VALICALC / MECHANICAL ENGINEERING SUITE / DS13

Planetary Gear Train Design Sheet

Identify the fixed, input and output members before interpreting ratio or torque. A simple sun–planet–ring set supports all six fixed-member arrangements and differential speed solving. A separate common-carrier constraint graph supports entered compound mesh/coupling equations without pretending a textbook topology preset is verified.

Verified mathematical models with explicit assumptions. Component capacity and applicability are shown as separate checks.

Labeled example inputs • SI calculations • Project revision 0 • No account or cloud upload

01 / ENGINEERING INPUTS

Define the operating point

Topology modelFixed-member arrangementDifferential member to solve

Actual sun teeth

Actual planet teeth

Actual ring teeth

Equally spaced planet count

Actual unshifted spur module

Signed input member RPM

rpm

Signed external input torque

N·m

Entered fixed-member motoring efficiency

02 / CALCULATE → SELECT → RECALCULATE

Calculation & checks

Required ring teeth for selected sun / planet

Equal-spacing phase quotient

Adjacent planet tip-circle clearance

46.70766 mm

Planet signed spin relative to carrier

-1,125 rpm

Sun tooth mesh events per hour

202,500

Ring tooth mesh events per hour

67,500

Signed input / output speed ratio

Loss from entered whole-drive efficiency

0 kW

Sun signed RPM

1,500 rpm

Ring signed RPM

0 rpm

Carrier signed RPM

375 rpm

Ideal external mechanical power residual

0 kW

Original schematic; not a manufacturing drawing. s-c-r · Sun / ring / carrier · Actual equally spaced planets. Actual dimensions and model checks are listed in the calculation record.

Intermediate values and comparisons - SI units
Member	Signed RPM	Ideal external T (N·m)	Ideal external P (W)	Entered-efficiency external T (N·m)	Entered-efficiency P (W)
Sun	1,500	100	15,707.963268	100	15,707.963268
Ring	0	300	0	300	0
Carrier	375	-400	-15,707.963268	-400	-15,707.963268

Criterion-specific verification

PASSED · Unshifted common-module coaxial geometry
Nr = Ns + 2Np; this simple-set relation must not be reused for compound graphs.
PASSED · Equally spaced planet phase condition
(Ns + Nr)/planet count must be an integer for this defined simple equally spaced set.
PASSED · Adjacent unshifted planet tip clearance
Checks standard full-depth tip circles only, not tooth interference or pin/carrier envelopes.
PASSED · Ideal torque / virtual-work balance
External torques act on the listed members; ideal power sum and torque reaction follow the no-slip graph.
BLOCKED · Planet load sharing, mesh and bearing rating
No empirically validated load-sharing factor, pin/carrier/bearing geometry or gear strength data; equal load capacity is not assumed.
BLOCKED · Named A1/A2/A3/B/C preset qualification
Generic entered constraints are functional. Named textbook compound topology/assembly presets require separate source and geometry verification.
UNKNOWN · Loss-data qualification
Whole-drive efficiency is supplied, not derived from a generic per-mesh coefficient.

Method and calculation trace

Simple set: Ns(ns−nc)+Nr(nr−nc)=0. Signed ratio always means input RPM / output RPM.

Simple ideal external torques are proportional to [Ns, Nr, −(Ns+Nr)]. Differential mode uses the entered sun external torque, with all ports explicitly listed.

Graph external mesh: zi(ni−nc)+zj(nj−nc)=0; internal mesh changes + to −; rigid coupling uses ni−nj=0. The entered graph must be fully determined by its fixed/input ports.

Selected actual integer teeth update speed, phase and adjacency. A failed assembly check remains failed even if the ratio is numerically valid.

Fixed-case output power equals minus input power times entered motoring efficiency; fixed-member reaction balances external torque. This does not qualify internal circulating losses or capacity.

Assumptions & scope

Simple geometry uses common-module unshifted spur gears: Nr = Ns + 2Np. Equal-spacing phase and adjacent tip-circle clearance are necessary checks; tooth interference, carrier/pins and dynamic load sharing remain unverified.

Ideal torques are signed external torques acting on each member. Fixed-case loss-adjusted output torque uses only the entered whole-drive motoring efficiency; it does not invent per-mesh efficiency or equal planet-load sharing.

Common-carrier graph solves entered ideal no-slip mesh constraints and rigid coupling. It validates algebraic consistency, not physical coaxial/assembly geometry. Book A1/A2/A3/B/C presets and detailed compound support/rating remain source-gated.

Differential mode needs two known member speeds. Power-flow/loss distribution with multiple driven ports needs more information and is blocked.

Worked example

24 sun / 24 planet / 72 ring teeth with three equally spaced planets satisfy coaxial and phase conditions. With ring fixed, 1500 RPM sun input gives 375 RPM carrier output. Ideal external torques are +100 N·m sun, +300 N·m ring reaction and −400 N·m carrier; their power sum is zero.

Calculation methods and sources

Ns(ns-nc)+Nr(nr-nc)=0; ideal external torques proportional to [Ns,Nr,-Ns-Nr]

Simple set, six fixed-member arrangements or two known differential speeds. Signed external torques and virtual work are explicit; whole-drive efficiency is user supplied.

Tập 1 6.72-6.77 printed pp119-120 / PDF118-119; independent no-slip and virtual-work derivation; MIT gear-train lecture context.

Nr=Ns+2Np; (Ns+Nr)/planetCount integer; adjacent tip gap = 2 orbitRadius sin(pi/planetCount) - planetTipDiameter

Same-module unshifted spur simple set with equally spaced planets only; necessary phase/circle-clearance checks, not a strength/interference approval.

Tập 1 6.69-6.71 printed p118 / PDF117; independent coaxial/circular-spacing derivation.

external: zi(ni-nc)+zj(nj-nc)=0; internal: zi(ni-nc)-zj(nj-nc)=0; rigid coupling: ni=nj

Bounded common-carrier linear constraints, explicit fixed/input/output ports, consistent tooth IDs, full-rank and residual checks. No arbitrary named topology/physical assembly claim.

Independent rolling-constraint derivation and scoped generalization of Willis; Tập 1 Chapter 6 planetary context pp118-126.

Textbook references identify the method context. Historical numerical catalog, material and service-factor tables have not been copied or treated as current product ratings.

Related calculators and references

Existing component-selection Jobs → · All mechanical worksheets →

Common questions

Does this approve a real component?

No. The worksheet separates mathematical results from criterion-specific checks. Actual motor, belt, gear, shaft, bearing and joint capacity need applicable current source data and engineering review.

What changes after choosing a physical size?

The worksheet recalculates the outputs and geometry from the entered actual dimensions or discrete tooth/link count. Dependent checks are reevaluated; previously saved results are not restored as approvals.