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I have been trying to model a custom gear to fit on to another physical gear. I having been using this 3d model gear generator. What I know about my physical gear is that it has:

  • (what I believe to be a diametral) Pitch of 32
  • Pitch Diameter of 1.5" (38.1mm)
  • Outer Diameter of 1.563" (39.7002mm)
  • 20° Pressure Angle
  • 48 Teeth

I have access to a 3D printer and am trying to calculate a gear that will mesh with my physical gear given these specs. I printed a smaller first gear that happened to mesh perfectly with the physical gear. When I increased the number of teeth (thus increasing the PD and OD of the gear in the generator) the teeth and distance between the teeth appeared to increase as well, not meshing well with the physical gear at all.

New gear specs:

  • Pitch Diameter of 1.2" (30.48mm)
  • Outer Diameter (Auto calculated, but I think it should be) 1.2" + .063" (30.48mm + 1.6002mm)
  • Same Pressure Angle
  • *No blacklash

Is there a way to calculate a gear that will mesh, or will I have to empirically derive the gear tooth and pitch by printing out gear after gear to see if it fits?

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It is important to remember that, when you design a set of meshing gears you need to keep the size and shape of the teeth the same, irrespective of the diameter. There is a temptation to design a gear template and simply scale the whole thing to get the diameter you want but this does not work.

One implication of this is that for any particular design the range of available diameters available to you is limited by the need to have an integer number of teeth. For example if you start with a gear with diameter D=10 and N = 10 teeth then if you are locked into that ratio so you can't have a diameter of 20.5 as that would imply 20.5 teeth and you can't have half a tooth.

The concept of module is widely used to simplify this design process

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Gears will only mesh together when they both share the same Diametral Pitch. There are many online descriptions for this term, that is what you want to learn about. Here is an example of one: https://www.bostongear.com/pdf/gearology/chapter02.pdf

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