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započeta konstrukcija naprave za smik

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Niko Vujic
2025-08-23 14:32:25 +02:00
parent acd12da62f
commit 35d7dec29a
35 changed files with 2557 additions and 624 deletions
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29
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.aux
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49
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl
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49
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl-SAVE-ERROR
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radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf
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1
radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf-SAVE-ERROR
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30
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'
[42] biber:342> INFO - === Thu Aug 21, 2025, 11:07:22
[50] Biber.pm:420> INFO - Reading 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf'
[80] Biber.pm:994> INFO - Found 20 citekeys in bib section 0
[88] Biber.pm:4463> INFO - Processing section 0
[93] Biber.pm:4654> INFO - Looking for bibtex file 'literatura.bib' for section 0
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[180] UCollate.pm:68> INFO - Overriding locale 'hr-HR' defaults 'normalization = NFD' with 'normalization = prenormalized'
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[195] bbl.pm:780> INFO - Output to ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl
[196] Biber.pm:131> WARN - Duplicate entry key: 'kuznetsov2018strengthPLA' in file 'literatura.bib', skipping ...
[196] Biber.pm:131> WARN - legacy year field '1963.' in entry 'bazjanacNauka1' is not an integer - this will probably not sort properly.
[196] Biber.pm:133> INFO - WARNINGS: 2
[48] biber:342> INFO - === Sat Aug 23, 2025, 14:16:35
[59] Biber.pm:420> INFO - Reading 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bcf'
[92] Biber.pm:994> INFO - Found 21 citekeys in bib section 0
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[227] Biber.pm:4283> INFO - Sorting list 'nty/global//global/global/global' of type 'entry' with template 'nty' and locale 'hr-HR'
[243] bbl.pm:677> INFO - Writing 'ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl' with encoding 'UTF-8'
[248] bbl.pm:780> INFO - Output to ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.bbl
[248] Biber.pm:131> WARN - Duplicate entry key: 'kuznetsov2018strengthPLA' in file 'literatura.bib', skipping ...
[248] Biber.pm:131> WARN - legacy year field '1963.' in entry 'bazjanacNauka1' is not an integer - this will probably not sort properly.
[248] Biber.pm:133> INFO - WARNINGS: 2

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radno/ispitivanje_cvrstoce_fdm_3d_printanog_uzorka.fdb_latexmk
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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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@@ -1073,8 +1103,108 @@ Charpy unnotched [kJ/m$^2$] & 23 °C & 10.4 \\ \
\end{tabular}
\end{table}
\subsection{Metode ispitivanja čvrstoće}\label{subsec:metode_ispitivanja_cvrstoce}
\subsection{Postav za ispitivanje smične čvrstoće}\label{subsec:postav_za_ispitivanje_smicne_cvrstoce}
%---- → UBACITI DIO SA JIGOM ZA SMIK
Pošto je jedini dostupni stroj za ispitivanje čvrstoće univerzalna kidalica, ispitivanje smične čvrstoće biti će izvedeno uzorkom s V-utorom na linearnim vodilicama.
Potrebno je iz tog razloga napraviti napravu za univerzalnu kidalicu koji će omogućiti da se razvlačenjem naprave ostvari smik u kritičnom presjeku ispitnog uzorka.
Po uzoru na \cite{Stamopoulos2020} napravljena je naprava prikazana na slici \ref{fig:naprava_smik} koja pomoću dvije čeljusti steže ispitni uzorak opisan
u poglavlju \ref{subsubsec:konstrukcija_epruveta} te ju pomoću dvaju linearnih vodilica razvlači na način da u kritičnom presjeku (V-utoru) ostvaruje (gotovo) čisto
smično naprezanje.\\
\begin{figure}[H]
\centering
\includegraphics[width=0.7\textwidth]{media/imgs/planiranje_eksperimenta/naprava_smik.jpg}
\caption{Prikaz naprave za smično opterečenje epruvete}
\label{fig:naprava_smik}
\end{figure}
\begin{flushleft}
Pošto obrada odvajanjem čestica nije dostupna na korištenje u ovom radu, naprava će biti izrađena metodom FDM 3D printanja. Iz istog je razloga potrebno voditi
računa o čvrstoći iste kako ne bi došlo do deformacije naprave u razini u kojoj bi dovela točnost mjerenja pomaka u ispitnom uzorka u pitanje.\\
\end{flushleft}
\pagebreak
\section{Provedba eksperimenta}\label{sec:provedba_eksperimenta}
\pagebreak
\section{Analiza podataka}\label{sec:analiza_podataka}
\subsection{Računalna analiza poprečnog presjeka}\label{subsec:racunalna_analiza_poprecnog_presjeka}
Za proračun naprezanja potrebno je odrediti stvarne površine poprečnih presjeka ispitnih uzoraka, koje su ovisne o geometriji ispune (vrsti ispune), širini ekstruzije
(širini traga), postotku ispune, broju stijenki i orijentaciji slojeva. U tu svrhu napisan je Python alat koji simulira unutarnju strukturu 3D printanog uzorka u 2D
rasteru. Na temelju navedenih parametara, program generira booleovu masku koja prikazuje raspored materijala u poprečnom presjeku.\\
\begin{flushleft}
Alat nakon generiranja booleove maske izračunava:
\begin{itemize}
\item ukupnu površinu presjeka u XY ravnini (pošto je XY ravnina normalna na Z-os ispisa, ova je površina konstantna u 2D ispunama)
\item površine presjeka u ravninama paralelnim s XZ i YZ ravninama (što je relevantno za različite orijentacije ispisa)
\end{itemize}
Primjer vizualizacije presjeka za obije orijentacije potrebne za vlačno testiranje nalazi se na slikama \ref{fig:vlak_2d_stojeci}, \ref{fig:vlak_2d_lezeci}.\\
\end{flushleft}
\begin{figure}[H]
\centering
\includegraphics[width=0.5\textwidth]{media/imgs/analiza_podataka/vlak_2d_stojeci.jpg}
\caption{2D prikaz ispune ispitnog uzorka u orijentaciji uspravnog ispisa.}
\label{fig:vlak_2d_stojeci}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=0.5\textwidth]{media/imgs/analiza_podataka/vlak_2d_lezeci.jpg}
\caption{2D prikaz ispune ispitnog uzorka u orijentaciji ležećeg ispisa.}
\label{fig:vlak_2d_lezeci}
\end{figure}
\begin{flushleft}
Iako 2D ispune ne mijenjaju površinu poprečnog presjeka kroz Z-os, u ostale dvije dimenzije ona se svakako mijenja, kako bi se odredilo koliko se točno mijenja,
napravljen je graf promjene površine u odnosu na duljinu modela, te automatski proračun površine paralelne sa XZ i YZ ravninama za zadanu x i y dimenziju.
Na slikama \ref{fig:promjena_povrsine_10x10}, \ref{fig:promjena_povrsine_10x70} prikazane su promjene površina u odnosu na njihove referentne ravnine.\\
\end{flushleft}
\begin{figure}[H]
\centering
\includegraphics[width=0.6\textwidth]{media/imgs/analiza_podataka/promjena_povrsine_10x10.jpg}
\caption{Promjena površine po X i Y osi za bazu 10x10mm.}
\label{fig:promjena_povrsine_10x10}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=0.6\textwidth]{media/imgs/analiza_podataka/promjena_povrsine_10x70.jpg}
\caption{Promjena površine po X i Y osi za bazu 10x70mm.}
\label{fig:promjena_povrsine_10x70}
\end{figure}
Za slučaj potrebe izračuna površine poprečnog presjeka u točnoj koordinati, moguć je upis zasebne visine na x i y osi, te je nakon izvršavanja programa ispisana i
površina u odnosu na te referentne osi u sljedećem formatu:\\
\begin{verbatim}
==== Grid ispuna 30.0% ====
XY ukupna povrsina = 301.7364 mm^2
Povrsina ljuski = 132.4033 mm^2
Povrsina ispune = 169.3331 mm^2
-- Presjeci kroz Z (uzorak konstantan po Z) --
Duzina po X @ y=1.000 mm: 4.0801 mm
Duzina po Y @ x=-2.000 mm: 19.0989 mm
Povrsina XZ @ y=1.000: 40.8010 mm^2 (Z=10.000 mm)
Povrsina YZ @ x=-2.000: 190.9887 mm^2 (Z=10.000 mm)
A_xz(y=1mm) = 40.80100125156456 mm^2
A_yz(x=-2mm) = 190.9887359198926 mm^2
\end{verbatim}
Uzevši u obzir da je Bambu Lab Slicer program otvorenog koda, matematički model i način generiranja mrežaste (Grid) ispune preuzet je iz istog, te prepisan iz
programskog jezika C++ u programski jezik Python, te dorađen za 2D prikaz. \\
Izračun površina i geometrijskih momenata presjeka proveden je pomoću vlastitog Python programa izvršavanog u JupyterLab okruženju (vidi Prilog A).
%---------------------------------------------------------------------
%----------------------LITERATURA-------------------------------------
@@ -1083,4 +1213,228 @@ Charpy unnotched [kJ/m$^2$] & 23 °C & 10.4 \\ \
\newpage
\newpage
\printbibliography[title={Literatura}]
\pagebreak
\appendix
\section*{Prilog A – Python skripta za analizu poprečnih presjeka}
\addcontentsline{toc}{section}{Prilog A – Python skripta za analizu poprečnih presjeka}
Sljedeći kod izvršavan je unutar okruženja \textbf{JupyterLab}, a koristi biblioteku \texttt{NumPy} i \texttt{Matplotlib}. Skripta služi za generiranje simuliranog rasporeda ispune FDM ispisa i izračun površina presjeka i geometrijskih momenata inercije.
\begin{lstlisting}[style=python, caption={Python skripta za analizu poprečnih presjeka.}]
import numpy as np
import matplotlib.pyplot as plt
def _udaljenost_mod(u, razmak):
r = np.mod(u, razmak)
return np.minimum(r, razmak - r)
def _pravocrtna_maska(XX, YY, razmak, sirina_linije, kut_stupnjevi=0.0, faza=0.0):
th = np.deg2rad(kut_stupnjevi)
u = XX * np.cos(th) + YY * np.sin(th)
dist = _udaljenost_mod(u + faza, razmak)
return dist <= (sirina_linije / 2.0)
def _razmak_za_gustocu_mreze(sirina_linije, f):
f = float(np.clip(f, 0.0, 1.0))
if f <= 0.0:
return np.inf
if f >= 1.0:
return sirina_linije
r = 1.0 - np.sqrt(1.0 - f)
return sirina_linije / r
def izracun_povrsine(XX, YY, maska):
if not np.any(maska):
return {"A": 0.0}
dx = XX[0, 1] - XX[0, 0]
dy = YY[1, 0] - YY[0, 0]
dA = dx * dy
A = float(np.count_nonzero(maska) * dA)
return {"A": A}
def prusa_mreza_ili_pravocrtna(
sirina, visina,
udio_ispune,
sirina_linije=0.42,
slojevi_ljuske=2,
osnovni_kut_ispune_stupnjevi=45.0,
mreza=True,
z_visina=0.0,
faza_po_mm=0.0,
z_visina_objekta=None,
y_ravnina=0.0,
x_ravnina=0.0,
N=800,
graficki_prikaz=True,
detaljno=True
):
xs = np.linspace(-sirina/2, sirina/2, N)
ys = np.linspace(-visina/2, visina/2, N)
XX, YY = np.meshgrid(xs, ys)
shell_mask = np.zeros_like(XX, dtype=bool)
for i in range(slojevi_ljuske):
off = (i + 0.5) * sirina_linije
shell_mask |= np.abs(XX - (-sirina/2 + off)) <= (sirina_linije / 2)
shell_mask |= np.abs(XX - ( +sirina/2 - off)) <= (sirina_linije / 2)
shell_mask |= np.abs(YY - (-visina/2 + off)) <= (sirina_linije / 2)
shell_mask |= np.abs(YY - ( +visina/2 - off)) <= (sirina_linije / 2)
unutarnji_pomak = slojevi_ljuske * sirina_linije
unutarnji_pravokutnik = (
(np.abs(XX) <= (sirina/2 - unutarnji_pomak)) &
(np.abs(YY) <= (visina/2 - unutarnji_pomak))
)
if udio_ispune <= 0.0:
infill_mask = np.zeros_like(XX, dtype=bool)
elif udio_ispune >= 1.0:
razmak = sirina_linije
maske = []
kutevi = [osnovni_kut_ispune_stupnjevi] + ([osnovni_kut_ispune_stupnjevi + 90] if mreza else [])
faza = faza_po_mm * z_visina
for a in kutevi:
maske.append(_pravocrtna_maska(XX, YY, razmak, sirina_linije, kut_stupnjevi=a, faza=faza))
infill_mask = np.logical_or.reduce(maske) & unutarnji_pravokutnik
else:
razmak = _razmak_za_gustocu_mreze(sirina_linije, udio_ispune) if mreza \
else sirina_linije / udio_ispune
maske = []
kutevi = [osnovni_kut_ispune_stupnjevi] + ([osnovni_kut_ispune_stupnjevi + 90] if mreza else [])
faza = faza_po_mm * z_visina
for a in kutevi:
maske.append(_pravocrtna_maska(XX, YY, razmak, sirina_linije, kut_stupnjevi=a, faza=faza))
infill_mask = np.logical_or.reduce(maske) & unutarnji_pravokutnik
konacna_maska = shell_mask | infill_mask
if graficki_prikaz:
plt.figure(figsize=(6, 6))
img = np.where(konacna_maska, 1.0, np.nan)
plt.imshow(img, origin='lower',
extent=[-sirina/2, sirina/2, -visina/2, visina/2],
interpolation='nearest')
naslov = "Grid" if mreza else "Pravocrtna"
plt.title(f"{naslov} @ {udio_ispune*100:.1f}% | ljuske={slojevi_ljuske}*{sirina_linije:.2f} kut={osnovni_kut_ispune_stupnjevi:.0f}deg")
plt.xlabel("X (mm)")
plt.ylabel("Y (mm)")
plt.gca().set_aspect('equal', 'box')
plt.grid(True)
plt.hlines(y_ravnina, -sirina/2, sirina/2, linestyles='--')
plt.vlines(x_ravnina, -visina/2, visina/2, linestyles='--')
plt.show()
total = izracun_povrsine(XX, YY, konacna_maska)
ljuske = izracun_povrsine(XX, YY, shell_mask)
A_ispuna = total["A"] - ljuske["A"]
dx = XX[0, 1] - XX[0, 0]
dy = YY[1, 0] - YY[0, 0]
ys_centered = YY[:, 0]
xs_centered = XX[0, :]
row = int(np.argmin(np.abs(ys_centered - y_ravnina)))
col = int(np.argmin(np.abs(xs_centered - x_ravnina)))
duzina_x_na_y = float(np.count_nonzero(konacna_maska[row, :]) * dx)
duzina_y_na_x = float(np.count_nonzero(konacna_maska[:, col]) * dy)
povrsina_xz_na_y = None
povrsina_yz_na_x = None
if z_visina_objekta is not None and z_visina_objekta > 0:
povrsina_xz_na_y = duzina_x_na_y * z_visina_objekta
povrsina_yz_na_x = duzina_y_na_x * z_visina_objekta
duzina_x_vs_y = np.count_nonzero(konacna_maska, axis=1) * dx
duzina_y_vs_x = np.count_nonzero(konacna_maska, axis=0) * dy
if z_visina_objekta is not None and z_visina_objekta > 0:
povrsina_xz_vs_y = duzina_x_vs_y * z_visina_objekta
povrsina_yz_vs_x = duzina_y_vs_x * z_visina_objekta
y_oznaka = "Povrsina XZ presjeka (mm^2)"
x_oznaka = "Povrsina YZ presjeka (mm^2)"
else:
povrsina_xz_vs_y = duzina_x_vs_y
povrsina_yz_vs_x = duzina_y_vs_x
y_oznaka = "Duzina po X (mm) [postavi z_visina_objekta za povrsinu]"
x_oznaka = "Duzina po Y (mm) [postavi z_visina_objekta za povrsinu]"
y_os_0_do_H = ys_centered + visina/2.0
x_os_0_do_W = xs_centered + sirina/2.0
if graficki_prikaz:
plt.figure(figsize=(7, 3.5))
plt.plot(y_os_0_do_H, povrsina_xz_vs_y)
plt.xlabel("y od donjeg zida (mm)")
plt.ylabel(y_oznaka)
plt.title("Varijacija prema y")
plt.grid(True)
plt.xlim(0, visina)
plt.tight_layout()
plt.show()
plt.figure(figsize=(7, 3.5))
plt.plot(x_os_0_do_W, povrsina_yz_vs_x)
plt.xlabel("x od lijevog zida (mm)")
plt.ylabel(x_oznaka)
plt.title("Varijacija prema x")
plt.grid(True)
plt.xlim(0, sirina)
plt.tight_layout()
plt.show()
if detaljno:
print(f"==== {('Grid' if mreza else 'Pravocrtna')} ispuna {udio_ispune*100:.1f}% ====")
print(f"XY ukupna povrsina = {total['A']:.4f} mm^2")
print(f" Povrsina ljuski = {ljuske['A']:.4f} mm^2")
print(f" Povrsina ispune = {A_ispuna:.4f} mm^2")
print(f"-- Presjeci kroz Z (uzorak konstantan po Z) --")
print(f"Duzina po X @ y={y_ravnina:.3f} mm: {duzina_x_na_y:.4f} mm")
print(f"Duzina po Y @ x={x_ravnina:.3f} mm: {duzina_y_na_x:.4f} mm")
if povrsina_xz_na_y is not None:
print(f"Povrsina XZ @ y={y_ravnina:.3f}: {povrsina_xz_na_y:.4f} mm^2 (Z={z_visina_objekta:.3f} mm)")
if povrsina_yz_na_x is not None:
print(f"Povrsina YZ @ x={x_ravnina:.3f}: {povrsina_yz_na_x:.4f} mm^2 (Z={z_visina_objekta:.3f} mm)")
print()
return {
"maska": konacna_maska,
"XX": XX, "YY": YY,
"dx": dx, "dy": dy,
"povrsina_ukupno_xy": total["A"],
"povrsina_ljuske_xy": ljuske["A"],
"povrsina_ispune_xy": A_ispuna,
"duzina_x_na_y": duzina_x_na_y,
"duzina_y_na_x": duzina_y_na_x,
"povrsina_xz_na_y": povrsina_xz_na_y,
"povrsina_yz_na_x": povrsina_yz_na_x,
"y_os_mm": y_os_0_do_H,
"x_os_mm": x_os_0_do_W,
"povrsina_xz_vs_y": povrsina_xz_vs_y,
"povrsina_yz_vs_x": povrsina_yz_vs_x,
}
# Konfiguracija
if __name__ == "__main__":
W, H = 10.0, 70.0
Z = 10.0
res = prusa_mreza_ili_pravocrtna(
sirina=W, visina=H,
udio_ispune=0.2,
sirina_linije=0.42,
slojevi_ljuske=2,
osnovni_kut_ispune_stupnjevi=45.0,
mreza=True,
z_visina_objekta=Z,
y_ravnina=+1.0,
x_ravnina=-2.0,
N=800,
graficki_prikaz=True, detaljno=True
)
print("A_xz(y=1mm) =", res["povrsina_xz_na_y"], "mm^2")
print("A_yz(x=-2mm) =", res["povrsina_yz_na_x"], "mm^2")
\end{lstlisting}
\end{document}

11
radno/literatura.bib
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@@ -221,4 +221,15 @@
doi = {10.5937/fme2502326C},
note = {ISSN 1451-2092}
}
@article{Stamopoulos2020,
author = {Antonios G. Stamopoulos and Luca Glauco Di Genova and Antoniomaria Di Ilio},
title = {Assessment of the shear properties of thermoplastic composites using the ±45° tension and the V-notched rail shear methods},
journal = {Manufacturing Rev.},
volume = {7},
pages = {10},
year = {2020},
publisher = {EDP Sciences},
doi = {10.1051/mfreview/2020007},
url = {https://doi.org/10.1051/mfreview/2020007}
}

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