This project is a continuation of "90:1 Compound Cycloidal Reducer"
In the configuration shown, it is only useful as a desk toy. This is because I designed it to be a desk toy and I am going to give it to an old friend who is a great engineer.
The first development is a modification of the cycloidal profile of the disks. As you can see in the figure above, the lobes are no longer rounded. I have truncated the cycloidal profile of each lobe using a straight line. The truncation is selected such that 3 lobes of each cycloidal disk may be in mesh with the stator teeth.
In the previous work, all lobes of each cycloidal disk had a small area of contact with all stator teeth. This is interesting and satisfying geometrically but the structural analysis shows that only 2 or 3 lobes are carrying any load. The other lobes are sliding at a high speed which is a source of parasitic drag. Thus the truncated cycloidal disks represent an efficiency improvement over unmodified cycloidal disks.
The next development is the application of integrally printed ball bearings. In this configuration, there are two 4-point contact ball slewing ring bearings and two 2-point angular contact ball bearings. You can see these in the figure above.
The previous work aimed to eliminate the need for an expensive discrete off the shelf slewing ring bearing because the cost of that class of component makes them less accessible. By 3D printing integral ball bearing races into the components, we can implement a much stiffer gearbox without significantly altering print time.
The rolling elements are next-level inexpensive. They are 6mm Airsoft pellets which can be purchased for around 15 dollars for 5000 quantity. This assembly uses ~55 in total for a total added cost of 16.5 cents.
The first 4-point contact ball slewing ring bearing is easily seen in the figure above. It is the largest diameter set of rolling elements, there are 31 rolling elements in the figure above. This large bearing supports the output stator.
You can see a cross section of this assembly at the left side of the figure below. The 4-points of contact allow each rolling element to support axial axial loads in both directions with zero backlash. This allows for thrust and even overhung loads to be supported on the gearbox. The compromise is that by utilizing 4 points of contact in the ball bearing race, there are much larger areas of sliding contact which gives rise to parasitic drag torque.
The second 4-point contact ball slewing ring bearing connects the cycloid stack to the eccentric. You can see it to the right of the figure above, in between the top and bottom angular contact ball bearings. It supports the cycloid stack against tipping over inside the assembly under load which would cause the assembly to jam.
This is a very bad place to put a 4-point contact ball slewing ring bearing because it is the highest angular velocity interface, so the increased drag torque of the bearing represents a proportionally large parasitic power loss. I used it here because this is a desk toy and I wanted the assembly to have minimum axial dimensions. With more axial space I would use two opposed and preloaded 2-point angular contact ball bearings.
The two 2-point angular contact ball bearings support the eccentric input shaft at either end of the assembly. They have higher efficiency than 4-point contact bearings because the rolling element is free to spin about an axis that minimizes sliding contact. Separately, 2-point angular contact ball bearings can only support axial loads in one direction and radial loads in no directions which is why they are found assembled in preloaded and opposed pairs. As you can see in the figure above, they are opposed so that the bottom bearing supports axial loads upwards and the top bearing supports axial loads downwards. Thus the eccentric input shaft is constrained concentrically and axially inside of the assembly. These end support bearings react all of the loads from the eccentric.
I leave it as an exercise to the reader to derive a formula for reduction ratio given A lobes on the large side and B lobes on the small side. In this example, there are 10 lobes on the large side and 9 lobes on the small side. The total gear reduction is 90:1. Please leave your formula in the comments section below.
