The formula for calculating the output RPM of a gearbox, based on the input RPM and the gear ratio as defined in the reference, is straightforward: Output RPM = Input RPM × Gear Ratio.
Understanding the Gearbox RPM Formula
To determine how fast the output shaft of a gearbox spins, you need to know the speed of the input shaft (usually connected to a motor) and the mechanical advantage or disadvantage provided by the gears within the gearbox, known as the gear ratio.
The provided reference explains the calculation as follows: "To find the RPM of an output shaft/mechanism, take the input RPM (i.e. the motor speed), and multiply it by the gear ratio (the ratio of the number of teeth on the input gear to the number of teeth on the output gear)."
This gives us the core relationship:
Output RPM = Input RPM × (Number of Teeth on Input Gear / Number of Teeth on Output Gear)
Key Components of the Formula
Let's break down the terms used in the formula:
- Input RPM: Revolutions Per Minute of the shaft entering the gearbox (e.g., motor speed).
- Output RPM: Revolutions Per Minute of the shaft exiting the gearbox. This is what you are calculating.
- Gear Ratio: As defined in the reference, this is the ratio of the number of teeth on the gear attached to the input shaft compared to the number of teeth on the gear attached to the output shaft.
- Gear Ratio = Number of Teeth on Input Gear / Number of Teeth on Output Gear
Illustrative Example
The reference provides a clear example: "600 RPM * (60/12) = 3000 RPM."
Let's analyze this example using the formula:
- Input RPM: 600 RPM
- Number of Teeth on Input Gear: 60
- Number of Teeth on Output Gear: 12
- Gear Ratio: 60 / 12 = 5
- Calculation: Output RPM = 600 RPM × 5 = 3000 RPM
This confirms that with an input gear having more teeth than the output gear, the output shaft spins faster than the input shaft.
Summary Table
| Component | Description | How to Find |
|---|---|---|
| Input RPM | Speed of the shaft entering the gearbox | Known (e.g., motor specification) |
| Output RPM | Speed of the shaft exiting the gearbox (Result) | Calculated |
| Gear Ratio | Ratio of Input Gear Teeth to Output Gear Teeth | Calculated from gear specifications |
| Input Gear Teeth | Number of teeth on the driving gear | Known (from gear design) |
| Output Gear Teeth | Number of teeth on the driven gear on the output shaft | Known (from gear design) |
Practical Implications of Gear Ratio
Understanding the relationship between teeth count and RPM is crucial for gearbox design and selection:
- If Input Gear Teeth > Output Gear Teeth, the Gear Ratio is > 1. The Output RPM will be higher than the Input RPM (speed increase). This is often called an "overdrive" or "speed-up" ratio.
- If Input Gear Teeth < Output Gear Teeth, the Gear Ratio is < 1. The Output RPM will be lower than the Input RPM (speed reduction). This is the most common scenario for increasing torque.
- If Input Gear Teeth = Output Gear Teeth, the Gear Ratio is = 1. The Output RPM will be equal to the Input RPM.
The reference notes, "The consideration of a “slow” or “fast” RPM depends on the mechanism," highlighting that the desired output speed is relative to the application's needs.
