Gear Ratios
Gear ratios are a core science behind almost every machine in the modern era. They can maximize power and efficiency and are based on simple mathematics. So, how do they work?
If you work with gear ratios every single day, this post probably isn’t for you. But, if you want to improve your understanding of this essential element of machine design, keep reading.
Gear ratios are simple as long as you understand some of the math behind circles. I’ll spare you the grade school math, but it is important to know that the circumference of a circle is related to a circle’s diameter. This math is important in gear ratio design.
To begin to understand gear ratios, it’s easiest if we start by removing the teeth from the gears. Imagine two circles rolling against one another, and assuming no slippage, just like college Physics 1. Give circle one a diameter of 2.54 inches. Multiplying this by pi leaves us with a circumference of 8 inches or, in other words, one full rotation of the circle one will result in 8 inches of displacement.
Give circle two a diameter of .3175 inches, giving us a circumference of 1 inch. If these two circles roll together, they will have a gear ratio of 8:1, since circle one has a circumference 8 times as big as circle two. A gear ratio of 8:1 means that circle two rotates 8 times for every time circle one rotates once. Don’t fall asleep on me yet; we are going to get more and more complex.
Gears aren’t circles because, as you know, they have teeth. Gears have to have teeth because, in the real world, there isn’t infinite friction between two rolling circles. Teeth also make exact gear ratios very easy to achieve.
Rather than having to deal with the diameters of gears, you can use the number of teeth on a gear to achieve highly precise ratios. Gear ratios are never just arbitrary values, they are highly dependent on the needed torque and power output, as well as gear and material strength. For example, if you need a gear ratio of 3.57:1, it would be possible to design two compatible gears, one with 75 teeth and another with 21.