Short update this week (although I’ve gotten a lot done), since I need to keep machining! Over the past week and change, I’ve finished mechanical design of the X axis; received a whole bunch of stock & components; started cutting parts; and talked to some very helpful bearing manufacturers.
PUPS 8/Lab 8
I’m mostly done with analysis & am actually cutting parts now – which means this PUPS is going to be heavy on the pictures and light on the text. First, the pictures:
First, I’ve (almost entirely) finished detailed design for the X axis! I completed both the motor mount & ball nut mount modules this week – this is a big deal, since both of these modules will be largely re-used in the Y and Z axes. The X axis presents an interesting design challenge that I won’t see in the Y and Z axes – namely, that the ball screw is quite honestly too short for the axis. I’ve made up for this by extending the ball screw bearing mounts under the table significantly (the two yellow T-shaped pieces at either end of the screw), and using the same mount block (albeit with different bearings & clamp components at each end).
I still need to finish detailing the handwheel mount (the right side of the table): thankfully, this isn’t hard, as I just need to add shorter spacers + a custom shaft to support my handwheel. I also need to add in mounts for the linear encoder I bought (not shown), although this is really an optional component – it won’t be used to close the control loop in any meaningful way, and it’s really just for my convenience.
I spent a fair amount of time detailing the motor mount assembly. It’s broken into two modules. The first is an upper module that bolts directly to the table using existing holes (well, on one side, at least). It supports the upper pulley at 2 points, and also holds the ball screw bearing mount. The lower module supports the lower pulley & motor. It swings from one of the spacers in the upper module on preloaded bushings, and is guided by slots cut into the mounts which travel along a different spacer. The drive belt keeps it from swinging away, and a pair of band clamps run between the spacers on the upper and lower modules to provide belt tension. (I may replace this with a lever or other cam-type locking mechanism someday – but for now, the band clamps will do fine!)
My last major victory for the week was coming up with a flexure mount for the X-axis ball nut. I’ve never designed a flexure before, and certainly not a multi-DOF flexure, so this was a useful exercise, which I’m excited to revisit in the future. After a few rounds of discussion with my PREP group, I finally put together a flexure design that is small enough to fit under the table of my machine; provides constraint in Z and C while allowing X/Y motion; and can be machined on the Media Lab waterjet. It’s loosely based on the Dancing Man flexure from the 2.72 lathe, although heavily modified for my particular geometry. Aaron walked me through determining that although the Stage 1 flexure (between the table mount and the intermediate stage) allows for translation and rotation, the presence of a second, matching flexure on the opposite side of the nut mount means that the rotation is constrained.
As I’m sure is clear from the images above, my design isn’t finished yet – I still need to optimize the thickness of the flexure beams. Right now, I’ve cut sample parts out of aluminum (I’m waiting for the steel I’ll use in the final version to come in), and I’m going to be experimenting with assembling the flexure. Because space is so limited, I can’t effectively screw the inner & outer layers of the flexure together at each stage. Instead, I’m planning to epoxy the layers together at each stage, and supplement with press-fit dowel pins to take some of the shear load.
Finally, for people just starting out with flexure design: Marcel Thomas’ introduction to flexures is an excellent first resource to read through, with links to other important works in the field.
Finally, some parts!
The other thing I did this week worth noting (detailed further in my PUPS) was test the on-axis stiffness & backlash of my mill in its original state, before I rip it apart & start bolting new components on. I measured .022″ of backlash and 5 x 10^7 N/m stiffness on the X axis; and .0175″ of backlash and 1.67 x 10^7 N/m of stiffness on the Y axis. For comparison, my spreadsheet estimates 1.76 x 10^7 N/m of stiffness in the X and Y axes. I am definitely concerned about this: my spreadsheet is designed to be extremely conservative, but I’d also feel a lot better if my expected stiffness was an order of magnitude – or two! – higher than what I’m currently seeing on the machine. This is largely due to the many constraints I’ve wrestled with in this design – particularly limited availability of non-flanged ball screws in the correct length at reasonable prices. My guess is that at the end of the day, though, the fact that the loads I’ve based my design around are outlandishly high – the motor required is 3 times the size of the one currently on the mill, and I’m cutting full-bore with a 5/8″ endmill – will give me more than acceptable performance for the light-duty machining I do at home.
For S&G this week, I wanted to showcase an extremely pleasant interaction I had with the folks at Timken Bearings regarding the spindle bearings of my machine. The spindle of the Benchmaster uses two Timken tapered roller bearings in the spindle. I was curious about the correct way to model these bearings, particularly given that their stiffness changes with preload. After calling Timken & explaining my situation, an extremely helpful application engineer got me all of the information I had requested – for both the TRBs my spindle uses, as well as a drop-in precision angular contact bearing replacement – along with information on correct bearing preload setting practice and more. The following plots are from the application sheet that Timken provided me:
(The plots show the stiffness of the smaller rear bearing in blue/red, and the larger front bearing in black) Unfortunately, as both the engineer and I noticed, the second plot seems to claim that the bearing stiffness actually decreases with preload. The engineer is currently confirming for me that this plot actually shows compliance, not stiffness – I’ll update as soon as I hear back from him. Regardless, though, the takeway from this for me is always get on the phone and call – companies are generally incredibly helpful if you’re willing to take a little time to get in touch with them. Thanks, Timken!