ME3263_Lab-02.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm, t\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import pretty_plots # script to set up LaTex and increase line-width and font size\n",
    "\n",
    "pretty_plots.setdefaults()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ME 3263 Introduction to Sensors and Data Analysis (Fall 2018)\n",
    "=====================================\n",
    "\n",
    "Lab #2 - Static beam deflections with strain gage\n",
    "=====================================\n",
    "\n",
    "# What is a Strain Gage?\n",
    "\n",
    "A strain gage consists of a looped wire that is embedded in a thin backing. Two\n",
    "copper coated tabs serve as solder points for the leads. See Figure 1a. The\n",
    "strain gage is mounted to the structure, whose deformation is to be measured. As\n",
    "the structure deforms, the wire stretches (increasing its net length ) and its\n",
    "electrical resistance changes: $R=\\rho L/A$, where $\\rho$ is the material\n",
    "resistivity, $L$ is the total length of the wire, and $A$ is the cross sectional\n",
    "area of the wire.  Note that as $L$ increases, the cross sectional area changes as\n",
    "well due to the Poisson contraction; the resistivity also changes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Figure 1: a) A typical strain gage. b) One common setup: the gage is\n",
    "mounted to measure the x-direction strain on the top surface. It's\n",
    "engaged in a quarter bridge configuration of the Wheatstone bridge\n",
    "circuit.](./figure_01.png)\n",
    "\n",
    "*Figure 1: a) A typical strain gage. b) One common setup: the gage is\n",
    "mounted to measure the x-direction strain on the top surface. It's\n",
    "engaged in a quarter bridge configuration of the Wheatstone bridge\n",
    "circuit.*\n",
    "\n",
    "# Validate static strain gage measurements\n",
    "\n",
    "In this lab we will calibrate strain measurements using Euler-Bernouli beam theory\n",
    "kinematics. The axial strain in a beam is directly proportional to the distance\n",
    "from the neutral axis and curvature as such"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\epsilon_x=-\\kappa z$. (1)\n",
    "\n",
    "The curvature of the beam is approximated as such\n",
    "\n",
    "$\\kappa=\\frac{d^2 w}{dx^2}$. (2)\n",
    "\n",
    "Equations 1 and 2 relate beam deflection to axial strain. These are called\n",
    "kinematic equations because they define the geometry of the beam deflection. \n",
    "\n",
    "The Euler-Bernouli beam theory uses Newton's second law (kinetics) and Hooke's\n",
    "law (constitutive) to derive the linear equations of motion for one dimensional\n",
    "deformable objects. The relation between a static applied force q(x) and static\n",
    "deflection w(x) is as such\n",
    "\n",
    "$\\frac{\\partial^2}{\\partial x^2}\\left(EI\\frac{\\partial^2 w}{\\partial\n",
    "x^2}\\right)=q(x)$ (3)\n",
    "\n",
    "where $E$ is the Young's modulus, $x$ is the distance along the neutral axis,\n",
    "and $I$ is the second moment of area of the beam's cross-section. For a\n",
    "rectangular cross-section $b \\times t$, width by thickness the second moment of\n",
    "area is\n",
    "\n",
    "$I=\\frac{bt^3}{12}$. (4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will design our strain gage validation such that $E$ and $I$ are not necessary. The boundary conditions for a clamped beam that is\n",
    "deflected by a distance $\\delta$ are $w(0)=0$, $w'(0)=0$, $w(L)=\\delta$, and\n",
    "$w''(L)=0$. Therefore, the functions $w(x)$ and $w''(x)$ can be determined by\n",
    "integrating equation 3 four times and using the four boundary conditions as such\n",
    "\n",
    "$w(x)=-\\frac{1}{2}\\left(\\frac{\\delta}{L^3}x^3-3\\frac{\\delta}{L^2}x^2\\right)$ (5a)\n",
    "\n",
    "and the curvature \n",
    "\n",
    "$w''(x)=-\\left(3\\frac{\\delta}{L^3}x-3\\frac{\\delta}{L^2}\\right)$ (5b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using equations 5a-b, the only quantities needed to determine strain at a given\n",
    "location on a linear, homogeneous beam are $z$, $\\delta$, $w(L)$, and $L$. \n",
    "\n",
    "![Figure 2: Diagram of the validation process. The strain gage is placed at a distance $x_{SG}$ from the cantilever support. A linear-elastic beam of length $L$ is deflected by distance, $\\delta$.](./figure_02.png)\n",
    "\n",
    "*Figure 2: Diagram of the validation process. The strain gage is placed at a distance $x_{SG}$ from the cantilever support. A linear-elastic beam of length $L$ is deflected by distance, $\\delta$.*\n",
    "\n",
    "-   Apply a known tip displacement by applying a load on the beam at multiple\n",
    "    locations as seen in Figure 2.  Measure and record the strain at your strain\n",
    "    gage location, the displacement, $\\delta$ and length where load was applied,\n",
    "    $L$.\n",
    "\n",
    "-   Calculate the strain at the location of the strain gage using equations 1,2,\n",
    "    and 5a-b.\n",
    "    \n",
    "Below are two functions that calculate displacement and curvature given a bar of length `L`, that is deflected by a distance, `delta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def disp_at_x(x,L,delta):\n",
    "    '''returns the displacement w(x) given the position, x, \n",
    "    length of bar, L, and displacement at L, delta'''\n",
    "    wx=-1/2*(delta/L**3*x**3-3*delta/L**2*x**2)\n",
    "    return wx\n",
    "\n",
    "def k_at_x(x,L,delta):\n",
    "    '''returns the curvature w''(x) given the position, x, \n",
    "    length of bar, L, and displacement at L, delta'''\n",
    "    wx=-(3*delta/L**3*x-3*delta/L**2)\n",
    "    return wx\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "displacement of 400 mm bar deflect`ed 10 mm, 20 mm from support =0.037 mm\n",
      "   curvature of 400 mm bar deflected 10 mm, 20 mm from support =0.178 1/m\n"
     ]
    }
   ],
   "source": [
    "w20mm=disp_at_x(20,400,10)\n",
    "k20mm=k_at_x(20,400,10)\n",
    "print('displacement of 400 mm bar deflect`ed 10 mm, 20 mm from support =%1.3f mm'%w20mm)\n",
    "print('   curvature of 400 mm bar deflected 10 mm, 20 mm from support =%1.3f 1/m'%(k20mm*1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Shape of deflected cantilever beam')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0,400)\n",
    "wx=disp_at_x(x,400,10)\n",
    "plt.plot(x,wx)\n",
    "plt.xlabel('position along beam (mm)')\n",
    "plt.ylabel(r'deflection of \\\\neutral axis w(x) (mm)')\n",
    "plt.title('Shape of deflected cantilever beam')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Curvature of deflected cantilever beam')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0,400)\n",
    "kx=k_at_x(x,400,10)\n",
    "plt.plot(x,kx*1000)\n",
    "plt.xlabel('position along beam (mm)')\n",
    "plt.ylabel(r'curvature \\\\of neutral axis \\\\w(x) (1/m)')\n",
    "plt.title('Curvature of deflected cantilever beam')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Measure constitutive properties\n",
    "\n",
    "## Constitutive Model\n",
    "Now the strain gage should be calibrated. We need to determine the Young's modulus, $E$ and second moment of area, $I$. This measurement requires three components: kinematic (which we solved in the validation), kinetic ($\\sum{F}=0$), and a constitutive model (Hooke's Law). The constitutive equation for a linear-elastic beam subject to a moment is as such\n",
    "\n",
    "$M=EI\\kappa$. (6)\n",
    "\n",
    "In equation 6, $M$ is the applied moment, $E$ is the Young's modulus, $I$ is the second moment of inertia of the area of the beam, and $\\kappa$ is the curvature of the beam. The constant $I$ is based upon the geometry from equation 4. The material constant $E$ is unknown. \n",
    "\n",
    "Use the weights to apply forces at different distances, $r$, from the support as seen in Figure 3. Increasing the weight or the distance the weight is applied will increase the applied moment. Use Table 1 to record the trial no., strain, force, distance, and moment. Use at least two trials per measurement. \n",
    "\n",
    "![Figure 3: A linear-elastic beam of length $L$ has a force applied at distance, $r$. \n",
    "The strain gage is placed at a distance $x_{SG}$ from the cantilever support.](./figure_03.png)\n",
    "\n",
    "*Figure 3: A linear-elastic beam of length $L$ has a force applied at distance, $r$. \n",
    "The strain gage is placed at a distance $x$ from the cantilever support.*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting your data to your model\n",
    "\n",
    "Once you have filled in a number of data points for $\\kappa$ and $M$, you can use a linear regression to determine the slope of the data. The constitutive model in equation (6) predicts that the moment and curvature will be related by a proportional constant, $EI$. If we know $EI$, the total squared error is as such\n",
    "\n",
    "$SSE=\\sum_i^N{(M_i-EI\\kappa_i)^2}$ (7)\n",
    "\n",
    "where SSE is the sum of squares error between the predicted moment and measured moment for the $i^{th}$ measurement with $N$ total measurements [2](https://www.amazon.com/Numerical-Methods-Engineers-Steven-Chapra/dp/0073401064). We can choose a of $EI$ that minimizes $SSE$, but it will never be zero. Below is an example calculation for a linear least squares regression in python for a beam with cross-section $12\\times3$ mm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "k=np.array([6.95685737e-07, 9.93992373e-06, 3.25200211e-05, 3.55750721e-05,\n",
    "       5.32023782e-05, 7.48128585e-05, 7.61625461e-05, 8.54476229e-05,\n",
    "       1.02089509e-04, 1.02841452e-04, 1.32351731e-04, 1.43996022e-04,\n",
    "       1.45204793e-04, 1.56867759e-04, 1.73435915e-04, 1.95625232e-04,\n",
    "       2.00670618e-04, 2.12900332e-04, 2.24582886e-04, 2.41141396e-04,\n",
    "       2.45991618e-04, 2.55608426e-04, 2.76117673e-04, 2.96128593e-04,\n",
    "       3.07157389e-04, 3.20509718e-04, 3.20363196e-04, 3.35535814e-04,\n",
    "       3.53706984e-04, 3.64130433e-04])\n",
    "M=np.array([ 0.        ,  23.82866379,  47.65732759,  71.48599138,\n",
    "        95.31465517, 119.14331897, 142.97198276, 166.80064655,\n",
    "       190.62931034, 214.45797414, 238.28663793, 262.11530172,\n",
    "       285.94396552, 309.77262931, 333.6012931 , 357.4299569 ,\n",
    "       381.25862069, 405.08728448, 428.91594828, 452.74461207,\n",
    "       476.57327586, 500.40193966, 524.23060345, 548.05926724,\n",
    "       571.88793103, 595.71659483, 619.54525862, 643.37392241,\n",
    "       667.20258621, 691.03125   ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit for Young's Modulus is 70.2 +/- 0.3 GPa\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Moment (N-mm)')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "\n",
    "def func(x,EI):\n",
    "    return EI*x\n",
    "\n",
    "EI,pcov=curve_fit(func, k, M)\n",
    "EI_error=np.sqrt(pcov[0,0])\n",
    "I=12*3**3/12.0\n",
    "print(\"Best fit for Young's Modulus is %1.1f +/- %1.1f GPa\"%(EI/I*1e-3,EI_error/I*1e-3))\n",
    "\n",
    "plt.plot(k*1e3,M,'o',label='experiment')\n",
    "plt.plot(k*1e3,func(k,EI),label='model')\n",
    "plt.legend()\n",
    "plt.xlabel('curvature (1/m)')\n",
    "plt.ylabel('Moment (N-mm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Note:*\n",
    "\n",
    "The least-squares method used above can be used to fit any function to a data set. You would just need to update the `func` definition to return the desired function based upon your unkown fitting constants. \n",
    "\n",
    "The outout `popt` is the covariance matrix [\\[3\\]](./least_squares-error_with_covariance.pdf). In practice, we can use the square root of the diagonal terms to estimate the error in our least-squares fit. We make a few assumptions when performing this best-fit:\n",
    "\n",
    "1. There is a random error in the measured  dependent variable (here the moment $M$). \n",
    "\n",
    "2. There is no error in the reported independent variable (here the curvature $\\kappa$).\n",
    "\n",
    "3. The measured dependent variables are uncorrelated with the measured error\n",
    "\n",
    "4. The random error has a mean of zero\n",
    "\n",
    "We can test assumption 4 by plotting the \"residuals\" of the fit i.e. the error. The plot below demonstrates that our data has a mean error of 0 and is uncorrelated with the "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Error=$M-EI\\\\kappa$')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(k*1e3,M-func(k,EI),'o')\n",
    "plt.xlabel('curvature (1/m)')\n",
    "plt.ylabel(r'Error=$M-EI\\kappa$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Table 1: Fill in the measured and calculated values.*\n",
    "\n",
    "|trial|distance, $r$| force= $mg$|strain (mm/mm)|curvature (1/mm)|Moment=$r\\times F$|\n",
    "|---|---|---|---|---|---|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|1|\n",
    "|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n",
    "|2|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Your Report \n",
    "\n",
    "1. Introduction\n",
    "\n",
    "  a. What assumptions are used in Euler-Bernoulli beam theory?\n",
    "  \n",
    "  b. How does a strain gage measure strain?\n",
    "  \n",
    "  c. How does the Euler-Bernoulli beam theory apply to the experiment?\n",
    "\n",
    "  \n",
    "\n",
    "2. Procedure\n",
    "\n",
    "  a. Description of experimental set-up\n",
    "\n",
    "  b. Description of materials and measurements\n",
    "\n",
    "  c. If someone repeated the experiment he/she would read only this section\n",
    "\n",
    "3. Results and Discussion\n",
    "\n",
    "  a. Present experimental results succinctly\n",
    "\n",
    "  b. Present propagation of error clearly\n",
    "\n",
    "  b. Interpret results clearly\n",
    "\n",
    "  c. Compare predicted strain and measured strain\n",
    "  \n",
    "  d. Compare your measured Young's modulus to published values for your beam material\n",
    "\n",
    "4. Conclusion\n",
    "\n",
    "  a. Is this a good method to calibrate a strain gage?\n",
    "\n",
    "  b. What other applications would benefit from this technique/these results?\n",
    "  \n",
    "  c. What could you use this beam for now that it is calibrated?\n",
    "  \n",
    "  d. Why is beam theory used in this experiment (when is it not appropriate)?\n",
    "\n",
    "You must get reasonable agreement between predicted and measured strains otherwise you cannot\n",
    "proceed to next week's lab.\n",
    "\n",
    "### References\n",
    "\n",
    "References\n",
    "\n",
    "1. F.P. Beer and E.R. Johnson, Mechanics of Materials, 2nd Edition,\n",
    "McGraw-Hill, 1992.\n",
    "\n",
    "2. S. Chapra, Numerical Methods for Engineers, ch. 14-15, 6th Edition, McGraw-Hill, 2009.\n",
    "\n",
    "3. [C. Salter, Error Analysis Using the Variance–Covariance Matrix, J. of Chem. Ed., 2000.](./least_squares-error_with_covariance.pdf)\n",
    "\n",
    "3. [Euler-Bernoulli Beam Theory - Wikipedia](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory) \n",
    "\n",
    "4. [Uncertainty\n",
    "Notes courses.washington.edu](https://courses.washington.edu/phys431/uncertainty_notes.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}