From 131686881f868dce7e5a9ac2c2da93997bb97a39 Mon Sep 17 00:00:00 2001 From: Rahix Date: Sat, 7 Jun 2025 16:58:48 +0200 Subject: [PATCH] Add data and graphs --- Spring-Dimensioning.ipynb | 93 ++++++++++++++++++++++++++++++++++----- 1 file changed, 83 insertions(+), 10 deletions(-) diff --git a/Spring-Dimensioning.ipynb b/Spring-Dimensioning.ipynb index 7bd44e8..a91901d 100644 --- a/Spring-Dimensioning.ipynb +++ b/Spring-Dimensioning.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 60, "id": "5bef2913-4855-471d-9594-5ec45c029048", "metadata": {}, "outputs": [ @@ -17,27 +17,36 @@ ], "source": [ "import math\n", + "import numpy as np\n", + "from pint import UnitRegistry\n", + "unit = UnitRegistry()\n", + "unit.formatter.default_format = \"~\"\n", + "\n", "\n", "# Parameters\n", - "spring_constant_n_mm = 1.1 * 4\n", - "spring_length_resting_mm = 112\n", + "spring_constant = 1.1 * 4 * unit.N / unit.mm\n", + "spring_length_resting = 112 * unit.mm\n", + "\n", + "weight_total = 14 * unit.kg\n", + "\n", + "dampening = 1 * unit.N / (unit.m / unit.s)\n", "\n", "def spring_length_at(weight):\n", - " return weight * 9.81 / spring_constant_n_mm + spring_length_resting_mm\n", + " return (weight * unit.standard_gravity / spring_constant + spring_length_resting).to(unit.mm)\n", "\n", "def resonant_freq_at(weight):\n", - " return 1 / (2 * math.pi) * math.sqrt(spring_constant_n_mm * 1000 / weight)\n", + " return (1 / (2 * math.pi) * np.sqrt(spring_constant / weight)).to(unit.Hz)\n", "\n", - "# Environment\n", - "weight_total_kg = 14\n", + "spring_length = spring_length_at(weight_total)\n", + "f0 = resonant_freq_at(weight_total)\n", "\n", - "print(f\"Length: {spring_length_at(weight_total_kg):.1f} mm\")\n", - "print(f\"Freq: {resonant_freq_at(weight_total_kg):.3f} Hz\")" + "print(f\"Length: {spring_length:~.1f}\")\n", + "print(f\"Freq: {f0:~.3f}\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 61, "id": "f21d84d9-c7a1-4fd2-aa32-136f04db32e5", "metadata": { "editable": true, @@ -46,6 +55,70 @@ }, "tags": [] }, + "outputs": [ + { + "data": { + "text/html": [ + "0.00201455741006345" + ], + "text/latex": [ + "$0.00201455741006345$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def lehr_dampening_factor(d, k, m):\n", + " return d / (2 * np.sqrt(m * k))\n", + "\n", + "lehr_dampening = lehr_dampening_factor(dampening, spring_constant, weight_total)\n", + "lehr_dampening.ito_reduced_units()\n", + "lehr_dampening" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "b71de7db-a7fb-4d3a-9dd2-de8e107700a6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def amplitude_ratio(lehr, f0, f):\n", + " eta = f / f0\n", + " return 1 / np.sqrt((1 - eta**2)**2 + (2 * eta * lehr)**2)\n", + "\n", + "f_in = np.logspace(0, 4, 100) * unit.Hz\n", + "ratio = amplitude_ratio(lehr_dampening, f0, f_in)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(f_in, ratio)\n", + "plt.xscale('log')\n", + "plt.ylim(0.00001, 10)\n", + "plt.yscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fea96fd4-46e1-4f07-8fb4-25ccc0ee82a5", + "metadata": {}, "outputs": [], "source": [] }