This post builds on Gear Ratio Basics and explains how gear ratios affect speed (velocity), torque, and efficiency. Understanding these concepts helps you design gear systems that work the way you need them to.

🔄 Gear Ratio and Velocity

The gear ratio controls how fast the output gear turns compared to the input gear. The formula for calculating this is shown below: \[\text{Gear Ratio} = \frac{\text{Input Speed}}{\text{Output Speed}}\]

For example, if your input gear rotates at 200 revolutions per minute (RPM) and you use a 2:1 gear ratio, you can calculate the output speed like this: \[\text{Output Speed} = \frac{200\, \text{RPM}}{2} = 100\, \text{RPM}\]

This means the output gear turns at 100 RPM. A higher gear ratio slows down the output gear because the driven gear rotates fewer times for each turn of the driver gear. That’s how gear reductions let you decrease speed when needed, like in a robot’s drivetrain or a power tool’s gearbox.

💪 Gear Ratio and Torque

Gear ratios also affect torque, which is the twisting force transmitted through the gears. The relationship between gear ratio and torque is: \[\text{Output Torque} = \text{Input Torque} \times \text{Gear Ratio}\]

For example, if your motor produces 1 newton-meter (Nm) of torque and you use a 3:1 gear ratio, you calculate the output torque like this: \[\text{Output Torque} = 1\, \text{Nm} \times 3 = 3\, \text{Nm}\]

This means you get 3 Nm of torque at the output. By slowing the rotation, the gear system lets the same power apply more force. In practical terms, a gear reduction gives you more torque at the cost of slower speed, which is essential when you need to move something heavy.

⚠️ Direction Reminder

Whenever gears mesh, they change the direction of rotation. Every time you add a gear between the driver and the driven gear, the direction reverses again. For example, if you connect your driver gear to an idler gear, the idler reverses the direction, and the next gear will spin the opposite way compared to the driver. An idler gear does not change the gear ratio, but it flips the rotation direction once more. An even number of gears in the train means the output spins in the same direction as the input. An odd number of gears means the output spins in the opposite direction.

⚙️ Gear Efficiency

No gear system is perfectly efficient. Energy is lost through friction, heat, and flexing of materials, so it is important to understand gear efficiency. Spur gears usually operate at 95 to 98 percent efficiency for each gear mesh. Worm gears have much lower efficiency, often below 70 percent, because of the sliding friction that happens between the worm and worm wheel.

To calculate the total efficiency of a gear train with multiple stages, multiply the efficiency of each gear pair together. For example, if you have two spur gear pairs with 97 percent efficiency each, you calculate the total efficiency like this: \[\text{Total Efficiency} = 0.97 \times 0.97 = 0.9409 \quad (\text{or } 94.1\%)\]

This means your gear train will deliver about 94.1 percent of the input power to the output. Lower efficiency means more heat and less useful power, which can become a problem in systems where energy savings or heat management are important.

✅ Summary

A higher gear ratio reduces the output speed but increases the output torque. Gears reverse rotation direction with each mesh, and the total number of gears in a train determines whether the output spins in the same or opposite direction as the input. Efficiency losses add up with every gear pair, so always include them in your calculations when designing a gear system.