Torsion_bar_simulator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Unitful: m, Length, N, inch,rad,°,@u_str,lbf, lb,s, ustrip, psi,uconvert\n",
    "using CSV\n",
    "using DataFrames\n",
    "using DSP\n",
    "using GR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bar Info\n",
    "Very average information on bar actually, nothing new here\n",
    "Unit packages are freaking nice, obviously. Is your input in inches? cm? miles? run- |>u\"m\", now it is in meters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#approximate, but close enough\n",
    "function yeild_strength_to_shear_yeild(yeild_strength)\n",
    "    yeild_strength*.58\n",
    "end\n",
    "bar_diameter=.75u\"inch\"|>u\"m\"\n",
    "bar_radius=bar_diameter/2\n",
    "poisson_ratio=.33\n",
    "youngs_modulus=29*(10^6)u\"psi\"|>u\"Pa\"\n",
    "bar_density= .284u\"lb/inch^3\"|>u\"kg/m^3\"\n",
    "transmitted_strain_gauge_distance=36u\"inch\"|>u\"m\"\n",
    "incident_strain_gauge_distance=24u\"inch\"|>u\"m\"\n",
    "yeild_strength=50800u\"psi\"|>u\"Pa\"\n",
    "shear_yeild_strength=yeild_strength_to_shear_yeild(yeild_strength)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shot information\n",
    "Two big driving variables, length of bar twisted and how far the bar was twisted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "length_of_bar_twisted=12u\"inch\"|>u\"m\"\n",
    "twist_angle=20u\"°\"|>u\"rad\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function compute_shear_modulus(youngs_modulus,poisson_ratio)\n",
    "    youngs_modulus/2/(1+poisson_ratio)\n",
    "end\n",
    "shear_modulus= compute_shear_modulus(youngs_modulus,poisson_ratio)\n",
    "shear_wave_speed=√((shear_modulus|>u\"(kg*m/s^2)/m^2\")/(bar_density))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shot Prediction\n",
    "Note shear strain is in radians. That is not a typo.\n",
    "The incident pulse would be twice the duration of crossing the twisted area,\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Important function\n",
    "function polar_moment_inertia_bar(bar_radius)\n",
    "    π*bar_radius^4/2\n",
    "end\n",
    "#Important function\n",
    "function surface_strain_to_bar_torque(surface_strain,bar_radius,shear_modulus)\n",
    "    torque_bar=(shear_modulus|>u\"N/m^2\")*polar_moment_inertia_bar(bar_radius)*surface_strain/bar_radius\n",
    "end\n",
    "function bar_torque_to_surface_strain(torque_bar,bar_radius,shear_modulus)\n",
    "    torque_bar*bar_radius/((shear_modulus|>u\"N/m^2\")*polar_moment_inertia_bar(bar_radius))\n",
    "end\n",
    "#counter part of \"speed limit\" for shear test- how much can you torque the bar befor it dies?\n",
    "function predicted_max_torque(shear_yeild_strength,bar_radius)\n",
    "    (shear_yeild_strength|>u\"N/m^2\")*polar_moment_inertia_bar(bar_radius)/bar_radius\n",
    "end\n",
    "function predicted_strain_of_shot(bar_radius,twist_angle,length_of_bar_twisted)\n",
    "    bar_radius*twist_angle/length_of_bar_twisted\n",
    "end\n",
    "shear_strain_surface=bar_radius*twist_angle/length_of_bar_twisted\n",
    "duration_pulse= 2*length_of_bar_twisted/shear_wave_speed\n",
    "shear_stress_surface=ustrip(shear_strain_surface)*shear_modulus*bar_radius\n",
    "J_bar=polar_moment_inertia_bar(bar_radius)\n",
    "torque_bar=surface_strain_to_bar_torque(shear_strain_surface,bar_radius,shear_modulus)\n",
    "predicted_max_torque(shear_yeild_strength,bar_radius)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sample parameters\n",
    "The sample is a tube or a hollow cylinder of metal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_inner_diameter=10u\"mm\"|>u\"m\"\n",
    "sample_outer_diameter=12u\"mm\"|>u\"m\"\n",
    "sample_length=5u\"mm\" |>u\"m\"\n",
    "sample_mean_radius=(sample_inner_diameter+sample_outer_diameter)/4\n",
    "sample_thickness=(sample_outer_diameter-sample_inner_diameter)/2\n",
    "sample_youngs_modulus=10*(10^6)u\"psi\"|>u\"Pa\"\n",
    "sample_shear_modulus=compute_shear_modulus(sample_youngs_modulus,.33)\n",
    "\n",
    "#this isnt a parameter\n",
    "sample_flow_shear_stress=200u\"MPa\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Important function\n",
    "function polar_moment_of_tube(inner_radius,outer_radius)\n",
    "    polar_moment_inertia_bar(outer_radius)-polar_moment_inertia_bar(inner_radius)\n",
    "end\n",
    "function sample_stress_to_sample_torque(sample_outer_diameter,sample_inner_diameter,shear_stress)\n",
    "    moment_of_inertia=polar_moment_of_tube(sample_inner_diameter/2,sample_outer_diameter/2)\n",
    "    torque_sample=(shear_stress|>u\"N/m^2\")*moment_of_inertia/((sample_outer_diameter+sample_inner_diameter)/4)\n",
    "end\n",
    "#Important function\n",
    "function sample_torque_to_sample_stress(torque_sample,sample_outer_diameter,sample_inner_diameter)\n",
    "    moment_of_inertia=polar_moment_of_tube(sample_inner_diameter/2,sample_outer_diameter/2)\n",
    "    torque_sample/moment_of_inertia*((sample_outer_diameter+sample_inner_diameter)/4)\n",
    "end\n",
    "#incident and reflected pulses to sample shear strain rate\n",
    "function compute_shear_strain_rate(reflected_shear_strain,bar_diameter,sample_average_diameter,\n",
    "        shear_wave_speed,length_of_sample)\n",
    "    4*(sample_average_diameter/2)*shear_wave_speed/(bar_diameter/2*length_of_sample)*(reflected_shear_strain) \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulated Shot  \n",
    "Twist 12 inches of bar 2 degrees  \n",
    "sample as described above.  \n",
    "Expect flow stress of 200 MPa  \n",
    "total strain of .66, strain rate of 3360  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "length_of_bar_twisted=12u\"inch\"|>u\"m\"\n",
    "twist_angle=2u\"°\"|>u\"rad\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "transmitted_torque=sample_stress_to_sample_torque(sample_outer_diameter,sample_inner_diameter,sample_flow_shear_stress)\n",
    "transmitted_strain=bar_torque_to_surface_strain(transmitted_torque,bar_radius,shear_modulus)\n",
    "predicted_strain=predicted_strain_of_shot(bar_radius,twist_angle,length_of_bar_twisted)\n",
    "reflected_strain=predicted_strain-transmitted_strain\n",
    "compute_shear_strain_rate(reflected_strain,bar_diameter,sample_mean_radius*2,\n",
    "        shear_wave_speed,sample_length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lead_time=collect(0u\"s\":1u\"μs\":0.0001u\"s\")\n",
    "duration_pulse=length_of_bar_twisted*2/shear_wave_speed\n",
    "lead_in=map(time->0.0,0u\"s\":1u\"μs\":0.0001u\"s\")\n",
    "incident_pulse=map(time->ustrip(predicted_strain),0u\"s\":1u\"μs\":duration_pulse)\n",
    "gap=map(time->0.0,0u\"s\":1u\"μs\":(2*incident_strain_gauge_distance/shear_wave_speed))\n",
    "reflected_pulse = map(time->-ustrip(reflected_strain),0u\"s\":1u\"μs\":duration_pulse)\n",
    "end_out=map(time->0.0,0u\"s\":1u\"μs\":0.0001u\"s\")\n",
    "transmitted_pulse=map(time->ustrip(transmitted_strain),0u\"s\":1u\"μs\":duration_pulse)\n",
    "gap_transmitted=map(time->0.0,0u\"s\":1u\"μs\":(1u\"μs\"+2*incident_strain_gauge_distance/shear_wave_speed+duration_pulse))\n",
    "\n",
    "time=map(time->ustrip(time),0u\"s\":1u\"μs\":(4u\"μs\"+0.0001u\"s\"*2+duration_pulse*2+(2*incident_strain_gauge_distance/shear_wave_speed)))\n",
    "#quick little filter so it doesn't look dumb\n",
    "proto=Butterworth(1)\n",
    "zpk = digitalfilter(Lowpass(0.2), proto)\n",
    "tf = convert(PolynomialRatio, zpk)\n",
    "\n",
    "incident_bar_strain_history=filt(tf,cat(dims=1,lead_in,incident_pulse,gap,reflected_pulse,end_out))\n",
    "transmitted_bar_strain_history=filt(tf,cat(dims=1,lead_in,gap_transmitted,transmitted_pulse,end_out));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "GR.setviewport(0.1, 0.95, 0.1, 0.95)\n",
    "GR.setwindow(-2, 2, -2, 2)\n",
    "GR.setspace(-0.5, 0.5, 0, 90)\n",
    "GR.setmarkersize(1)\n",
    "GR.setmarkertype(-1)\n",
    "GR.setcharheight(0.024)\n",
    "GR.settextalign(2, 0)\n",
    "GR.settextfontprec(3, 0)\n",
    "\n",
    "\n",
    "plot(time,incident_bar_strain_history)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "GR.setviewport(0.1, 0.95, 0.1, 0.95)\n",
    "GR.setwindow(-2, 2, -2, 2)\n",
    "GR.setspace(-0.5, 0.5, 0, 90)\n",
    "GR.setmarkersize(1)\n",
    "GR.setmarkertype(-1)\n",
    "GR.setcharheight(0.024)\n",
    "GR.settextalign(2, 0)\n",
    "GR.settextfontprec(3, 0)\n",
    "\n",
    "plot(time,transmitted_bar_strain_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "data_frame=DataFrame(time_seconds=time,incident_strain_gauge=incident_bar_strain_history,transmitted_strain_gauge=transmitted_bar_strain_history)\n",
    "CSV.write(\"example_data.csv\",data_frame)"
   ]
  }
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