477 lines
38 KiB
Text
477 lines
38 KiB
Text
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "9d2d29bc-6859-4281-92b3-8a374912f46a",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from scipy import constants\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"gasses = { \n",
|
||
" \"air\": {\n",
|
||
" \"c_p\": 1.005e3, # J/kgK\n",
|
||
" \"c_v\": 0.718e3, # J/kgK\n",
|
||
" \"m_mol\": 28.949e-3 , # kg/mol\n",
|
||
" },\n",
|
||
"}\n",
|
||
"\n",
|
||
"gas = gasses['air']\n",
|
||
"temp_r = 273.15+25\n",
|
||
"r_s = constants.R / gas['m_mol']"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d1e8fb76-4f11-4882-b78a-ade315f4dc46",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Berechnungen zu Impact Teststand\n",
|
||
"\n",
|
||
"## Aufgabenstellung\n",
|
||
"\n",
|
||
"Es gilt einen Teststand für das Aufprallverhalten von heißgepressten Kunststoff Briketts zu entwerfen.\n",
|
||
"\n",
|
||
"Die Briketts sind 120mm im durchmesser und 300mm lang. Sie treffen mit 100m/s auf.\n",
|
||
"\n",
|
||
"## Lauflänge\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "01be7156-9cec-4beb-b874-0cad2fcfd6e2",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Probenenergie: 30 kJ\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"sample_d = 0.2 #m \n",
|
||
"sample_l = 0.3 #m \n",
|
||
"sample_vel = 100 #m/s\n",
|
||
"sample_m = 6 #kg\n",
|
||
"\n",
|
||
"\n",
|
||
"chamber_p = 20e5 # Pa \n",
|
||
"\n",
|
||
"sample_a = (sample_d/2)**2 * np.pi\n",
|
||
"sample_v = sample_a * sample_l\n",
|
||
"density = sample_m / sample_v #kg/m³\n",
|
||
"e_kin = sample_m * sample_vel**2 / 2\n",
|
||
"print(f\"Probenenergie: {e_kin/1000:.0f} kJ\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a140e327-e966-4d7b-9e97-08244084b13b",
|
||
"metadata": {},
|
||
"source": [
|
||
"$W = -\\int_{V_0}^{V_1} p \\, dV = -p \\Delta V = -p A \\Delta L$\n",
|
||
"\n",
|
||
"$W = E_{kin}$\n",
|
||
"\n",
|
||
"$V_c = -\\frac{E_{kin}}{p_c}$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "d2f98c9e-3294-49cf-868a-ef7234af193b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Chamber Volume = 15.0 l\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"chamber_v = e_kin/ chamber_p\n",
|
||
"# chamber_v = 0.05\n",
|
||
"print(f\"Chamber Volume = {chamber_v*1000:.1f} l\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3305659e-ffdc-4391-bf52-96499c27165f",
|
||
"metadata": {},
|
||
"source": [
|
||
"Mitrechnung der Beschleunigung des Gases in die kinetische Energie:\n",
|
||
"\n",
|
||
"$$E_{kin, Gas} = \\frac{1}{2} \\int m_g v_{x_g}^2$$\n",
|
||
"Balistics, pp.66 löst dies auf: \n",
|
||
"$$E_{kin, Gas} = \\frac{1}{6} m_g v_{sample}^2$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "2b632e0e-e4a3-4999-ae5d-98a03ebd550b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Gas-Masse = 0.350 kg = 5.52 % der Systemmasse\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"m_g = chamber_v*chamber_p / (r_s * temp_r)\n",
|
||
"print(f\"Gas-Masse = {m_g:.3f} kg = {m_g / (sample_m+m_g) *100:.2f} % der Systemmasse\")\n",
|
||
"\n",
|
||
"# e_kin = (sample_m * sample_vel**2 / 2) + (m_g * sample_vel**2 /6)\n",
|
||
"# print(f\"kinetische System-energie = {e_kin:.0f} J\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "21572b57-eb01-48d7-86b2-6cc651103674",
|
||
"metadata": {},
|
||
"source": [
|
||
"## isothermer Ansatz\n",
|
||
"\n",
|
||
"Ausgangsenergie in Kammer:\n",
|
||
"$ p_0 V_0 = E_{pot}$\n",
|
||
"\n",
|
||
"$p s A = const$\n",
|
||
"\n",
|
||
"$p(s) = \\frac{p_0 V_0}{A s} = \\frac{E_{pot}}{A} \\frac{1}{s}$\n",
|
||
"\n",
|
||
"Fiktive Kammerlänge $l_f = \\frac{V_c}{A}$ für einen konstanten Rohrsurchmesser. Die Probe befindet sich also an $s=l_f$ eines fiktiven Laufes mit Kammerdruck $p$ hinter sich.\n",
|
||
"\n",
|
||
"$W = \\int p \\, dV = \\int_{l_f}^{L+l_f} p(s) A \\, ds = \\int_{l_f}^{L+l_f} E_{pot} \\frac{1}{s} \\, ds$\n",
|
||
"\n",
|
||
"$W = E_{pot} \\left[\\ln(L+l_f) - \\ln(l_f)\\right]$\n",
|
||
"\n",
|
||
"$W = E_{pot} \\ln(\\frac{L+l_f}{l_f}) = E_{kin}$\n",
|
||
"\n",
|
||
"$L =l_f \\exp\\left(\\frac{E_{kin}}{E_{pot}} \\right) - l_f$\n",
|
||
"\n",
|
||
"$L =l_f (\\exp\\left(\\frac{E_{kin}}{E_{pot}} \\right) - 1)$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "df2f1bba-170b-4c90-853a-edcbbcc51b4d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"p V = 30000.0 J\n",
|
||
"l_f = V_c / A = 0.477 m\n",
|
||
"Lauflänge = 0.820 m\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"e_pot = chamber_p * chamber_v\n",
|
||
"print(f\"p V = {e_pot} J\")\n",
|
||
"l_f = chamber_v / sample_a\n",
|
||
"print(f\"l_f = V_c / A = {l_f:.3f} m\")\n",
|
||
"barrel_l = l_f * np.exp(e_kin / e_pot)-l_f\n",
|
||
"print(f\"Lauflänge = {barrel_l:.3f} m\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cc53cecd-e6f4-40e0-bf20-128bb455cde8",
|
||
"metadata": {},
|
||
"source": [
|
||
"## adiabatischer Ansatz\n",
|
||
"\n",
|
||
"$$Q = \\Delta U + W$$\n",
|
||
"Wobei Q = 0, da es ein verbrennungsfreier Ablauf ist.\n",
|
||
"\n",
|
||
"Nun können wir die ideale Gasgleichung in das Integral der Arbeit einsetzen:\n",
|
||
"$$pV = n\\mathfrak{R}T = m_gR_sT $$\n",
|
||
"\n",
|
||
"$$W = \\int p \\, dV = \\int m_gR_sT \\, \\frac{dV}{V}$$\n",
|
||
"\n",
|
||
"da es sich um ein adiablitsches System handelt ist die absolute Temperatur abhängig vom Volumen:\n",
|
||
"$$T = T_0 \\left(\\frac{V_{c}}{V}\\right)^{(\\gamma - 1)}$$\n",
|
||
"wobei $\\gamma$ das spezifische Wärmeverhältnis $\\frac{c_p}{c_v}$ist. Das führt zu einer Vereinfachung des Intergals:\n",
|
||
"\n",
|
||
"$$W = m_gR_sT_0V_c^{(\\gamma -1)} \\int_{V_c}^{V} V^{-\\gamma} dV$$\n",
|
||
"\n",
|
||
"unter Annahme eines zylindrischen Laufs mit konstantem Durchmesser und einer Fictiven Kammerlänge $l_f = \\frac{V_c}{A}$ kann man das Integral auf den Weg reduzieren:\n",
|
||
"$$W = m_gR_sT_0l_f^{(\\gamma -1)} \\int_{0}^{L} \\left(l_f + x\\right)^{-\\gamma} \\,dx$$\n",
|
||
"$$W = \\frac{m_gR_sT_0l_f^{(\\gamma -1)}}{1-\\gamma} \\left[\\left(l_f + L\\right)^{1-\\gamma} - \\left(l_f \\right)^{1-\\gamma}\\right]$$\n",
|
||
"\n",
|
||
"die errechnete Arbeit kann man wieder der kinetischen energie gleichsetzen\n",
|
||
"$$E_{kin} = W$$\n",
|
||
"$$\\frac{m v_0^2}{2} = \\frac{m_gR_sT_0l_f^{(\\gamma -1)}}{1-\\gamma} \\left[\\left(l_f + L\\right)^{1-\\gamma} - l_f^{1-\\gamma}\\right]$$\n",
|
||
"\n",
|
||
"Diesen Zusammenhang kann man nu nach beliben umformen um zB die mundungsgeschwindigkeit bei bekannter Lauflänge und InnenDruck zu errechnen, oder in diesem Fall für die benötigte Lauflänge bei gegebenen Anfangsdruck und gewünschter Mündungsenergie:\n",
|
||
"$$L = \\left[E_{kin}\\cdot\\frac{1-\\gamma}{m_gR_sT_0l_f^{(\\gamma -1)}}+l_f^{1-\\gamma}\\right]^\\frac{1}{1-\\gamma} - l_f$$\n",
|
||
"$$L = \\left[\\frac{E_{kin}}{E_{pot}}\\cdot\\frac{1-\\gamma}{l_f^{(\\gamma -1)}}+l_f^{1-\\gamma}\\right]^\\frac{1}{1-\\gamma} - l_f$$\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "f5faae92-41c7-48fe-9c63-e53673d67bb9",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"γ = 1.3997214484679665\n",
|
||
"Lauflänge L = 1.234\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"gamma = gas['c_p']/gas['c_v']\n",
|
||
"print(f\"γ = {gamma}\")\n",
|
||
"\n",
|
||
"l_f = chamber_v / sample_a\n",
|
||
"const = chamber_v*chamber_p *(l_f**(gamma-1)) / (1-gamma)\n",
|
||
"L = (e_kin/const + l_f**(1-gamma))**(1/(1-gamma)) - l_f\n",
|
||
"\n",
|
||
"print(f\"Lauflänge L = {L:.3f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "24b4b3ac-a53e-4b9b-a016-f7bf8914a2b5",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"1.2343053902013508"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"l_f * ((e_kin/e_pot * (1-gamma) +1)**(1/(1-gamma)) -1)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fd2716ee-5b8f-44ef-82f0-b8b97714604b",
|
||
"metadata": {},
|
||
"source": [
|
||
"Reibungsarbeit\n",
|
||
"\n",
|
||
"$$F_R = \\mu \\cdot F_n$$\n",
|
||
"$$W_R = \\int F_R \\, ds$$\n",
|
||
"\n",
|
||
"Annahme: $F_n$ ist unabhängig vom Kammerduck\n",
|
||
"\n",
|
||
"$$W_R = F_R \\cdot s$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "14d46de4-8f55-47e4-8950-05ff27de74d8",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Lauflänge L = 1.234305\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"mu = 0.04\n",
|
||
"f_n = 100000# N compression force of briquette in barrel\n",
|
||
"L = ((e_kin)/const + l_f**(1-gamma))**(1/(1-gamma)) - l_f\n",
|
||
"\n",
|
||
"print(f\"Lauflänge L = {L:f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "618d3d65-0298-4494-8b9a-a6b8f0d949ec",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"L = 1.234\n",
|
||
"W(x=1.234, p=2e+06) = 30000.000\n",
|
||
"p(x=1.234, p=2e+06) = 1.20e+06\n",
|
||
"V(x=1.234, p=2e+06) = 5.38e-02\n",
|
||
"ΔT(x=1.234, p=2e+06) = 178.97\n",
|
||
"94562.17620021079\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"def work(x):\n",
|
||
" return const *((l_f + x)**(1-gamma) - l_f**(1-gamma))\n",
|
||
"\n",
|
||
"def vel(x):\n",
|
||
" return np.sqrt(2*work(x) /sample_m)\n",
|
||
"\n",
|
||
"def vol(x):\n",
|
||
" return chamber_v + sample_a*x\n",
|
||
"\n",
|
||
"t_0 = 273.15+25\n",
|
||
"\n",
|
||
"def temp(x):\n",
|
||
" return t_0 * (chamber_v / vol(x))**(gamma-1)\n",
|
||
"\n",
|
||
"def pres(x):\n",
|
||
" return e_pot * (chamber_v / vol(x))**(gamma-1) / chamber_v\n",
|
||
" \n",
|
||
"\n",
|
||
"print(f\"L = {L:.3f}\")\n",
|
||
"\n",
|
||
"l_v = 3\n",
|
||
"print(f\"W(x={L:.3f}, p={chamber_p:.0e}) = {work(L):.3f}\")\n",
|
||
"print(f\"p(x={L:.3f}, p={chamber_p:.0e}) = {pres(L):.2e}\")\n",
|
||
"print(f\"V(x={L:.3f}, p={chamber_p:.0e}) = {vol(L):.2e}\")\n",
|
||
"print(f\"ΔT(x={L:.3f}, p={chamber_p:.0e}) = { temp(L):.2f}\")\n",
|
||
"\n",
|
||
"print(e_kin + vol(L)*pres(L))\n",
|
||
"\n",
|
||
"\n",
|
||
"l_array = np.linspace(0,L,400)\n",
|
||
"plt.plot(l_array, vel(l_array))\n",
|
||
"plt.ylabel('Speed [m/s]')\n",
|
||
"plt.xlabel('Sample Travel [m]')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8092e400-264c-45f2-8709-f384a8af042e",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Wandstärke - Kesselgleichung\n",
|
||
"\n",
|
||
"Gültig für $t \\ll r$\n",
|
||
"\n",
|
||
"Wöhlerkurven!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "a218c0aa-8802-423f-b74c-277d2b795cc1",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"sig_streck = 175e6 #Pa\n",
|
||
"sig_zul = 25e6\n",
|
||
"sicherheit = 2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f133254f-52c4-4bdf-b440-b323795bba0b",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\\sigma_t = \\frac{p\\cdot d_m}{2\\cdot s}$$\n",
|
||
"\n",
|
||
"$$\\sigma_a = \\frac{p\\cdot d_m}{4\\cdot s}$$\n",
|
||
"\n",
|
||
"$$s_{min} = \\frac{p \\cdot d_m}{2 \\cdot \\sigma_{zul}}$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "66a38636-8468-4b0c-898f-f9929ed7edf5",
|
||
"metadata": {
|
||
"jupyter": {
|
||
"source_hidden": true
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"mindest wandstärke lauf: 4.0 mm\n",
|
||
"mindest wandstärke kammer: 4.4 mm\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"s_min_l = chamber_p * (sample_d) / (2 * sig_zul * sicherheit - chamber_p/2)\n",
|
||
"print(f\"mindest wandstärke lauf: {s_min_l*1000:.1f} mm\")\n",
|
||
"\n",
|
||
"chamber_l = .4\n",
|
||
"chamber_d = np.sqrt(4*chamber_v/(chamber_l*np.pi))\n",
|
||
"s_min_c = chamber_p * (chamber_d) / (2 * sig_zul * sicherheit - chamber_p/2)\n",
|
||
"print(f\"mindest wandstärke kammer: {s_min_c*1000:.1f} mm\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d492aedb-f040-494f-953f-563bb99b1f6a",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Risikoanalyse / Gefahren\n",
|
||
"- Entladung mit Person zwischen Apparat und Endstopp\n",
|
||
"- Entladen im geöffneten Zustand\n",
|
||
"- Entladen ohne Beton Platte -> dicke Backplate\n",
|
||
"- Versagen von druckführenden Bauteilen\n",
|
||
"- Einklemmen / Einzwicken in Mechanik\n",
|
||
"- Stromstoß an Elektronik\n",
|
||
"- Falsches Beladen"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (ipykernel)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.10.12"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|