This revision separates this page from the generic portable-drill ledger. It models one exact simple planetary stage with sun input, a fixed ring and carrier output, while removing unsupported component ratings, failures, field stories and operating advice.
Exact Fixed-Ring Planetary Drill Stage
Enter sun and planet tooth counts plus declared sun speed and torque. The worksheet derives the required ring count, exact carrier reduction, carrier speed and ideal lossless carrier torque for one simple planetary stage.
Equation Used
- Sun, planet and ring use a common module and compatible pressure angle, and the displayed circles are pitch circles.
- One planet is shown so arbitrary entered tooth-count pairs do not imply an unsupported equally spaced multi-planet assembly condition.
- The ring is fixed to the housing, the sun is the input and the carrier is the output.
- Gears are rigid, coaxial and backlash-free for the ideal kinematic result.
- Ideal carrier torque follows lossless power conservation and excludes efficiency.
- Tooth form, module, pressure angle, undercut, contact ratio, strength, bearing loads, planet count/spacing, balance, noise, lubrication, backlash, efficiency, motor curve, clutch, multi-stage shifting, spindle/chuck limits, bit/material interaction, heat, duty cycle, reaction torque, guarding and safe operation are excluded.
Recasts a duplicate generic drill page as an exact one-stage fixed-ring planetary kinematics model with enforced pitch geometry.
One exact fixed-ring planetary stage
The motor shaft drives the sun gear. A planet meshes externally with the sun and internally with the ring, which is fixed to the housing. The planet centre rides on the carrier, so its orbital motion turns the connected output shaft, chuck and bit.
The drawing shows one planet to avoid implying that every entered tooth-count pair supports a particular equally spaced multi-planet assembly. The pitch circles remain tangent and the sun, planet and carrier angle markers follow the exact ideal closure.
Use this page to study planetary geometry
This worksheet is distinct from the whole-drill shaft page: it isolates one simple planetary stage and derives its ring count and ratio from entered tooth counts. It can audit ideal geometry and kinematics, not design or rate a gearbox.
OSHA requires drills and other power tools to be maintained safely and hazardous exposed power-transmission parts to be guarded. Follow the tool manufacturer's instructions and a task-specific hazard assessment.
Enforce pitch geometry before calculating speed
The ring pitch radius equals the sun radius plus two planet radii when all gears share a module.
NASA's planetary table gives this exact ratio for sun input, fixed ring and carrier output. Ideal lossless torque multiplication is the same positive magnitude R.
A transparent tooth-count example
For Ns=18 and Np=21, the required ring has Nr=60 teeth. The exact reduction is 4.333:1. At a declared sun speed of 20,000 rpm and torque of 0.50 N-m, carrier speed is 4615.4 rpm and ideal lossless carrier torque is 2.17 N-m.
These results describe one ideal stage only and are not a drill rating.
Tooth counts do not complete a gearbox design
A buildable gearset also needs module, pressure angle, tooth form, undercut and contact-ratio checks, material and strength analysis, planet-pin and bearing sizing, backlash, lubrication, efficiency, tolerances, balance and housing stiffness. Multiple planets add spacing and load-sharing conditions.
The former universal drill ratios, chuck torque, runout thresholds, failure hours, battery-sag claims, industry deployments, product comparisons and operating instructions are removed because they were not supported for a specific tested plant.
Planetary-stage questions
Why is ring tooth count derived?
Equal-module coaxial pitch geometry requires Nr=Ns+2Np.
Why is only one planet drawn?
It preserves the exact mesh without asserting a multi-planet spacing condition.
Is ideal carrier torque a real output rating?
No. It excludes every loss and limit.
Does this model a multi-speed drill gearbox?
No. It is one declared stage.
Planetary drill-stage references
- NASA CR-195200: planetary members and the sun-input, fixed-ring, carrier-output ratio 1+Nr/Ns.
- US Patent 9,415,448: drill motor drives the sun, planets roll on a housing-fixed ring and the carrier drives the downstream member.
- OSHA 29 CFR 1926.300: power-tool condition, guarding and drill-control requirements.
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