chip3 actuator: bearings, and initial design components [updates]
Okay so yesterday: https://www.adim.io/post/chip3-actuator-back-to-cad-and-design-speccing-bearings-updates we looked at some initial forces on parts of this gearbox, we looked at. Yesterday we specced out some bearings for the middle part of the gearbox but part of me says those are way too big and we didn't look at our own dimensions closely enough so let's go re-look.
Pitch Diameter Planetary Gears: 59.5mm
Yea so we messed that up a little bit. So we need to go find some bearings that aren't 2in on the outside because those wouldn't work so well. Ball bearings that can take the axial force we required of 2680N. So if its. 59.5mm on the outer diameter of the gear we don't want to go above 30mm. And we don't want to go less than 10mm on those inner diameters so let's see: https://www.amazon.com/PGN-6200-2RS-Sealed-Ball-Bearing/dp/B07CHSPJF3/ref=sr_1_1_sspa?dchild=1&keywords=10mmx30mm+bearing&qid=1594911593&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyR0kwR0o3Sks3QTlNJmVuY3J5cHRlZElkPUEwMzI3MDkyM1M3M0pIQ1dMUjFLNiZlbmNyeXB0ZWRBZElkPUEwMzkyNjUyMzlaMlo5MlJJMFdWQSZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU= here's a 10x30x9mm bearing on amazon. There doesn't seem to be any specs anywhere on if this ball bearing can survive loads so we need to look harder or we need to look elsewhere. Okay found it on AST bearings:
"Dynamic load ratings are determined by bearing geometry, number and size of balls, bearing pitch diameter, and ring and ball material. This load rating is used in conjunction with the actual applied radial load to calculate bearing fatigue life."- AST Bearings
"The static load rating relates to limiting loads applied to non-rotating bearings. The static load rating depends on the maximum contact stress between the balls and either of the two raceways. It is affected by material, number and size of balls, raceway curvatures, raceway depths, and contact angles. It is also based on using clean, high quality bearing steel with typical hardness levels of 58-64 HRC for rings and 60-65 HRC for balls."
"Basic Static Load Rating
The basic static radial load rating(Cor) applies to bearings which rotate at very slow speeds, subjected to very slow oscillations, or stationary under load. It should be considered when heavy shock loading occurs to a rotating bearing."
So what this means is, since the 2680N load would be applied when the bearing is STATIONARY since that's stall torque we need to consider that number. And this bearing will fail at this rate so onto another. We'll come back to the formulas above though:
Looking at bearings here:
https://www.grainger.com/product/BL-Radial-Ball-Bearing-35JA14? --> this one doesn't have a high enough static load rating.
https://www.grainger.com/product/BL-Angular-Contact-Ball-Bearing-35HY85? here's an ANGULAR CONTACT BEARING - 10x30x14.3mm and it has a 850lbs Static Load Capacity. Which means: 3780.993134N which is a safety factor of 3780.993134/2680N = 1.41! So that does pass.
I also want to calculate the life-span of the bearing like it says above. This bearing has a dynamic load rating of 7117.154592N. We can do this with the torque-speed curve of the motor and find the most efficient location of operation of the bearing, we'll do this later.
The MAX RPM of the bearing is: 19000 RPM, the max speed of the Falcon 500 is 6380 RPM, the speed of the planetary gear is less than that since it is larger than the sun gear. So we have a safety factor there of at least 3. Let's calculate it anyways.
14 teeth/119 teeth*6380RPM = 750.5RPM 19000RPM/750.5RPM = 25
Ya that's a safety factor in speed of 25 so I think we're doing OK. And that's at free-running speed of the planetary gearbox.
So we've decided on our bearing for the planetary gears as a 5200 ZZ/C3 PRX Angular Contact Bearing. Which has a 30mmOD and a 10mmID. So now we can do more actual calculations on the shaft requirements we need.
So what this shows is the bearing itself and the design of the inside of an angular contact bearing. Angular contact bearings need to be mounted in a very specific way because of their interior design.
To counteract certain loads we need to mount them in certain directions: https://www.sciencedirect.com/topics/engineering/angular-contact-ball-bearings
To counteract theaxial load, these bearings are must be fitted in pairs. Normally three types of pairs are made: face to face, and tandem and back to back.
1 Back-to-back arrangement - It can accommodate radial loads and axial loads in either direction. As it has a large distance between the acting load centre of the bearing, and therefore a large momentary force load capacity. Allowable misalignment angle is small.
2 Face-to-face arrangement - It can accommodate radial loads and axial loads in either direction. As it has a smaller distance between the acting load centre of the bearing, and therefore a smaller momentary force load capacity. But it can be used where more misalignment angle is required.
3 Tandom arrangement - It can accommodate radial loads and single direction axial loads. Axial loads are received by both bearings as a set, and therefore it can handle heavy axial loads.
So this is more if this bearing needs to sustain axial loading. Since we don't think the bearings inside the gearbox will need to sustain much axial load, we'll load the bearings like this and only use one:
If we look at how an angular contact bearing actually works this makes a lot and a lot of sense. Just scroll up and look at the lines but now that I'm looking at this - there might be a big problem with this design. The load center of the bearing is past the assembly. I don't know enough about bearings to know if the load center of the bearing needs to be within the assembly. So the question is, we aren't loading the bearing on the load-center what happens if we load it off center?
So time to go ask a friend who's a MechE what this means and learn something new :))) I really don't know that much about these bearings if I'm being honest.
Another thing I just noticed while staring at this is it really isn't preloaded properly because that's only true if that gear is rigid but it isn't so we're actually looking at THIS kind of a design.
This is the correct mounting of an angular contact bearing IT's two bearings mounted opposite because one angular contact bearing will not be able to constrained correctly in the above design. I don't think we want to use two bearings so what that means is we probably should go looking for a different type of bearing.
INSERT ANSWER TO ABOVE QUESTION ABOUT LOADING:
While they're responding I want to do the next step which is FEA a 10mm steel shaft and see if it passes the loading conditions. Because if the shaft is 10mm (or if we end up using a 10mm bolt) that'll be made of steel. We'll also try aluminum to see what would happen. We'll FEA this with bolt preload properly later - but for now I want to just see what a 10mm steel shaft can sustain. We're going to FEA with Carbon Steel and change that to the steel they use in bolts later. So we're going to solve this FEA similar to if there was a bolt in here taking that kind of load and see what this means for our design.
So it does barely pass. I don't think we'll ever be reaching these loading conditions but since it barely passes it's going to require some testing to see if this will actually work. We're going to need to re-evaluate this design after we properly FEA it with things like a bolt and the spacers. It's also important to note where this thing has a minimum safety factor of 1.08 - it's at that seam because it's a sharp edge. If we filleted something like this it might raise the minimum safety factor. We won't do it right now for purposes of FEA and etc.
Looking for new bearings. Because the bearings above, the angular contact ones, won't really work well in our design because we won't be able to mount them how they're designed to be mounted... now looking online I came across this... https://www.grainger.com/product/INA-Needle-Roller-Bearing-4XFH2?
These roller bearings have a much higher Static Load Capacity than the angular contact bearings or the ball bearings. There's also combination ball/needle roller bearings which: "reduces the wear from adjacent shaft components while the needle roller bearing supports radial forces." - McMaster.
So these are likely the kind of bearings we want to use with a 0.5in shaft. Why do we not want to use the angular contact bearing? Because weight matters in this application. So we can now come up with a much better design than before for this assembly.
So the shaft gets glued into the Planet Carrier, the bearings get glued into the gear, the gear slides onto the shaft and is held in place, constrained by spacers on the shaft and the back-wall of the gearbox. And these bearings are more than rated for the axial forces they will be assuming.
Now that we've chosen a ball bearing we want to choose a shaft for that bearing. We need a 0.5in steel shaft and we're going to figure out the length later and then spec the shaft. Since we haven't figured out the length we can't actually spec the shaft yet since we'd prefer we bought them and didn't have to cut them.
So now that we've specified the bearings we're going to use for the gears in the drive trains itself. We're going to work on specifying the bearing for the outside of the whole frame as well after we do some calculations on the kinds of forces and moments that thing needs to withstand. So we're going to work on that tomorrow. We've also been looking at the design of this: https://hackaday.io/project/159404-opentorque-actuator just to see. I'm really worried about plastic gears with such small teeth stripping away so we're going to have to see what we can come up with - maybe we even need to drop the ratio down but since the whole platform would be lighter this is OK.