[RCaffin]

Harmonic Design Mounting and Performance

Recall the coloured drawing of the HD unit from the previous chapter. The largest diameter part was in blue, and is the obvious part to bolt down to the frame. It not only supports the magic spline, it also supports the Crossed Roller Bearing (CRB). In fact, the 16 M4 cap head bolts used to hold it onto the frame are also required to hold the CRB together. Yeah - this thing is engineered. The green bit is equally the obvious bit to be the rotating output, and the 16 cap head M4 bolts there are also required for holding the bearings and the Harmonic Spline together. (So I went and bought a bag of non-Chinese M4 cap head bolts and matching nuts.)

Which is all very well, but this configuration means the division ratio is actually N+1:1, not N:1, so my unit has a slightly awkward 51:1 reduction, not the basic 50:1 shown in the unit designation. That is due to the way the spline inside works, and there is no getting around the N+1 bit. That means that a unit quoted as being 100:1 will, if used this way, have an actual reduction of 101:1, and so on.

I did look at mounting the unit off the green part (to get the 50:1 ratio), but putting a chuck onto the blue part was mechanically more difficult. While thinking about this I discovered that the 51:1 ratio was actually quite manageable, so I left it like that. More on that later.

Attachment 272012

Obviously, the thing to do here is to carve a shaped hole in a thick plate of metal to hold the HD and be a 'front panel' for the rotary table. Yes, the outside rim is on the other side of this plate. With no less than 16 cap head bolts holding the HD into the front panel, the basic design looked fairly robust. A thick front panel will be needed of course to handle the profile of the mounting.

In this context it is worth checking the details on the engineering drawing I showed before. Certain dimensions have a fairly tight h7 tolerance quoted: these are the probably best faces to use for the mounting. So machining the big hole and drilling the small bolt holes to that accuracy was an obvious requirement.

Attachment 272014

So I will just mention here that all the machining was done on my CNC, which easily holds 10 microns. That meant everything was machined to 10 - 20 microns accuracy, and all the parts just went together without any adjustment. Bolt holes were perfect: holes for M6 were drilled 6.0 mm and so on. I could not do that with manual marking and machining - no way!

Having bought the HD unit and decided on using it, I wanted some preliminary idea of how good the HD might really be. In particular, what sort of backlash does it have and what sort of load compliance does it have. Backlash is reasonably well known, so I won't explain that, but maybe I should explain what I mean by 'load compliance'. It means rotational stiffness: how many degrees will the output twist when torque is applied to the output?

The easiest way to measure small rotations is to measure small movements at the end of an arm bolted to the output stage - while placing the load somewhere else! You can't use the same arm for creating torque by loading the arm and for measuring the rotation: all you will do is measure the bending of the arm. I tried using a conventional dial indicator for this at the end of an ~200 mm arm, but the DI was only sensitive to 0.01 mm (smallest unit on dial). "Only", he says. So I made up an electro-optical sensor able to go down to well under 1 micron. You can skip the description if you wish.

Attachment 272016

I had some old IR LED emitters and photo diode detectors designed for fibre optic cables. These have fibre-optic-type glass fibres at the output and input, and the fibres are about 100 microns in diameter. The fibre diameter means you go from unblocked to blocked in 100 microns. That's moderately sensitive. I mounted one of each in a coaxial arrangment and put a blocking vane through the gap between them, as shown here.

Some electronic circuitry was needed to drive the emitter and to amplify the sensor output: this is not shown in the photo (because the photo was taken while I was building the sensor). The output was read with a DVM.

Technical explanation: when you shine X amount of light on a photo diode, it gives out a current Y. Within broad limits, any changes in the amount X will cause similar changes in Y.

Do I really expect to get sub-micron accuracy out of a lash-up like this? In short, yes. But note the restrictions on use: there are no forces on the sensor and it is not meant to be a commercial unit, able to withstand rough treatment. It works for me, but that is because I built it and I understand its limitations.

Attachment 272018

Then I mounted the HD on a steel plate, added some arms and the sensor, and was ready to measure. Well, actually, this photo was taken only part way through the construction as well, as the gold leads on the emitter don't yet go anywhere. Note that the upper arm going to the black sensor block is purely for sensing: any loads go on the lower arm. Note also that all metrology stuff is referenced to the flat vertical plate to which the HD is bolted. They are out of the bendable regions. Trying to put a magnetic DI stand on the horizontal base part was a complete failure, due to flexing of the steel around the bend.

Before going any further I had to calibrate the sensor: convert microns of movement at the flag to milliVolts out of the sensor. Better note here that this calibration will apply only to this exact arrangement. If I change the arms at all, I have to recalibrate. But this set up gave me an idea of how well the sensor arrangement worked, and it also gave me some idea of how well the HD worked. That's all I wanted at this stage.

Attachment 272020

To do the calibration I mounted a third arm, at the back on the input, and drove it with a long-throw (Mitutoyo) micrometer. Now I could rotate the input axle in steps of 100 microns at the input arm radius (or smaller), go through the known 51:1 reduction ratio, and measure the change in output voltage from the sensor. By knowing the length of the input arm I could convert the microns of movement at the micrometer to degrees of rotation at the input to the HD. In addition, by knowing the 51:1 reduction ratio, I could also get the output rotation in degrees from the input rotation. Yes, that assumes that the reduction ratio is as claimed, but that seemed reasonable.

(Interpolation: I am a retired PhD physicist, and I have spent most of my career developing measurement technologies. They all worked, so this is 'fun games' to me, and I had all the necessary stuff in stock.)



The first thing to do was to look at the linearity of the sensor. Since the light beam is round, I did not expect a simple straight line between input movement and output signal: rather I expected an S-shaped curve. And the graph here shows just that: the vertical axis is mV while the horizontal axis is microns of movement at the end of the output sensing arm. Microns of movement at the output were calculated from microns of movement at the input micrometer, the ratio of the lever arm lengths, and the HD reduction ratio.

Don't pay a lot of attention to the actual numbers, as they depend on several factors which could and did change later; just note the nice S-shape of the curve. Obviously this is not a general-purpose linear sensor, but the middle region is quite usable, even if the outer edges are less so. The shape is what matters, and it confirmed my expectation of an S-shaped curve.

Around here I had to repeat the whole first set of measurements. I was finding a steady drift in the results: a drift I did not believe. (Long experience helps.) After some ferreting around I realised that I was driving the IR LED emitter rather hard, and that it was warming up. That meant its output was slowly changing. Oops. So I reduced the drive current and the sensor became satisfactorily stable. If I left the system just sitting there for 5 minutes, the DVM reading stayed about the same (give or take 0.1 mV). The moral here is to never believe the results from the first few experiments: always repeat them a few more times until the results are stable - ie until you have the bugs out!



Having first driven the HD in one direction to look at the shape of the sensor response (to see what was happening), I was then able to drive the HD back and forth a few times to look at the hysteresis in the drive. That is, the micrometer went up and down a few times, in very small steps. The bent bits at the extremes of the loops are probably the non-linearity of the sensor, but the fact that the loop does not retrace exactly on itself in the middle tells me that there is some hysteresis in the spline drive. The path in the forward direction is not exactly the same as the path in the reverse direction.

The data starts at the top open-ended curve and goes in a 'loop' anti-clockwise. The 'loop' actually represents data from about 5 cycles. After the first lead-in, the loops overlay each other, which was really pleasing. It meant the data was fairly reproducible.

Well, it would be pretty amazing if there was no hysteresis at all. In fact, this preliminary graph suggests there is about 0.0062 degrees (0.37 arc-minutes or 22 arc-seconds) of hysteresis, under no load. To be sure, the result might be out by 10 - 20% but it is not incompatible with what I was able to get from the Harmonic Drive data sheets. I dare say some commercial RT units can do much better than this - but they also cost a whole lot more.

Actually, getting this sort of information from the HD data sheets is difficult: they are far more concerned about operation under high torque loads and lifetime under overloads. I guess that makes some sense: this is a gearbox, after all. I was not expecting to load the HD spline quite that hard anyhow.

If we are going to fuss about the details, I had better add that it is possible that the hysteresis might be slightly different if I rotated the HD output by 90 degrees. I don't have any guarrantee that the HD spline is absolutely uniform all the way around. Well, true, but I am not quite that fanatical.

You might say 'so what?' to all these measurements. Well there are good reasons for knowing about this. If the rest of the hardware (ie the motor) could only turn the HD in 10 arc-minute steps, I would be wasting some of the performance available. On the other hand, if I tried to get a resolution of 0.05 arc-minutes from the system, I would wasting a lot of my effort and getting no-where. The thing to do is to find what is a reasonable expectation from the HD, and to design everything else accordingly. Equally, with this sort of good performance, the rest of the housing had better be rigid enough to match. Tin plate will not do.

In the next chapter I will look at the performance under load. How much will the HD deflect when machining? (The answer to that question really depends on how hard you bash the cutter into the workpiece! If using a small cutter - say 5 mm, I suspect the cutter would break before the HD suffered.)