*}{3.4473} & \multirow{2}{*}{2} \\ \cline{2-4}
& 2 & 29.3413 & 29.88 & & \\ \hline
\multirow{3}{*}{Visina sloja [mm]}
& 0.08 & 25.9672 & 23.76 & \multirow{3}{*}{3.2725} & \multirow{3}{*}{0.14} \\ \cline{2-4}
& 0.14 & 28.8463 & 27.96 & & \\ \cline{2-4}
& 0.28 & 28.0395 & 26.02 & & \\ \hline
\multirow{3}{*}{Širina ekstruzije [mm]}
& 0.4 & 26.8063 & 23.92 & \multirow{3}{*}{2.8791} & \multirow{3}{*}{0.6} \\ \cline{2-4}
& 0.6 & 29.0385 & 29.19 & & \\ \cline{2-4}
& 0.8 & 27.0081 & 24.62 & & \\ \hline
\multirow{3}{*}{Postotak ispune [\%]}
& 20 & 26.2701 & 22.49 & \multirow{3}{*}{2.3673} & \multirow{3}{*}{55} \\ \cline{2-4}
& 55 & 28.6374 & 27.18 & & \\ \cline{2-4}
& 85 & 27.9454 & 28.07 & & \\ \hline
\multirow{3}{*}{Broj slojeva stijenke}
& 2 & 26.2286 & 22.06 & \multirow{3}{*}{2.2322} & \multirow{3}{*}{4} \\ \cline{2-4}
& 4 & 29.5010 & 30.22 & & \\ \cline{2-4}
& 6 & 27.1234 & 25.46 & & \\ \hline
\end{tabular}
\caption{Analiza faktora s prosječnim vrijednostima SNR i čvrstoće}
\label{tab:snr_vlak}
\end{table}
\subsubsection{ANOVA analiza rezultata vlačnog ispitivanja}\label{subsubsec:anova_analiza_rezultata_vlacnog_ispitivanja}
ANOVA metodu provesti ćemo po postupku opisanom u poglavlju \ref{subsec:anova_analiza}
Izračunamo li srednju srednju vrijednost ($\mu$) naprezanja $\sigma$ svakog eksperimenta te zbroj kvadrata odstupanja točaka od srednje vrijednosti za skup svih
$\sigma$, uz broj uzoraka $\mathrm{N}=18$, dobivamo vrijednosti iz izraza \ref{eq:sst} te izraza \ref{eq:sigma_avg}.\\
\begin{equation}\label{eq:sigma_avg}
\mu = \bar{\sigma} = \frac{\sum_{i=1}^{N} (\sigma_i)}{N} = 25.912 \mathrm{MPa}
\end{equation}
\begin{equation}\label{eq:sst}
SS_{ukupno} = \sum_{i=1}^{N} (\sigma_i) = 1233.228 \mathrm{MPa^2}
\end{equation}
Sada je moguće izračunati zbrojeve kvadrata za svaki faktor ($\mathrm{SS_f}$) prema izrazu \ref{eq:ssf} koji predstavlja dio ukupne varijacije koji se može pripisati
glavnom učinku faktora za koji se računa.\\
\begin{equation}\label{eq:ssf}
SS_f = \sum_{j=1}^{l} n_j (\bar{\sigma}_j - \bar{\sigma})^2
\end{equation}
Srednji kvadrat definiran je izrazima \ref{eq:msf} i \ref{eq:mse} te opisuje prosječni varijabilitet koji objašnjava faktor po jednom stupnju slobode i "ostatak", tj.
preostali varijabilitet koji model nije objasnio.\\
\begin{equation}\label{eq:msf}
\mathrm{MS_f} = \frac{\mathrm{SS_f}}{\mathrm{SL_f}}
\end{equation}
\begin{equation}\label{eq:mse}
\mathrm{MS_E} = \frac{\mathrm{SS_E}}{\mathrm{SL_E}}
\end{equation}
Stupnjevi slobode govore koliko je neovisnih informacija dostupno za procjenu varijabilnosti. Ukupni broj stupnjeva slobode (definiran izrazom \ref{eq:sl_ukupno}
je zapravo ukupan broj ispitnih uzoraka, umanjen za jedan jer jedno od $\mathrm{N}$ mjerenja koristimo za procjenu ukupnog prosjeka $\mu$, dok je broj
stupnjeva slobode faktora s $\mathrm{a}$ razina (definiran izrazom \ref{eq:sl_faktor}) umanjen za jedan jer se jedna razina koristi za kontrast u odnosu na $\mu$.\\
\begin{equation}\label{eq:sl_ukupno}
\mathrm{SL_{ukupno}} = \mathrm{N} - 1
\end{equation}
\begin{equation}\label{eq:sl_faktor}
\mathrm{SL_{faktor}} = \mathrm{a} -1
\end{equation}
U tablici \ref{tab:anova_ssf_vlak} prikazane su vrijednosti zbroja kvadrata, stupnjeva slobode te srednjih kvadrata za svaki faktor i njegove razine.\\
\begin{table}[H]
\centering
\caption{Rezultati vlačnih ispitivanja (primjer vrijednosti → moram ubaciti prave nakon kidanja, ali ovo bi trebao biti format tablice)}
\label{tab:rezultati_vlacni}
\begin{tabular}{|c|c|c|c|c|}
\hline
Eksperiment & Orijentacija & $F_\text{max}$ [N] & Površina presjeka $A$ [mm$^2$] & $\sigma$ [MPa] \\
\hline
1 & Orijentacija 1 & 1420 & 25.0 & 56.8 \\
2 & Orijentacija 1 & 1280 & 25.0 & 51.2 \\
3 & Orijentacija 1 & 1630 & 25.0 & 65.2 \\
... & ... & ... & ... & ... \\
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Faktor & $\bar{\sigma}$ & n & $\mu^2$ & $\mathrm{n} \cdot \mu^2$ \\ \hline
\multicolumn{5}{|l|}{\textbf{Orijentacija}} \\ \hline
1 & 21.9411 & 9 & 15.7697 & 141.9275 \\ \hline
2 & 29.8833 & 9 & 15.7697 & 141.9275 \\ \hline
\textbf{Zbroj kvadrata} & & & & 283.8550 \\ \hline
\textbf{Stupnjevi slobode} & & & & 1 \\ \hline
\textbf{Srednji kvadrat} & & & & 283.8550 \\ \hline
\multicolumn{5}{|l|}{\textbf{Visina sloja [mm]}} \\ \hline
0.08 & 23.7583 & 6 & 4.6392 & 27.8354 \\ \hline
0.14 & 27.9617 & 6 & 4.2002 & 25.2013 \\ \hline
0.28 & 26.0167 & 6 & 0.0109 & 0.0655 \\ \hline
\textbf{Zbroj kvadrata} & & & & 53.1022 \\ \hline
\textbf{Stupnjevi slobode} & & & & 2 \\ \hline
\textbf{Srednji kvadrat} & & & & 26.5511 \\ \hline
\multicolumn{5}{|l|}{\textbf{Širina ekstruzije [mm]}} \\ \hline
0.4 & 23.9233 & 6 & 3.9557 & 23.7347 \\ \hline
0.6 & 29.19 & 6 & 10.7438 & 64.4629 \\ \hline
0.8 & 24.6233 & 6 & 1.6612 & 9.9674 \\ \hline
\textbf{Zbroj kvadrata} & & & & 98.1644 \\ \hline
\textbf{Stupnjevi slobode} & & & & 2 \\ \hline
\textbf{Srednji kvadrat} & & & & 49.0822 \\ \hline
\multicolumn{5}{|l|}{\textbf{Postotak ispune [\%]}} \\ \hline
20 & 22.4883 & 6 & 11.7230 & 70.3381 \\ \hline
55 & 27.18 & 6 & 1.6073 & 9.6436 \\ \hline
85 & 28.0683 & 6 & 4.6489 & 27.8929 \\ \hline
\textbf{Zbroj kvadrata} & & & & 107.8745 \\ \hline
\textbf{Stupnjevi slobode} & & & & 2 \\ \hline
\textbf{Srednji kvadrat} & & & & 53.9377 \\ \hline
\multicolumn{5}{|l|}{\textbf{Broj slojeva stijenke}} \\ \hline
2 & 22.0583 & 6 & 14.8525 & 89.1148 \\ \hline
4 & 30.215 & 6 & 18.5139 & 111.0834 \\ \hline
6 & 25.4633 & 6 & 0.2015 & 1.2090 \\ \hline
\textbf{Zbroj kvadrata} & & & & 201.4071 \\ \hline
\textbf{Stupnjevi slobode} & & & & 2 \\ \hline
\textbf{Srednji kvadrat} & & & & 100.7036 \\ \hline
\end{tabular}
\caption{Sume kvadrata faktora vlačnog testa}
\label{tab:anova_ssf_vlak}
\end{table}
Za svaki rezultat izračunat je S/N omjer (pripadajuč za taj slučaj) prema kriteriju što je vrijednost viša, to je bolja.\\
\begin{equation}
\text{S/N} = -10 \cdot \log_{10}\left( \frac{1}{n} \sum_{i=1}^{n} \frac{1}{y_i^2} \right)
\label{eq:sn_ratio}
Pogreška predstavlja sve što nije objašnjeno glavnim učincima u modelu, te je definirana izrazom \ref{eq:pogreska}. Uzevši u obzir da (zbog ograničennja eksperimenta)
nemamo više ispitivanja istih epruveta, pogreška će sadržavati interakcije među faktorima (jer ih ne procjenjujemo), stohastični šum procesa (varijacije u ispisu,
temperaturama, mjerenju itd.) te neubrojene kovarijante (neidealnu adheziju, točne poprečne presjeke, interakciju geometrije ispune i stijenke itd.). Pogreška u
ovome slučaju zato neće predstavljati grešku u mjerenju, već neobjašnjene varijacije u rezultatu.
\begin{equation}\label{eq:pogreska}
\mathrm{SS_E} = \mathrm{SS_{ukupno}} - \sum_f \mathrm{SS_f}
\end{equation}
F-omjer, opisan izrazom \ref{eq:f-ratio}, predstavlja usporedbu varijabilnosti zbog faktora te preostale (rezidualne) varijabilnosti. Velika F vrijednost govori
da se razine u tome faktoru razlikuju više nego što bi se očekivalo od slučajnog šuma, te je kao takva pokazatelj statističke značajnosti faktora na finalni rezultat.\\
\begin{equation}\label{eq:f-ratio}
\mathrm{F_f} = \frac{\mathrm{MS_f}}{\mathrm{MS_e}}
\end{equation}
Sažetak cijele analize, te udio varijabiliteta svakog faktora prikazan je u tablici \ref{tab:anova_sazetak_vlak}.\\
\begin{table}[H]
\centering
\scriptsize
\begin{tabular}{|l|c|c|c|c|c|}
\hline
\textbf{Faktor} & \textbf{Zbroj kvadrata (SS)} & \textbf{Stupnjevi slobode (df)} & \textbf{Srednji kvadrat (MS)} & \textbf{F-omjer} & \textbf{Udio varijabiliteta [\%]} \\ \hline
Orijentacija & 283.8550 & 1 & 283.8550 & 4.6455 & 23.0172 \\ \hline
Visina sloja & 53.1022 & 2 & 26.5511 & 0.4345 & 4.3060 \\ \hline
Širina ekstruzije & 98.1644 & 2 & 49.0822 & 0.8033 & 7.9600 \\ \hline
Postotak ispune & 107.8745 & 2 & 53.9373 & 0.8827 & 8.7473 \\ \hline
Broj slojeva stijenke & 201.4071 & 2 & 100.7036 & 1.6481 & 16.3317 \\ \hline
Pogreška (rezidual) & 488.8245 & 8 & 61.1031 & & 39.6378 \\ \hline
\textbf{Ukupno} & 1233.2279 & 17 & & & 100.0000 \\ \hline
\end{tabular}
\caption{ANOVA tablica sa SS, df, MS, F-omjerom i udjelom varijabiliteta}
\label{tab:anova_sazetak_vlak}
\end{table}
\subsection{Obrada rezultata smičnog ispitivanja}\label{subsec:obrada_rezultata_smičnog_ispitivanja}
Rezultati smičnog ispitivanja obratiti će se na isti način kao i kod vlačnog, dakle prema poglavlju \ref{subsec:obrada_rezultata_vlačnog_ispitivanja}. \\
@@ -1399,12 +1618,28 @@ Eksperiment & Orijentacija & $F_\text{max}$ [N] & Površina presjeka $A$ [mm$^2$
\subsection{Obrada rezultata i S/N omjer}\label{subsec:obrada_rezultata_i_sn_omjer}
Za svaku eksperimentalnu kombinaciju iz ortogonalnih matrica L18 i L27 (tablice \ref{tab:taguchi_l18_vlacni} i \ref{tab:taguchi_l27}) prikupljeni su podaci
vlačne i smične čvrstoće (prema poglavljima \ref{subsec:obrada_rezultata_vlačnog_ispitivanja} i \ref{subsec:obrada_rezultata_smičnog_ispitivanja}) te je na temelju istih
izračunat signal-šum (S/N) omjer prema izrazu \ref{eq:sn_ratio}. Gdje je $y_i$ izmjerena vrijednost čvrstoće u $i$-tom ponavljanju, a $n$ broj ponavljanja.\\
izračunat signal-šum (S/N) omjer prema izrazu \ref{eq:sn_ratio}. Gdje je $y_i$ izmjerena vrijednost čvrstoće u $i$-tom ponavljanju, a $n$ broj ponavljanja. Budući da
je svaki ispitni uzorak (zbog ograničenih resursa) ispitivan samo jednom, izraz \ref{eq:sn_ratio} možemo pretvoriti u izraz \ref{eq:sn_ratio_vlak} (za
vlak) te izraz \ref{eq:sn_ratio_smik} (za smik).\\
\begin{equation}
\text{S/N} = -10 \cdot \log_{10}\left ( \frac{1}{\sigma^2}\right) = 20\cdot log_{10} \left (\sigma \right )
\label{eq:sn_ratio_vlak}
\end{equation}
\begin{equation}
\text{S/N} = -10 \cdot \log_{10}\left ( \frac{1}{\tau^2}\right) = 20\cdot log_{10} \left (\tau \right )
\label{eq:sn_ratio_smik}
\end{equation}
\subsection{ANOVA analiza}\label{subsec:anova_analiza}
Kako bi se kvantificirao doprinos svakog pojedinog parametra, na ukupnu varijabilnost čvstoće, provedena je analiza varijance (ANOVA).\\
ANOVA postupak obuhvaća sljedeće postupke:\\
ANOVA postupak obuhvaća sljedeće korake:\\
\begin{enumerate}
\item Izračun ukupne sume kvadrata (SST), koja predstavlja ukupnu varijabilnost rezultata:
\begin{equation}