Gear Face Width

[Chris is me]

Originally Posted by Andrew Lawrence

All VP/WCP gears are .5 total width, but a .375 face width. This is because of the two .0625 thick nubs on either end of the gear.

This is only true for gears above 24 teeth. Pinions and gears under 24T from Vex are .475 face width, with just a .0125" nub on either side to get the total width to .500".

As for the OP's question about gear strength, if no one gets to it I'll answer that in a day or two, but someone smarter will probably beat me to it. A good first order approximation is to use Lewis numbers and model gears as cantilevered beams.

With regard to making gears, unless you want a different diametrical pitch (e.g. coarser teeth for an arm gear) you're probably better off just doubling the number of Vex gears on the shaft to double the effective face width. Very hard to speak in generalities here; it depends on the mechanism.

[asid61]

I looked into using just 32 pitch, 20* pressure angle gears for the initial reduction stage once.
The problem is that your design actually won't get any smaller or lighter. This is because the CIM shaft is 8mm. A 20p or 32p gear that has an 8mm bore will have a diameter of around 0.6" regardless of its pitch. Then the mating gear will need to have a pitch diameter of between 2-4", regardless of pitch again, because the speed ratio is determined by the pitch diameters, not pitch.
If you want to experience this for yourself, just make a CAD model of a basic, single-stage gearbox and see what happens.

If you wanted to have a lighter primary reduction, making the 20p gears thinner would work much better. Or you could turn down the CIM shaft, but I don't know if that's legal. I know you can change mounting, but messing around with a cim shaft is iffy.

Cutting your own gears: depends. Involute gear cutters are expensive, and for a full FRC set of cutters (20 pitch, 14.5* PA, 12-100 teeth) it costs upwards of $400. I believe you can CNC them with a small ballnose endmill, but that takes up valuable CNC time. If you have access to a wire EDM machine that would be best. Those can cut gears quickly and effectively.
Waterjetting might work too. I know my local community college used to have a hobbing machine for gears.

I use this calculator for gear strength: http://www.botlanta.org/converters/dale-calc/gear.html
I have absolutely no idea about its accuracy, but I use it to compare the relative strengths of different pitch, pressure angle and face width gears. The most common Vex/Andymark gears in use in FRC today can withstand massive loads (such as my team's 600lb spring winch).

[Chris is me]

Originally Posted by asid61

I looked into using just 32 pitch, 20* pressure angle gears for the initial reduction stage once.
The problem is that your design actually won't get any smaller or lighter. This is because the CIM shaft is 8mm. A 20p or 32p gear that has an 8mm bore will have a diameter of around 0.6" regardless of its pitch. Then the mating gear will need to have a pitch diameter of between 2-4", regardless of pitch again, because the speed ratio is determined by the pitch diameters, not pitch.

In short, this isn't true.

In this case, two factors determine the minimum diameter (and by extension pitch diameter) of a gear. You are right in that the first factor is the shaft size - obviously the pitch diameter can't be smaller than 8mm. The second factor determining the minimum diameter of the gear is the tooth size. In theory, the smallest possible gear would have an outer diameter equal to the bore plus 2x the tooth height. Since a 32 DP gear tooth is much smaller than a 20T gear tooth (that's the point!), the pinion can be smaller as well.

In the real world, there needs to be some material between the bore and the root of the gear teeth for a gear to hold up, but not a lot. Let's say 1mm of material is needed between the bore and the teeth making the minimum root diameter 10mm, or .393 inches.

This root diameter is just shy of the root diameter of a 15 tooth pinion. A 15 tooth 32DP gear has an outer diameter of ~.531 inches and a pitch diameter of ~.469 inches. Compare these to the smallest practical 20 DP pinion*, 12 tooth, which has an outer diameter of .7 inches and a pitch diameter of .6 inches, and you can see that the 32DP pinion can be much smaller.

This allows for a reduction in a smaller space, even accounting for the greater number of teeth on the 32DP gear. Say you want a 4:1 reduction. That would be a 15:60 pair in the 32DP example and a 12:48 in the 20DP example. The 32DP gearset center distance would be ~1.172 inches, while the 20DP gearset center distance would be ~1.5 inches.

If you want to experience this for yourself, just make a CAD model of a basic, single-stage gearbox and see what happens.

This is a great way to demonstrate that a 32DP initial reduction saves space. Just use the AndyMark 15T and 60T models (they're just pitch circles, by the way) and compare them to either AndyMark or VexPro models for 12T and 48T gears. On 2791's 2014 robot, we used the 32DP gearset to save space in several large reduction gearboxes. Our winch would not have been able to nicely package itself at the back of our shooter, with the winch rope popping out around the middle of the gearbox, if we did not use the 32DP gearset.

Also, some tips on lightening gears: If you can, I would pocket the gears at their current thickness before thinning them. You can take a lot of material out of a gear by turning the gear on a lathe and thinning the material between the bore and the root, or by drilling a hole circle into the gear. Done right, strength shouldn't be compromised at all (teeth still fail first) and you'll save a dramatic amount of weight.

* An 11 tooth pinion that doesn't use the 12T pitch circle is possible, but it gets a bit weaker than I'm comfortable with, especially when the 11T with 12T pitch circle gear is both COTS and much stronger.

[asid61]

Originally Posted by Chris is me

In short, this isn't true.

In this case, two factors determine the minimum diameter (and by extension pitch diameter) of a gear. You are right in that the first factor is the shaft size - obviously the pitch diameter can't be smaller than 8mm. The second factor determining the minimum diameter of the gear is the tooth size. In theory, the smallest possible gear would have an outer diameter equal to the bore plus 2x the tooth height. Since a 32 DP gear tooth is much smaller than a 20T gear tooth (that's the point!), the pinion can be smaller as well.

In the real world, there needs to be some material between the bore and the root of the gear teeth for a gear to hold up, but not a lot. Let's say 1mm of material is needed between the bore and the teeth making the minimum root diameter 10mm, or .393 inches.

This root diameter is just shy of the root diameter of a 15 tooth pinion. A 15 tooth 32DP gear has an outer diameter of ~.531 inches and a pitch diameter of ~.469 inches. Compare these to the smallest practical 20 DP pinion*, 12 tooth, which has an outer diameter of .7 inches and a pitch diameter of .6 inches, and you can see that the 32DP pinion can be much smaller.

This allows for a reduction in a smaller space, even accounting for the greater number of teeth on the 32DP gear. Say you want a 4:1 reduction. That would be a 15:60 pair in the 32DP example and a 12:48 in the 20DP example. The 32DP gearset center distance would be ~1.172 inches, while the 20DP gearset center distance would be ~1.5 inches.



This is a great way to demonstrate that a 32DP initial reduction saves space. Just use the AndyMark 15T and 60T models (they're just pitch circles, by the way) and compare them to either AndyMark or VexPro models for 12T and 48T gears. On 2791's 2014 robot, we used the 32DP gearset to save space in several large reduction gearboxes. Our winch would not have been able to nicely package itself at the back of our shooter, with the winch rope popping out around the middle of the gearbox, if we did not use the 32DP gearset.

Also, some tips on lightening gears: If you can, I would pocket the gears at their current thickness before thinning them. You can take a lot of material out of a gear by turning the gear on a lathe and thinning the material between the bore and the root, or by drilling a hole circle into the gear. Done right, strength shouldn't be compromised at all (teeth still fail first) and you'll save a dramatic amount of weight.

* An 11 tooth pinion that doesn't use the 12T pitch circle is possible, but it gets a bit weaker than I'm comfortable with, especially when the 11T with 12T pitch circle gear is both COTS and much stronger.

Wow, that's a much more dramatic effect than what I have experienced. I stand corrected.
I think I said what I said, than 32p does not save space, because I'm used to designing side-by-side CIM gearboxes. This makes 32p impractical, because you need a minimum center-to-center distance of 2.56 inches anyway.

[scottandme]

Originally Posted by asid61

Wow, that's a much more dramatic effect than what I have experienced. I stand corrected.
I think I said what I said, than 32p does not save space, because I'm used to designing side-by-side CIM gearboxes. This makes 32p impractical, because you need a minimum center-to-center distance of 2.56 inches anyway.

Sure, but only for that one usage case (2+ CIMS on a single gearbox).

If you're using non-CIM motors, or only 1 CIM, you can realize those gains.

See here for an example: http://media.team254.com/2012/08/gearbox.jpg

[Tristan Lall]

Originally Posted by Chris is me

You are right in that the first factor is the shaft size - obviously the pitch diameter can't be smaller than 8mm.

For the more adventurous, you can turn down the shaft diameter, and add an aftermarket gear (like the ones for the RS-series motors). You could also cut gear teeth in it directly.<sup>1

1</sup> For the most adventurous, if you really want to go crazy to prove the point that we aren't limited by the shaft diameter, and aren't averse to some creative fixturing and metallurgy, you might even be able to machine it, then harden it in place, and finish-grind the diameter (to maintain concentricity) and the teeth (to clean up the profile). That would permit a very small, strong shaft. This isn't remotely easy or cheap, and it's virtually inconceivable that any FRC team has ever tried it. You'd need a lot of very direct heat and a lot of heatsinking ability to avoid cooking the varnish in the motor or demagnetizing the magnets, while still changing the phase of the steel at the tip of the shaft. Then you'd need to quench it fast. And finish grinding of gear teeth essentially requires a custom fixture, which you'd have to build. (Note that if the next set of FRC rules have a definition of modification that allows disassembly of motors, this becomes a fair bit easier.)

[asid61]

Originally Posted by Tristan Lall

For the more adventurous, you can turn down the shaft diameter, and add an aftermarket gear (like the ones for the RS-series motors). You could also cut gear teeth in it directly.<sup>1

1</sup> For the most adventurous, if you really want to go crazy to prove the point that we aren't limited by the shaft diameter, and aren't averse to some creative fixturing and metallurgy, you might even be able to machine it, then harden it in place, and finish-grind the diameter (to maintain concentricity) and the teeth (to clean up the profile). That would permit a very small, strong shaft. This isn't remotely easy or cheap, and it's virtually inconceivable that any FRC team has ever tried it. You'd need a lot of very direct heat and a lot of heatsinking ability to avoid cooking the varnish in the motor or demagnetizing the magnets, while still changing the phase of the steel at the tip of the shaft. Then you'd need to quench it fast. And finish grinding of gear teeth essentially requires a custom fixture, which you'd have to build. (Note that if the next set of FRC rules have a definition of modification that allows disassembly of motors, this becomes a fair bit easier.)

Actually, you can open up the CIM and remove the shaft for machining. I distinctly remember one team did this. I think is was to allow CIM mounting to a versaplanetary.

[Tristan Lall]

Originally Posted by asid61

Actually, you can open up the CIM and remove the shaft for machining. I distinctly remember one team did this. I think is was to allow CIM mounting to a versaplanetary.

There are two issues: firstly, the definition of modification and secondly, the utility of removing the rotating portion of the CIM.

Modification isn't straightforwardly defined, particularly because it's difficult to account for the cases where something is disassembled, and then reassembled in a functionally-identical way. When the assembly was apart, it was clearly modified, but it is arguable whether reassembly restores it to an unmodified state, leaves it in a functionally-identical modified state that negates the illegal modification, or leaves it in a functionally-identical illegally-modified state.

As for removing the CIM shaft, although it's straightforward to open the motor up and detach the rotating parts from the fixed ones, I don't recall it being practical to remove the CIM shaft from the armature. As a result, overheating the varnish is still a concern (but overheating the magnets would not be). But you're correct that this would nevertheless simplify the process significantly.