{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[](https://drivetrainhub.com)\n", "\n", "
© 2020 Drivetrain Hub LLC
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Tooling / Basic Rack\n", "---\n", "\n", "**Authors**: [Chad Glinsky](https://github.com/glinskyc)\n", "\n", "**Description**: Review of basic racks and their significance to manufacturing of cylindrical involute gears." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Table of Contents\n", "\n", "1. [Introduction](#Introduction)\n", "2. [Geometry](#Geometry)\n", "3. [Types](#Types)\n", " 1. [Standard](#Standard)\n", " 2. [Non-standard](#Non-standard)\n", "4. [References](#References)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide_cell" ] }, "source": [ "#### Notebook imports and settings" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "hide_cell" ] }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from math import radians\n", "\n", "# notebook modules\n", "from helper import html_table\n", "import basic_rack as br\n", "\n", "# settings\n", "FIGSIZE = (6, 6) # size of plots\n", "plt.rcParams.update({'font.size': 12}) # set default font size" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "hide_cell" ] }, "outputs": [], "source": [ "# DEVELOPMENT USE: %autoreload 1\n", "# PRODUCTION USE: %autoreload 0\n", "%load_ext autoreload\n", "%autoreload 0\n", "%aimport basic_rack" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "A basic rack defines the tooth profile of a gear with infinite diameter and forms the basis of a family of gears. A basic rack is merely a set of geometric properties for describing gear tooth proportions. It is particularly useful for defining the parameters of a generating cutting tool capable of manufacturing cylindrical involute gears. Later chapters explain such manufacturing methods in detail.\n", "\n", "
\n", " The geometry of a cylindrical involute gear is directly dependent on the manufacturing tooling and processes used to make the gear. \n", "

\n", "The cost of manufacturing would be prohibitive if every gear required a different tool to make it, hence why the basic rack is of interest to gear manufacturing. Several common methods of gear manufacturing are reviewed in later chapters.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometry\n", "\n", "The geometry of a basic rack tooth profile is reviewed here.\n", "\n", "### Nomenclature\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SymbolDescription
$m_n$Module
$\\alpha_n$Pressure angle
$p$Pitch
$p_b$Base pitch
$h_a$Addendum
$h_f$Dedendum
$c$Bottom clearance
$\\rho_F$Root radius
$\\alpha_{FP}$Undercut angle
$U_{FP}$Undercut size
$p_{bP}$Undercut base pitch
\n", "\n", "Any symbols combined with a superscript asterisk refer to a *coefficient*, a term normalized by the module. For example, $\\rho_F^*$ is the root radius coefficient." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Basic\n", "

Basic rack tooth profile

\n", "\n", "
\n", " Notice the geometric definition of a basic rack does not include information about number of gear teeth, gear tooth thickness, tip diameter, or root diameter. This means a given basic rack can be referenced for many possible gear designs, and hence why it serves a good basis for gear tooling.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Bottom Clearance\n", "\n", "Bottom clearance is defined as the distance between the basic rack root line and the tip line of the reciprocal mating rack.\n", "\n", "\"Basic\n", "

Basic rack with mating rack and bottom clearance

\n", "\n", "As observed in the figure above, the mathematical expression for bottom clearance can be written as:\n", "\n", "$$c = h_f - h_a$$\n", "\n", "Additionally, the root radius height is equal to the bottom clearance, thus the root radius can be expressed as:\n", "\n", "$$\\rho_F = \\frac{c}{1 - \\sin\\alpha_n}$$\n", "\n", "
\n", " Rack generation gear cutting tools consider the reciprocal mating rack for tool geometry. In that case, the basic rack root radius represents the tool tip radius, a feature important to the generated shape of a gear tooth root. A deeper understanding of this will be developed in later notebooks.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Maximum Root Radius\n", "\n", "When designing a gear or its tooling, the maximum root radius of the basic rack is often of interest. The maximum root radius is constrained by the basic rack tooth profile geometry, and may be limited by the bottom clearance to ensure the root radius starts at or below the common tooth depth. The bottom clearance constraint is observed in the previous section.\n", "\n", "\"Basic\n", "

Full root radius of basic rack

\n", "\n", "If root radius is not limited by bottom clearance, the maximum root radius corresponds to a full root radius. The solution of a full root radius can be obtained by formulating a system of equations. First, an equation can be written for the horizontal coordinate:\n", "\n", "$$\\rho_F = \\frac{s_\\text{fillet}}{2 \\cos\\alpha_n}$$\n", "\n", "where $s_\\rm{fillet}$ is the spacewidth at the start of the root fillet, an unknown parameter. Next, an equation can be written for the vertical coordinate:\n", "\n", "$$\\rho_F = \\frac{h_\\text{fillet}}{1 - \\sin\\alpha_n}$$\n", "\n", "where $h_\\text{fillet}$ is the height of the root fillet, an unknown parameter. This equation was applied in the case of a root radius limited by bottom clearance, where $h_\\rm{fillet} = c$. We currently have two equations with three unknowns, so we need to introduce additional expressions to create a solvable system of equations. By observing that $s_\\text{fillet}$ and $h_\\text{fillet}$ can be expressed as functions of a vertical coordinate, $f\\{y\\}$, we can create a solvable system.\n", "\n", "$$s_\\text{fillet} = \\frac{p}{2} + 2 y_\\text{fillet} \\tan\\alpha_n$$\n", "\n", "$$h_\\text{fillet} = h_f + y_\\text{fillet}$$\n", "\n", "where $y_\\text{fillet}$ is a negative value of the vertical coordinate from the basic rack datum line to the start of the full root fillet. By solving the system of equations, we obtain an expression for $y_\\text{fillet}$, which can then be used to find the full root radius.\n", "\n", "$$y_\\text{fillet} = \\frac{e_p \\tan\\alpha_n - e_p \\sec\\alpha_n + 2 h_f}{2 (\\tan\\alpha_n \\sec\\alpha_n -\\tan^2\\alpha_n - 1)}$$\n", "\n", "where $e_p = \\pi m_n / 2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Basic Rack Plot\n", "\n", "By parametrically defining a basic rack, we can produce a piece-wise plot of the resulting geometry. Below is a such a plot, drawn in the Cartesian xy-plane per the table of input parameters used to define the basic rack." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "data": { "text/html": [ "
$m_n$$\\alpha_n$$h_a^*$$h_f^*$$\\rho_F^*$$\\rho_{F,\\rm{max}}^*$$p$$p_b$$c^*$
$1\\text{mm}$$20^\\circ$$1$$1.25$$0.38$$0.38$$3.14\\text{mm}$$2.95\\text{mm}$$0.25$
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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# INPUTS\n", "# ------\n", "module = 1\n", "pressure_angle_deg = 20\n", "addendum_coefficient = 1\n", "dedendum_coefficient = 1.25\n", "root_radius_coefficient = 0.38\n", "\n", "# compute properties\n", "pressure_angle = radians(pressure_angle_deg)\n", "addendum = addendum_coefficient * module\n", "dedendum = dedendum_coefficient * module\n", "root_radius_coefficient_max = round(br.max_root_radius(module, pressure_angle, addendum, dedendum) / module, 2)\n", "pitch = round(br.pitch_fcn(module), 2)\n", "base_pitch = round(br.base_pitch_fcn(module, pressure_angle), 2)\n", "bottom_clearance_coefficient = br.bottom_clearance_fcn(addendum, dedendum) / module\n", "\n", "# display input variables\n", "headings = ['$m_n$', '$\\\\alpha_n$', '$h_a^*$', '$h_f^*$', '$\\\\rho_F^*$', '$\\\\rho_{F,\\\\rm{max}}^*$', '$p$', '$p_b$', '$c^*$']\n", "rows = [[f'${module}\\\\text{{mm}}$', f'${pressure_angle_deg}^\\\\circ$', f'${addendum_coefficient}$', f'${dedendum_coefficient}$', f'${root_radius_coefficient}$', f'${root_radius_coefficient_max}$', f'${pitch}\\\\text{{mm}}$', f'${base_pitch}\\\\text{{mm}}$', f'${bottom_clearance_coefficient}$']]\n", "html_table(headings, rows)\n", "\n", "# basic rack coordinate data \n", "x, y = br.basic_rack_coordinates(module, pressure_angle_deg, addendum_coefficient, dedendum_coefficient, root_radius_coefficient)\n", "\n", "# create figure and axes\n", "fig = plt.figure(figsize=[2 * x for x in FIGSIZE])\n", "ax = fig.add_subplot(1, 1, 1)\n", "\n", "# plot reference lines (datum, tip, root) and basic rack\n", "xlimits = [min(x), max(x)]\n", "ax.plot(xlimits, [0] * 2, '-.')\n", "ax.plot(xlimits, [addendum] * 2, '--')\n", "ax.plot(xlimits, [-dedendum] * 2, ':')\n", "ax.plot(xlimits, [-addendum] * 2, 'k--')\n", "ax.plot(x, y, 'k', linewidth=3)\n", "\n", "# format plot\n", "ax.set_aspect('equal')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend(['datum line', 'tip line', 'root line', 'mating tip line'], loc='upper left')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Undercut\n", "\n", "The geometry of an undercut basic rack tooth profile is reviewed here. Undercut is a geometric feature in the root of a basic rack. Undercut exists when the rack tooth profile is not tangent to the root geometry, but instead intersects a line oriented at a pressure angle less than the tooth profile pressure angle.\n", "\n", "Undercut angle, $\\alpha_{FP}$, and undercut size, $U_{FP}$, are used to define the undercut of a basic rack. These are illustrated in the undercut basic rack below.\n", "\n", "\"Undercut\n", "

Undercut basic rack tooth profile

\n", "\n", "Notice the base pitch of the undercut profile, $p_{bP}$, differs from the tooth profile base pitch, $p_b$, despite each profile having the same pitch, $p$. As we will see in the chapters on spur and helical gear geometry, this difference explains why only gears of the same module and reference pressure angle can mesh. However, there are some exceptions for the generating tool geometry that will be discussed in the relevant notebooks. \n", "\n", "
\n", " Undercut is of particular interest when using a basic rack as a basis for a generating cutting tool, in which case it is referred to as protuberance. Later notebooks on gear tooling will elaborate on the usefulness of protuberance for gear manufacturing and design, and its influence on gear root geometry. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Undercut Basic Rack Plot\n", "\n", "By parametrically defining an undercut basic rack, we can produce a piece-wise plot of the resulting geometry. Below is a such a plot, drawn in the Cartesian xy-plane per the table of input parameters used to define the undercut basic rack." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "data": { "text/html": [ "
$m_n$$\\alpha_n$$h_a^*$$h_f^*$$\\rho_F^*$$\\alpha_{FP}$$U_{FP}$
$1\\text{mm}$$20^\\circ$$1$$1.25$$0.38$$10^\\circ$$0.15\\text{mm}$
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# INPUTS\n", "# ------\n", "module = 1\n", "pressure_angle_deg = 20\n", "addendum_coefficient = 1\n", "dedendum_coefficient = 1.25\n", "root_radius_coefficient = 0.38\n", "undercut_angle_deg = 10\n", "undercut_size = 0.15\n", "\n", "# display input variables\n", "headings = ['$m_n$', '$\\\\alpha_n$', '$h_a^*$', '$h_f^*$', '$\\\\rho_F^*$', '$\\\\alpha_{FP}$', '$U_{FP}$']\n", "rows = [[f'${module}\\\\text{{mm}}$', f'${pressure_angle_deg}^\\\\circ$', f'${addendum_coefficient}$', f'${dedendum_coefficient}$', f'${root_radius_coefficient}$', f'${undercut_angle_deg}^\\\\circ$', f'${undercut_size}\\\\text{{mm}}$']]\n", "html_table(headings, rows)\n", "\n", "# undercut basic rack coordinate data \n", "x, y = br.undercut_basic_rack_coordinates(module, pressure_angle_deg, addendum_coefficient, dedendum_coefficient, root_radius_coefficient, undercut_angle_deg, undercut_size)\n", "\n", "# create figure and axes\n", "fig = plt.figure(figsize=[2 * x for x in FIGSIZE])\n", "ax = fig.add_subplot(1, 1, 1)\n", "\n", "# plot reference lines (datum, tip, root) and basic rack\n", "xlimits = [min(x), max(x)]\n", "ax.plot(xlimits, [0] * 2, '-.')\n", "ax.plot(xlimits, [addendum_coefficient * module] * 2, '--')\n", "ax.plot(xlimits, [-dedendum_coefficient * module] * 2, ':')\n", "ax.plot(xlimits, [-addendum_coefficient * module] * 2, 'k--')\n", "ax.plot(x, y, 'k', linewidth=3)\n", "\n", "# format plot\n", "ax.set_aspect('equal')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend(['datum line', 'tip line', 'root line', 'mating tip line'], loc='upper left')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Types\n", "\n", "There are standard and non-standard basic rack tooth profiles. The standard back rack types have been established by gearing organizations, such as International Standards Organization (ISO) and American Gear Manufacturing Association (AGMA). Gear manufacturers commonly have tools available to cut cylindrical involute gears with the tooth proportions defined by the standard basic rack types.\n", "\n", "Depending on the manufacturing method and manufacturer, non-standard basic racks may be used to define the gear tooth proportions. A non-standard basic rack is any basic rack that is not a standard type." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Standard\n", "\n", "Standard basic rack types per ISO 53 are defined and illustrated below. Refer to the standard for complete details.\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ABCD
Pressure angle, $\\alpha_n$$20^\\circ$$20^\\circ$$20^\\circ$$20^\\circ$
Addendum coefficient, $h_a^*$$1.00$$1.00$$1.00$$1.00$
Dedendum coefficient, $h_f^*$$1.25$$1.25$$1.25$$1.40$
Root radius coefficient, $\\rho_F^*$$0.38$$0.30$$0.25$$0.39$
\n", "\n", "
\n", " Notice the basic rack standard types are only concerned with tooth proportions, not tooth size. This is why module is excluded. \n", "
" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# INPUTS [A, B, C, D]\n", "# -------------------\n", "types = ['A', 'B', 'C', 'D']\n", "modules = [1, 1, 1, 1] # arbitrary\n", "pressure_angles_deg = [20, 20, 20, 20]\n", "addendum_coefficients = [1, 1, 1, 1]\n", "dedendum_coefficients = [1.25, 1.25, 1.25, 1.4]\n", "root_radius_coefficients = [0.38, 0.3, 0.25, 0.39]\n", "\n", "# create figure and axes\n", "fig = plt.figure(figsize=[12, 6])\n", "\n", "for i in range(4) :\n", " ax = fig.add_subplot(2, 2, i+1)\n", " \n", " # plot basic rack \n", " x, y = br.basic_rack_coordinates(modules[i], pressure_angles_deg[i], addendum_coefficients[i], dedendum_coefficients[i], root_radius_coefficients[i])\n", " ax.plot(x, y, 'k', linewidth=3)\n", " \n", " # annotate\n", " ax.text(0, 0, types[i], fontsize=25, horizontalalignment='center')\n", "\n", " # format plot\n", " ax.set_aspect('equal')\n", " plt.xlim([-3.3, 3.3])\n", " plt.ylim([-1.5, 1.2])\n", " plt.xlabel('x')\n", " plt.ylabel('y')\n", " plt.grid()\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Non-standard\n", "\n", "Non-standard basic rack tooth profiles are defined and illustrated below. These non-standard racks were arbitrarily defined.\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
IIIIIIIV
Pressure angle, $\\alpha_n$$25^\\circ$$15^\\circ$$20^\\circ$$20^\\circ$
Addendum coefficient, $h_a^*$$0.90$$1.10$$1.00$$1.00$
Dedendum coefficient, $h_f^*$$1.15$$1.35$$1.25$$1.25$
Root radius coefficient, $\\rho_F^*$$0.30$$0.30$$0.30$$0.30$
Undercut angle, $\\alpha_{FP}$--$10^\\circ$$5^\\circ$
Undercut size, $U_{FP}$--$0.15$$0.15$
" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# INPUTS [I, II, III, IV]\n", "# -----------------------\n", "types = ['I', 'II', 'III', 'IV']\n", "modules = [1, 1, 1, 1] # arbitrary\n", "pressure_angles_deg = [25, 15, 20, 20]\n", "addendum_coefficients = [0.9, 1.1, 1, 1]\n", "dedendum_coefficients = [1.15, 1.35, 1.25, 1.25]\n", "root_radius_coefficients = [0.3, 0.3, 0.3, 0.3]\n", "undercut_angles_deg = [25, 15, 10, 5]\n", "undercut_sizes = [0, 0, 0.15, 0.15]\n", "\n", "# create figure and axes\n", "fig = plt.figure(figsize=[12, 6])\n", "\n", "for i in range(4) :\n", " ax = fig.add_subplot(2, 2, i+1)\n", " \n", " # plot basic rack \n", " if undercut_angles_deg[i] == pressure_angles_deg[i]:\n", " x, y = br.basic_rack_coordinates(modules[i], pressure_angles_deg[i], addendum_coefficients[i], dedendum_coefficients[i], root_radius_coefficients[i])\n", " else:\n", " x, y = br.undercut_basic_rack_coordinates(modules[i], pressure_angles_deg[i], addendum_coefficients[i], dedendum_coefficients[i], root_radius_coefficients[i], undercut_angles_deg[i], undercut_sizes[i])\n", " \n", " ax.plot(x, y, 'k', linewidth=3)\n", " \n", " # annotate\n", " ax.text(0, 0, types[i], fontsize=25, horizontalalignment='center')\n", "\n", " # format plot\n", " ax.set_aspect('equal')\n", " plt.xlim([-3.3, 3.3])\n", " plt.ylim([-1.5, 1.3])\n", " plt.xlabel('x')\n", " plt.ylabel('y')\n", " plt.grid()\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "
\n", "

Learn More


\n", " Continue reading the Drivetrain Hub | Notebook Series to further understand the significance of the basic rack for gear geometry and manufacturing.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Model Basic Racks


\n", " Accurately model, analyze, and print 3-dimensional gears defined from standard and non-standard basic racks with the Drivetrain Hub | Gears App, a modern drivetrain modeling environment 100% online at drivetrainhub.com.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Improve Notebook


\n", " Our gear geometry notebooks are publicly hosted in a GitHub repository, available for anyone to view and propose edits.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. [ISO 53:1998 Cylindrical gears for general and heavy engineering -- Standard basic rack tooth profile](https://www.iso.org/standard/22643.html)\n", "2. [Gears and Gear Drives, 1st Edition. Damir Jelaska](https://www.wiley.com/en-us/Gears+and+Gear+Drives-p-9781119941309)\n", "3. Handbook of Practical Gear Design and Manufacture, 1st Edition. Darle W. Dudley" ] } ], "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": "3.7.2" }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } } }, "nbformat": 4, "nbformat_minor": 2 }