Pulley Transmission Ratio: How to Calculate It Correctly
The transmission ratio in a pulley and belt system is the ratio between the input speed and output speed, or equivalently, the ratio between the pulley diameters. Calculating it correctly is the fundamental step to designing a transmission that delivers the required speed and torque for the application.
Difference Between Transmission Ratio and Reduction Ratio
A transmission ratio greater than 1 means speed reduction (the driven pulley is larger than the driving pulley). A transmission ratio less than 1 means speed increase (the driven pulley is smaller than the driving pulley). In most industrial applications, the motor rotates at a higher RPM than required by the load, so the transmission reduces speed. A 3:1 ratio means the output speed is one-third of the input speed, and the output torque is three times the input torque (excluding friction losses in the system, which in a properly tensioned belt transmission are typically 2 to 5%).
Maximum Recommended Transmission Ratio in a Single Stage
The maximum recommended transmission ratio in a single pair of pulleys is 7:1 for V-belt pulleys and up to 10:1 for synchronous pulleys in some cases. Above these values, the contact angle on the smaller pulley decreases significantly, reducing friction-based transmission capacity. For higher ratios, the correct solution is to use two stages: a first stage that reduces speed to an intermediate value and a second stage that reaches the final value. This allows maintaining proper contact angles in both stages and using reasonably sized pulleys.
How to Calculate Actual Speed When Installed Diameters Are Known
If an existing pulley system is being analyzed and the actual output speed needs to be determined, the formula is: Output RPM = Input RPM × (Driving pulley diameter / Driven pulley diameter) Example: Motor speed of 960 RPM, driving pulley diameter of 150 mm, and driven pulley diameter of 400 mm. Output speed = 960 × (150/400) = 360 RPM If the slip factor is added (estimated at 2%): Actual output speed = 360 × (1 - 0.02) = 352.8 RPM
MARTIN Standard Pulley Diameter Tables
MARTIN manufactures pulleys in standard diameters for each belt section. The calculated diameter for the required transmission ratio almost never matches exactly with an available catalog diameter. The correct procedure is: Calculate the theoretical diameter of the driven pulley. Select the closest standard diameter available in the MARTIN catalog. Recalculate the actual output speed using that standard diameter. Verify that the resulting speed is within the acceptable tolerance for the application. If the resulting speed with the standard diameters is not acceptable, the solution is to adjust the driving pulley diameter and recalculate. The BIOSA technical team can support this selection process.