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 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 testing of this 39:1 dual cycloidal drive (see Test Results section) as I'm exploring 3D printed gear train types for an application requiring ~16Nm of torque, with a 30:1 to 40:1 ratio in a ~120x120x60mm (~4.7x4.7x2.4") 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 allow to almost double the eccentricity value.

Although most of them present performance drawbacks compared to cycloidal, like high friction losses or much higher 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, for specific applications.

Below is a casual exploration of tooth profiles for a 39:1 reducer with a 120mm outside diameter. 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 materials and require neither tight tolerances, nor low backlash, nor industrial reliability.

Happy abnormal explorations to all !

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ACG Profiles Exploration

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

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

An internal spur gear profile provides much more tooth engagement but would not work due to tooth tip interference:

One way to avoid interferences is to reduce further the number of internal teeth, like in this 40/38 example. However, that would halve the reduction rate 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 eccentricty is back down to 1.8mm, a value not very suitable when 3D printing plastics.

So, back to the 40/39 case: the tip interference can be reduced by increasing the pressure angle, but that's still not enough:

Decreasing the module of the internal gear would make it smaller, therefore 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 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 eccentricity is now significantly higher, which should be benefitial when 3D printing the gears. However, now the fully engaged teeth on the right side of the pic are clashing pretty substantially and will bind.

This can be improved by chopping off and rounding the tooth tips:

Success, the interferences are gone, and the eccentricity 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.

So let's switch to a trapezoidal profile, whose shape can easily be modified:

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

Interestingly, the first tooth to engage has shifted from the eccentric direction by ~38°. I'm unclear as to the consequences. We'll see how the load test goes.

The pressure angle is constant at 24.6°, which is a big plus over cycloidal drives with the same number of 'teeth'. It could even be decreased down to almost 0 by using a quasi-square trapezoid:

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

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, and I am planning to put that profile to the test, like was done for the dual cycloidal gear train (see Test Results section)

For comparison, here are the forces exerted on a traditional cycloidal disc at the contact points with the stator pins. They are far from tangential to the rotation of the output, unlike in most of the abnormal tooth shapes we just explored:

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 papers published in Asia, so no idea if it is the proper name or not ?

Change-speed gearing by Alfred Laukhuff, 1922