Intro to Gear Ratios
Spur Gears
A few days ago, a co-worker asked me if I could help him with some gear ratio calculations. This will be a great opportunity to brush up on gearing.
Well, let’s start with a little basics. The concept of gears only works directly between two gears. If you have 3 gears whose teeth are locked, absolutely nothing can happen; they will not turn. That is obvious, I hope. That’s not to say that we can’t use gears in series (i.e. gear to gear to gear…); we can, and we probably should at times.
Here’s a few facts about gears:
- The larger gear is called the idler gear and the smaller gear is called the pinion.
- Not all gears need teeth, but they are generally considered to have them. We’ll assume teeth here.
From HowStuffWorks, gears can be used to perform the following functions:
- To reverse the direction of rotation
- To increase or decrease the speed of rotation
- To move rotational motion to a different axis
- To keep the rotation of two axis synchronized
Gear ratios come into play only when there is a different number of teeth on the two gears, i.e. the gears are of different size. Otherwise, if they are the same size, the gear ratio is 1:1, and our calculations get boring. Both Wikipedia and HowStuffWorks do a heck of a job explaining gear ratios, so if you like a little geometry, pay them a visit. (We’ll take a second more in-depth look at this in a future post.)
But the bottom line is this: in designing for gear ratios, we need to know the speed at which we are driving the system and the speed we want coming out of it (changing the speed is the whole point at looking at gear ratios in the first place).
Rotating the Pinion
The gear ratio is fundamentally the ratio of the number of revolutions over a given period of time. This can translate to a ratio of the circumference of the circles.
From this we can go two ways. First, as you’ll remember from math class, the circumference and the diameter of a circle are related by pi (3.14159…). We can eliminate the factor of pi, and arrive at a the exact same ratio, a ratio of diameters. Second, knowing the gear’s circumference and the size of each tooth of the gear, we can take the gear ratio to simply be the ratio of the number of teeth on each gear.
The larger gear rotates slower; the smaller gear is rotates faster. If we want a slower rotation, we will need to drive the smaller gear and output from the larger gear. If we want a faster rotation, we will need to drive the larger gear and output from the smaller gear. In fact, knowing the desired rotational velocity, the gear ratio is simply the inverse of the ratio of gear speed. (Inverse means you flip the numerator and denominator!)
Gear image from Gear Design.
I feel like having gear ratios is usually not so much about changing gear speed, but more about changing torque.
I agree with John that gears are also used to change torque, but I think the big equation you’re missing is:
P=T*w
where P = power, T = torque, w = angular velocity (or gear speed). Gears ratios are used to change power from one form to another. You can add torque by reducing speed, or add speed by reducing torque, but the overall power must remain constant.
Yes, you are both accurate. I was biased in the writing of this topic in that gear speed was the main purpose on my mind when I was writing this. I guess I only covered one aspect of the gear concept. I want to tackle this topic more in-depth in the future.