{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[](https://drivetrainhub.com)\n", "\n", "
Planetary geartrain modeled in Gears App
\n", "\n", "\n", "Most commonly, planetary geartrains have a sun gear (yellow), ring gear (blue), and multiple planet gears (orange) on a carrier (gray). Spur or helical gears are used for a planetary gearset, with each type having advantages. This notebook reviews the unique geometric attributes of planetary gears and their significance to planetary gear mesh operation.\n", "\n", "Standard planetary modeled in Gears App
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Nomenclature \n", "\n", "This table provides a set of parameters commonly used to define the geometry of planetary geartrains.\n", "\n", "Symbol | \n", "Description | \n", "
---|---|
$i$ | \n", "Transmission ratio | \n", "
$u$ | \n", "Base ratio | \n", "
$\\omega$ | \n", "Angular velocity | \n", "
$m_n$ | \n", "Normal module | \n", "
$z$ | \n", "Number of teeth | \n", "
$\\beta$ | \n", "Helix angle | \n", "
$d_a$ | \n", "Tip diameter | \n", "
$p_t$ | \n", "Transverse pitch | \n", "
$d_w$ | \n", "Pitch diameter | \n", "
$a$ | \n", "Center distance | \n", "
$l$ | \n", "Planet distance | \n", "
$N$ | \n", "Number of planets | \n", "
Planetary layout diagram of 4-planet geartrain
\n", "Planetary geartrain phasing types modeled in Gears App
\n", "Description | \n", "Symbol | \n", "Value | \n", "Units | \n", "
---|---|---|---|
Target ratio | \n", "$i_{1v_o}$ | \n", "4.000 | \n", "- | \n", "
Target ratio deviation | \n", "$\\Delta i_{1v_o}$ | \n", "3.000 | \n", "% | \n", "
Target pitch diameter, ring | \n", "$d_{w3_o}$ | \n", "-104.000 | \n", "$\\mm$ | \n", "
Target pitch diameter, sun | \n", "$d_{w1_o}$ | \n", "34.667 | \n", "$\\mm$ | \n", "
Target pitch diameter, planets | \n", "$d_{w2_o}$ | \n", "34.667 | \n", "$\\mm$ | \n", "
Target pitch diameter, carrier | \n", "$d_{wV_o}$ | \n", "69.333 | \n", "$\\mm$ | \n", "
Target reference center distance | \n", "$a_{0_o}$ | \n", "34.667 | \n", "$\\mm$ | \n", "
Helix angle, min | \n", "$\\beta_\\text{min}$ | \n", "15.000 | \n", "$\\deg$ | \n", "
Helix angle, max | \n", "$\\beta_\\text{max}$ | \n", "15.000 | \n", "$\\deg$ | \n", "
Number of planets, target | \n", "$N_o$ | \n", "4.000 | \n", "- | \n", "
Number of planets, max | \n", "$N_\\text{max}$ | \n", "5.000 | \n", "- | \n", "
# | \n", "z1 | \n", "z2 | \n", "z3 | \n", "ratio | \n", "beta | \n", "N | \n", "space | \n", "phase | \n", "fx | \n", "fy | \n", "trq | \n", "mn | \n", "CD | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | \n", "14 | \n", "~14.0 | \n", "-42 | \n", "4.00 | \n", "15.0 | \n", "4 | \n", "E | \n", "C | \n", "0.00 | \n", "0.0 | \n", "0.00 | \n", "2.392 | \n", "34.667 | \n", "
2 | \n", "15 | \n", "~15.0 | \n", "-45 | \n", "4.00 | \n", "15.0 | \n", "4 | \n", "E | \n", "S | \n", "1.00 | \n", "1.0 | \n", "0.00 | \n", "2.232 | \n", "34.667 | \n", "
3 | \n", "16 | \n", "~16.0 | \n", "-48 | \n", "4.00 | \n", "15.0 | \n", "4 | \n", "E | \n", "I | \n", "0.00 | \n", "0.0 | \n", "1.00 | \n", "2.093 | \n", "34.667 | \n", "
4 | \n", "17 | \n", "~16.0 | \n", "-49 | \n", "3.88 | \n", "15.0 | \n", "4 | \n", "X | \n", "M | \n", "1.03 | \n", "1.0 | \n", "0.00 | \n", "2.050 | \n", "35.020 | \n", "
5 | \n", "17 | \n", "~17.0 | \n", "-51 | \n", "4.00 | \n", "15.0 | \n", "4 | \n", "E | \n", "S | \n", "1.00 | \n", "1.0 | \n", "0.00 | \n", "1.970 | \n", "34.667 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
136 | \n", "50 | \n", "~49.0 | \n", "-148 | \n", "3.96 | \n", "15.0 | \n", "4 | \n", "X | \n", "M | \n", "0.00 | \n", "0.0 | \n", "0.39 | \n", "0.679 | \n", "34.784 | \n", "
137 | \n", "49 | \n", "~50.0 | \n", "-149 | \n", "4.04 | \n", "15.0 | \n", "4 | \n", "X | \n", "M | \n", "1.01 | \n", "1.0 | \n", "0.00 | \n", "0.674 | \n", "34.550 | \n", "
138 | \n", "51 | \n", "~49.0 | \n", "-149 | \n", "3.92 | \n", "15.0 | \n", "4 | \n", "E | \n", "S | \n", "1.00 | \n", "1.0 | \n", "0.00 | \n", "0.674 | \n", "34.899 | \n", "
139 | \n", "50 | \n", "~50.0 | \n", "-150 | \n", "4.00 | \n", "15.0 | \n", "4 | \n", "E | \n", "C | \n", "0.00 | \n", "0.0 | \n", "0.00 | \n", "0.670 | \n", "34.667 | \n", "
140 | \n", "52 | \n", "~49.0 | \n", "-150 | \n", "3.88 | \n", "15.0 | \n", "4 | \n", "X | \n", "M | \n", "0.00 | \n", "0.0 | \n", "0.92 | \n", "0.670 | \n", "35.013 | \n", "
Description | \n", "Symbol | \n", "Value | \n", "Units | \n", "
---|---|---|---|
Candidate | \n", "# | \n", "8 | \n", "- | \n", "
Sun tooth count | \n", "$z_1$ | \n", "18 | \n", "- | \n", "
Ring tooth count | \n", "$z_3$ | \n", "-54 | \n", "- | \n", "
Planet tooth count | \n", "$z_2$ | \n", "~18.0 | \n", "- | \n", "
Transmission ratio | \n", "$i_{1V}$ | \n", "4.0 | \n", "- | \n", "
--- | \n", "\n", " | \n", " | \n", " |
Number of planets | \n", "$N$ | \n", "4 | \n", "- | \n", "
Planet spacing | \n", "- | \n", "E | \n", "- | \n", "
Planet angles | \n", "$\\theta_i$ | \n", "[0.0, 90.0, 180.0, 270.0] | \n", "$\\deg$ | \n", "
--- | \n", "\n", " | \n", " | \n", " |
Phasing type | \n", "- | \n", "C | \n", "- | \n", "
Phase angles, ring | \n", "$\\phi_{3i}$ | \n", "[0.0, 180.0, 0.0, 180.0] | \n", "$\\deg$ | \n", "
Phase angles, sun | \n", "$\\phi_{1i}$ | \n", "[0.0, 180.0, 0.0, 180.0] | \n", "$\\deg$ | \n", "
--- | \n", "\n", " | \n", " | \n", " |
Helix angle | \n", "$\\beta$ | \n", "15.0 | \n", "$\\deg$ | \n", "
Normal module | \n", "$m_n$ | \n", "1.86 | \n", "$\\mm$ | \n", "
Transverse module | \n", "$m_t$ | \n", "1.926 | \n", "$\\mm$ | \n", "
Reference center distance | \n", "$a_0$ | \n", "34.667 | \n", "$\\mm$ | \n", "
Compound planetary modeled in Gears App
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Nomenclature \n", "\n", "This table provides a set of parameters commonly used to define the geometry of compound planetary geartrains.\n", "\n", "*TODO need to add parameters pertaining to the planet gear / pinion*\n", "\n", "Symbol | \n", "Description | \n", "
---|---|
$i$ | \n", "Transmission ratio | \n", "
$u$ | \n", "Base ratio | \n", "
$\\omega$ | \n", "Angular velocity | \n", "
$m_n$ | \n", "Normal module | \n", "
$z$ | \n", "Number of teeth | \n", "
$\\beta$ | \n", "Helix angle | \n", "
$d_a$ | \n", "Tip diameter | \n", "
$p_t$ | \n", "Transverse pitch | \n", "
$d_w$ | \n", "Pitch diameter | \n", "
$a$ | \n", "Center distance | \n", "
$l$ | \n", "Planet distance | \n", "
$N$ | \n", "Number of planets | \n", "