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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Chapter 17: Rolling of Metals"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "collapsed": true
- },
- "source": [
- "### Example 17.1, Forces in rolling, Page No. 596"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "Maximum possible reduction when mu is 0.08 = 0.0768 in\n",
- "\n",
- "Maximum possible reduction when mu is 0.5 = 3 in\n"
- ]
- }
- ],
- "source": [
- "\n",
- "from math import atan\n",
- "\n",
- "#variable declaration\n",
- "mu1=0.08;\n",
- "mu2=0.5;\n",
- "R=12;\n",
- "\n",
- "#calculation\n",
- "alpha=atan(mu1);\n",
- "dh1=mu1**2*R;\n",
- "dh2=mu2**2*R;\n",
- "\n",
- "#result\n",
- "print('\\nMaximum possible reduction when mu is 0.08 = %g in\\n')%(dh1);\n",
- "print('Maximum possible reduction when mu is 0.5 = %g in')%(dh2);\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Example 17.2, Rolling Load, Page No. 598"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "Rolling Load = 3039.51 kips\n",
- "\n",
- "Rolling Load if sticking friction occurs = 5509.54 kips\n"
- ]
- }
- ],
- "source": [
- "\n",
- "from math import sqrt\n",
- "from math import exp\n",
- "\n",
- "#variable declaration\n",
- "h0=1.5;\n",
- "mu=0.3;\n",
- "D=36;\n",
- "s_en=20;\n",
- "s_ex=30;\n",
- "\n",
- "#calculation\n",
- "h1=h0-0.3*h0;\n",
- "dh=h0-h1;\n",
- "h_=(h1+h0)/2;\n",
- "Lp=sqrt(D/2*dh);\n",
- "Q=mu*Lp/h_;\n",
- "sigma0=(s_en+s_ex)/2;\n",
- "P=sigma0*(exp(Q)-1)*s_ex*Lp/Q;\n",
- "Ps=sigma0*(Lp/(4*dh)+1)*s_ex*Lp;\n",
- "\n",
- "#result\n",
- "print('\\nRolling Load = %g kips')%(P);\n",
- "print('\\nRolling Load if sticking friction occurs = %g kips')%(Ps);\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Example 17.3, Rolling Load, Page No. 599"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "P2 = 1410.35\n",
- "R2 = 18.6281\n"
- ]
- }
- ],
- "source": [
- "\n",
- "\n",
- "from math import sqrt\n",
- "from math import exp\n",
- "\n",
- "#variable declaration\n",
- "h0=1.5;\n",
- "mu=0.3;\n",
- "D=36;\n",
- "s_en=20;\n",
- "s_ex=30;\n",
- "C=3.34*10**-4;\n",
- "P_=1357;\n",
- "\n",
- "#calculation\n",
- "h1=h0-0.3*h0;\n",
- "dh=h0-h1;\n",
- "h_=(h1+h0)/2;\n",
- "R=D/2;\n",
- "R1=R*(1+C*P_/(s_ex*(dh)));\n",
- "Lp=sqrt(R1*dh);\n",
- "Q=mu*Lp/h_;\n",
- "sigma0=(s_en+s_ex)/2;\n",
- "P2=sigma0*(exp(Q)-1)*s_ex*Lp/Q;\n",
- "P2=P2*0.45359 #conversion to tons\n",
- "R2=R*(1+C*P2/(s_ex*(dh)));\n",
- "\n",
- "#result\n",
- "print('\\nP2 = %g\\nR2 = %g')%(P2,R2);\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Example 17.4, Torque and Horsepower, Page No. 614"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "Rolling Load = 540.012\n",
- "Horsepower = 1713.63\n"
- ]
- }
- ],
- "source": [
- "\n",
- "from math import sqrt\n",
- "from math import pi\n",
- "from math import log\n",
- "\n",
- "#variable declaration\n",
- "w=12;\n",
- "hi=0.8;\n",
- "hf=0.6;\n",
- "D=40;\n",
- "N=100;\n",
- "\n",
- "#calculation\n",
- "R=D/2;\n",
- "dh=abs(hf-hi);\n",
- "e1=log(hi/hf);\n",
- "r=(hi-hf)/hi;\n",
- "sigma=20*e1**0.2/1.2;\n",
- "Qp=1.5;\n",
- "P=2*sigma*w*sqrt(R*(hi-hf))*Qp/sqrt(3);\n",
- "a=0.5*sqrt(R*dh);\n",
- "a=a/12; #conversion to ft\n",
- "hp=4*pi*a*P*N*1000/33000;\n",
- "\n",
- "#result\n",
- "print('\\nRolling Load = %g\\nHorsepower = %g')%(P,hp);\n"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.9"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}