MechanicalTLM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.container { width:100% !important; }</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.core.display import display, HTML\n",
    "display(HTML(\"<style>.container { width:100% !important; }</style>\"))\n",
    "\n",
    "__author__ = \"Peter Nordin\"\n",
    "__license__ = \"GPL\"\n",
    "__email__ = \"peter.nordin@liu.se\"\n",
    "\n",
    "'''The purpose of this script is to allow easy calulation of the parasitic inductance and/or capacitance that\n",
    "   will result from the choice of time step and material properties in Hopsan'''\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from TLMclasses import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         k &         Ts &         Par. Ind &         Par. Cap &       Perc. Mass &  Perc. Stiffness &        Resonance\n",
      "2.6389E+11 &      1E-12 &  2.638937829E-13 &                0 &  2.638937829E-13 &  2.638937829E+11 &            1E+12\n",
      "2.6389E+11 &      1E-11 &  2.638937829E-11 &                0 &  2.638937829E-11 &  2.638937829E+11 &            1E+11\n",
      "2.6389E+11 &      1E-10 &  2.638937829E-09 &                0 &  2.638937829E-09 &  2.638937829E+11 &            1E+10\n",
      "2.6389E+11 &      1E-09 &  2.638937829E-07 &                0 &  2.638937829E-07 &  2.638937829E+11 &       1000000000\n",
      "2.6389E+11 &      1E-08 &  2.638937829E-05 &                0 &  2.638937829E-05 &  2.638937829E+11 &        100000000\n",
      "2.6389E+11 &      1E-07 &   0.002638937829 &                0 &   0.002638937829 &  2.638937829E+11 &         10000000\n",
      "2.6389E+11 &    2.5E-07 &    0.01649336143 &                0 &    0.01649336143 &  2.638937829E+11 &          4000000\n",
      "2.6389E+11 &      5E-07 &    0.06597344573 &                0 &    0.06597344573 &  2.638937829E+11 &          2000000\n",
      "2.6389E+11 &    7.5E-07 &     0.1484402529 &                0 &     0.1484402529 &  2.638937829E+11 &      1333333.333\n",
      "2.6389E+11 &      1E-06 &     0.2638937829 &                0 &     0.2638937829 &  2.638937829E+11 &          1000000\n",
      "2.6389E+11 &    2.5E-06 &      1.649336143 &                0 &      1.649336143 &  2.638937829E+11 &           400000\n",
      "2.6389E+11 &      5E-06 &      6.597344573 &                0 &      6.597344573 &  2.638937829E+11 &           200000\n",
      "2.6389E+11 &    7.5E-06 &      14.84402529 &                0 &      14.84402529 &  2.638937829E+11 &      133333.3333\n",
      "2.6389E+11 &      1E-05 &      26.38937829 &                0 &      26.38937829 &  2.638937829E+11 &           100000\n",
      "2.6389E+11 &    2.5E-05 &      164.9336143 &                0 &      164.9336143 &  2.638937829E+11 &            40000\n",
      "2.6389E+11 &      5E-05 &      659.7344573 &                0 &      659.7344573 &  2.638937829E+11 &            20000\n",
      "2.6389E+11 &    7.5E-05 &      1484.402529 &                0 &      1484.402529 &  2.638937829E+11 &      13333.33333\n"
     ]
    },
    {
     "data": {
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124BPg+Occ5WIWbictmEDvPxy5Uo46eZJxznnyun222HGjHAvTnWd3iZZnnScc64cHnoo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\nxznnKpFK09JxzjlXBZhZ7C+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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9232640f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For a single step Mechanical Spring TLM modelled as a pure capacitance (linear elastic spring), calculate parasitic inductance\n",
    "\n",
    "# Spring\n",
    "k=2.63893782902e+11\n",
    "n=1\n",
    "\n",
    "Tdesired = 1e-12\n",
    "\n",
    "kvec = [1e6, 1e7, 1e8, 1e9, 1e10, 1e11, k]\n",
    "kvec = [k]\n",
    "\n",
    "for k in kvec:\n",
    "    #Ts = [Tdesired/n, Tdesired/n*2, Tdesired/n*4, Tdesired/n*8, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 5e-4, 1e-3, 1e-2, 1e-1, 1e-0]\n",
    "    Ts = [Tdesired/n, Tdesired/n*10, Tdesired/n*100, Tdesired/n*1000, Tdesired/n*10000, 1e-7, 2.5e-7, 5e-7, 7.5e-7, 1e-6, 2.5e-6, 5e-6, 7.5e-6, 1e-5, 2.5e-5, 5e-5, 7.5e-5]\n",
    "    Ts = sorted(Ts)\n",
    "\n",
    "    templatehead = \"{0:>10} & {1:>10} & {2:>16} & {3:>16} & {4:>16} & {5:>16} & {6:>16}\"\n",
    "    template = \"{0:10.5G} & {1:10.10G} & {2:16.10G} & {3:16.10G} & {4:16.10G} & {5:16.10G} & {6:16.10G}\"\n",
    "    print(templatehead.format(\"k\", \"Ts\", \"Par. Ind\", \"Par. Cap\", \"Perc. Mass\", \"Perc. Stiffness\", \"Resonance\"))\n",
    "    paraind = list()\n",
    "    for t in Ts:\n",
    "        #zc_desired = K/volume*t\n",
    "        tp = TLMMechanicSpring(k, t)\n",
    "        #tp = TLMMechanicLine(E, rho, X, A, zctype='pureinductance')\n",
    "        #tp = TLMMechanicLine(E, rho, X, A, zctype='normal')\n",
    "        tp.calcStuff(t, n)\n",
    "\n",
    "        print(template.format(k, t, tp.parasitic.ind, tp.parasitic.cap, tp.percived.ind, tp.percived.stiffness, np.sqrt(tp.percived.stiffness/tp.percived.ind)))\n",
    "        template2 = \"{0:>23.5G}  {1:>17.10G}\"\n",
    "        #print(template2.format(tp.percived.zc,tp.parasitic.ind2))\n",
    "        paraind.append(tp.parasitic.ind)\n",
    "\n",
    "fig, axL = plt.subplots()\n",
    "#plt.title('Length and parasitic mass realtive to simualtion timestep')\n",
    "axL.plot(Ts, paraind, label='Parasitic Inductance')\n",
    "axL.set_ylabel('Inductance (mass)')\n",
    "axL.set_xlabel('Simulation Timestep in micro seconds')\n",
    "axL.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Desired Mass:  12.084136142033142\n",
      "              Ts &         Par. Ind &         Par. Cap &       Perc. Mass &  Perc. Stiffness &               Zc &        Resonance\n",
      "           1E-10 &     -12.08413614 &                0 &  2.020436775E-11 &       2020436775 &     0.2020436775 &            1E+10\n",
      "           1E-09 &     -12.08413614 &  1.033975766E-25 &  2.020436775E-09 &       2020436775 &      2.020436775 &       1000000000\n",
      "           1E-08 &     -12.08413594 &                0 &  2.020436775E-07 &       2020436775 &      20.20436775 &        100000000\n",
      "           1E-07 &     -12.08411594 &                0 &  2.020436775E-05 &       2020436775 &      202.0436775 &         10000000\n",
      "         2.5E-07 &     -12.08400986 &                0 &  0.0001262772985 &       2020436775 &      505.1091938 &          4000000\n",
      "           5E-07 &     -12.08363103 &                0 &  0.0005051091938 &       2020436775 &      1010.218388 &          2000000\n",
      "         7.5E-07 &     -12.08299965 &                0 &   0.001136495686 &       2020436775 &      1515.327582 &      1333333.333\n",
      "           1E-06 &     -12.08211571 &                0 &   0.002020436775 &       2020436775 &      2020.436775 &          1000000\n",
      "         2.5E-06 &     -12.07150841 &                0 &    0.01262772985 &       2020436775 &      5051.091938 &           400000\n",
      "           5E-06 &     -12.03362522 &                0 &    0.05051091938 &       2020436775 &      10102.18388 &           200000\n",
      "         7.5E-06 &     -11.97048657 &                0 &     0.1136495686 &       2020436775 &      15153.27582 &      133333.3333\n",
      "           1E-05 &     -11.88209246 &                0 &     0.2020436775 &       2020436775 &      20204.36775 &           100000\n",
      "         2.5E-05 &     -10.82136316 &                0 &      1.262772985 &       2020436775 &      50510.91938 &            40000\n",
      "           5E-05 &     -7.033044204 &                0 &      5.051091938 &       2020436775 &      101021.8388 &            20000\n",
      "         7.5E-05 &    -0.7191792807 &                0 &      11.36495686 &       2020436775 &      151532.7582 &      13333.33333\n",
      " 7.733661734E-05 &                0 &                0 &      12.08413614 &       2020436775 &      156253.7457 &      12930.48538\n",
      "          0.0001 &      8.120231611 &                0 &      20.20436775 &       2020436775 &      202043.6775 &            10000\n",
      "          0.0005 &      493.0250577 &                0 &      505.1091938 &       2020436775 &      1010218.388 &             2000\n",
      " 0.0007733661734 &      1196.329478 &                0 &      1208.413614 &       2020436775 &      1562537.457 &      1293.048538\n",
      "           0.001 &      2008.352639 &                0 &      2020.436775 &       2020436775 &      2020436.775 &             1000\n",
      "           0.005 &      50498.83525 &                0 &      50510.91938 &       2020436775 &      10102183.88 &              200\n",
      "  0.007733661734 &      120829.2773 &                0 &      120841.3614 &       2020436775 &      15625374.57 &      129.3048538\n",
      "   0.07733661734 &      12084124.06 &                0 &      12084136.14 &       2020436775 &      156253745.7 &      12.93048538\n",
      "    0.7733661734 &       1208413602 &                0 &       1208413614 &       2020436775 &       1562537457 &      1.293048538\n"
     ]
    }
   ],
   "source": [
    "# A solid mechanic TLM element, with typical solid material properties\n",
    "# If modelled as a pure capacitance (linear elastic spring) then we get parasitic inductance\n",
    "# If modelled as a pure inductance (rigid mass) then we get parasitic capacitance (reduced stiffness, so its not really rigid anymore)\n",
    "# If modelled as a pure impedance (normal way) then we get both pparasitic inductance and capacitance \n",
    "\n",
    "# Solid properties\n",
    "E=2.1e11\n",
    "rho=7850\n",
    "X=0.4\n",
    "D=0.070*1\n",
    "A=np.pi*D*D/4\n",
    "n=1\n",
    "\n",
    "waveSpeed = np.sqrt(E/rho)\n",
    "Tdesired = X/waveSpeed\n",
    "massdesired = A*X*rho\n",
    "\n",
    "#Ts = [Tdesired/n, Tdesired/n*2, Tdesired/n*4, Tdesired/n*8, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 5e-4, 1e-3, 1e-2, 1e-1, 1e-0]\n",
    "#Ts = [Tdesired/abs(n), 2e-6, 1e-5, 1e-4, 5e-4, 1e-3, 1e-2]\n",
    "Ts = [Tdesired/n, Tdesired/n*10, Tdesired/n*100, Tdesired/n*1000, Tdesired/n*10000, 1e-10, 1e-9, 1e-8, 1e-7, 2.5e-7, 5e-7, 7.5e-7, 1e-6, 2.5e-6, 5e-6, 7.5e-6, 1e-5, 2.5e-5, 5e-5, 7.5e-5, 1e-4, 5e-4, 1e-3, 5e-3]\n",
    "Ts = sorted(Ts)\n",
    "\n",
    "print('Desired Mass: ', massdesired)\n",
    "templatehead = \"{0:>16} & {1:>16} & {2:>16} & {3:>16} & {4:>16} & {5:>16} & {6:>16}\"\n",
    "template = \"{0:16.10G} & {1:16.10G} & {2:16.10G} & {3:16.10G} & {4:16.10G} & {5:16.10G} & {6:16.10G}\"\n",
    "print(templatehead.format(\"Ts\", \"Par. Ind\", \"Par. Cap\", \"Perc. Mass\", \"Perc. Stiffness\", \"Zc\", \"Resonance\"))\n",
    "for t in Ts:\n",
    "    #zc_desired = K/volume*t\n",
    "    tp = TLMMechanicLine(E, rho, X, A, zctype='purecapacitance')\n",
    "    #tp = TLMMechanicLine(E, rho, X, A, zctype='pureinductance')\n",
    "    #tp = TLMMechanicLine(E, rho, X, A, zctype='normal')\n",
    "    tp.calcStuff(t, n)\n",
    "\n",
    "    print(template.format(t, tp.parasitic.ind, tp.parasitic.cap, tp.percived.ind, tp.percived.stiffness, tp.percived.zc, np.sqrt(tp.percived.stiffness/tp.percived.ind)))\n",
    "    template2 = \"{0:>16.5G}  {1:>17.10G} {2:>18.10G} {3:>18.10G}\"\n",
    "    #print(template2.format(tp.percived.zc, tp.parasitic.ind2, tp.parasitic.cap2, tp.percived.ind2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time step            & Par.Cap              & Par.Ind              & Percived Stiffness   & Percived Mass        \\\\\n",
      "1e-09  1:            & 0.0                  & -0.9999999999        & 100000000.0          & 1.0000000000000002e-10 \\\\\n",
      "1e-09  2:            & 1.3234889800848443e-23 & -21.99999999999      & 10000000.0           & 1.0000000000000001e-11 \\\\\n",
      "1e-08  1:            & 0.0                  & -0.99999999          & 100000000.0          & 1e-08                \\\\\n",
      "1e-08  2:            & 0.0                  & -21.999999999        & 10000000.0           & 1e-09                \\\\\n",
      "1e-07  1:            & 0.0                  & -0.999999            & 100000000.0          & 1e-06                \\\\\n",
      "1e-07  2:            & 0.0                  & -21.9999999          & 10000000.0           & 1e-07                \\\\\n",
      "1e-06  1:            & 0.0                  & -0.9999              & 100000000.0          & 9.999999999999999e-05 \\\\\n",
      "1e-06  2:            & 0.0                  & -21.99999            & 10000000.0           & 9.999999999999999e-06 \\\\\n",
      "1e-05  1:            & 0.0                  & -0.99                & 100000000.0          & 0.010000000000000002 \\\\\n",
      "1e-05  2:            & 0.0                  & -21.999              & 10000000.0           & 0.0010000000000000002 \\\\\n",
      "3e-05  1:            & 0.0                  & -0.91                & 100000000.0          & 0.09                 \\\\\n",
      "3e-05  2:            & 1.3234889800848443e-23 & -21.991              & 10000000.0           & 0.009000000000000001 \\\\\n",
      "0.0001  1:           & 0.0                  & 0.0                  & 100000000.0          & 1.0                  \\\\\n",
      "0.0001  2:           & 1.3234889800848443e-23 & -21.9                & 10000000.0           & 0.1                  \\\\\n",
      "0.00015  1:          & 0.0                  & 1.2499999999999996   & 100000000.0          & 2.2499999999999996   \\\\\n",
      "0.00015  2:          & 1.3234889800848443e-23 & -21.775              & 10000000.0           & 0.22499999999999995  \\\\\n",
      "0.0002  1:           & 0.0                  & 3.0                  & 100000000.0          & 4.0                  \\\\\n",
      "0.0002  2:           & 1.3234889800848443e-23 & -21.6                & 10000000.0           & 0.4                  \\\\\n",
      "0.0004  1:           & 0.0                  & 15.0                 & 100000000.0          & 16.0                 \\\\\n",
      "0.0004  2:           & 1.3234889800848443e-23 & -20.4                & 10000000.0           & 1.6                  \\\\\n",
      "0.0005  1:           & 0.0                  & 24.0                 & 100000000.0          & 25.0                 \\\\\n",
      "0.0005  2:           & 0.0                  & -19.5                & 10000000.0           & 2.5                  \\\\\n",
      "0.001  1:            & 0.0                  & 99.0                 & 100000000.0          & 100.0                \\\\\n",
      "0.001  2:            & 0.0                  & -12.0                & 10000000.0           & 10.0                 \\\\\n"
     ]
    }
   ],
   "source": [
    "# Two-mass-spring system test\n",
    "m1 = 1\n",
    "m2 = 22\n",
    "kGain = 1000000\n",
    "k1 = 100*kGain\n",
    "k2 = 10*kGain\n",
    "\n",
    "Ts = [1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1.5e-4, 2e-4, 3e-5, 4e-4, 5e-4, 1e-3]\n",
    "Ts = sorted(Ts)\n",
    "\n",
    "template = \"{0:20} & {1:20} & {2:20} & {3:20} & {4:20} \\\\\\\\\"\n",
    "print(template.format(\"Time step\", \"Par.Cap\", \"Par.Ind\", \"Percived Stiffness\", \"Percived Mass\"))\n",
    "for t in Ts:\n",
    "    tp1 = TLMLineParameters(1e99, 1e-20, np.sqrt(m1/k1), m1, 1.0/k1, 'purecapacitance')\n",
    "    tp1.calcStuff(t,1)\n",
    "    tp2 = TLMLineParameters(1e99, 1e-20, np.sqrt(m2/k2), m2, 1.0/k2, 'purecapacitance')\n",
    "    tp2.calcStuff(t,1)\n",
    "    \n",
    "    print(template.format(str(t)+'  1:', str(tp1.parasitic.cap), str(tp1.parasitic.ind), str(tp1.percived.stiffness), str(tp1.percived.ind)))\n",
    "    print(template.format(str(t)+'  2:', str(tp2.parasitic.cap), str(tp2.parasitic.ind), str(tp2.percived.stiffness), str(tp2.percived.ind)))\n"
   ]
  }
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