Overview
This work computes tooth-number combinations for planetary gear trains. We follow an “exhaustive-first” approach—generate as many feasible combinations as possible, then filter by design needs. After presenting classification and symbols, three methods are introduced: brute-force enumeration, equal-strength & minimum-envelope principles, and an ANN-based ratio selection. For trains without compound planets, brute force is often enough; for double-row systems with compound planets, the latter two are preferable. Ratio distribution for double-row systems follows standard handbook practices.
1. Classification of Gear Trains and Symbols
Two schemes are used: (i) by basic components of planetary transmission (Kudryavtsev), and (ii) by meshing type. For the component-based scheme, see Table 1.
| Name | Central gear | Carrier | Output shaft |
|---|---|---|---|
| Letter | Z | X | V |
*In the original notation, K denotes the central gear and H denotes the carrier. Based on combinations we obtain 2Z-X, 3Z, and Z-X-V types (see Figs. 1–3).
For the meshing-type scheme, see Table 2.
| Name | Internal mesh pair | External mesh pair | Common gear (meshing two central gears) |
|---|---|---|---|
| Letter | N | W | G |
This yields NGW, NW, NN, WW, NGWN, and N forms; here N denotes a structure with only one internal mesh and no sun gear. Allocation typically focuses on adjacency limits.
2. Brute-Force Enumeration — NGW Trains
For standard (non-shifted) spur gears, allocation must satisfy ratio, coaxiality, adjacency, and assembly constraints.
Given the exact ratio and the number of planets, the total allocation can follow:
The formula applies when all tooth counts are integers. Bound the search from the sun’s minimum teeth, propagate others, enumerate combinations, and accept those matching the proportion.
3. Strength Principle — Automatic Solution for Double-Row Systems
We auto-screen tooth counts under contact and root-bending strength and compactness constraints, coupled with ratio distribution.
4. Artificial Neural Networks — Imitating Human Designers
An ANN module regresses designer heuristics and preferred regions, accelerating convergence from a large to a small candidate set.
5. Other Gears — Profile Shift, Helical, etc.
For shifted and helical gears, replace geometry and coaxiality constraints within the same framework; the method remains consistent.
References
(To be populated as needed.)
Disclaimer
(1) This article and associated code are for reference only.
(2) The referenced standard is ISO 53.
(3) If discrepancies arise between the Chinese and English versions, the Chinese version prevails.
(4) Datasets come from publicly available literature with no conflict of interest; only algorithms and ideas are open-sourced, with no commercial use or profit.