From 2c3f692beba4b154b7db73d8477b4fef7c159bef Mon Sep 17 00:00:00 2001 From: javalsai <jvssxxi@gmail.com> Date: Sat, 23 Nov 2024 21:09:00 +0100 Subject: [PATCH] =?UTF-8?q?add=20notes=20=F0=9F=91=8D?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- notes/math/U0_Exercises.html | 34 +++++ notes/math/U0_Exercises.md | 38 ++++++ notes/tech/Ensayos de Tracción.html | 138 +++++++++++++++++++++ notes/tech/Ensayos de Tracción.md | 63 ++++++++++ notes/tech/Pasted image 20241017201832.png | Bin 0 -> 73774 bytes notes/tech/Pasted image 20241017202224.png | Bin 0 -> 54523 bytes notes/tech/Pasted image 20241017205944.png | Bin 0 -> 238323 bytes notes/tech/Pasted image 20241017210008.png | Bin 0 -> 232226 bytes notes/tech/Pasted image 20241017210211.png | Bin 0 -> 19545 bytes notes/tech/Pasted image 20241017210225.png | Bin 0 -> 17657 bytes notes/tech/Pasted image 20241017211222.png | Bin 0 -> 51722 bytes notes/tech/Pasted image 20241017211235.png | Bin 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20241017214311.png create mode 100644 notes/tech/Pasted image 20241017220307.png create mode 100644 notes/tech/Pasted image 20241017220332.png diff --git a/notes/math/U0_Exercises.html b/notes/math/U0_Exercises.html new file mode 100644 index 0000000..7569cf4 --- /dev/null +++ b/notes/math/U0_Exercises.html @@ -0,0 +1,34 @@ +<!--# include virtual="/components/md-pre.html" --> +<h1 id="exercise-86-page-30">Exercise 86 page 30</h1> +<p>Calcula el rango de estas matrices:</p> +<ul> +<li><p>Apartado A +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><mn>2</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>2</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex"> +A = \begin{pmatrix} +2 & 0 \\ +0 & 2 +\end{pmatrix} +</annotation></semantics></math> Rango 2.</p></li> +<li><p>Apartado B +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><mn>1</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>2</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>1</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>2</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex"> +B = \begin{pmatrix} +1 & 2 \\ +1 & 2 +\end{pmatrix} +</annotation></semantics></math> Rango 1.</p></li> +<li><p>Apartado C +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><mn>1</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex"> +C = \begin{pmatrix} +1 & 0 \\ +0 & 0 +\end{pmatrix} +</annotation></semantics></math> Rango 1.</p></li> +<li><p>Apartado D +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>1</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>2</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex"> +B = \begin{pmatrix} +0 & 1 \\ +2 & 0 +\end{pmatrix} +</annotation></semantics></math> Rango 2.</p></li> +</ul> +<!--# include virtual="/components/md-post.html" --> diff --git a/notes/math/U0_Exercises.md b/notes/math/U0_Exercises.md new file mode 100644 index 0000000..2c89492 --- /dev/null +++ b/notes/math/U0_Exercises.md @@ -0,0 +1,38 @@ +# Exercise 86 page 30 +Calcula el rango de estas matrices: + +- Apartado A +$$ +A = \begin{pmatrix} +2 & 0 \\ +0 & 2 +\end{pmatrix} +$$ +Rango 2. + +- Apartado B +$$ +B = \begin{pmatrix} +1 & 2 \\ +1 & 2 +\end{pmatrix} +$$ +Rango 1. + +- Apartado C +$$ +C = \begin{pmatrix} +1 & 0 \\ +0 & 0 +\end{pmatrix} +$$ +Rango 1. + +- Apartado D +$$ +B = \begin{pmatrix} +0 & 1 \\ +2 & 0 +\end{pmatrix} +$$ +Rango 2. diff --git a/notes/tech/Ensayos de Tracción.html b/notes/tech/Ensayos de Tracción.html new file mode 100644 index 0000000..b6df7bc --- /dev/null +++ b/notes/tech/Ensayos de Tracción.html @@ -0,0 +1,138 @@ +<!--# include virtual="/components/md-pre.html" --> +<p><strong>Ley de Hooke:</strong> +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mi>E</mi><mi>ε</mi></mrow><annotation encoding="application/x-tex">\sigma=E\varepsilon</annotation></semantics></math> +<img src="Pasted%20image%2020241017210008.png" /> <img +src="Pasted%20image%2020241017201832.png" /></p> +<ul> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mi>l</mi></mrow><msub><mi>l</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">A = \frac{\Delta l}{l_0}</annotation></semantics></math>: +Alargamiento de rotura +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>%</mi><annotation encoding="application/x-tex">\%</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Z</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mi>S</mi></mrow><msub><mi>S</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">Z = \frac{\Delta S}{S_0}</annotation></semantics></math>: +Estricción de rotura +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>%</mi><annotation encoding="application/x-tex">\%</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo>=</mo><mo>∫</mo><mrow><mi>σ</mi><mspace width="0.222em"></mspace><mi>d</mi><mi>ε</mi></mrow></mrow><annotation encoding="application/x-tex">w = \int{\sigma\ d\varepsilon}</annotation></semantics></math>: +Trabajo realizado al alcanzar una tensión +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mtext mathvariant="normal">deformación</mtext><mtext mathvariant="normal">unidad de volumen</mtext></mfrac><annotation encoding="application/x-tex">\frac{\text{deformación}}{\text{unidad de volumen}}</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo>=</mo><mo>∫</mo><mrow><mi>F</mi><mspace width="0.222em"></mspace><mi>d</mi><mi>l</mi></mrow></mrow><annotation encoding="application/x-tex">w = \int{F\ dl}</annotation></semantics></math>: +Trabajo de deformación</li> +</ul> +<h1 id="ensayos-de-dureza">Ensayos de Dureza</h1> +<h3 id="ensayo-de-brinell">Ensayo de Brinell</h3> +<table> +<colgroup> +<col style="width: 50%" /> +<col style="width: 50%" /> +</colgroup> +<thead> +<tr class="header"> +<th><img src="Pasted%20image%2020241017210211.png" /></th> +<th><img src="Pasted%20image%2020241017210225.png" /></th> +</tr> +</thead> +<tbody> +</tbody> +</table> +<p>Los grados Brinell se calculan como +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi><mi>B</mi><mo>=</mo><mfrac><mi>F</mi><mi>S</mi></mfrac></mrow><annotation encoding="application/x-tex">HB=\frac{F}{S}</annotation></semantics></math> +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo>=</mo><mi>k</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">F = kp</annotation></semantics></math>, +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>=</mo><mi>m</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">S = mm^2</annotation></semantics></math>), +siendo la superficie calculada con +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>=</mo><mi>π</mi><mi>D</mi><mi>f</mi></mrow><annotation encoding="application/x-tex">S=\pi D f</annotation></semantics></math>.</p> +<p>Para calcular a +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>f</mi><annotation encoding="application/x-tex">f</annotation></semantics></math> +en función de los diámetros de la bola y de la huella se puede usar +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo>=</mo><mfrac><mrow><mi>D</mi><mo>±</mo><msqrt><mrow><msup><mi>D</mi><mn>2</mn></msup><mo>−</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></msqrt></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex"> +f = \frac{D \pm \sqrt{D^2 - d^2}}{2} +</annotation></semantics></math></p> +<h5 id="inconvenientes">Inconvenientes</h5> +<ul> +<li>No se pueden usar en piezas de espesores pequeños</li> +<li>No se puede utilizar en superficies curvas</li> +<li>Solo se puede usar en material de dureza baja (menor que el +penetrador)</li> +</ul> +<h3 id="ensayo-de-vickers">Ensayo de Vickers</h3> +<table> +<colgroup> +<col style="width: 50%" /> +<col style="width: 50%" /> +</colgroup> +<thead> +<tr class="header"> +<th><img src="Pasted%20image%2020241017211222.png" /></th> +<th><img src="Pasted%20image%2020241017211235.png" /></th> +</tr> +</thead> +<tbody> +</tbody> +</table> +<p>En este caso se utiliza como penetrador una pirámide de base cuadrada +cuyas caras laterales forman un ángulo de 136º. Lo que se hace es medir +la diagonal de la huella que deja el penetrador sobre el material. Se +usan fuerzas pequeñas +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi>k</mi><mi>p</mi><mo>−</mo><mn>120</mn><mi>k</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">1kp - 120kp</annotation></semantics></math>), +normalmente +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mi>k</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">30 kp</annotation></semantics></math>.</p> +<p>Con respecto a Brinell: - Se puede usar con materiales duros y +blandos. - Los espesores de las piezas pueden ser pequeños.</p> +<p>Se calcula con +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi><mi>V</mi><mo>=</mo><mfrac><mrow><mn>1.854</mn><mo>⋅</mo><mi>F</mi></mrow><msup><mi>d</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">HV=\frac{1.854 \cdot F}{d^2}</annotation></semantics></math> +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo>=</mo><mi>k</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">F = kp</annotation></semantics></math>, +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mo>=</mo><mi>m</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">d = mm</annotation></semantics></math>)</p> +<h3 id="ensayo-de-rockwell">Ensayo de Rockwell</h3> +<ul> +<li>El ensayo de Brinell no permite medir la dureza de los aceros +templados porque se deforman las bolas. Con el ensayo de Rockwell se +mide la profundidad de la huella.</li> +<li>Es fácil y rápido, pero poco preciso.</li> +<li>Se puede usar en materiales: +<ul> +<li>Duros: Para los que se usa un cono de diamante (HRC)</li> +<li>Blandos: Para el que se usa una bola (HRB)</li> +</ul></li> +</ul> +<p><img src="Pasted%20image%2020241017214311.png" /> 👍</p> +<h3 id="ensayo-de-charpy-o-de-resiliencia">Ensayo de Charpy o de +resiliencia</h3> +<table> +<colgroup> +<col style="width: 50%" /> +<col style="width: 50%" /> +</colgroup> +<thead> +<tr class="header"> +<th><img src="Pasted%20image%2020241017220307.png" /></th> +<th><img src="Pasted%20image%2020241017220332.png" /></th> +</tr> +</thead> +<tbody> +</tbody> +</table> +<p>El punto medio se suele entallar en forma de V o de U, a esta +resistencia se la llama KCU o KCV respectivamente. Se calcula dividiendo +la energía consumida por el material en la rotura en sus posiciones +inicial y final. +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi><mo>=</mo><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>−</mo><msub><mi>h</mi><mi>f</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mi>P</mi><mo>⋅</mo><mi>L</mi><mo>⋅</mo><mrow><mo stretchy="true" form="prefix">(</mo><mo>cos</mo><mi>β</mi><mo>−</mo><mo>cos</mo><mi>α</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex"> +W = P(h_0-h_f) = P \cdot L \cdot (\cos\beta - \cos\alpha) +</annotation></semantics></math></p> +<ul> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>P</mi><annotation encoding="application/x-tex">P</annotation></semantics></math>: +peso del péndulo +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mi>g</mi></mrow><annotation encoding="application/x-tex">kg</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>: +longitud del péndulo +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>m</mi><annotation encoding="application/x-tex">m</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>W</mi><annotation encoding="application/x-tex">W</annotation></semantics></math>: +energía de rotura +(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mi>g</mi><mo>⋅</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">kg \cdot m</annotation></semantics></math>)</li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math> +y +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>β</mi><annotation encoding="application/x-tex">\beta</annotation></semantics></math>: +ángulos del péndulo +<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi><mi>C</mi><mi>V</mi><mi>/</mi><mi>K</mi><mi>C</mi><mi>U</mi><mspace width="0.222em"></mspace><mrow><mo stretchy="true" form="prefix">(</mo><mfrac displaystyle="false"><mi>J</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mi>W</mi><msub><mi>S</mi><mn>0</mn></msub></mfrac><mo>→</mo><mi>ρ</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><msub><mi>E</mi><mi>P</mi></msub></mrow><mi>S</mi></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi><mo>⋅</mo><mi>g</mi><mo>⋅</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>H</mi><mo>−</mo><mi>h</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mi>S</mi></mfrac></mrow><annotation encoding="application/x-tex"> +KCV/KCU\ (\tfrac{J}{m^2}) = \frac{W}{S_0} \longrightarrow \rho = \frac{\Delta E_P}{S} = \frac{m \cdot g \cdot (H - h)}{S} +</annotation></semantics></math></li> +<li><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>/<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>S</mi><mn>0</mn></msub><annotation encoding="application/x-tex">S_0</annotation></semantics></math>: +Sección en la zona de entrada (sin contar la entalladura)</li> +</ul> +<!--# include virtual="/components/md-post.html" --> diff --git a/notes/tech/Ensayos de Tracción.md b/notes/tech/Ensayos de Tracción.md new file mode 100644 index 0000000..592cd27 --- /dev/null +++ b/notes/tech/Ensayos de Tracción.md @@ -0,0 +1,63 @@ +**Ley de Hooke:** $\sigma=E\varepsilon$ + + + +* $A = \frac{\Delta l}{l_0}$: Alargamiento de rotura ($\%$) +* $Z = \frac{\Delta S}{S_0}$: Estricción de rotura ($\%$) +* $w = \int{\sigma\ d\varepsilon}$: Trabajo realizado al alcanzar una tensión ($\frac{\text{deformación}}{\text{unidad de volumen}}$) +* $w = \int{F\ dl}$: Trabajo de deformación + +# Ensayos de Dureza +### Ensayo de Brinell +|  |  | +| ------------------------------------ | ------------------------------------ | +Los grados Brinell se calculan como $HB=\frac{F}{S}$ ($F = kp$, $S = mm^2$), siendo la superficie calculada con $S=\pi D f$. + +Para calcular a $f$ en función de los diámetros de la bola y de la huella se puede usar +$$ +f = \frac{D \pm \sqrt{D^2 - d^2}}{2} +$$ + +##### Inconvenientes +- No se pueden usar en piezas de espesores pequeños +- No se puede utilizar en superficies curvas +- Solo se puede usar en material de dureza baja (menor que el penetrador) + +### Ensayo de Vickers +|  |  | +| ------------------------------------ | ------------------------------------ | +En este caso se utiliza como penetrador una pirámide de base cuadrada cuyas caras laterales forman un ángulo de 136º. Lo que se hace es medir la diagonal de la huella que deja el penetrador sobre el material. Se usan fuerzas pequeñas ($1kp - 120kp$), normalmente $30 kp$. + +Con respecto a Brinell: +- Se puede usar con materiales duros y blandos. +- Los espesores de las piezas pueden ser pequeños. + +Se calcula con $HV=\frac{1.854 \cdot F}{d^2}$ ($F = kp$, $d = mm$) + +### Ensayo de Rockwell +* El ensayo de Brinell no permite medir la dureza de los aceros templados porque se deforman las bolas. Con el ensayo de Rockwell se mide la profundidad de la huella. +* Es fácil y rápido, pero poco preciso. +* Se puede usar en materiales: + * Duros: Para los que se usa un cono de diamante (HRC) + * Blandos: Para el que se usa una bola (HRB) + + +👍 + +### Ensayo de Charpy o de resiliencia + +|  |  | +| ------------------------------------ | ------------------------------------ | +El punto medio se suele entallar en forma de V o de U, a esta resistencia se la llama KCU o KCV respectivamente. Se calcula dividiendo la energía consumida por el material en la rotura en sus posiciones inicial y final. +$$ +W = P(h_0-h_f) = P \cdot L \cdot (\cos\beta - \cos\alpha) +$$ + +* $P$: peso del péndulo ($kg$) +* $L$: longitud del péndulo ($m$) +* $W$: energía de rotura ($kg \cdot m$) +* $\alpha$ y $\beta$: ángulos del péndulo +$$ +KCV/KCU\ (\tfrac{J}{m^2}) = \frac{W}{S_0} \longrightarrow \rho = \frac{\Delta E_P}{S} = \frac{m \cdot g \cdot (H - h)}{S} +$$ +* $S$/$S_0$: Sección en la zona de entrada (sin contar la entalladura) diff --git a/notes/tech/Pasted image 20241017201832.png b/notes/tech/Pasted image 20241017201832.png new file mode 100644 index 0000000000000000000000000000000000000000..328d222aa44313e1017e07b2f49c14622c00cb82 GIT binary patch literal 73774 zcmc$G_dnHr_`khZlAU>Ql5vuZoNPii3E3fgB~da%2q8OrC)wFMTO=XL%F4<(Wb?Un ze?EV}_owgqp~szW@AE#d_v>|C&vl(pP4(O4B#b0jSXkuBO7hxRSU8hdSlF3FIPeo8 z<MaS5EH*4<c^O^Lw`+}KkC^TypG}fyL|=?1@-tJnpzUCb$wKPHJC65m-&{wGy|TZR 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