Designing Gears for 3D Printing

Hello makers, today we will learn how to design and 3D print gears from scratch. As we all know gears are one of the main components in motion translation. However, the design of the gears is not simple especially tooth design. But, this instructable will guide you and provide you all the necessary formulas and techniques for 3D printing gears. This instructable is a bit based on theory as I am trying to write something which can be helpful to the people who want to learn things from the basics and another reason is that when I tried to design gear a few weeks back I could not found any proper guide where I can find all the formulas to design a custom gear and eventually I had to read a couple of books. So, I decided to write about it where people like me can find formulas and theory easily in one place. Also, it's my first time writing such instructable do criticize me in the comment section below (Open to all the suggestions) :P

List of the items which are required or used in this instructable is:

1. 3D printer

2. PLA filament 1.75mm

A gear has many variables, and in this part, we will understand each of them and design two gears. To design and calculate, we must fix some of our prerequisites. Let dive into it. First, we have 3 circles as shown in the figure, the middle circle is known as the pitch circle, and when the gear meshes with another gear the pitch circle of both gear coincides(touches). Okay, So now we have known about pitch circle let's begin with our prerequisites. First, we have to decide our pitch circle dimension and for that, we need center distance which means that we must decide how apart these gears are or the distance between the two shafts of the gear.

For the starters, we will make a gear with a center distance of 25mm and it should have 10 teeth and we will keep the gear ratio to 1:1. So, now we have our 2 most important dimensions let's find out the dimensions of the upper and lower circle but first, we need to find the module of the gear, the module is nothing but the ratio of pitch circle to the number of teeth. So in our case.

Module(m) = 25/10 =2.5 (as in our case, the center distance is equal to pitch circle diameter because the gear ratio is 1:1)

In Engineering terms, the upper circle is known as the addendum circle, and the addendum which is the distance between the pitch circle and addendum circle is equal to our module.

So the dimension of the addendum circle will be:

addendum circle = 2*m+pitch circle = 30mm

Now, the lower circle is a little bit complex as it consists of 2 dimension dedendum and clearance. As shown in the second picture, that there is a gap between two gears after meshing this gap is known as the clearance and the distance between the lower circle a.k.a root circle is the summation of dedendum and clearance.

dedendum is formulated as 1.25*module and clearance is addendum - dedendum.

so now we have dedendum as 3.125 and clearance of 3.125-2.5 = 0.625.

And our root circle will became = pitch circle - 2*(0.625+3.125) = 17.5.

Now we have all the circle dimensions next we have to find the dimension of teeth

Illusion, we are still at the second step, I just split it because I thought it was already too big. Okay, now we already have our three circles so now let's make the tooth geometry. From the figure, you may see that the gear tooth has two different thicknesses. One at the very top and another at the pitch circle, so the thickness at the pitch circle can be obtained using the formula 1.5708*module. In our case, it would be 1.9635 mm.

We need to do some trigonometry for the top thickness, but believe me, it is not that hard. Okay, so as shown in the diagram (where a is the length of addendum), the upper thickness can be deduced easily if we just have to subtract 2 times the x length from circular thickness, and in our case, it will be 1.054 mm.

So now we are done with the paperwork, the next step is to design it in CAD. Well, this part is pretty easy, if you know how to use any CAD software. It is basically just drawing circles and extrude. The only tricky part which I can think of is to draw the tooth geometry, and for the tooth, geometry I have used 3 point arc as shown in the gif. However, I have attached the video in which I have shown all the steps and how to design it in CAD you can refer to it and now our gear is ready for the print.

I hope you have learned something from this instructable. Thank you for your time. Till next time