Make a Gear From Scratch (in Fusion 360!)

Hello and welcome to my first instructable! Today I will be showing you how to model a gear in fusion 360.

Before we get to the steps you will need the following:

• Microsoft Excel for calculating the values that define your gear
• Fusion 360, or any other CAD program for drawing your gear
• 3D printer (optional) for printing your gear

If you are unfamiliar with gears please see the list below for some basic terms, otherwise feel free to skip this step

Terms:

Diametral pitch - the ratio of the number of teeth on the gear to the pitch diameter (units are teeth per mm)

Addendum - the radial distance between the top land (top part of tooth) and pitch circle

Dedendum - the radial distance between the bottom land (bottom part of tooth) and pitch circle

Base circle - a circle that can be found using the pitch circle and pressure angle, it is the start for drawing the involute profile of a gear

Pitch circle - the theoretical circle of a gear that is in contact with another (this is somewhere between the top and bottom of the teeth)

Clearance circle - circle that is tangent to the addendum circle of the mating gear, when two gears are in mesh the ends of their teeth should never meet their bottom lands (dedendum circles) so this clearance is between the top of the teeth on one gear and the bottom valley of the other

Backlash - the difference between the tooth space and tooth thickness (which is always positive because the space needs to be greater for the gears to properly mesh

Circular pitch - the distance, as an arc on the pitch circle, from a point on one tooth to the same point on the next tooth (please see image for clarity) - NOT THE SAME AS DIAMETRAL PITCH, THIS IS AN ARC

Involute - the curve traced out by the end of a taut string if unraveled around a cylinder

Line of action - the line that is perpendicular to the point of contact between gears (this is tangent to the base circles of the gears)

Pressure angle - the angle between the line of action and a line perpendicular to the line of centers

Line of centers - the line that connects the centers of both gears

Like other mechanical parts, gears have a specific function, they transfer motion. It's pretty simple but also quite useful since it allows them to change the speed, torque and direction of motion in things like cars, clocks and instruments.

Before we draw the gears we will decide on their size and number of teeth. In this example, I want to keep things simple so we will use two 40 mm gears, each with 20 teeth. This results in a gear ratio of 1:1 meaning the output gear moves at the same speed as the input gear.

In the spreadsheet that I have attached below you'll notice that the inputs are:

• pressure angle
• number of teeth
• pitch circle diameter
• tooth thickness to circular pitch ratio

You may be wondering why there are four inputs instead of the two that I just mentioned. This is because pressure angle and tooth spacing (tooth to pitch ratio) are usually pretty constant across involute gears. For convenience, we will use a pressure angle of 20 degrees (since this is a commonly used value) and tooth to pitch ratio of 0.49 since the teeth are generally a little less than half as wide as the circular pitch (which means the spaces are a bit wider than the teeth themselves).

The spreadsheet should already have all of the values in it but play around with the numbers for diameter and teeth so you can see for yourself how the gears parameters change.

For instructions on how to model the gear please see the video above.

A list of steps for making the gear is also shown below (and every value can be found in the spreadsheet);

1. Draw the base circle of one gear (since the gear ratio is 1:1, we only need to draw one).
2. Create 5 equally-spaced segments that extend from the center of the circle to it's outer circumference
3. Draw a chord (a line whose endpoints lie on a circular arc) from a point of intersection (between one of the radial lines and circle) to the furthest point
4. Repeat making these chords for the remaining points on the circle so that you have 4 chords that share the same endpoint
5. Dimension the length of each chord and move these dimensions out of the way
6. Draw a tangent perpendicular from one of the points of intersection
7. Repeat making these tangents for the rest of the points on the circle
8. Make the length of each tangent equal to the length of it's respective chord - this will form the outer profile of the tooth
9. Use the spline tool to create a curve that intersects the endpoints of those tangents
10. Create a circle with the same center as the base circle, this will be the addendum circle which will form the end surface of the tooth
11. Trim the excess lines
12. Make a radius to the addendum
13. Mirror the spline over the addendum radius
14. Dimension the distance between the point and addendum radius (this is the half-width of the tooth)
15. Change that dimension to half of the tooth thickness that you have in the spreadsheet
16. Close the shape of the tooth
17. Extrude the tooth and dedendum circle
18. Pattern the tooth
19. Fillet the corners of the tooth - use the "Clearance" value in the spreadsheet for the fillet radius
20. Save the file

Optional:

Export model as an stl file to slice and print

When gears are designed the space between teeth is just as important as the teeth themselves. The reason for this is backlash, if the gap between teeth is too large there will be significant backlash which will unnecessarily wear down the teeth. On the other hand, if the gap between teeth is too small then the gears will not mesh properly which also causes unnecessary wear. The ideal spacing between teeth is one that produces the smoothest motion, which is a little wider than the tooth width.

If you want to see this difference first hand, you can print a few gears using the files I have attached below. Here is a brief description of each;

1. Just enough clearance (smooth, proper meshing) - #1
2. Tooth space = tooth thickness (gears "stick" when meshing) - #2
3. Too little space (meshing is too jumpy, not constant) - #3
4. Too much space (excessive backlash) - #4

To "feel" the difference grab two gears with the same number (same tooth spacing) and rotate one against the other. As you rotate them you should feel the teeth making and breaking contact. This feedback will be different from pair to pair, but will be more noticeable for pairs 3 and 4 since they have more space between teeth which results in both sets of teeth not always being in contact.

The print settings for the gears are in the csv file below (and the screenshot above). The brim values are included but may not be needed to get a good print.

Thanks for reading and I hope I was able to share something new with you.