• aditya mehrotra.

chip3 actuator updates: so now we might want to re-design everything! [updates]

In the last post: https://www.adim.io/post/chip3-actuator-bearings-and-initial-design-components-updates we talked about bearings, speccing bearings, and etc. But there are a few things in this design that I am genuinely worried about before we get to even anything else.

  • I'm worried about the plastic gears and I'm worried they'll strip after some time especially with how small the teeth are. WE might want to use larger gears but using helical gears for smoother transmission these are also better for higher load applications - which this is.

  • I'm mostly worried because of the max torque and the need for this gearbox to change direction quickly will shred the gears inside.

Important info for helical gears:

  • The helix may be cut either right hand or left hand. ... The maximum efficiency is a helix angle between 40 and 45 degrees, however a reasonable efficiency is achieved above 15°. Due to difficulties in forming the thread, helix angle greater than 30° are rarely used. So let's do some math on if we made a helical gear as the sun gear which fit over the shaft of the Falcon 500...

This is using the Sunderland system and module of 1mm. This gear has 16 teeth. So that means we can do some math to figure out the pitch diameter. D = N/P, N = D/m, so 16 = D/1 so D = 16mm. That seems abut right for this gear...

Now let's say we want the maximum outer diameter to be 126mm that's a helical gear with a module of 1mm and the number of teeth will be: N = 126/1 = 126 teeth. And the gear ratio would be (RING+STAR)/START = (126+16)/16 = 8.875:1 gear ratio. And that would produce a total of 8.875*4.69N = 41Nm of output torque which is the same as the open-torque actuator but I'm feeling better about this gear train than the last one. I also think we're doing our gear force calculations wrong so let's re-do them too. After we make a few more helical gears in CAD. The pitch diameter of the planetary gears would be 126. We're going to make the thickness of this outer gear as 30mm. Also since we know the pitch diameter of the outer gear is 126mm, and the inner gear is 16mm. PD of the planet gears would be 126/2-16/2 = 55mm. So we'll need some of those gears as well and we'll make them 25mm thick. We're doing this because we need to know how many planet gears we will have so we can actually do proper gear calculations. I think the last time we forgot to divide the force felt at one part of a gear by the number of gears there were. We should probably pop this up to a 9:1 gear ratio so the gears actually mesh.

  • (N+16)/16 = 9, 128teeth + 128mm. Which makes the planet gears need to be 56mm in diameter each with 56 teeth. So let's do that change too.

Now there are three gears which means each one will hold 1/3 of the force instead of 1/2. Yes we have a smaller may torque of 40Nm but we can also calculate exactly how much weight a robot leg could hold with 40Nm of torque... we'd just need to design whatever robot we were using to be light and nimble and isn't that what we want anyways? Since we're using the Sunderland standard for gears we can think about making a herringbone gear later.

  • herringbone gears do not produce an additional axial load. Like helical gears, they have the advantage of transferring power smoothly, because more than two teeth will be in mesh at any moment in time.

So this is the difference and I think we will take advantage of it using the herringbone gears and not the straight helical gears because we don't want to produce axial load on the gears themselves. Especially because the bearings inside the box will assume that no axial load is produced! So now lets do some math and then we can go back to square one when it comes to speccing bearings. The question is now, is 40Nm of torque enough for most of our robotics applications. Let's run this through Matlab to see. We made a script before that tells us the torque required to hold one of chip's legs up. Now let's assume the robot is the current weight of chip and that's 25kgs. At most we should see half of that on each leg. So that's 12kgs on each leg if two legs are down at the same time. And if we make the robot even lighter this time, it'll be less.

That's 30Nm of torque required to keep the platform standing. More to accelerate it at any speed right? And initially when getting up this thing spikes to:

47 Nm... see thats more than 40 which means this actuator is cutting is close for a design like chip2 because we'd never get up with only two legs but since the minimum to stand is two legs we should design for that. So we're looking at an actuator with 60Nm of torque at least which means...

60/4.69 = 12.79~13 --> a gear ratio of at least 13:1. Which would mean the following changes if we wanted the outer gear to stay at 128 teeth - we can't make the box much bigger:

  • (128+N)/N = 13, 13N-N = 128, 12N = 128, N = 10.66 teeth.. This would work if the outer gear was 120 teeth and the inner gear was 10. Let's see if that would fit on out shaft.

With a module of 1 - this gear is way too small at 10 teeth to be able to work for our application. It honestly might be better to go with the original design and give ourselves 89Nm of may torque. We're going to do that but we're also going to re-do the gear math and the bearing specs because I think we messed that up.

  • It's always good to verify what we are thinking with math... even if the above proved worthless for robots like what we want to make.

Now let's redo the calculations for what kind of forces the gears and shafts and etc will need to width stand. This will help us designate gearbox properly, spec the bearings, and then get to actually CADing the box, making it, and testing it! So now we have some more reasonable numbers:

  • The tooth force these gears need to survive is 670N and the force at the center of the planetary gear is 1340N. These are much more reasonable numbers. We might not even re-spec the bearings because I kind of like the design we came up with today. Because of how light it is.

Here's the right gear calculation - that was a dumb mistake but it does give me more hope that this design is actually going to be useful and survive. We'll have to 3D print it out of NYLON or some material that is strong with good layer adhesion.

So that's that!

#updates #omgrobots #design

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