32DP gears have seemed appealing for lightweight, compact reductions. However, my team has stuck to 20DP gears just because that’s what we’ve always used.
I’d like to avoid settling for this sort of propriety, so my question: besides empirical testing, how can I take a system for which I know the necessary gear ratio, max torque to be applied through the gearbox, and an estimate for max load (e.g., on impact), and determine whether a 32DP gearbox would be suitable? (Are these reasonable parameters to define a system?)
The tables provided by manufacturers make this sort of analysis quite easy for belts, but I’d like to be able to do similarly and justify the selection of 32DP.
To extend that further, is there an analytical way to determine if certain stages of a gearbox (such as the earlier stages, which should see less torque), would satisfy the torque spec we’re looking for with 32DP gears? Most of the 32DP gears sold contain a 3/8" hex bore, so would it be necessary to consider the torsional stiffness of the 3/8" hex axle in case that is a limiting factor (as opposed to 32DP gear teeth)?
This is not the answer to your question at all, but it’s an important and related point: while in theory, 32DP gears can provide a more compact reduction than 20DP gears, in practice in FRC, it’s often not the case.
Consider that if you are trying to create a significant reduction in a small space, (which is part of the premise of your question), you will largely be limited by how small the driving gear is. That, in turn, is limited by the shaft you are using. So, for example, on a half inch hex shaft, the smallest you can generally go is 18 teeth on 20DP gears. (maybe 16 or 17 if you push it). Let’s use 20T to keep the math simple, so a 1” diameter. To get a 2:1 reduction, you need to use a 40T gear, with a 2” diameter. So total space is 3”. For a 32DP gear, you can get 32 teeth on that 1” gear (which is roughly the smallest you can put on a half inch hex shaft), and to get the 2:1 reduction you need a gear with 64 teeth, which would be 2”… for a total of 3” of space - the same as with the 20DP gears!
This is a bit of an oversimplification because you can squeeze things a bit more because the shaft can get closer to the edge of the gear with the smaller teeth on 32DP, but that is just a marginal advantage.
Even on the 550/750 types of motors, the 32DP pinions aren’t much better. The smallest 32DP pinion I know of is 12T, and the smallest 20DP is 6T, which allow for very similar reductions in a given space.
For a few years some of the common FRC vendors were really pushing the 32DP gears as a way to save space, but I think that as people started to recognize this concept, you saw them being marketed less and less.
We’ve used 32DP gears frequently in the first stage of gearboxes. In that application, it’s hard to get a bigger reduction in the same space using 20DP gears. Andymark sells a 15 tooth pinion in 32DP for a CIM-size motor which has a PCD of 0.46". If you’re using a 550 or 750 size motor, you can get PCDs down to 0.325"
Compare that to a 10 tooth 20DP pinion which is 0.5". So making a comparable reduction in one stage from a CIM is going to need ~8% more width in 20DP, which isn’t much, but not nothing.
Some caveats:
The press on pinions may not fit NEO 1.1 motors well because of a shaft tolerance change. With a key, you’re back up to 20 teeth / 0.625" PCD.
The new Vortex motor apparently will offer a 7t 20DP pinion with a PCD of only 0.35"
The AM Sport and Rev Max Planetary gearboxes are reliable and reusable, so making your own spur gearboxes is less valuable than it used to be.
32DP gears have weaker teeth, and may not be suitable for second or third stages that apply more torque. (There are standard gear formulas to calculate this.)
There is something to be said about only having one gear system in stock for future reuse, and if that’s your preference, go with 20DP.
Where are you finding a gear this small? That would be a very undercut tooth profile
[Edit] found it, for 775 and 550 motors. Neat. I know that some teams have reported more wear with pitch-shifted pinions, so I’d love to hear any opex about these in particular.
I personally haven’t seen a strong need to use 32dp gears since moving to 100% NEOs in 2022 (were already getting away from it in 2020). Back when we were using 775s, 550s, BAGs, etc we would use 32dp gears regularly as our first stage. Most of the press fit pinion gears for those motors were 32dp and we found tons of compatible RC car pinions. I can’t remember ever using a 32dp pinion on anything larger than a 5mm shaft.
2022 and onwards we’ve been using timing belts in place of 32dp gears. For us they offer similar enough reduction options, more flexibility for mounting, and we have had a lot of success printing the larger driven sprockets allowing us do dial reductions in better.
That’s not to say there isn’t a place for 32dp gears but it’s not as prominent of a place as it was 5 years ago.
@SndMndBdy put it well, every time I tried to design with 32 DP in mind I ended up not really saving much space. I see it the same as GT2 3mm belts, sure I can use them, and they are technically smaller, but at the end of the day I’m not saving much and the downside is needing to worry about stocking components for an entirely different standard.
I’m sticking with HTD 5mm and 20DP for now and spending my time on other optimizations.
-I don’t have the math to prove it, but anecdotally I’m pretty sure that the 20DP gears are more forgiving to imperfections in machining. For example, if your center-to-center distance on 20DP gears is machined 0.005” too small, it won’t be too big of a deal. But the same inaccuracy on a 32DP gear will really bind it up.
-As mentioned above, the 7T pinion for the Vortex is really exciting here because it allows for significant reductions in the smallest spaces we’ve ever seen in FRC spur gear boxes. They are able to achieve this because the gear doesn’t need to fit on a shaft - it is the shaft!
-All this being said, if I need a mechanism that’s going to be driven by a 550/750 motor with a single reduction, I’ll still often consider the 32DP gears, particularly if I don’t have any of the 6T 20DP pinions on hand, or if the ratios don’t quite work out with the 20DP gears that I have on hand. The 32DP gears are generally fine in such a case.
As I found out several years ago, it’s not just the centre distance: if your gear bore is not concentric to the teeth, you can spend a lot of time applying lapping compound to expensive hardened steel gears to make it work. (188 used a wire EDM to enlarge a bore and cut a keyway; our alignment in the machine was imperfect. We therefore mounted the gears in their plates, and lapped the teeth against each other until the binding subsided. It worked well enough as a salvage operation.)
There is definitely a way to make robots with nothing but 32 pitch gears all the way through, if you’re so inclined. But consider the requirements in more detail:
Why 32 pitch, specifically? If you could have similar weight or moment of inertia out of a coarser pitch gear, in a similar packaging volume, with maybe a little less efficiency, would you be satisfied?
Are you trying to hit a cost target, or just not run afoul of the parts utilization rules?
Are you trying to standardize on a single product line or system?
Are you willing to spend (possibly a lot of) money on custom parts, or custom tooling?
Do you want to spend a lot of time learning how, or are you more interested in the ultimate performance of the robot?
How many copies of this do you want?
My feeling is that given the sizes of motors likely to be encountered, and the reductions you’re likely to want, a first stage in something like 32 pitch or 0.8 module (31.75 pitch) is perfectly reasonable without much difficulty using minimally modified stock parts. Making the rest of the drivetrain out of this same size gear is what is going to trigger all the special considerations.
For analytical methods, the Lewis-Barth bending calculation estimates the strength needed for a tooth, conservatively. The AGMA method is more about gears in long-term service. If you just want stresses, it is possible to do finite element analysis of the teeth. You can extend these methods with dynamics (to physically represent shock loads and material elasticities), or you can somewhat arbitrarily select a large design factor to guess at the effect of an impact.
The only reason to use 32 dp in frc is backlash imo, but it’s worth it in scenarios you want very fine control
" As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch; the minimum being 0.03 divided by the diametral pitch and the maximum 0.05 divided by the diametral pitch.[3] In metric, you can just multiply the values with the module:"