Planetary Gearboxes: Design, Function and Selection
A planetary gearbox consists of a sun gear, planet gears, ring gear, and planet carrier, and achieves efficiencies of 95–98% through parallel power flow in a coaxial, compact design. Their high power density and versatility make them the first choice for demanding applications – from robot joints and wind turbines to high-precision machine tool drives.
The operating principle of a planetary gearbox differs fundamentally from conventional spur or bevel gear designs. While spur gearboxes mesh two gears in fixed bearings, planetary gearboxes have multiple planet gears orbiting a central sun gear while simultaneously rotating about their own axes – an elegant solution for high power density in minimum installation space.
Design and Operating Principle
A planetary gearbox consists of four main components:
- Sun gear: The central gear, connected to the drive (motor). Transmits torque to the planet gears.
- Planet gears: 3 to 6 gears arranged evenly around the sun gear. They mesh with both the sun gear and the ring gear simultaneously.
- Ring gear (annulus): The outer gear with internal teeth. In standard operation, it is fixed to the housing.
- Planet carrier: Connects the planet gear axles. In standard reduction operation, it is the output element.
The torque is distributed across all planet gears simultaneously. With 3 planet gears, each carries only 1/3 of the total torque – enabling a much higher total torque capacity than a comparable simple spur gearbox.
Gear ratio formula
i = 1 + (zring / zsun)
Where zring = number of ring gear teeth, zsun = number of sun gear teeth
Calculating the gear ratio: the Willis equation
The gear ratio of a planetary gearbox follows from the tooth counts of the sun gear (zS) and the ring gear (zH). The most common operating mode — fixed ring gear, input via the sun gear, output via the planet carrier — is described by the Willis equation:
i = 1 + zH / zS
i = gear ratio (ring gear fixed) · zH = tooth count of ring gear · zS = tooth count of sun gear
The underlying fixed-carrier ratio (planet carrier held stationary) is i0 = − zH / zS; the minus sign indicates the direction reversal caused by the internal teeth of the ring gear. For coaxial meshing, the tooth counts must additionally satisfy the assembly condition zH = zS + 2 · zP (zP = tooth count of the planet gears).
Worked example: zS = 24, zH = 72
- Gear ratio (ring gear fixed): i = 1 + 72/24 = 4.0
- Tooth count of planet gears: zP = (72 − 24)/2 = 24
- Assembly condition for evenly spaced planets: (zS + zH)/p = 96/p must be an integer — satisfied for p = 3 (result 32) and p = 4 (result 24).
Tooth counts may be chosen freely as long as both the meshing condition and the assembly condition are met. Load capacity must be verified in accordance with ISO 6336 or DIN 3990; the values given here are design guidelines only.
Design Types
Single-Stage Planetary Gearbox
The simplest design with one set of planet gears. Gear ratios of i = 3:1 to 10:1 are achievable. It is compact, efficient (up to 97%), and available in standard sizes for direct servo motor mounting.
Multi-Stage Planetary Gearbox
Multiple stages in series multiply the gear ratios. Two-stage designs achieve i = 9:1 to 100:1, three-stage designs up to i = 1000:1. Each stage reduces efficiency slightly (approx. 97% per stage). Used for high torques at low speeds.
Angle Planetary Gearbox
Combines a planetary stage with an integrated bevel gear stage for 90° shaft redirection. Compact design without separate angle gearbox. Efficiency slightly lower than inline design due to the additional bevel gear stage.
Coaxial Design
Input and output shafts are coaxial (on the same axis). This is the most common design for servo applications. Very compact and allows direct flange mounting to servo motors according to IEC standard.
Selection Criteria
- Gear ratio (i): Determine from motor speed and required output speed.
- Output torque (M2): Calculate from load and required acceleration. Include safety factors (typically 1.5 to 2.0).
- Backlash: For precision positioning: < 1 arcminute (precision gearbox); for standard positioning: 2–5 arcminutes; for conveyor technology: up to 10 arcminutes. For custom gear geometries with tight tolerances, TEA offers custom gears to drawing.
- Torsional stiffness: Important for dynamic applications with position reversals. Higher stiffness means better positioning accuracy under changing loads.
- Motor interface: IEC flange dimension, input shaft diameter, and coupling type must match the motor.
Planetary vs. Other Gearbox Types
| Criterion | Planetary | Worm | Bevel |
|---|---|---|---|
| Efficiency | Up to 97% | 50–90% | Up to 98% |
| Backlash | < 1 arcmin | Higher | Medium |
| Power density | Very high | Medium | High |
| Cost | Medium–High | Low | Medium |
Planetary vs. worm gearbox: direct comparison
Choosing between a planetary and a worm gearbox is one of the most common fundamental decisions in drive sizing. Both achieve comparable gear ratios, but they differ fundamentally in efficiency, self-locking behaviour and design layout. The following comparison summarises the properties that are decisive for the selection.
| Criterion | Planetary gearbox | Worm gearbox |
|---|---|---|
| Efficiency (single stage) | 95–98 % | approx. 45–90 %, drops sharply as the ratio increases |
| Ratio per stage | approx. 3:1 to 10:1 | approx. 5:1 to 70:1 (single stage) |
| Self-locking | no (back-drivable) | possible at a small lead angle (γ < friction angle ρ′) |
| Shaft arrangement | coaxial (in line) | right-angle, crossing |
| Power density | very high (load shared across 3–5 planets) | medium, high sliding component in mesh |
| Wear / lubrication | predominantly rolling friction, low heat generation | high sliding component, often requires special oils (e.g. polyglycol) |
| Noise | moderate (multiple tooth engagements) | very quiet (continuous sliding contact) |
The key distinguishing feature is self-locking: a worm gearbox locks statically when the lead angle γ of the worm is smaller than the effective friction angle ρ′. Planetary gearboxes, by contrast, are inherently back-drivable and require a separate brake for holding tasks.
Self-locking (static): γ ≤ ρ′ with ρ′ = arctan(μ / cosαn)
γ = lead angle of the worm at the mean diameter · ρ′ = effective (tooth-related) friction angle · μ = sliding friction coefficient in the tooth mesh · αn = normal pressure angle (typically 20°). The relationship follows classical screw mechanics after Roloff/Matek (the worm = a rotating inclined plane); for steel/bronze pairings μ lies, depending on lubrication and sliding speed, at roughly 0.03–0.08.
Worked example: lead angle γ = 4°, μ = 0.05, αn = 20°
- cosαn = cos 20° = 0.9397
- ρ′ = arctan(0.05 / 0.9397) = arctan(0.0532) ≈ 3.05°
- Condition γ ≤ ρ′: 4° > 3.05° → not self-locking (the worm back-drives).
- A shallower lead of just γ = 2.5° would already produce static self-locking with γ < ρ′ — so the transition is narrow and strongly dependent on the actual friction value.
Practical note: static self-locking (at standstill) does not automatically imply dynamic self-locking (during run-out). It should never be relied upon as the sole brake for safety-relevant holding tasks. You will find a more in-depth comparison in the guide Worm gearbox vs. planetary gearbox.
Lubricant viscosity: ISO VG selection per standard
The lubricant viscosity largely determines the load-carrying capacity of the lubricating film, the efficiency and the thermal behaviour of a planetary gearbox. Industrial oils are classified into standardised viscosity grades (ISO VG) according to ISO 3448 (national: DIN 51519). The grade number corresponds to the kinematic mid-point viscosity in mm²/s (cSt) at the reference temperature of 40 °C.
ISO VG n → ν(40 °C) = n mm²/s (tolerance ±10 %), step factor ≈ ⁶√10 ≈ 1.5 (six grades per decade; ISO 3448 / DIN 51519)
The grades are geometrically stepped: each next-higher ISO VG grade has roughly 1.5 times the mid-point viscosity of the preceding one (series …32 – 46 – 68 – 100 – 150 – 220…). Within a grade, the actual viscosity at 40 °C may deviate by ±10 % from the grade value.
Reference values for planetary gearboxes
| ISO VG grade | ν at 40 °C (mm²/s) | Typical application |
|---|---|---|
| ISO VG 32 | 28.8 – 35.2 | high speeds, low load, low churning losses |
| ISO VG 46 / 68 | 41.4 – 74.8 | all-round range, medium speed and load |
| ISO VG 100 / 150 | 90 – 165 | low speed, high load/shock, elevated temperatures |
| ISO VG 220 | 198 – 242 | heavy slow runners, high flank pressure |
Viscosity ranges of the grades per ISO 3448 / DIN 51519 (grade mid-point ±10 %). The application column is a sizing orientation — the binding oil selection follows from the required minimum operating viscosity at the actual bulk temperature that occurs and is to be made according to the manufacturer's specification or tribological design (e.g. per ISO/TR 13989, ISO 6336 lubricant film verification).
Viscosity index (VI) and temperature behaviour
The ISO VG grade describes the viscosity only at the 40 °C reference point. How sharply the viscosity drops as the temperature rises is characterised by the dimensionless viscosity index (VI) per ISO 2909 / DIN ISO 2909, calculated from the kinematic viscosity at 40 °C and 100 °C. A high VI (mineral oils typically 90–105, modern synthetic oils >140) means a flatter temperature behaviour — decisive when the gearbox runs through a wide operating-temperature range, so that a sufficient lubricating film is still carried at operating temperature.
Application Examples
- Robot joints: High power density and low backlash for precise positioning of robot arms
- CNC machine tools: Servo axes with high dynamic performance and positioning accuracy
- Printing machines: Precise register control with high torsional stiffness
- Solar trackers: Long-term reliable drives for solar panel positioning
- Medical technology: Low-backlash drives for diagnostic and therapy equipment
- Conveyor technology: High-torque wheel drives for heavy transport tasks
TEA Recommendation
TEA offers planetary gearboxes in various sizes and precision classes – from standard series for general automation to high-precision versions for demanding servo applications. We also supply pre-assembled motor-gearbox combinations with verified interfaces.
Request Gearbox ConsultationFrom design to enquiry: procurement notes
- Cost drivers: Precision class and number of stages determine the price – high-precision versions with <1 arcmin backlash cost significantly more than standard types; multi-stage units require more manufacturing effort than single-stage ones.
- Standard vs. custom: Catalogue types (single-stage, coaxial, i = 3–10) are available as standard catalogue items and cost-effective. Custom versions with modified tooth counts, flank geometry, or angle output are worthwhile only for specific installation constraints or special ratio requirements.
- Enquiry checklist: Please specify rated torque (Nm) and peak torque, desired gear ratio, input speed, required backlash (arcmin), mounting orientation, and ambient temperature range.
- TCO note: Oil change intervals and bearing service life vary considerably with speed and load profile – plan maintenance costs early for applications with frequent reversing cycles.
- Further reading: Enquiries about custom gears for high-precision gearboxes: custom gears to drawing or directly to the contact form.
Frequently Asked Questions about Planetary Gearboxes
Planetary gearboxes achieve 95–98% efficiency per stage thanks to parallel power flow. Two-stage units multiply the individual stage efficiencies, typically yielding 90–95% overall.
A single-stage planetary gearbox typically achieves ratios of i = 3:1 to 10:1. Multi-stage designs (2 or 3 stages) reach up to i = 1000:1 or higher. The exact achievable ratio depends on the tooth counts of sun gear, planet gears, and ring gear.
Backlash is the clearance between meshing gear flanks. In positioning applications it causes errors on direction reversal, since the drive must first close the gap before the output responds. Precision planetary gearboxes achieve less than 1 arcmin; standard versions 2–5 arcmin.
The coaxial arrangement (input and output on the same axis) enables a compact, space-saving design and simplifies integration into existing machines. This is especially valuable in robotics and machine tool drives where installation space is limited.
Yes, planetary gearboxes are inherently reversible and can run under load in both directions. Dimensioning and lubrication must account for symmetric load distribution across all planet gears.
About the Author
Senior Sales & Application Engineer · Technische Antriebselemente GmbH
Specialises in gear technology and drive system selection for automation and robotics.