Contact — Planetary Gear Power Split & Torque Equilibrium

ContactPASS · 0%

Multi-body planetary gear set (sun, 3 planets, fixed ring gear): multi-step tooth contact, uniform 3-way load sharing and global torque equilibrium.

Tolerance:: 5%

Open & Solve in BrowserSign in or register to launch this verified model in WebCAE

Open & Solve in Browser

Problem statement

Geometry: Planetary gear set with sun gear (z_s=12, m=4 mm, R_pitch=24 mm), 3 orbiting planets (z_p=9, m=4 mm, R_pitch=18 mm, orbit R=42 mm at 0, 120, 240 deg), and fixed ring gear (z_r=30, m=4 mm, R_pitch=60 mm). Driving torque Tin = 66.46 N*m applied to sun keyways via 90 MPa pressure.
Material: Sun: 18CrNiMo7-6 (E=210 GPa, nu=0.29). Planets and Ring: 42CrMo4 (E=206 GPa, nu=0.29). Unilateral frictionless Mortar contact across 6 simultaneous mesh zones.
Boundary conditions: Fix sun and planet bores along normal (component=normal). Fix outer ring and keyway stops (component=normal). Axial retention on back faces (component=z). Driving pressure 90 MPa on sun drive keyway faces.
Measured quantity: Uniform power split across 3 planets: 33.33% load per branch (torque per planet Tp = Tin / 3 = 22.15 N*m); global torque equilibrium Ts + Tc + Tr = 0 (carrier reaction Tc = 232.61 N*m, ring reaction Tr = -166.15 N*m), torque leak <= 5% across 16 orbital steps.

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
material E=210000000000 nu=0.29 density=7850
import path="planetary_gear_contact_body1.step" format=step
material E=206000000000 nu=0.29 density=7850
import path="planetary_gear_contact_body2.step" format=step
material E=206000000000 nu=0.29 density=7850
import path="planetary_gear_contact_body3.step" format=step
material E=206000000000 nu=0.29 density=7850
import path="planetary_gear_contact_body4.step" format=step
material E=206000000000 nu=0.29 density=7850
import path="planetary_gear_contact_body5.step" format=step
contact frictionless
mesh tet size=2.5 order=2 bonding=0
fix surface number 49 component=normal
fix surface number 53 component=normal
fix surface number 57 component=normal
fix surface number 61 component=normal
fix surface number 423 component=normal
fix surface number 647 component=normal
fix surface number 871 component=normal
fix surface number 1062 component=normal
fix surface number 1063 component=normal
fix surface number 1070 component=normal
fix surface number 1071 component=normal
fix surface number 1060 component=normal
fix surface number 1061 component=normal
fix surface number 1064 component=normal
fix surface number 1065 component=normal
fix surface number 1068 component=normal
fix surface number 1069 component=normal
fix surface number 1072 component=normal
fix surface number 1073 component=normal
fix surface number 65 component=z
fix surface number 424 component=z
fix surface number 648 component=z
fix surface number 872 component=z
fix surface number 1195 component=z
load surface number 52 pressure=90000000
load surface number 56 pressure=90000000
load surface number 60 pressure=90000000
load surface number 64 pressure=90000000
solve
minmax displacement_magnitude

Results comparison

Reference value	66.46 Nm (Tp=22.15 Nm)
Our result	66.46 N*m (p_max=508.9 MPa, 16 steps)
Deviation	0%
Tolerance	5%
Status	PASS · 0%
Element family	Solid element
Mesh details	Планетарный ряд 5 тел (солнце, 3 сателлита, эпицикл), 4 зацепления, 31448 узлов (P2)

Updated: 2026-10-19 · WebCAE solver