chip3 actuator: back to CAD and design - speccing bearings! [updates]
Yesssss we know we wanted to do some design work - mechanical design work this summer and now before time runs out we want to start doing some work on the actuator design. Here's the plan for the actuator to design it from beginning to end:
First, design the parts of the actuator themselves, attempt to design the actuator for use with the Falcon 500 motor and with minimum backlash we want zero to as little backlash as possible.
Second, do assembly FEA on this design to improve assembly FEA skills and to actually see if this is something we'll be able to do. Try to FEA it as if it was 3D printed - do the research into that so we can design the component properly. If necessary, put in some hand-calcs.
We're going to 3D print a version of it and test for things like backlash and etc. We want to be able to quantify the backlash and re-design it if there is any.
Finally, we're going to get to software and to actually testing to see if the actuator works - verifying the FEA, the torque limits, generating torque speed curves and all the other good motor stuff. Relating torque to current and etc.
Let's start with the past work we did so we can get on track without re-doing all the calculations:
And without doing previous CAD:
Let's start with some of the engineering drawings we and Vex Pro did earlier and let's open up Fusion 360 so we can get started on actually designing this thing :). The plan is to make full-fledged part and assembly CAD, and then do assembly FEA, and then try to actually manufacture this thing. We'll need to spec bearings for this assembly later let's draw out a very basic parts diagram - exploded for the thing so we know what the CAD is going to look like. We're going to see below there are three bearings in the design so we'll need to spec them correctly: http://guide.directindustry.com/choosing-the-right-bearing/
Now I think, at first, it's important to decide what kind of bearings we want because knowing what bearings we want means we can find the bearings before we start designing most of the parts, and then we can actually put them into the CAD. So here's what I think we're going to do. Start with the bearings and then move to actually CADing parts.
There are three total bearings in the design, two of which are identical meaning there are two different bearings in the design.
The first bearing goes in-between the outer housing and the planet carrier - the center part of this bearing would either go around the planet carrier or connect to it making the it essentially the output of the actuator.
The other two bearings go in-between the planet carrier and the planet gears themselves which just allow them to rotate easier and makes the gearbox operation a lot smoother.
I will say some of this design is based off of the open torque actuator however, the idea is this actuator will be an all-in-one actuator with no need for an ODrive motor controller or things like that. Now let's get to what kind of loads these bearings will be sustaining.
So these are the types of loads on any bearing. The bearing at the end of this design has to support all three types of these loads because in robotics usually this actuator will be connected to a leg or an arm and from the FBDs from Chip - we can see that all three of these kind of loads will exist at the bearing. The other reason this one bearing needs to support all three is because in this actuator, we are theoretically trying to design something where this bearing holds all three of those kind of forces and allows the insides of the gearbox to operate in a simply radial fashion. Meaning the planetary gears and the sun gear should not have to bear any of those outside loads - they simply will transfer the torque.
So the loading at the interior bearings will look something like this:
Which means that that bearing in the middle of the planetary gear will be undergoing mostly radial loading - it shouldn't theoretically have to undergo anything else as long as the outermost bearing does its job. So let's start by speccing the inner bearing since we already came up with the gear ratios for this system and the number of teeth - here is that data: https://www.adim.io/post/chip3-actuator-updates-so-we-re-going-to-try-modeling-the-large-gears-yes-updates
So the MODULE of the gear is 0.5, the number of teeth on the inner gear is 14, the number of teeth on the outer-most gear is 252 and each of the planets have around 119 teeth for a total ratio of 19:1. The Falcon 500 has a max stall torque output of: 4.69Nm! And we can calculate the pitch diameters of all of the gears in the setup. In the last post we calculated the following:
Pitch Diameter Planetary Gears: 59.5mm
Pitch Diameter Sun Gear: 7mm
Pitch Diameter Ring Gear: 126mm
So now we can draw a FBD and figure out what the forces at the center of the planetary gears are so we know what forces the bearings will need to be able to width-stand so we can then spec them.
So now there's a few design considerations we need to have here. First - we now know that the teeth of the gears are experiencing a contact force at full-torque of like 1340N. That will be distributed over a few teeth and we configure out exactly how many teeth later but that's something to keep in mind along with these other things:
Gear contact force = 1340N
Force at center of planet gear = 2680N
So what this means is we need to design the planet carrier to be able to withstand that force and we need to be able to have the bearings withstand that force. This does tell me that while there are parts of the actuator that may be able to be 3D printed (possibly the gears) the shaft holding the bearings on the planetary carrier may very well have to be like steel or something. Let's do some hand-calc to find out what we're really looking for here in terms of material as well as what to design.
https://my3dmatter.com/fea-for-fdm-3d-printing/ this is something we really want to look at if we want to consider 3D printing these things instead of manufacturing them. We can use OptiMatter Forecast apparently to try to FEA 3D printed things. At the moment we're going to forecast with: https://www.amazon.com/eSUN-1-75mm-Printer-Filament-2-2lbs/dp/B01EKEMDA6/ref=pd_sim_b2b_2/143-2196587-5521301?_encoding=UTF8&pd_rd_i=B01EKEMDA6&pd_rd_r=9ee65763-1b4d-4be2-9393-5ad7607c708a&pd_rd_w=aIRq1&pd_rd_wg=a3Fa1&pf_rd_p=a07701e4-f565-442a-b97f-93ab23cbb7ef&pf_rd_r=1TSYKKP492GMX94XB6VD&psc=1&refRID=1TSYKKP492GMX94XB6VD ESUN PLA + just because we can't really print ABS.
Settings for FEA:FDM / PLA / Esun PLA+ / 100% / 0.1 / Honeycomb / Very small (1cm2)
So according to this chart our max stress is looking to be for PLA+ (which is the red) to be something like 44.9MPa in the x/y direction and it will yield at 38.5 mpa. And this is assuming a 1mm cross section for the part with 100% hexagon infill. In fact since we're comparing let's change the infill type and see what happens. Okay nothing happened diagonal was slightly less on the Max Stress and linear is the same. Remember this is at 100% infill and properly printed. What's our stress right now?
Stress: 2680N / 1e-6 m^2 = 2.9GPa
So that's like two orders of magnitude above the max breaking strength that print will definitely shatter if it is printed out of PLA. Let's compare it to ABS+. Okay for some reason ABS is less strong than the PLA in the x/y direction maybe because the layer bonding is harder. Either way it seems 3D printing out of PLA is not a good idea for this we might need to manufacture the planet carrier out of metal like aluminum. The shear strength of aluminum is 207 MPa - that's still too low for 1mm^2 if we make it 4mm^2 then we get
Stress: 2680N / 4e-6 m^2 = 2.9GPa/4 = 0.725GPa = 725MPa
And that number is still too high so now we're looking at steel for at least the actual interface between the planet carrier, the bearing, and the planetary gears. WE might have to look at steel for the gears as well since that's around 1340N. We'll also need to check if the shaft can handle that kind of force - the shaft of the Falcon 500 motor itself. Let's answer all of those questions before we even get to designing anything. These forces are very high.
NOTE: the above is inaccurate because it assumes all of the shear force is on one plane of the part which is incorrect. But we will verify this with FEA. This might not matter because at the base of the part we might need to widstand this kind of force anyways (at x=0).
We're going to start by FEA'ing the shaft of the motor itself using the materials listed on the website which is: Zinc plated steel. We're going to put the 4.69 Nm of torque on the one end and see what happens to the shaft if its only held by one tooth on either side.
We're just running with the material "steel" for right now - this will give us an idea if this amount of force is too much to handle for steel or if it will be OK. Remember the area of concern is really where the shaft meets the base because there's (a) a sharp transition, and (b) it'll be holding the full moment at that point. We are also concerned with the teeth. I'm going to assume VexPro designed this such that it would be able to widstand this kind of force on the teeth - however - because whatever this motor shaft is used for it would need to widstand the full stall torque. But that may be distributed over all of the teeth we are now checking if its okay when distributed over just TWO of the teeth.
Here are the results of the FEA and as we can see there's a large location where the safety factor is much less than one. But I do want to compare this to if we spread it across all the teeth as fixed. I want to see if that will fix it or if that will not fix it. And then we want to see at what point does it pass FEA because if this doesn't we may need to reach out to VexPro and ask what the material of the shaft is - the exact alloy.
As guessed. This thing also fails because I don't think we have the right alloy of steel not because the design wouldn't pass FEA. I do want to direct our attention to something though. In both this and the other one the teeth of the gear do pass FEA so we shouldn't be worried about the teeth breaking at the very limit of this motor's performance.
Let's do some analysis on a steel pin that could be able to hold the carriers. Just for kicks. So what we did was CAD a small pin with a 1in base and a 0.75in shaft and place 2680N of force on one half face of the shaft. We fixed the base but only the cylindrical outward facing face that would actually be holding forces in the planetary gear design.
So we can see here that:
And the maximum von mises stress is 113.6 MPa
The maximum stress in the XY plane is 17.66 MPa
And the maximum stress in the Z-direction is 59.52 MPa
Now we need to find a material - the lightest cheapest material that will pass this FEA. We want to use a pre-made part we don't want to machine anything because machining would drive the cost up and we're trying to keep the cost down. Now I want to go back to my 2.001 notes and check out what all this means.
Essentially what you'd have to do for any material is compare the yield stress of the material to the max Von Mises stress and you get a pretty good idea of if it is going to yield or not. Now this is mostly for metals so it's probably better to make the shafts of the planet carrier out of aluminum or steel. We'll find something after we spec the bearings. Bearings first and then we get to design the rest of this stuff.
Okay so back to the bearings - we need the inside bearings to be minimal in slop and we need them to widstand an axial load of 2680N. We also need them to be less than 126mm in diameter. Something not too small something like this: https://www.amazon.com/PGN-R16-2RS-Sealed-Bearing-Lubricated/dp/B07MWH2G8Z/ref=sr_1_9?dchild=1&keywords=1in+bearing&qid=1594846382&sr=8-9
We don't know if this supports the load of course let's see how we can figure that out. "The bearing Dynamic Capacity, C, is defined as the constant stationary radial load which a rolling bearing can theoretically endure for a basic rating life of one million revolutions."
According to amazon that bearing above with an ID of 1" and OD of 2" gives us a rated capacity of 5000N while stationary and 80000N while rotating. That's pretty much a safety factor of 3: https://www.linearmotiontips.com/difference-between-dynamic-load-capacity-and-static-load-capacity/ here's some more on dynamic vs static load capacity but either way I think we're OK.
So that's a R16-2RS bearing and it has an OD=2.00in and ID=1.00in and a W=0.5in. We'll go figure out what the tolerances are when we actually end up designing the part. But that does give us a 1in circular diameter inside. So this is a possible bearing. If we want to make it smaller we can go with others this bearing weighs around 4.1 ounces. There are 2 bearings for like 12 dollars.
The next bearing is much trickier because it needs to survive axial, radial, and moment loads. And the outer diameter needs to be like 240mm or something. We're looking at bearings that are like: HRE18025 or the: HRE20025 the second one being probably around the right size. This type of bearing is not a regular ball bearing but a crossed roller bearing because those can withstand forces in the axial and radial directions as well as moments. Ideally we would've wanted something like: https://www.vxb.com/RU445UU-Cross-Roller-Slewing-Bearing-350x540x45mm-p/RU445UU.htm?gclid=Cj0KCQjw0rr4BRCtARIsAB0_48PxKT-m-5h2TPPmH1URmJ0viOB7L8Bc779YTxH5gfL4QOt5JibZO6oaAp96EALw_wcB (of course in the right size) but for an open source actuator this just seems like too much money.
We're really going to look more into those kind of bearings tomorrow though.