Published: September 11, 2026
A common custom gearbox request sounds simple:
“Can you change this planetary gearbox from 20:1 to 21:1?”
The difference in output speed appears small. With a motor operating at 6,000 rpm:
- A 20:1 gearbox gives a theoretical output speed of 300 rpm.
- A 21:1 gearbox gives approximately 285.7 rpm.
From a gear-design and manufacturing perspective, however, that one-point change may require a completely different tooth combination.
The 20:1 ratio might be assembled from an existing ring gear, module and validated stage family. Achieving 21:1 in the same package could require a smaller sun gear, profile modification, a new internal ring gear, a different module or additional tooling and validation.
The real engineering question is therefore not simply whether the requested ratio can be calculated. It is:
Can the ratio be produced within the existing diameter, length, torque, life and manufacturing platform without creating a less reliable gearbox?
This article explains how engineers evaluate a custom planetary gearbox ratio through stage combinations, integer tooth counts, gear geometry, planet arrangement, load capacity and manufacturing constraints.
Wichtigste Erkenntnisse
- A target ratio is a system requirement, not a finished gear specification.
- Planetary gearbox ratios are constrained by integer tooth counts and are not continuously adjustable.
- Two numerically similar ratios may require different gears, modules or stage arrangements.
- Passing the ratio equation does not prove that the gears can be assembled, manufactured or loaded safely.
- Small sun gears require undercut, tip-thickness, profile-shift and strength checks.
- Planet quantity does not directly change the ratio, but it affects phasing, clearance and load sharing.
- Reusing a validated platform is often preferable to developing new gearing solely to reach an exact number.
- A custom ratio should solve a measurable operating-point problem.
A Target Ratio Is Not Yet a Gear Design
The initial ratio requirement normally comes from output speed:
Target ratio = Actual motor speed under load ÷ Required output speed
For example:
6,000 rpm ÷ 300 rpm = 20:1
The calculation should use the motor speed at the intended load—not simply the no-load speed. If the input speed is unrealistic, the resulting gearbox ratio will not match the final operating point.
Before selecting tooth counts, determine:
- Is the required output speed exact, or is a range acceptable?
- Is the stated motor speed a no-load or loaded value?
- What are the continuous and short-duration peak torque requirements?
- What gearbox diameter and length are available?
- What backlash, noise and service-life limits apply?
- Is an existing standard ratio already close enough?
For example, a target speed of 286 rpm does not necessarily require an exact 21:1 ratio. If the system can accept 285–305 rpm, an existing 20:1 design may already satisfy the application.
Four Levels of Planetary Ratio Customization
Not every custom-ratio request requires a completely new gearbox.
| Customization Level | Main Change | Engineering Impact |
|---|---|---|
| Use an existing ratio | No internal gearing changes | Lowest development risk |
| Recombine validated stages | Existing single-stage gearsets are rearranged | Length, efficiency, backlash and load must be checked |
| Develop a new tooth combination | Sun, planet or ring tooth counts change | Geometry, strength and manufacturing require validation |
| Develop a new gear platform | Module, ring gear, stage count or package changes | Approaches a complete gearbox-development project |
Customization should therefore begin with a platform search rather than a blank design.
TSL Motor first evaluates whether the requested operating point can be reached using an existing custom planetary gearbox platform. New tooth combinations or a new gearbox architecture are considered when the established options cannot meet the requirement.
Planetary Ratios Form a Discrete Design Space
For a common arrangement with the ring gear fixed, the sun gear as the input and the carrier as the output, the theoretical single-stage ratio is:
i = 1 + Zr ÷ Zs
Where:
- i is the single-stage reduction ratio;
- Zr is the ring-gear tooth count;
- Zs is the sun-gear tooth count.
For gears using the same module and basic standard geometry, the tooth counts must also satisfy:
Zr = Zs + 2Zp
Where Zp is the planet-gear tooth count.
Gear teeth must be integers. An engineer cannot normally choose every value between 20.00:1 and 21.00:1 as though the gearbox were an electronically programmable reducer.
Some ratios fit naturally within an existing ring-gear and module family. Another numerically close ratio may require a smaller sun, a different ring or an additional stage.
The ISO 21771 series provides terminology and geometric concepts for cylindrical involute gears. The current standard can be located through the official ISO standards catalogue.
This creates what can be described as manufacturable ratio regions: many ratios are mathematically possible, but only a smaller group fits an established production platform cleanly.
Why 20:1 and 21:1 May Require Different Designs
Consider an illustrative two-stage planetary gearbox with:
- A 72-tooth ring gear;
- Three equally spaced planets per stage;
- The same module in both stages;
- Standard unshifted geometry for the initial screening.
Possible single-stage combinations include:
| Ring Gear | Sun Gear | Planet Gear | Stage Ratio |
|---|---|---|---|
| 72 | 36 | 18 | 3.0:1 |
| 72 | 30 | 21 | 3.4:1 |
| 72 | 24 | 24 | 4.0:1 |
| 72 | 18 | 27 | 5.0:1 |
| 72 | 12 | 30 | 7.0:1 |
All five rows satisfy the basic tooth-count relationship. That does not mean they have the same engineering risk.
A 20:1 Design
A two-stage combination can be:
4 × 5 = 20
Stage 1:
72-tooth ring, 24-tooth sun and 24-tooth planets
Stage 2:
72-tooth ring, 18-tooth sun and 27-tooth planets
Both sun gears remain within the conventional initial screening range for an unmodified 20° full-depth involute tooth form.
A 21:1 Design
If the same 72-tooth ring family is retained, one direct combination is:
3 × 7 = 21
The 7:1 stage requires:
72-tooth ring, 12-tooth sun and 30-tooth planets
The requested ratio is only 5% higher than 20:1, but the sun has decreased from 18 to 12 teeth. Undercut, root strength, tip thickness, profile shift and working contact conditions now require closer analysis.
This does not mean that 21:1 is impossible. It means:
A 21:1 ratio may not fit this particular 72-tooth platform as naturally as 20:1.
Could the Ring Gear Be Changed?
A 90-tooth ring could be used to create 6:1 and 3.5:1 stages:
6 × 3.5 = 21
This arrangement can avoid the 12-tooth sun. However, the ring tooth count is now 25% higher.
The reference diameter of a gear is approximately:
d = m × Z
If a 72-tooth ring uses a module of 0.30, its reference diameter is 21.6 mm. To fit a 90-tooth ring into approximately the same diameter, the module would need to decrease to about 0.24.
The request has now changed more than the tooth count. It may also change:
- Tooth size;
- Root thickness;
- Contact geometry;
- Cutting tools;
- Strength calculations;
- Inspection requirements;
- Production capability.
The best way to achieve 21:1 therefore depends on the allowable diameter, module, torque and existing manufacturing platform.
Small Tooth Counts, Profile Shift and Internal Meshes
The frequently repeated statement that a sun gear must have at least 17 teeth is not a universal rule.
For a 20° pressure angle, standard full-depth external gear with no profile shift, 17 teeth is a useful conventional screening value for avoiding significant undercut. Miniature planetary gearboxes, however, may use:
- Positive profile shift;
- Modified addendum;
- Different pressure angles;
- Non-standard tooth proportions;
- Dedicated cutting tools.
A 12-tooth sun is therefore not automatically incorrect. It means that the design has moved beyond a standard unmodified screening case.
Positive profile shift can improve the root geometry of a small sun gear, but it also affects:
- Tooth thickness;
- Tip thickness;
- Working pressure angle;
- Working center distance;
- Contact ratio;
- Backlash;
- Internal and external interference.
Profile shift should be selected as part of the complete gear-mesh design rather than added as a late correction after the tooth counts have been frozen.
A planetary stage also contains two different mesh types:
- External mesh between the sun and planets;
- Internal mesh between the planets and ring gear.
The geometry must therefore be evaluated as a complete sun–planet–ring system. ISO geometry terminology is useful for defining these parameters consistently, while the AGMA standards library provides additional industry standards covering gear rating, accuracy and enclosed-drive applications.
Every candidate tooth combination should answer three questions:
- Can the gears mesh with acceptable working geometry?
- Can the intended tooling generate the required tooth forms?
- Can the finished gears be inspected and reproduced consistently?
Planet Count Affects Assembly and Load Sharing
The number of planets does not appear in the basic ratio equation. Three planets do not make the reduction ratio three times larger.
Multiple planets do, however, introduce assembly-phasing and adjacent-clearance requirements.
For a common arrangement using equally spaced, identical and in-phase planets, the following expression can be used as an initial assembly check:
(Zs + Zr) ÷ N must be an integer
Where N is the number of planets.
This is a screening condition for a common equal-spacing arrangement—not a universal substitute for complete phasing analysis.
Passing the phasing condition also does not prove that the planets physically fit. Their outside diameters must have sufficient clearance at the selected carrier-pin radius.
The design sequence is therefore:
Ratio → Pitch geometry → Planet phasing → Adjacent-planet clearance
These are separate checks.
Multiple planets provide parallel load paths, but real load is rarely divided perfectly. Load sharing can be affected by:
- Planet-pin position error;
- Sun or ring eccentricity;
- Gear runout;
- Carrier deformation;
- Bearing and housing stiffness;
- Profile and lead deviations.
Research available through the NASA Technical Reports Server examines planetary-gear tooth geometry, planet-position errors and static or dynamic load sharing.
More recent planetary-actuator research also treats ratio, gearbox architecture, package size, efficiency, backlash and stiffness as linked design variables rather than independent values. One example is the COMPAct planetary actuator design study.
A three-planet stage should therefore not be designed on the assumption that each planet will always carry exactly one-third of the load.
Passing the Ratio Equation Does Not Validate the Gearbox
A tooth combination that passes the kinematic and geometric checks is only ready for further engineering—not for production release.
The complete gearbox must still be evaluated for:
- Tooth-flank contact fatigue;
- Tooth-root bending strength;
- Planet-pin and carrier strength;
- Output-shaft and bearing loads;
- Ring-gear support stiffness;
- Backlash and transmission error;
- Lubrication and temperature rise;
- Noise and service life.
ISO 6336-1 provides general principles and influence factors for calculating the load capacity of involute spur and helical gears. The standard also states that these calculations are intended to compare and rate gear designs; they do not independently guarantee the performance of a complete assembled drive system.
The small sun gear may be the first visible concern, but it is not always the final torque-limiting component. Other possible limits include:
- Planet pins;
- Planet carrier;
- Output shaft;
- Bearings or bushings;
- Ring support;
- Housing;
- Mechanical connections.
Later stages in a multistage gearbox normally transmit more torque than earlier stages. Using identical tooth widths, materials and carrier structures in every stage may therefore result in an unbalanced design.
Why Reusing a Validated Ring Gear and Platform Matters
A production gearbox platform contains more validated engineering than its nominal ratio.
It may already have a proven:
- Ring gear and housing;
- Module and tooth system;
- Planet-center radius;
- Carrier assembly method;
- Lubrication strategy;
- Cutting and inspection process;
- Assembly tolerance chain.
If a requested ratio can be produced by changing compatible sun and planet gears—or by recombining existing stages—the number of variables requiring complete revalidation may be reduced.
A practical development hierarchy is:
- Use an existing complete ratio.
- Recombine validated stage ratios.
- Retain the ring, module and housing while evaluating compatible sun and planet gears.
- Develop a new tooth system only where necessary.
- Change the ring, module or complete architecture only when the earlier options cannot meet the requirement.
Internal ring gears may require shaping, broaching, power skiving or another suitable process. Tool-workpiece interference, workholding, cycle time and inspection must be considered before the ring design is released.
Die Gleason Power Skiving Technology overview provides a useful visual reference for the production of internal and external gears. It is included as a manufacturing-process reference, not as a planetary gearbox product recommendation.
Manufacturing quality is also separate from nominal ratio. ISO 1328-1 defines a flank-tolerance classification system for cylindrical involute gears; the standard can be found through the official ISO catalogue.
A nominal 20:1 gearset does not normally become a nominal 19:1 gearset because of manufacturing deviations. Instead, those deviations affect:
- Transmission error;
- Backlash;
- Runout;
- Noise and vibration;
- Contact pattern;
- Load sharing;
- Efficiency.
For more detail on material, size and application trade-offs, see Micro Planetary Gearbox: Materials, Sizes and Selection.
When Is a Custom Ratio Worth Developing?
A custom ratio is justified when the nearest standard option creates a measurable system-level problem.
Examples include:
- The loaded output-speed window is narrow.
- The standard ratio moves the motor outside an acceptable efficiency or temperature range.
- The ratio forms part of the mechanism’s kinematic relationship.
- Axial length prevents the addition of another reduction stage.
- Standard ratios do not provide sufficient speed or torque margin.
- The control system requires a defined mechanical relationship.
An existing ratio should receive priority when:
- Loaded output speed is already within tolerance;
- Continuous torque is sufficient;
- Motor current and temperature remain acceptable;
- Package length is suitable;
- Backlash, noise and life meet the requirement;
- A new ratio provides no measurable system benefit.
Die TSL-24GP-370-EN planetary gear motor is available with discrete ratios including 4:1, 16:1, 25:1, 64:1, 88:1, 110:1, 138:1, 256:1, 320:1, 400:1 and 500:1.
These published configurations should not be treated as a controlled experiment showing the effect of ratio alone. Stage count, motor loading and gearbox limits also affect the operating data.
They demonstrate a more fundamental production reality:
A validated gearbox family provides discrete configurations—not every theoretical value between its minimum and maximum ratios.
Custom Ratio Manufacturability Checklist
| Design Gate | Main Question |
|---|---|
| Operating point | Was the ratio derived from actual loaded motor speed? |
| Acceptable range | Is a ratio or output-speed tolerance available? |
| Existing platform | Can a validated standard ratio meet the requirement? |
| Stage count | Can the required stages fit within the allowed length? |
| Integer teeth | Are practical integer tooth combinations available? |
| Basic geometry | Can the sun, planets and ring share valid working geometry? |
| Planet phasing | Can the required planets be assembled at the intended positions? |
| Adjacent clearance | Is there sufficient clearance between neighboring planets? |
| Small-tooth design | Are undercut, tip thickness and profile shift acceptable? |
| Internal mesh | Have working and manufacturing interference been checked? |
| Gear strength | Do root and flank capacity calculations pass? |
| Load sharing | Have manufacturing and assembly errors been considered? |
| System capacity | Do the carrier, pins, bearings and output shaft pass? |
| Manufacturing | Can the gears be cut, treated and inspected consistently? |
| Prototype testing | Do efficiency, backlash, noise, temperature and life meet the targets? |
What Information Should Be Provided for a Custom Ratio?
A request should include more than:
“Please quote a 47:1 planetary gearbox.”
Provide the engineering boundary conditions:
| Required Input | Why It Matters |
|---|---|
| Rated and operating voltage | Defines motor operating conditions |
| Motor speed at the intended load | Determines the actual ratio requirement |
| Required output speed | Establishes the ratio target |
| Acceptable output-speed range | Determines whether a standard ratio can be retained |
| Continuous output torque | Defines the main long-term gearbox load |
| Peak or starting torque | Defines short-duration tooth, carrier and shaft loads |
| Duty cycle | Affects temperature and fatigue |
| Maximum gearbox diameter | Limits ring-gear and module space |
| Maximum gearbox length | Limits the number of stages |
| Backlash requirement | Influences precision design |
| Radial and axial shaft loads | Influences bearings and output support |
| Noise requirement | Influences geometry, materials and lubrication |
| Required service life | Determines design margin |
| Expected quantity | Influences tooling and production-process decisions |
One of the most valuable—and most frequently omitted—inputs is the allowable range.
For example:
Target ratio: 21:1
Acceptable range: 20.5:1 to 21.5:1
is a very different request from:
Required ratio: exactly 21.000:1
A clearly defined tolerance may allow the design to remain within a validated platform.
Common Mistakes
| Common Mistake | Why It Is Incorrect |
|---|---|
| Treating the target ratio as a tooth-count specification | Different architectures can produce the same ratio |
| Starting customization before checking standard ratios | It may create unnecessary parts and validation |
| Assuming a 5% ratio change means a 5% design change | Integer tooth and platform constraints are nonlinear |
| Adding ring teeth while keeping diameter fixed | The module, root geometry and manufacturing process may change |
| Treating 17 teeth as an absolute minimum | It applies only to a defined standard tooth system |
| Adding profile shift late in the design | Profile shift changes the complete working geometry |
| Checking only the external mesh | Planetary stages also contain an internal mesh |
| Checking phasing but not planet clearance | Correct phasing does not guarantee sufficient physical space |
| Dividing load equally by planet quantity | Real load sharing is affected by errors and deflection |
| Rating only the gear teeth | The carrier, pins, bearings and shaft may limit capacity |
| Assuming CAD assembly proves manufacturability | Cutting, treatment, inspection and repeatability still matter |
| Requesting an exact ratio without a tolerance | It may eliminate a simpler validated solution |
FAQ
Q1:Can any planetary gearbox ratio be customized?
Many ratios are mathematically possible, but not every ratio is practical within a fixed diameter, length and manufacturing platform. A candidate ratio must also satisfy integer tooth geometry, planet assembly, interference, strength and manufacturing requirements.
Q2:Why can a small ratio change require new gears?
Gear tooth counts are integers. A small ratio change may require a different sun or ring tooth count, which can affect planet geometry, profile shift, module, diameter, stage arrangement and tooling.
Q3:Can profile shift solve every small-sun-gear problem?
No. Positive profile shift can improve undercut and root geometry, but it also changes tooth thickness, tip thickness, working pressure angle, contact ratio and backlash. The complete internal and external mesh must be evaluated.
Q4:Does adding more planet gears increase the reduction ratio?
No. Planet quantity does not directly change the theoretical ratio of a common fixed-ring planetary stage. It mainly affects load paths, assembly phasing, adjacent clearance and load distribution.
Q5:What is the most important information for a custom-ratio request?
Provide the loaded motor speed, acceptable output-speed range, continuous and peak torque, duty cycle, diameter, length, backlash, shaft loads and required life. The allowable ratio or speed range is especially valuable.
Fazit
A planetary gearbox gear ratio is easy to describe as a number, but a production-ready custom ratio is the result of several connected design decisions.
A viable solution must satisfy more than kinematics. It must also pass tooth-count, center-distance, planet-phasing, adjacent-clearance, small-tooth geometry, internal-mesh interference, gear-strength, load-sharing and manufacturing checks.
The 20:1 and 21:1 example shows why two ratios separated by only 5% can have very different consequences when ring gear, module and outside diameter are fixed. One ratio may use validated stage combinations, while the other may require a small sun, profile modification or a different ring-gear platform.
A custom project should begin with the actual operating point and an acceptable speed range—not an exact ratio with no stated tolerance. TSL Motor can first compare the requirement with its existing planetary gear motor range and then evaluate new stage combinations, tooth combinations or a complete gear platform where standard configurations are insufficient.
For the initial engineering review, provide the loaded motor speed, target output speed and tolerance, continuous and peak torque, duty cycle, maximum diameter and length, backlash, shaft loads and expected service life. All new ratios and gear geometries remain subject to engineering assessment and prototype validation.
