Abnormal Cycloidal Gear Profiles

A main inconvenient of Cycloidal Gear Trains is that, for a given volume, the higher the reduction ratio the lower the eccentricity value. This can result in a very short tooth engagement and, consequently, small tooth contact areas that can only handle light loads.

Although this isn't much of a problem for metal parts, which can be produced with exquisite precision on CNC / EDM machines, it soon becomes an issue when using softer PLA / ABS / PA materials like in 3D printing. This was demonstrated to failure during the test of this 39:1 dual cycloidal drive (see Test Results section) (as I'm exploring 3D printed gear trains for an application requiring ~16Nm of torque, with a ~36:1 ratio in a ~120x120x60mm volume).

Meet Abnormal Cycloidal Gears (not sure that's the right name, see Resources section) that replace the cycloidal tooth profile with profiles such as spur gear, trapezoidal, square, etc, and can almost double the eccentricity value:

Although most of them present performance drawbacks compared to cycloidal, like high friction losses or backlash, they can significantly increase the tooth contact area, widen the tooth root, and produce a pressure angle almost tangential to the pitch diameter. All this can translate into much higher max load torque and longevity, in specific situations.

Below is a casual exploration of tooth profiles for a 39:1 reducer. The techniques covered can be applied to other drives.

This post is just an introduction, and applies only to 'sloppy' production techniques fit for applications that use plastic and require neither tight tolerances, nor low backlash, nor industrial reliability.

Fun abnormal explorations to all !

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ACG Profiles Exploration

All profiles assume a ~120mm pitch diameter for the stator, 40 stator 'teeth' and 39 for the disc, unless otherwise mentioned.

A cycloidal gear train with a 39:1 ratio and a ~124mm pin ring diameter is limited to a 1.45mm max eccentricity. That doesn't leave much overlap between the disc teeth and the stator pins:

Alternatively, an internal spur gear (ISP) profile provides much more tooth engagement but would not work due to tooth tip interference:

Many studies have been published about the conditions to meet to avoid tooth tip interference in ISPs, several are listed in the Resources section below. But they all require a level of familiarity with profile equations that I don't have, and I couldn't find an online easy-to-use ISP generator. So this exploration will consist in monkeying around: tooth shape, module, modified profiles, etc.

Let's start McGyving this: one way to avoid interference is to reduce further the number of internal teeth, like in this 40/38 example. However, that would halve the reduction ratio from 39:1 down to 19.5:1.

Or one could use smaller teeth, and maintain the 40:1 ratio by doubling the number of teeth. But now eccentricity is back down to 1.8mm, a value not very suited to 3D printed plastic parts.

So, back to the 40/39 case: the tip interference can be reduced a bit more by increasing the spur gear's pressure angle. But that's still not enough:

In addition, decreasing the module of the internal gear would make it smaller, which should lower the amount of tip interference. However, mixing gears with different modules is mechanical engineering anathema (poor meshing, backlash, losses...) but, since my application only uses ductile plastic and performance is not critical, let's give it a shot:

This is trending in the right direction as the tip interferences are much smaller. Also, the 2.5mm eccentricity is now significantly higher. However, the fully engaged teeth on the right side of the pic are now clashing substantially and will bind.

This can be improved by chopping off and rounding the tooth tips, and shifting the internal gear left a smidge or reducing its eccentricity a tad:

Success, the interferences are gone, and the eccentricity actually even increased. However, the teeth now have a smaller contact area.

At this point there's only little that can be improved further when using spur gear profiles.

But since the shape of the teeth in the previous attempts evolved more and more toward a trapeze, let's switch to a pure trapezoidal profile and see if further 'gains' can be had:

That profile results in no interference, large tooth contact areas, and a manageable 2.7mm eccentricity. Great !

Interestingly, that's when I realized that the first tooth to engage was now ~38° off from the eccentric's direction. This is one of the drawbacks from mixing different module values. I'm not clear about the consequences yet. Will see what happens later during testing (update: no issue, see test results).

The pressure angle is now constant at 24.6°, which is a big plus over cycloidal drives with the same number of 'teeth'.

For comparison, here are the force vectors on a traditional cycloidal disc at the contact point with each stator pin. They are far from tangential to the pitch diameter, resulting in a high average pressure angle, unlike in most of the abnormal tooth shapes explored here:

And we could even get the pressure angle down to almost 0 by using a quasi-square trapezoid:

However, when designing for high load torque, the root of the square teeth might now be too narrow and fragile. But, since in my winch-like application only one direction of rotation experiences the highest torque (when pulling the rope, not so much when unspooling), the shape of the teeth can be asymmetrical, thus allowing for much larger tooth roots:

Et voila, c'est emballé. Thanks to its large tooth roots, large contact areas, and extremely low pressure angle, this gear profile would likely fare well if 3D printed with plastic.

Of course it is absolutely not optimized for wear or backlash. And the substantial sliding-under-load motion experienced by the teeth will noticeably impact efficiency and lead to fast abrasion. But again, that's not the focus for this exploration. So next we'll put this profile to the test, like was done for the dual cycloidal gear train (see Test Results section), as the proof is in the pudding.

update both an ACG concept toy model and a robust version with bearings were designed and documented, including the 16Nm torture test, in this post: Dual Abnormal Cycloidal gear train

Note: all the spur gear profiles were generated in Fusion 360 via the Spur Gear add-in:

Resources

It is unclear to me if Abnormal Cycloidal Gear train is the proper name for this gear type. Couldn't find many references, and most papers are behind paywalls. The ACG moniker seems to show up mostly in translated papers from Asia, so no idea if it's the proper academic name or not ?

Change-speed gearing by Alfred Laukhuff, 1922