J Heikkala Method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "82d76f22",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "713e2efe",
   "metadata": {},
   "outputs": [],
   "source": [
    "class JH_Forces():\n",
    "    \n",
    "    def __init__(self, li=[None]):\n",
    "        '''Constructor for Forces Calculation as per J.Heikkala Method\n",
    "           Pass: List of Feed per Tooth, Cutting Speed, Diameter of Cutter, Depth of Cut, Width of Cut, \n",
    "                 Number of Teeth, Approach Angle, Radial Rake Angle, Axial Rake Angle and y.'''\n",
    "        # Parameters\n",
    "        self.li           = li\n",
    "        self.feed         = self.li[0]       # Feed in mm/tooth\n",
    "        self.cut_speed    = self.li[1]       # Cut Speeed in m/min\n",
    "        self.dia_cutter   = self.li[2]       # Diameter of Cutter in mm \n",
    "        self.doc          = self.li[3]       # Depth of Cut in mm\n",
    "        self.woc          = self.li[4]       # Width of Cut in mm\n",
    "        self.z            = self.li[5]       # Number of teeth\n",
    "        self.approach_ang = self.li[6]       # Approach angle in degrees\n",
    "        self.gamma_r      = self.li[7]       # Radial Rake Angle\n",
    "        self.gamma_a      = self.li[8]       # Axial Rake Angle\n",
    "        self.y            = self.li[9]       # Y distance in mm\n",
    "        \n",
    "        # Dataframes\n",
    "        self.df = pd.read_csv('Specific_Cutting_Forces.csv')   # Read CSV File\n",
    "        \n",
    "    def get_forces(self):\n",
    "        '''Calculates Forces, Power and Torques.\n",
    "           Pass: None\n",
    "           Return: DataFrame of Forces, Torques and Power.'''\n",
    "        \n",
    "        li = ['Material','Tangential Force (N)', 'Radial Force (N)', 'Axial Force (N)', 'Torque (N-m)', 'Power (kW)']\n",
    "        df = pd.DataFrame(columns = li)\n",
    "        \n",
    "        # Calculate Speed\n",
    "        speed = (self.cut_speed * 1000)/(np.pi * self.dia_cutter)\n",
    "        \n",
    "        # Calculate Rotating Angles\n",
    "        psi_min = np.pi*0.5 - np.arcsin((2*self.y)/self.dia_cutter)\n",
    "        psi_max = np.pi*0.5 + np.arcsin(2*(self.woc - self.y)/self.dia_cutter)\n",
    "        alpha = psi_max-psi_min\n",
    "        \n",
    "        # Number of Teeths in COntact\n",
    "        k = (alpha*self.z)/(2*np.pi) +1\n",
    "        k = int(k)\n",
    "        \n",
    "        # Calculate Forces \n",
    "        li_tang = []\n",
    "        li_rad = []\n",
    "        li_axi = []\n",
    "        li_torq = []\n",
    "        li_power =[]\n",
    "        for ksi, q in zip(self.df['Specific cutting force'], self.df['r']):\n",
    "            r = 1-q\n",
    "            ksi = ksi/1000\n",
    "            \n",
    "            # Calculate Coefficients\n",
    "            A = self.doc * ksi * (self.feed**r) * (np.sin(self.approach_ang * (np.pi/180)))**(r-1) * (1 - (0.01*self.gamma_r))\n",
    "            B = 0.44 - (0.013*self.gamma_r)\n",
    "            C = ((self.feed + (self.doc/np.tan(self.approach_ang*(np.pi/180))))/self.doc) * (0.88 - (0.013*self.gamma_a))\n",
    "            \n",
    "            # Calculate Angles\n",
    "            li_ang = []\n",
    "            for i in range(int(k)):\n",
    "                psi = psi_min + ((2*np.pi)/self.z)*(i+1-1)\n",
    "                li_ang.append(psi)\n",
    "            \n",
    "            # Calculate Forces\n",
    "            li_forces =[]\n",
    "            for i in range(int(k)):\n",
    "                force = A * (np.sin(li_ang[i]))**r\n",
    "                li_forces.append(force)\n",
    "            \n",
    "            # Tangential, Radial and Axial Forces\n",
    "            tang_force = sum(li_forces) * 1000\n",
    "            radial_force = tang_force * B\n",
    "            axial_force = tang_force * C\n",
    "            \n",
    "            # Torque\n",
    "            torque = tang_force * (self.dia_cutter/2000)\n",
    "            \n",
    "            # Power \n",
    "            power = (2*np.pi*speed*torque)/60000\n",
    "            \n",
    "            # Append to List\n",
    "            li_tang.append(tang_force)\n",
    "            li_rad.append(radial_force)\n",
    "            li_axi.append(axial_force)\n",
    "            li_torq.append(torque)\n",
    "            li_power.append(power)\n",
    "        \n",
    "        # Update the Dataframe\n",
    "        df['Material'] = self.df['Material']\n",
    "        df['Tangential Force (N)'] = li_tang\n",
    "        df['Radial Force (N)'] = li_rad\n",
    "        df['Axial Force (N)'] = li_axi\n",
    "        df['Torque (N-m)'] = li_torq\n",
    "        df['Power (kW)'] = li_power\n",
    "        \n",
    "        return df # Return Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a8414a5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "feed = 0.15           # Feed in mm/tooth\n",
    "cut_speed = 144        # Cut Speeed in m/min\n",
    "dia_cutter = 100         # Diameter of Cutter in mm \n",
    "doc = 2               # Depth of Cut in mm\n",
    "woc =80                # Width of Cut in mm\n",
    "z = 8                   # Number of teeth\n",
    "approach_ang = 67       # Approach angle in degrees\n",
    "gamma_r = -5            # Radial Rake Angle\n",
    "gamma_a = -7             # Axial Rake Angle\n",
    "ksi = 1.79            # Specific Cutting force in kN/mm2\n",
    "y = woc/2               # y value - woc/2\n",
    "r = 0.8                # r factor given tables\n",
    "\n",
    "li = [feed, cut_speed, dia_cutter, doc, woc, z, approach_ang, gamma_r, gamma_a, y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "77f2a89f",
   "metadata": {},
   "outputs": [],
   "source": [
    "force = JH_Forces(li)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4a2bbf5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = force.get_forces()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fbbed900",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Material</th>\n",
       "      <th>Tangential Force (N)</th>\n",
       "      <th>Radial Force (N)</th>\n",
       "      <th>Axial Force (N)</th>\n",
       "      <th>Torque (N-m)</th>\n",
       "      <th>Power (kW)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Steel Unalloyed C = 0.1 - 0.25%</td>\n",
       "      <td>1953.381269</td>\n",
       "      <td>986.457541</td>\n",
       "      <td>947.370473</td>\n",
       "      <td>97.669063</td>\n",
       "      <td>4.688115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Steel Unalloyed C = 0.25 - 0.55%</td>\n",
       "      <td>2083.606687</td>\n",
       "      <td>1052.221377</td>\n",
       "      <td>1010.528504</td>\n",
       "      <td>104.180334</td>\n",
       "      <td>5.000656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Steel Unalloyed C = 0.55 - 0.80%</td>\n",
       "      <td>2213.832105</td>\n",
       "      <td>1117.985213</td>\n",
       "      <td>1073.686536</td>\n",
       "      <td>110.691605</td>\n",
       "      <td>5.313197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;= 5%) No...</td>\n",
       "      <td>2213.832105</td>\n",
       "      <td>1117.985213</td>\n",
       "      <td>1073.686536</td>\n",
       "      <td>110.691605</td>\n",
       "      <td>5.313197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;=5%) Har...</td>\n",
       "      <td>2474.282941</td>\n",
       "      <td>1249.512885</td>\n",
       "      <td>1200.002599</td>\n",
       "      <td>123.714147</td>\n",
       "      <td>5.938279</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            Material  Tangential Force (N)  \\\n",
       "0                    Steel Unalloyed C = 0.1 - 0.25%           1953.381269   \n",
       "1                   Steel Unalloyed C = 0.25 - 0.55%           2083.606687   \n",
       "2                   Steel Unalloyed C = 0.55 - 0.80%           2213.832105   \n",
       "3  Steel-Low alloyed (alloying elements <= 5%) No...           2213.832105   \n",
       "4  Steel-Low alloyed (alloying elements <=5%) Har...           2474.282941   \n",
       "\n",
       "   Radial Force (N)  Axial Force (N)  Torque (N-m)  Power (kW)  \n",
       "0        986.457541       947.370473     97.669063    4.688115  \n",
       "1       1052.221377      1010.528504    104.180334    5.000656  \n",
       "2       1117.985213      1073.686536    110.691605    5.313197  \n",
       "3       1117.985213      1073.686536    110.691605    5.313197  \n",
       "4       1249.512885      1200.002599    123.714147    5.938279  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2c1e26f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_excel('Result Dataframe.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7cd481",
   "metadata": {},
   "source": [
    "# -----------------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "90b9b145",
   "metadata": {},
   "outputs": [],
   "source": [
    "class JH_Forces():\n",
    "    \n",
    "    def __init__(self, li=[None]):\n",
    "        '''Constructor for Forces Calculation as per J.Heikkala Method\n",
    "           Pass: List of Feed per Tooth, Cutting Speed, Diameter of Cutter, Depth of Cut, Width of Cut, \n",
    "                 Number of Teeth, Approach Angle, Radial Rake Angle, Axial Rake Angle and y.'''\n",
    "        # Parameters\n",
    "        self.li           = li\n",
    "        self.feed         = self.li[0]       # Feed in mm/tooth\n",
    "        self.dia_cutter   = self.li[1]       # Diameter of Cutter in mm \n",
    "        self.doc          = self.li[2]       # Depth of Cut in mm\n",
    "        self.woc          = self.li[3]       # Width of Cut in mm\n",
    "        self.z            = self.li[4]       # Number of teeth\n",
    "        self.approach_ang = self.li[5]       # Approach angle in degrees\n",
    "        self.gamma_r      = self.li[6]       # Radial Rake Angle\n",
    "        self.gamma_a      = self.li[7]       # Axial Rake Angle\n",
    "        self.y            = self.li[8]       # Y distance in mm\n",
    "        \n",
    "        # Dataframes\n",
    "        self.df = pd.read_csv('Specific_Cutting_Forces.csv')   # Read CSV File\n",
    "        \n",
    "    def get_forces(self):\n",
    "        '''Calculates Forces, Power and Torques.\n",
    "           Pass: None\n",
    "           Return: DataFrame of Forces, Torques and Power.'''\n",
    "        \n",
    "        li = ['Material','Specific cutting force','Cutting Speed (m/min)','Speed (RPM)','Tangential Force (N)', 'Radial Force (N)', 'Axial Force (N)', 'Torque (N-m)', 'Power (kW)']\n",
    "        df = pd.DataFrame(columns = li)\n",
    "        \n",
    "        # Lists to Store\n",
    "        li_tang = []\n",
    "        li_rad = []\n",
    "        li_axi = []\n",
    "        li_torq = []\n",
    "        li_power =[]\n",
    "        li_speed = []\n",
    "        li_cut_speed = []\n",
    "        \n",
    "        for ksi, q, speed in zip(self.df['Specific cutting force'], self.df['r'], self.df['Cutting Speed']):\n",
    "            r = 1-q\n",
    "            ksi = ksi/1000\n",
    "            \n",
    "            # Calculate Speed\n",
    "            rot_speed = (speed * 1000)/(np.pi * self.dia_cutter)\n",
    "\n",
    "            # Calculate Rotating Angles\n",
    "            psi_min = np.pi*0.5 - np.arcsin((2*self.y)/self.dia_cutter)\n",
    "            psi_max = np.pi*0.5 + np.arcsin(2*(self.woc - self.y)/self.dia_cutter)\n",
    "            alpha = psi_max-psi_min\n",
    "\n",
    "            # Number of Teeths in COntact\n",
    "            k = (alpha*self.z)/(2*np.pi) +1\n",
    "            k = int(k)\n",
    "\n",
    "            # Calculate Forces \n",
    "        \n",
    "            # Calculate Coefficients\n",
    "            A = self.doc * ksi * (self.feed**r) * (np.sin(self.approach_ang * (np.pi/180)))**(r-1) * (1 - (0.01*self.gamma_r))\n",
    "            B = 0.44 - (0.013*self.gamma_r)\n",
    "            C = ((self.feed + (self.doc/np.tan(self.approach_ang*(np.pi/180))))/self.doc) * (0.88 - (0.013*self.gamma_a))\n",
    "            \n",
    "            # Calculate Angles\n",
    "            li_ang = []\n",
    "            for i in range(int(k)):\n",
    "                psi = psi_min + ((2*np.pi)/self.z)*(i+1-1)\n",
    "                li_ang.append(psi)\n",
    "            \n",
    "            # Calculate Forces\n",
    "            li_forces =[]\n",
    "            for i in range(int(k)):\n",
    "                force = A * (np.sin(li_ang[i]))**r\n",
    "                li_forces.append(force)\n",
    "            \n",
    "            # Tangential, Radial and Axial Forces\n",
    "            tang_force = sum(li_forces) * 1000\n",
    "            radial_force = tang_force * B\n",
    "            axial_force = tang_force * C\n",
    "            \n",
    "            # Torque\n",
    "            torque = tang_force * (self.dia_cutter/2000)\n",
    "            \n",
    "            # Power \n",
    "            power = (2 * np.pi * rot_speed * torque)/60000\n",
    "        \n",
    "            # Append to List\n",
    "            li_tang.append(np.ceil(tang_force))\n",
    "            li_rad.append(np.ceil(radial_force))\n",
    "            li_axi.append(np.ceil(axial_force))\n",
    "            li_torq.append(np.ceil(torque))\n",
    "            li_power.append(np.ceil(power))\n",
    "            li_speed.append(np.ceil(rot_speed))\n",
    "            li_cut_speed.append(np.ceil(speed))\n",
    "            \n",
    "        \n",
    "        # Update the Dataframe\n",
    "        df['Material'] = self.df['Material']\n",
    "        df['Specific cutting force'] = self.df['Specific cutting force']\n",
    "        df['Tangential Force (N)'] = li_tang\n",
    "        df['Radial Force (N)'] = li_rad\n",
    "        df['Axial Force (N)'] = li_axi\n",
    "        df['Torque (N-m)'] = li_torq\n",
    "        df['Power (kW)'] = li_power\n",
    "        df['Cutting Speed (m/min)'] = li_cut_speed\n",
    "        df['Speed (RPM)'] = li_speed\n",
    "        \n",
    "        return df # Return Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4d36ec9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "feed = 0.15           # Feed in mm/tooth\n",
    "dia_cutter = 100        # Diameter of Cutter in mm \n",
    "doc = 1               # Depth of Cut in mm\n",
    "woc =100                # Width of Cut in mm\n",
    "z = 6                   # Number of teeth\n",
    "approach_ang = 45       # Approach angle in degrees\n",
    "gamma_r = -5            # Radial Rake Angle\n",
    "gamma_a = -7             # Axial Rake Angle\n",
    "y = woc/2               # y value - woc/2\n",
    "\n",
    "li = [feed, dia_cutter, doc, woc, z, approach_ang, gamma_r, gamma_a, y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6598ad36",
   "metadata": {},
   "outputs": [],
   "source": [
    "force = JH_Forces(li)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b07fca26",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = force.get_forces()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "687c2b99",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Material</th>\n",
       "      <th>Specific cutting force</th>\n",
       "      <th>Cutting Speed (m/min)</th>\n",
       "      <th>Speed (RPM)</th>\n",
       "      <th>Tangential Force (N)</th>\n",
       "      <th>Radial Force (N)</th>\n",
       "      <th>Axial Force (N)</th>\n",
       "      <th>Torque (N-m)</th>\n",
       "      <th>Power (kW)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Steel Unalloyed C = 0.1 - 0.25%</td>\n",
       "      <td>1500</td>\n",
       "      <td>490.0</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>744.0</td>\n",
       "      <td>376.0</td>\n",
       "      <td>830.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Steel Unalloyed C = 0.25 - 0.55%</td>\n",
       "      <td>1600</td>\n",
       "      <td>440.0</td>\n",
       "      <td>1401.0</td>\n",
       "      <td>793.0</td>\n",
       "      <td>401.0</td>\n",
       "      <td>886.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Steel Unalloyed C = 0.55 - 0.80%</td>\n",
       "      <td>1700</td>\n",
       "      <td>415.0</td>\n",
       "      <td>1321.0</td>\n",
       "      <td>843.0</td>\n",
       "      <td>426.0</td>\n",
       "      <td>941.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;= 5%) No...</td>\n",
       "      <td>1700</td>\n",
       "      <td>345.0</td>\n",
       "      <td>1099.0</td>\n",
       "      <td>843.0</td>\n",
       "      <td>426.0</td>\n",
       "      <td>941.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;=5%) Har...</td>\n",
       "      <td>1900</td>\n",
       "      <td>225.0</td>\n",
       "      <td>717.0</td>\n",
       "      <td>942.0</td>\n",
       "      <td>476.0</td>\n",
       "      <td>1052.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            Material  Specific cutting force  \\\n",
       "0                    Steel Unalloyed C = 0.1 - 0.25%                    1500   \n",
       "1                   Steel Unalloyed C = 0.25 - 0.55%                    1600   \n",
       "2                   Steel Unalloyed C = 0.55 - 0.80%                    1700   \n",
       "3  Steel-Low alloyed (alloying elements <= 5%) No...                    1700   \n",
       "4  Steel-Low alloyed (alloying elements <=5%) Har...                    1900   \n",
       "\n",
       "   Cutting Speed (m/min)  Speed (RPM)  Tangential Force (N)  Radial Force (N)  \\\n",
       "0                  490.0       1560.0                 744.0             376.0   \n",
       "1                  440.0       1401.0                 793.0             401.0   \n",
       "2                  415.0       1321.0                 843.0             426.0   \n",
       "3                  345.0       1099.0                 843.0             426.0   \n",
       "4                  225.0        717.0                 942.0             476.0   \n",
       "\n",
       "   Axial Force (N)  Torque (N-m)  Power (kW)  \n",
       "0            830.0          38.0         7.0  \n",
       "1            886.0          40.0         6.0  \n",
       "2            941.0          43.0         6.0  \n",
       "3            941.0          43.0         5.0  \n",
       "4           1052.0          48.0         4.0  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "06a0cfb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_excel('80 100/Result_Dataframe_100.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d03fba4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = pd.read_csv('Specific_Cutting_Forces.csv')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3caafba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Material</th>\n",
       "      <th>Class Iso</th>\n",
       "      <th>Specific cutting force</th>\n",
       "      <th>Brinnel Hardness</th>\n",
       "      <th>r</th>\n",
       "      <th>Cutting Speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Steel Unalloyed C = 0.1 - 0.25%</td>\n",
       "      <td>P</td>\n",
       "      <td>1500</td>\n",
       "      <td>125</td>\n",
       "      <td>0.25</td>\n",
       "      <td>490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Steel Unalloyed C = 0.25 - 0.55%</td>\n",
       "      <td>P</td>\n",
       "      <td>1600</td>\n",
       "      <td>150</td>\n",
       "      <td>0.25</td>\n",
       "      <td>440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Steel Unalloyed C = 0.55 - 0.80%</td>\n",
       "      <td>P</td>\n",
       "      <td>1700</td>\n",
       "      <td>170</td>\n",
       "      <td>0.25</td>\n",
       "      <td>415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;= 5%) No...</td>\n",
       "      <td>P</td>\n",
       "      <td>1700</td>\n",
       "      <td>175</td>\n",
       "      <td>0.25</td>\n",
       "      <td>345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steel-Low alloyed (alloying elements &lt;=5%) Har...</td>\n",
       "      <td>P</td>\n",
       "      <td>1900</td>\n",
       "      <td>300</td>\n",
       "      <td>0.25</td>\n",
       "      <td>225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            Material Class Iso  \\\n",
       "0                    Steel Unalloyed C = 0.1 - 0.25%         P   \n",
       "1                   Steel Unalloyed C = 0.25 - 0.55%         P   \n",
       "2                   Steel Unalloyed C = 0.55 - 0.80%         P   \n",
       "3  Steel-Low alloyed (alloying elements <= 5%) No...         P   \n",
       "4  Steel-Low alloyed (alloying elements <=5%) Har...         P   \n",
       "\n",
       "   Specific cutting force Brinnel Hardness     r  Cutting Speed  \n",
       "0                    1500              125  0.25            490  \n",
       "1                    1600              150  0.25            440  \n",
       "2                    1700              170  0.25            415  \n",
       "3                    1700              175  0.25            345  \n",
       "4                    1900              300  0.25            225  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f42538ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ceil(17.17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98ccfceb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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