In this video, Corey describes what is needed for gears to mesh properly, how to adjust backlash and how to calculate gear speeds.
Video Transcript
Hi and welcome back to Mentor and Engineer. We’re still talking about gears here. Still excited, woohoo! And now we’re going to talk about making sure that your gears mesh together. And so, before we can do that, we need to talk a little bit about terminology.
Alright, so the first thing I want to point out is these things called lands right here. Alright, this is a bottom land and a top land. They’re more or less a flattened section of our tooth. And then you will also notice that as they mesh together, you’re going to have a gap here, you’re going to have a gap up there, and you’re going to have a gap on the back side of the gear. Now I have my gear rotating clockwise here, which means this one’s going to rotate counterclockwise, and it’s pushing right here, and it’s pushing a little bit right there.
And you want to make sure that there’s a gap everywhere so that you don’t bind the teeth. It’s very important to have a gap right here so that you will be able to make adjustments. You can also adjust that gap by bringing these two gears closer or farther apart. You never want to get to a zero tolerance. So, this right here is where back glass comes into play.
I can adjust the center distances to increase or decrease that gap as I desire. Moving on, we’re going to talk about the pitch circle. The pitch circle is these two lines here, these dotted lines. That is right at the center here. These two will be tangent to each other.
That’s the theoretical angle where the gears mesh together. From there, we can determine how far our gears need to be apart based on their center to center. This value of a pitch circle will come from the manufacturer. and they will be something they readily give and it will allow you to figure out how far apart they are and you use this formula that the pitch circle represented by d d1 divided by 2 d2 divided by 2 equals the center to center distance of the two gears all right
and that’s just saying that the radius of this gear and the radius of that gear have to eat it may have to add up to be double that so you get that tangent line there no big deal we can all do that all right the second thing that we’re going to need to talk about is diametrical pitch and this is represented by the letters p and D, both capitalized. Sometimes you’ll just see the letter P for the pitch diameter. I like to use both just to indicate that’s exactly what I’m talking about. And that is the number of teeth, and that is divided by the pitch circle of the tooth, and that’s represented by lowercase d.
So, let’s do a little example. I have Lego gears here and I have two gears, and I know that they need to mesh together because I see the mesh and I want to figure out what is the diametrical pitch. So, I’m going to use unstandard units here. Just because I can count these very easy, I’m going to consider each space one.
So, this large gear right here, we’re going to start there. I just counted. It’s got 40 teeth. and it has from the center one two and a half spaces all right so I’m going to need to multiply that by two
and I get five, so I get 40 teeth five spaces and that equals eight, so that’s a pitch diameter of eight. Alright, on the small one, it’s got 24 teeth, and it is one and a half, so multiply by two, that’s three, so I’ve got 24, excuse me, I can’t write, 24 divided by three, and that also equals eight. Now it is very important that these two numbers add up are the same. That is how a gear will match.
The other thing that tells me if a gear will match or not is the pressure angle. So those both have to match. So, if I have a pressure angle of 20 and one of 14 and a half, those will not work together. If I have a pressure or a diametrical pitch of six and eight, those will not match together. They both have to match.
That is the only two things that have to have happen. The final component of this video is going to be doing the gear ratio. This is the ratio of the two gears and how the input drives the output. It’s very simple. It’s all based on the number of teeth.
Our ratio is going to be the number of teeth on the output gear. over the number of teeth on the input gear. So, in this case, I’m going to drive the 40-tooth gear by the 24-tooth gear. And that gives us a ratio of 3 to 5. So, I can divide both of those by 8, and I will get there.
Or what is that? 1.66. So, in our example, let’s just say that our input Gear is running at 100 RPM. All right, we’re going to do our output, which is V out equals V in over our gear ratio. All right, so we get, what is that?
It’s exactly 60 RPM. 60 rpm out now we can just use that formula to figure out you know so we get we will also get increased torque now it’s not exactly a one-to-one ratio because there is a power that is lost between the two gears and we’ll talk about that more in our next video so thank you for watching please stay tuned thanks bye.