{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Free Vibration of a Mass-Spring System
with Friction

\n", "

MCHE 485: Mechanical Vibrations

\n", "

Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\t\"A
\n", " Figure 1: A Mass-Spring System with Friction \n", "

\n", "\n", "This notebook simluates the free vibration of a simple mass-spring-damper system like the one shown in Figure 1. The mass in this system is attache to ground via a linear spring, k. The coefficient of friction between mass m and the surface on which it is moving is $\\mu$. The position of the mass is described by x(t).\n", "\n", "We'll first look at how the system response to non-zero initial conditions. We'll then compare its response to that of a similar system without friction, but with a viscous damper.\n", "\n", "The equation of motion for the system is:\n", "\n", "$ \\quad m \\ddot{x} + \\mu N sgn(\\dot{x}) + kx = 0 $\n", "\n", "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency $\\omega_n$.\n", "\n", "$ \\quad \\ddot{x} + \\frac{\\mu N}{m} sgn(\\dot{x}) + \\omega_n^2x = 0$\n", "\n", "For information on how to obtain this equation, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np # Grab all of the NumPy functions with nickname np\n", "from scipy.integrate import odeint " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We want our plots to be displayed inline, not in a separate window\n", "%matplotlib inline \n", "\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the System Parameters\n", "\n", "m = 1.0 # mass (kg)\n", "k = (1.0*2.0*np.pi)**2 # spring constant (N/m)\n", "mu = 0.1 # Friction coefficient\n", "g = 9.81 # gravity\n", "\n", "wn = np.sqrt(k/m) # natural frequency (rad/s)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the system as a series of 1st order ODES (beginnings of state-space form)\n", "def eq_of_motion(w, t, p):\n", " \"\"\"\n", " Defines the differential equations for the coupled spring-mass system.\n", "\n", " Arguments:\n", " w : vector of the state variables:\n", " w = [x, x_dot]\n", " t : time\n", " p : vector of the parameters:\n", " p = [m, k, mu, g]\n", " \"\"\"\n", " x, x_dot = w\n", " m, k, mu, g = p\n", "\n", " # Create sysODE = (x', x_dot'):\n", " sysODE = [x_dot,\n", " (-k * x - mu*m*g*np.sign(x_dot)) / m]\n", " return sysODE" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Set up simulation parameters \n", "\n", "# ODE solver parameters\n", "abserr = 1.0e-9\n", "relerr = 1.0e-9\n", "max_step = 0.01\n", "stoptime = 10.0\n", "numpoints = 10001\n", "\n", "# Create the time samples for the output of the ODE solver\n", "t = np.linspace(0.,stoptime,numpoints)\n", "\n", "# Initial conditions\n", "x_init = 1.0 # initial position\n", "x_dot_init = 0.0 # initial velocity\n", "\n", "# Pack the parameters and initial conditions into arrays \n", "p = [m, k, mu, g]\n", "x0 = [x_init, x_dot_init]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Call the ODE solver.\n", "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr, hmax=max_step)\n", "\n", "# Find the location of the last cycle peaks - we'll use to plot the linear decay envelope\n", "last_min = np.min(resp[:,0]* (t > 9))\n", "last_min_t = t[np.argmin(resp[:,0] * (t > 9))]\n", "last_max = np.max(resp[:,0]* (t > 8.5))\n", "last_max_t = t[np.argmax(resp[:,0]* (t > 8.5))]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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hiL90BQAgfvkyAIB95y6v4+MsEpbOycJDa+b7dMT21HbicGMPk3YegPezLzAX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\nSPiaU6z559tXjAWWO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel('Time (s)',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Position (m)',fontsize=22,weight='bold',labelpad=10)\n", "plt.yticks([-1.5, -1, -0.5, 0, 0.5, 1, 1.5], ['', r'$-x_0$', '', '0', '', r'$x_0$', ''])\n", "\n", "# plot the response\n", "plt.plot(t,resp[:,0],linewidth=2)\n", "\n", "# Add the (linear) decay envelopes\n", "plt.plot([0., last_max_t],[x_init, last_max], color = \"#377eb8\", linewidth=1.0, linestyle=\"--\")\n", "plt.plot([0., last_min_t],[-x_init, last_min], color = \"#377eb8\", linewidth=1.0, linestyle=\"--\")\n", "\n", "plt.annotate(r'Linear Decay Envelope',\n", " xy=(t[5001],resp[5001,0]), xycoords='data',\n", " xytext=(+10, +30), textcoords='offset points', fontsize=16,\n", " arrowprops=dict(arrowstyle=\"simple, head_width = 0.35, tail_width=0.05\", connectionstyle=\"arc3,rad=.2\", color=\"#377eb8\"),color = \"#377eb8\")\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# plt.savefig('CoulombDamping_Resp.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison to Viscous Damping\n", "Let's compare that response to the response from a system with a viscous damper and no friction, like the one in Figure 2.\n", "

\n", "\t\"A
\n", " Figure 2: A Mass-Spring-Damper System \n", "

\n", "\n", "As a reminder, the equation of motion for this system is:\n", "\n", "$ \\quad m \\ddot{x} + c \\dot{x} + k x = 0 $\n", "\n", "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency $\\omega_n$.\n", "\n", "$ \\quad \\ddot{x} + 2 \\zeta \\omega_n \\dot{x} + \\omega_n^2 x = 0 $" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Set up a system with viscous damping for comparison\n", "z = 0.025 # Define a desired damping ratio \n", " # z=0.025 to try to match first cycles of friction example\n", " \n", "c = 2*z*wn*m # calculate the damping coeff. to create it (N/(m/s))\n", "\n", "wd = wn*np.sqrt(1-z**2) # Damped natural frequency (rad/s)\n", "\n", "# Define the system as a series of 1st order ODES (beginnings of state-space form)\n", "def eq_of_motion_viscous(w, t, p):\n", " \"\"\"\n", " Defines the differential equations for the coupled spring-mass system.\n", "\n", " Arguments:\n", " w : vector of the state variables:\n", " w = [x, x_dot]\n", " t : time\n", " p : vector of the parameters:\n", " p = [m, k]\n", " \"\"\"\n", " x, x_dot = w\n", " m, k = p\n", "\n", " # Create sysODE = (x', x_dot'):\n", " sysODE = [x_dot,\n", " (-k*x - c*x_dot) / m]\n", " return sysODE\n", "\n", "\n", "\n", "# Set up simulation parameters \n", "# ODE solver parameters\n", "abserr = 1.0e-9\n", "relerr = 1.0e-9\n", "max_step = 0.01\n", "stoptime = 10.0\n", "numpoints = 10001\n", "\n", "\n", "# Initial conditions\n", "x_init = 1.0 # initial position\n", "x_dot_init = 0.0 # initial velocity\n", "\n", "# Pack the parameters and initial conditions into arrays:\n", "p = [m, k]\n", "x0 = [x_init, x_dot_init]\n", "\n", "# Call the ODE solver.\n", "resp_damped = odeint(eq_of_motion_viscous, x0, t, args=(p,), atol=abserr, rtol=relerr, hmax=max_step)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's compare this response to that with dry friction (Coulomb Damping)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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VOrbTM3yLq1JKYZplK2SuW63Vy34+Jq8Xs2V2QzWHl8eYSTPV1szbrure6K0A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\nWbsWD578GRR/De7qfjUAIHv6jDi2fr1j8ywGnNSdK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(t,resp[:,0], linewidth=2, linestyle = '-', label='Coulomb')\n", "plt.plot(t,resp_damped[:,0], linewidth=2, linestyle = '--', label='Viscous')\n", "\n", "# You may need to change your plot limits\n", "# plt.xlim(0,5)\n", "# plt.ylim(0,7)\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts() \n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# plt.savefig('DampingComparison_Resp.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (By Request) What if we have both viscous damping and friction?\n", "\n", "Let's look at a system that has both a viscous damper and friction, like the one shown in Figure 3.\n", "\n", "

\n", "\t\"A
\n", " Figure 3: A Mass-Spring-Damper System with Fricion\n", "

\n", "\n", "It's equation of motion is:\n", "\n", "$ \\quad m \\ddot{x} + c \\dot{x} + \\mu N sgn(\\dot{x}) + k x = 0 $\n", "\n", "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency $\\omega_n$.\n", "\n", "$ \\quad \\ddot{x} + 2 \\zeta \\omega_n \\dot{x} + + \\frac{\\mu N}{m} sgn(\\dot{x}) + \\omega_n^2 x = 0 $\n", "\n", "You can look at which form of damping is dominant by looking at the shape of the decay envelope. Change the values of $ \\mu $ and $\\zeta$ in the code block below to investigate." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Redefine the system parameters\n", "\n", "m = 1.0 # mass (kg)\n", "k = (1.0 * 2.0*np.pi)**2 # spring constant (N/m)\n", "mu = 0.025 # Friction coefficient\n", "g = 9.81 # gravity\n", "\n", "wn = np.sqrt(k/m) # natural frequency (rad/s)\n", "\n", "# Set up a system with viscous damping for comparison\n", "z = 0.02 # Define a desired damping ratio\n", "c = 2*z*wn*m # calculate the damping coeff. to create it (N/(m/s))\n", "\n", "wd = wn*np.sqrt(1-z**2) # Damped natural frequency (rad/s)\n", "\n", "\n", "\n", "# Define the system as a series of 1st order ODES (beginnings of state-space form)\n", "def eq_of_motion_both(w, t, p):\n", " \"\"\"\n", " Defines the differential equations for the coupled spring-mass system.\n", "\n", " Arguments:\n", " w : vector of the state variables:\n", " w = [x, x_dot]\n", " t : time\n", " p : vector of the parameters:\n", " p = [m, k, mu, g]\n", " \"\"\"\n", " x, x_dot = w\n", " m, k, mu, g = p\n", "\n", " # Create sysODE = (x', x_dot'):\n", " sysODE = [x_dot,\n", " (-k * x - mu*m*g*np.sign(x_dot) - c*x_dot) / m]\n", " return sysODE\n", "\n", "# Set up simulation parameters \n", "# ODE solver parameters\n", "abserr = 1.0e-9\n", "relerr = 1.0e-9\n", "max_step = 0.01\n", "stoptime = 10.0\n", "numpoints = 10001\n", "\n", "\n", "# Initial conditions\n", "x_init = 1.0 # initial position\n", "x_dot_init = 0.0 # initial velocity\n", "\n", "# Pack the parameters and initial conditions into arrays \n", "p = [m, k, mu, g]\n", "x0 = [x_init, x_dot_init]\n", "\n", "# Call the ODE solver.\n", "resp_both = odeint(eq_of_motion_both, x0, t, args=(p,), atol=abserr, rtol=relerr, hmax=max_step)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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RpOWksaXz67nccJoHxuU1D5Tr7ASK6+6shoqAk0bZrNX9yFjR3aP5cCfOGDgT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now, let's plot the results\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(t,resp_both[:,0], linewidth=2, linestyle = '-', label='Viscous and Friction')\n", "\n", "# You may need to change your plot limits\n", "# plt.xlim(0,5)\n", "# plt.ylim(0,7)\n", "\n", "# leg = plt.legend(loc='upper right', fancybox=True)\n", "# ltext = leg.get_texts() \n", "# plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# plt.savefig('FrictionAndViscous_Resp.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Licenses\n", "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n", "\n", "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This cell will just improve the styling of the notebook\n", "from IPython.core.display import HTML\n", "import urllib.request\n", "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n", "HTML(response.read().decode(\"utf-8\"))" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }