Reply with Quote? Check the last page of the brochure... They actually have an office a few hours from me.Originally Posted by RCaffin
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Harmonic Drive Gear Ratios
I mentioned in a previous chapter that I was using a 51:1 gear ratio when calculating out the movements of my HD, and this caused some discussion. So this chapter will be a brief sideways digression into how the HD gear ratios work. For a better explanation of how the Harmonic Drive itself works, see any of their literature. However, their literature does skip a few vital (imho) details.
I had better start by explaining my and their terminology. Previously I have been referring to red/pink bits and blue bits and green bits. I need to relate those terms to the 'official' HD ones.
The key to the whole system is the Flexspline, which I was calling the red bit with a pink fill. It is flexible - slightly. It is connected to what I was calling the blue bit, but which is not shown here. The connection is via the outer back rim, with all those (16) holes. The blue bit is rigid, and includes the outer race parts for the Crossed Roller Bearing. The Harmonic Drive itself does not have to include the CRB, but packaged units do have a CRB.
The Circular Spline is what I had drawn as green. It too is rigid, and in my drawing there are a couple more parts attached to it, including the inner race for the CRB.
The interesting and tricky bit seems to be the Wave Generator, which gets more detail in the next drawing.
The first diagram in this chapter shows a ball race between the Wave generator and the Flexspline. It looks round. This drawing shows the ball race all right, but it is elliptical. A moment's thought rings alarm bells here: just how do you have a elliptical ball race? Nonetheless, it is elliptical, and that is crucial to the whole design.
The inner race can be elliptical fairly easily: it sits on the Wave Generator and the balls go around it. That's easy enough to do with some CNC grinding. But the outer race has to flex as the Wave Generator goes around. A ball race flexes??? My mind boggled at first.
Yes indeed, the outer race has to flex. Here we have a 'printed' version of a Harmonic Drive (picture off the web, (c) Peter Heim), and you can clearly see the outer race distorted into an ellipse. I think the designer has put a bit too much ellipticity into the shape, but with that size teeth he had no choice. You could get a lower ellipticity by having a bigger number of teeth, as the difference between the inner and outer teeth rings is always just two. I count 32 teeth on the inner ring, so the reduction ratio should be (I think) 16:1. My HD is 50:1. I am not sure whether the plastic would support the finer teeth you would get with a 50 tooth version.
So how does the outer race in a real HD flex? You just make it very thin and out of spring steel. Very simple, and quite reasonable. Stay within the elastic limits of the steel and you are fine. They make springs that way too. Now try to find that explanation in the HD literature! (If you can, do please tell me where.) Very clever people, the Germans. (HD is a German company.)
Does it have to be made this way? No. You could make it with a couple of small ball race wheels as shown here, but the construction would be far weaker, and a bit more complex. But it would work.
You could also make it with just one ball race, so there is only one point of contact. That would allow the use of one ball race, which might be a whole lot simpler. I imagine that was tried and found lacking. I suspect the Flexspline did not like it, and failed after a while.
You could even make it like this, but beware! This design will have significant backlash at the input gears. We don't like backlash. Not good.
Well, how do they keep all the balls in line at the right separations? They use a Vespel TP ball cage. Vespel is a high-end engineering plastic by DuPont, able to handle the sideways forces the balls generate as they go around the ellipse. Unlike brass, which could fatigue and crack after a while, Vespel handles the flexing quite OK, and the grease, and the high temperatures sometimes encountered.
OK, moving right along to the original question of whether it is R:1 or R+1:1. Here we have the official explanation from the Harmonic Drive manual for the SHF & SHG drives of how the ratios work (PDF file on my disk drive, from the HD web site). Nice diagrams, but unfortunately the text under each diagram is wrong. Yes, I know that this is from the official company manual, but it is still wrong. Compare the text for each of the boxes with that in the first box. They are all the same, despite the arrangements being all different. They all say 'CS Fixed', 'Input and output in opposite directions', '1. Reduction Gearing', and so on. The text is right for the first box, and wrong for all the others.
Let me hasten to add here, that while the first two arrangements make engineering sense, none of the other arrangements would be viable in the real world. No engineer with an ounce of brains would even contemplate trying to use a HD unit to gear up by R:1, or even R+1:R. You would simply smash the Flexspline.
How? I guess the graphics designer who created the catalog was not an engineer, hadn't a clue, and simply did a cut-and-paste from the first box to all the other, changed the big red arrows and the equation numbers, and forgot (or did not know) to change the text. And no-one did any serious proof reading. I suspect this mistake has mislead many people. (End of slight rant.)
I used the arrangement shown in box 2. That's equation 2. R+1:1.
Well, yes, very fine, but does it work like that in practice, or am I up the creek? Leaping several chapters ahead, I will simply say this. If I give a command 'g0 a3600' (I am working in degrees), the RT spins exactly 10 revolutions if I use the 51:1 ratio. On the other hand, a 50:1 ratio is actually 2% short, which is 7.2 degrees per revolution. Over 10 revs, that's 72 degrees of error. Kinda visible, yes? And yes, that's what happened to me at first.
? Check the last page of the brochure... They actually have an office a few hours from me.
Good write-up... I checked and the CSD - HSD catalog got it right. Yes I'd agree that an almost 1:1 ratio may be a bit useless, unless maybe you need a compact rotation reversal. The differential setup looks interesting.Harmonic Drive Gear Ratios
I mentioned in a previous chapter that I was using a 51:1 gear ratio when calculating out the movements of my HD, and this caused some discussion. So this chapter will be a brief sideways digression into how the HD gear ratios work. For a better explanation of how the Harmonic Drive itself works, see any of their literature. However, their literature does skip a few vital (imho) details.
I had better start by explaining my and their terminology. Previously I have been referring to red/pink bits and blue bits and green bits. I need to relate those terms to the 'official' HD ones.
The key to the whole system is the Flexspline, which I was calling the red bit with a pink fill. It is flexible - slightly. It is connected to what I was calling the blue bit, but which is not shown here. The connection is via the outer back rim, with all those (16) holes. The blue bit is rigid, and includes the outer race parts for the Crossed Roller Bearing. The Harmonic Drive itself does not have to include the CRB, but packaged units do have a CRB.
The Circular Spline is what I had drawn as green. It too is rigid, and in my drawing there are a couple more parts attached to it, including the inner race for the CRB.
The interesting and tricky bit seems to be the Wave Generator, which gets more detail in the next drawing.
The first diagram in this chapter shows a ball race between the Wave generator and the Flexspline. It looks round. This drawing shows the ball race all right, but it is elliptical. A moment's thought rings alarm bells here: just how do you have a elliptical ball race? Nonetheless, it is elliptical, and that is crucial to the whole design.
The inner race can be elliptical fairly easily: it sits on the Wave Generator and the balls go around it. That's easy enough to do with some CNC grinding. But the outer race has to flex as the Wave Generator goes around. A ball race flexes??? My mind boggled at first.
Yes indeed, the outer race has to flex. Here we have a 'printed' version of a Harmonic Drive (picture off the web, (c) Peter Heim), and you can clearly see the outer race distorted into an ellipse. I think the designer has put a bit too much ellipticity into the shape, but with that size teeth he had no choice. You could get a lower ellipticity by having a bigger number of teeth, as the difference between the inner and outer teeth rings is always just two. I count 32 teeth on the inner ring, so the reduction ratio should be (I think) 16:1. My HD is 50:1. I am not sure whether the plastic would support the finer teeth you would get with a 50 tooth version.
So how does the outer race in a real HD flex? You just make it very thin and out of spring steel. Very simple, and quite reasonable. Stay within the elastic limits of the steel and you are fine. They make springs that way too. Now try to find that explanation in the HD literature! (If you can, do please tell me where.) Very clever people, the Germans. (HD is a German company.)
Does it have to be made this way? No. You could make it with a couple of small ball race wheels as shown here, but the construction would be far weaker, and a bit more complex. But it would work.
You could also make it with just one ball race, so there is only one point of contact. That would allow the use of one ball race, which might be a whole lot simpler. I imagine that was tried and found lacking. I suspect the Flexspline did not like it, and failed after a while.
You could even make it like this, but beware! This design will have significant backlash at the input gears. We don't like backlash. Not good.
Well, how do they keep all the balls in line at the right separations? They use a Vespel TP ball cage. Vespel is a high-end engineering plastic by DuPont, able to handle the sideways forces the balls generate as they go around the ellipse. Unlike brass, which could fatigue and crack after a while, Vespel handles the flexing quite OK, and the grease, and the high temperatures sometimes encountered.
OK, moving right along to the original question of whether it is R:1 or R+1:1. Here we have the official explanation from the Harmonic Drive manual for the SHF & SHG drives of how the ratios work (PDF file on my disk drive, from the HD web site). Nice diagrams, but unfortunately the text under each diagram is wrong. Yes, I know that this is from the official company manual, but it is still wrong. Compare the text for each of the boxes with that in the first box. They are all the same, despite the arrangements being all different. They all say 'CS Fixed', 'Input and output in opposite directions', '1. Reduction Gearing', and so on. The text is right for the first box, and wrong for all the others.
Let me hasten to add here, that while the first two arrangements make engineering sense, none of the other arrangements would be viable in the real world. No engineer with an ounce of brains would even contemplate trying to use a HD unit to gear up by R:1, or even R+1:R. You would simply smash the Flexspline.
How? I guess the graphics designer who created the catalog was not an engineer, hadn't a clue, and simply did a cut-and-paste from the first box to all the other, changed the big red arrows and the equation numbers, and forgot (or did not know) to change the text. And no-one did any serious proof reading. I suspect this mistake has mislead many people. (End of slight rant.)
I used the arrangement shown in box 2. That's equation 2. R+1:1.
Well, yes, very fine, but does it work like that in practice, or am I up the creek? Leaping several chapters ahead, I will simply say this. If I give a command 'g0 a3600' (I am working in degrees), the RT spins exactly 10 revolutions if I use the 51:1 ratio. On the other hand, a 50:1 ratio is actually 2% short, which is 7.2 degrees per revolution. Over 10 revs, that's 72 degrees of error. Kinda visible, yes? And yes, that's what happened to me at first.
As to the gears, IIRC for 50:1 it's 102 teeth for the CS and 100 for the flex spline. That would give you 51:1 if the CS is the output, our typical setup, and 50:1 if the FS is output. Unfortunately there doesn't seem to be a convenient way of accessing the tidy ratio without some modifications... On a typical cycloidal drive there's only 1 less tooth on the outer ring, and a counterweight is used to balance the system at high speeds.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
> They actually have an office a few hours from me.
Ah yes, maybe, but I live in Australia, I am not going to ring them in America.
They now have a new catalog for the light-weight versions of these models, and guess what? That page of diagrams has been omitted. Maybe they have been told?
Cheers
Roger
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Actually their sales office is about an hour from me! Their US corporate headquarters is about 5 hours away....
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Freebies?
Cheers
Roger
(Doubtful!)
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Performance Under Load
The last but one chapter covered performance without any load. A little bit of (expected) hysteresis was found and measured. Now, what happens when I put a load on the unit? Since the Crossed Roller Bearing is probably far stronger than the Harmonic Drive spline itself, I will only cover torque loads here. I don't think straight radial (sideways) loads will signify (once I have done up all 32 bolts tightly): the ratings shown by HD for the CRB are quite high. Response to torque loads could be called 'load compliance' or 'torsional stiffness'.
The simplest way to measure this would be to lock the input, put a varying torque onto the output and measure the rotation of the output while the torque varies. This may sound a bit technical and difficult, but it fact it is quite simple to do. The secret is to have a very clear understanding of what one is trying to measure. Knowing what can go wrong also helps.
I did make the assumption that the CRB inside the unit could be 'trusted'. This meant that I could create a torque on the output by attaching an arm to the output and putting a weight on the end of the arm. I did not need to extend the arm out both sides with matching forces.
You may recall this photo from the last chapter. There is a sensing arm going to the black optical position sensor, and there is a second arm below it. That second arm takes the load which converts to a torque. You can see a hole in the arm at the right hand end: that is at a fixed and known distance from the centre of rotation, so I can convert force at a distance to torque. In most cases I will be more interested in the forces from machining anyhow. Um ... just what sideways force does a 2 mm cutter spinning at 3000 rpm with a 0.2 mm depth of cut in 6061 aluminium exert when moving at 100 mm/min? Good question. An equally good question is what force on that cutter will break it?
Now this photo may surprise you: it looks terribly 'amateur', doesn't it? Actually, it isn't. Static force is static force; it does not matter how you transmit it. A piece of string is just as good as braided high-tensile stainless steel cable: both transmit a force from one end to the other end. The mineral water bottles might look clumsy, but each bottle weighed either 500 g or 1000 g, to within 1 g (digital scales are so useful). The string was not rubbing or dragging anywhere: it was going over a ball-race pully. With this arrangement I could go from 4.00 kg force downwards to 4.00 kg force upwards at the fixed distance from the centre in 0.50 kg steps. The voltmeter let me read the sensor output to better than 1 mV. The rest of the junk lying around is just my office workbench. You want sterile (or tidy)?
This graph shows the response of the HD to loads between +3000 g and -3000 g at the end of that arm. The vertical axis is calibrated in microns of movement at the sensor using the calibration coefficient obtained before. It's applicable because the sensor arm length has not changed. Several cycles from +3 kg to -3 kg and back are shown, and as before the cycles overlay each other. Yes, there is some 'compliance' or twist, as there is deflection (vertical axis) as the torque (horizontal axis) increases. The slight bend in the response visible at the ends of the loops is an artifact of the non-linear sensor, as seen before. The first test went up to 4 kg each way and the results showed that I was definitely running into the non-linear parts of the sensor response, so I scaled the forces down a bit. No harm is done by showing a little bit of the sensor non-linearity. (No electrons were harmed in collecting this data either.)
The slope of the curve shows the actual 'compliance' or torsional stiffness. In the ideal world that slope would be zero (no Y-axis movement in response to X-axis torque), but this is the real world. The way the 'eye' in the middle opens shows you (once again) the hysteresis in the load response.
Turning all that into numbers, that means the HD 'twists' about 11 microns at the sensor (at 141 mm) per kilogram at the load point (at 161 mm). Turning that into more comprehensible English (or engineering), applying a 1 kg sideways force at the periphery of a 100 mm diameter (50 mm radius) object in the chuck would cause about 1.2 microns of movement at the edge of the object. That seemed reasonable to me. OK, when you put it that way, it actually seemed pretty good to me!
I did check this against what data I could get from the HD data sheet. That was difficult, as Harmonic Drive are far more concerned about what loads the unit can take without breaking or skipping a tooth. My measured torsional stiffness was I think about (4 times higher (better)) just a little bit higher than the figure in the HD data sheet. However, the figure in the data sheet has to be a bit conservative so the customer does not come back complaining that the unit failed specs. It is also possible that the spline had bedded in slightly during it's previous use.
[Edit: data sheet stiffness value corrected]
The hysteresis due to the varying torsion as shown by the eye corresponds to about 5 microns at 141 mm or 1.8 microns at the periphery of a 100 mm diameter object, for the cyclic load of +/- 3 kgf. Given how heavy those water bottles felt when I was loading and unloading them again and again, I doubt that the forces due to a small cutter will be anywhere near that large.
Well, that was all very encouraging, and probably a bit better than a manual rotary table with a stepper motor and no clamps. I was encouraged. So in the next chapter I will discuss the motor drive.
Last edited by RCaffin; 03-17-2015 at 06:01 PM.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
What an excellent series of posts, thank you for taking the time to write all this up!
Just a quick calculation...
torque of 1 kg at a 161mm radius is 0.161 kg-m, or 1.58 N-m.
11 microns tangential movement at radius 141mm is 1.24e-5 of the circle, or 7.8e-5 radians
so the measured stiffness is 2.03e4 N-m / radian
the spec from the catalog looks like 2.5e4 N-m / radian
so they match up quite well!
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Hi Derek
I think I must have been using K3 rather than K1 for the rating. I have corrected the text. Thanks.
Cheers
Roger
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Great installment!
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Motors for a Rotary Table
We now consider motors, needed to make the Rotary Table move. There is a variety of different sorts of motors available, but the only two which make sense for a hobby system are DC servo motors and two-phase stepper motors. The others are either too complex, too expensive, or just not suitable. Fortunately, I had both sorts of motors available in the NEMA 23 size, which seemed to be just right. (They were left-overs from old research projects). But which sort to use?
DC servo motors need optical encoders, which cost a little money, and they need suitable drivers. Steppers just need drivers. However, as far as I can see, these days modern stepper drivers and DC servo drivers are not very different in pricing or shape. Each driver has a few gutsy power MOSFETs (right), some MOSFET driver chips, a couple of current-sensing resistors, a couple of opto-couplers, and a large FPGA (with dot, at left) to do all the thinking and control. The advantage of DC servo motors is that they can go much faster than steppers, but they can use more power (it depends ...) and they are not so powerful at very low speeds. Steppers are really good when you want very slow speeds at high torque.
Do I need high speed? The answer would be yes if I wanted to use the Rotary Table as a slow CNC lathe. However, my machining centre already has a quite a good CNC lathe spindle, so I didn't want to make any sacrifices in that direction. Do I want slow or very slow speed? Oh, definitely yes: there are many applications where a good Rotary Table can be used as a sophisticated indexer or at least just turn slowly while you machine all the way around the object. So it looked like a stepper motor would be best. I had lots of them.
What to use as a driver? Well, there are plenty of different brands on the market, all of which have their ardent supporters. OK, it seems not everyone is entirely happy with the Chinese stepper drivers, so I ruled them out. A consideration here was that I had recently rebuilt the electronics for my CNC, replacing everything after the big power transformer, and I had used Gecko 320X servo drivers for the X, Y and X axes. They worked fine, and the support I got from the local distributor (Homann Designs) was really wonderful.(One of the drives was DOA: there was arcing between the MOSFETs and the heatsink. You can see traces of the arcing on the left-hand MOSFET. A replacement was sent by Express Mail the next day.) So a Gecko stepper driver seemed like a reasonable gamble.
There are several stepper motor drivers available from Gecko. The 302V (Vampire Drive) is supposed to be bomb-proof, while only slightly more expensive. There is quite an interesting thread on that driver here at CNCZone, by the way. Marcus of Gecko challenged people to produce a dead one. They did, but as Marcus pointed out, if you scatter metal swarf across a powered PCB, anything can happen.) I've been through the pain and hassles of replacing drivers a few times. The extra cost seemed pretty small in that context.
One feature I do like with the Gecko 203V is the 'Disable' input. You do not unplug a stepper from the drive while it is powered up, nor do you 'switch' the power supply off and on: both can be damaging. And yet, I wanted to be able to unplug the stepper motor so I could remove or connect the Rotary Table while the system was live. I thought a simple little front panel switch on the Disable line could solve that requirement completely. (It works very well in fact.)
Having settled what sort of motor and driver to use, the next question was how to connect the stepper motor to the HD. There are two obvious ways to do this: a direct coupling or a belt drive. A direct coupling puts the motor in line with the HD axis, with a flexible coupling between the two to handle any minor misalignment. That's very simple: you can get flexible beam couplings (plus other varieties) from Hong Kong or Asia for a few dollars, or from America for 20-30 dollars plus postage - IF they ship to Australia. The Chinese and Hong vendors on eBay do ship to Australia: no prizes here. In addition, it does not take long with a slitting saw to make your own beam couplings, especially out of a nice engineering plastic like PET. The disadvantages of the direct coupling are twofold: you lose the through-hole or hollow shaft feature (because the coupling and motor block the hole), and you can't alter the gear ratio even slightly. But it is simple.
The advantages of the toothed belt drive are the same two factors in reverse: you keep the through-hole feature and you can vary the gear ratio. However, now you need two toothed belt pulleys and a toothed belt of the right size. These can be horribly expensive and on long delivery - from some suppliers.
But a funny thing happened on the way to the Forum: the RepRap 3D printer became extremely popular, and it uses the 2 mm GT2 belt in various loop sizes (and also as an open belt, as shown here). So, if your design can use one of the RepRap sizes of 6 mm wide 2 mm pitch GT2 belts, well, there are lots of eager Chinese vendors on eBay! And they sell a few sizes of toothed belt pulley as well, all for the proverbial 'a few dollars and free postage'. I managed to design my drive using one of these very inexpensive belts. (No, I have not bought from the vendor whose logo is showing.)
I will mention something in passing here: yes, you can get several different metric bores for flexible couplings and for pulleys (China is metric), but in deference to America you can also get 1/4". That's nice, because stepper motors very often have a 1/4" shaft (like, most often). I bowed to the inevitable - but only this once!
A flexible coupling may allow some torsional compliance, but given the 51:1 gear reduction in the HD, it did not seem likely that there would be huge forces on the coupling. Some of the very old designs of toothed belts (eg X, L) can have some backlash, but the modern GT2 series is far, far better. Most treat it as having zero backlash provided you match GT2 pulley to GT2 belt, with some tension. It's all in the tooth profile, for both the belt and the pulley. That's a subject for another day, or at least for a later chapter in this series.
So my plan was to make a motor mount which could provide both a direct coupling mounting point and an offset belt-drive coupling point. In the photo here the mounting plate is sitting above the chassis holding the HD (I'll get to that later). The servo-motor hole in the middle is for the direct drive, while the hole to the left is for the belt drive. The loose bit at the bottom at the right is the connection for the direct drive, using a bought flexible coupling and a custom attachment for the HD shaft. There is a 1/4" shaft hidden inside there. The toothed belt pulley on the left side was an early experiment with 100 teeth and rims: that experiment went well. The small pulley in the middle is for the motor, driving the larger pulley already mounted on the HD shaft in the middle. Apart from the bought coupling, all parts were machined on my CNC, and the toothed belt pulleys do have a proper GT2 profile (like, within microns). The data for the 2 mm GT2 profile is on the web. I did also machine up an integrated plastic flexible coupling, with lathe and slitting saw, but the metal one turned up at that stage so I used it.
So I put all this together and tested the drive system. That skips all the mechanical construction work (the 'box'), but I will get back to that later. In the next chapter I will cover gear ratios and stepper motor performance. Not everything went exactly as planned.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Steppers Motors, Old & New, and Pulleys
I am going to skip over a lot of details about the frame or structure of the rotary table for the moment and keep the focus on the motor drive. I'll get back to the mechanical engineering in due course. Not many pictures this time, but some equations and numbers.
I mentioned that I have a stack of old round stepper motors left over from past projects - some going back to the 80s. A stack, like a dozen or more, mostly Philips brand, although they got out of that market a long time ago. There's a picture of one of them in chapter 7 - this is chapter 10. I had bigger ones and smaller ones as well. Some of the motors have the NEMA 23 servo mount on the face, which is fully compatible with a wide range of other more modern motors (just in case). So I took an old round Philips stepper and hooked it up to the Gecko 203V driver with about the right current setting, as seen in chpater 7.
This is where things went slightly wrong. I do remember that when we bought these motors we could make them scream like a 747 jet taking off. That didn't seem to be happening any more. I could get them responding to about 3000 pulse/second, but that is with the 10 microsteps per step feature of the G203V. In other words, I was getting about 300 Hz performance without the microstepping. In addition, I found I could stop the stepper motor with my hand, and I am sure I could not do that back then. What had gone wrong? Some detective work followed.
Back in the 80s the material used for magnets in general was a ferrite. That is what was used for those round stepper motors (left photo). To keep ferrite's performance or magnetisation you need to 'close the gap' with an iron 'keeper' across the poles very carefully all the time, or the ferrite slowly loses its magnetisation. But the gap is never 'closed' in a stepper motor (there is always an small air gap), and as the good Marcus Freimanis of Gecko has pointed out, that means old round steppers lose their performance after 5 - 10 years. On the other hand, modern 'square' stepper motor (right photo) use rare earth magnets: these are far more powerful than the old ferrite and do not degrade with time.
Oh dear. Does that mean that my lovely collection of old round stepper motors of all sizes are all likely to be rather degraded now? They all cost quite a lot back then (although I was not paying the bill). Unfortunately, it would seem so. What to do?
Fortunately, even back in the 80s they were making servos and steppers with the NEMA 23 mechanical specifications. In theory this meant that I should be able to buy a modern square NEMA 23 stepper motor and just plug it in. Yeah, really? Since I had been buying all my Gecko stuff from the Australian distributor Homann Designs, I bought a small stepper of about the same (short) length from him to see if this was so. That's the motor to the right. It was not a Gecko motor as far as I know, but it was covered by the Homann Designs warranty (which I had tested very successfully). It turned up, I connected the wires, hooked it up to the direct coupling, and ... away we went. And yes, it could scream a bit. Ain't Standards and compatibility wonderful?
I wasn't going to bother mentioning just what stepper motor I had bought because the torque rating of the motor is really irrelevant. When you have a 51:1 reduction ratio, almost anything can drive it, and that includes my very weak old round stepper which I could stop with my hand. However, for the record, it is a 1.1 N.m (155 oz.in) stepper 2H256-28-4B, 56 mm long (body, not shaft), 50 V, 2.8 A, 0.8 ohm, 2.4 mH. In other words, it is a 'short' one. Given that it has far more torque than I need, I run it at about 2 A rather than 2.8 A. The power supply to the Gecko 203V is ~50 V - the same supply used for the XYZ axes.
Stepper motors are supposed to have a mid-band resonance, but this is not seen in the Rotary Table. That's because the motor is coupled quite tightly to the HD, which presents both a drag and losses. They damp out any resonance. The RT rotates very comfortably at 1 Hz (rev/sec) and can go faster.
Does that mean my collection of round steppers is just so much junk? Well, no, not really total junk. If I want a stepper motor to rotate something slowly without high forces, they will still do nicely - so I am keeping them for the moment. Yes, one of the round ones would be able to drive my Rotary Table - but far too slowly.
Leaping even further ahead, the first job for the Rotary Table (using the direct drive) was to make a 120-tooth pulley for the toothed belt. The material used was hard plastic; the tool was an inexpensive 1.1 mm ball-nosed milling cutter from China. (I bought 5, expecting a few hassles.) The new motor ran perfectly (and I didn't break a single cutter).
But why a 120 tooth pulley? About here is a good place to discuss the pulley ratio for the belt drive and some magic numbers. We have some basic numbers:
Steps per rev: 200 (from the motor)
Microstepping: 10 (from the driver)
Motor pulley teeth: N (by definition)
Harmonic Drive pulley teeth: M (by definition)
Harmonic Drive ratio: 51:1 (from the Harmonic Drive)
Now, putting these together to get steps per rev of the HD, we have:
steps/rev = 200 * 10 * 51 * N / M
steps/degree = 200 * 10 * 51 * N / M * 360
If I make the N/M ratio equal to 1:1, as for a direct drive, we find that I need 283.333 microsteps per degree. I investigated a bit, and I found that Mach3 could actually handle this correctly for the A axis. (It does not seem to like decimals for the linear axes though, which is a bit sad, but I am not 100% sure.) So I was able to make the 120 tooth pulley mentioned above using a direct drive, and I could make it very closely to the GT2 profile as well.
However, when I was testing the whole system with very small movements I found that 283.333 steps/degree was a just a bit coarse, and some of the results showed this up. Some of the tiny incremental moves I had programmed took two steps while other moves took one step. The results were therefore a bit bumpy. Yes, very fine bumps, but still a bit too coarse for my liking. But then, the direct drive was purely an interim step anyhow. I did not intend to keep it.
I thought 283.3333 steps.degree was a bit awkward, even if Mach3 can handle it. If I make the ratio N/M = 3:1 (gearing the stepper motor down a bit), then there are 850 microsteps per degree. That seems to be a nicer and cleaner number. However, it also means that one step is 0.001176 degrees, which is not so nice, at least from my point of view. Part of the problem is that 51 number on the top of the equation: it seemed like a most inconvenient number at first. However, after messing around with a spreadsheet for a while I suddenly realised that it is not a prime number: 51 = 3 * 17. So I took another look at that expression for steps/degree, and rearranged the equation slightly:
steps/degree = 100 * 10 * 2 * 3 * 17 * N / M * 3 *120
Put N = 120 and M = 34 = 2 * 17, and this big mess reduces to
steps/degree = 1000 * (6 * 17 * 120) / (6 * 17 * 120) = 1000
That means a motor pulley of 34 teeth and a HD pulley of 120 teeth gives me 1000 steps per degree. What could be nicer? I have no trouble thinking in terms of 1/1000 of a degree. The astute may notice that I could get the same result with pulleys of half the size: 17 and 60 teeth. That is true, but 17 teeth is not all that many to have around a toothed belt pulley, and a pulley with 60 teeth would be difficult to fit to the shaft on the HD while leaving the bore clear. (The OD for the HD shaft is 38 mm, and the OD for a 60 tooth pulley is also ~38 mm. Awkward.) And finally, the 34/120 ratio fitted an eBay-available belt length of 280 teeth (which I had already purchased on spec). It all came together so nicely.
Subsequent checking which I will cover in a later chapter showed that 1000 teeth worked perfectly. Yes, I do mean perfectly. So the next chapter will return to the mechanical engneering.
Addendum re machining GT2 pulleys
If machining a GT2 profile on an RT, you need to be able to cut a groove about 1.11 mm wide with a round bottom. The obvious thing to use is a 1.1 mm ball end cutter. The extra 10 micron width (1.10 mm to 1.11 mm) will probably happen due to flexing of the cutter, although one could program it in. There are other ways of doing this of course, starting with a 1.0 mm ball end and deliberately widening the slot. The problem for the 'ideal' method was to find 1.1 mm OD (0.55 mm radius) ball end cutters. They don't exactly grow on trees, and when they are available they tend to be rather expensive.
I found that I could get 1.0 mm ball ends and 1.2 mm ball ends quite cheaply from CarbideChiu on eBay, so I emailed him and asked about 1.1 mm ball ends. No, not in stock, but if I want to buy 5 of them he could get the factory to custom make them for me. They came out with an HRC 55 rating and coated, for $5 each, posted to Australia. I have to say, I was impressed by the service he provided. The cutters were OK too.
Last edited by RCaffin; 03-22-2015 at 11:14 PM. Reason: added motor details
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
LOL two long posts on motors and not a hint on the rated torque?! Still great posts...
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Hi Louie
OK, OK, I have added the motor details to the posting.
They are not really important as the motor has far more torque than is needed. However, I had overlooked the value of the information to other readers. So I have explained a bit as well.
Cheers
Roger
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
I had previously thought of the "tidy" ratio dilemma myself. Being that my reducer has a more oddball ratio. The simple solution for me would be to use the reciprocal ratio in the belt drive stage, 100 teeth at the motor, 101 at the input. I haven't checked to see if these are available yet. But since my reducer drive ratio is actually a prime number it didn't leave to many options to have a round number of steps/unit. Which was one consideration for use of servo. I may still go that route if for positioning speed.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
As to resonance, the GeckoDrive should have electronic mid band resonance damping, which pretty much eliminates problems found in lesser drives. Wasn't too long ago when we were making "shaker" dampers to help with resonance; it's ao much lesa prevalent nowadays.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
I couldn't get 120 tooth or 34 tooth pulleys, so I cut my own. Not hard. I used engineering PVC for that.I had previously thought of the "tidy" ratio dilemma myself. Being that my reducer has a more oddball ratio.
Cheers
Roger
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
The Mechanical Design for the Harmonic Drive Frame
First of all I had better explain that the moving table on my mill is on the Y-axis, not the more common X axis. There are some very sound engineering reasons for this which make the structure very solid, but it does mean the mill table is not all that long. To preserve as much milling room as possible, I needed to sit the chuck face on the HD as far 'back' as possible. The rather large chuck I ended up using further reduced the miling space - later for that.
For a start, the HD needs to be mounted securely to a solid plate. This is not a 'it would be nice'; it is a real engineering requirement. You see, the Crossed Roller Bearing has to be assembled from three parts, not two as in an ordinary DGB. There is the inner race in one piece and the outer race in two pieces. The split is in the middle of the outer race (red arrow). The drawing they give for the unit does not highlight this split, but it is there. (This drawing started off as a PDF, and I had to erase an awful lot of dimension lines to make it readable. There are a few ends left showing.)
There are four small bolts holding the two parts of the outer race together (blue arrow in previous drawing), but they are only there as 'place keepers'. You really need the 16 (green line) bolts around the rim to hold the outer race together properly. The 4 keeper bolts can be seen here as they have white centres where the paint has been chipped off.
This photo shows the 16 bolts holding the HD to the front plate, and the 4 keeper bolts which keep the two halves of the CRB together before assembly. These 4 keeper bolts have white marks on their heads. And you need a solid flat face to bolt the rim against, to keep it really flat. That's the machined front plate. It's actually 19 mm thick Fortal.
Finally, you also need the 16 (pink) bolts on the output stage (1st drawing) to hold it together properly. The 4 small bolts in place on the output stage are not enough for real use either. Once again, those bolts seem to have acquired 'white' marks on their heads. As you will see from these two photos, the holding bolts are in between the 16 holes in each case. Technical manuals on CRBs go into all this in great length (trust me) ...
What's with the white marks, or chipped paint on the keeper bolts? I don't know, but it suggests that someone has disassembled the HD at some stage - perhaps to apply fresh grease. It wasn't me, but I can see the fresh grease.
So we start off with a slab about 19 mm thick with a great big hole (110 mm & 92 mm) bored through the middle. Red circles are the bolt holes, while black bolt heads show nominally where the keeper bolts go. Such a large hole needs a reasonable amount of meat around the rim, so the whole plate has to be somewhat larger. In my case it came to 185 mm wide x 175 mm high. All of a sudden this thing has got a bit bigger! The purple rectangle bit at the top right shows a cross section at the centre line and what I mean by a 110/92 mm hole: there is a step. Inner diameter is 92 mm (which is clearance), the outer diameter is 110.00 mm. But the requirement for a wide and strong rim does mean the centre line is a fair distance above the table, which could be useful. In lathe terms, the swing is fairly large. This is the 'front plate'.
Incidentally, some of the diameters on the HD are spec'd to h7 tolerance, so these dimensions were emphasised in the design and machining. The HD ended up being a tight fit into its socket. That's why there are three extra holes visible in the ring of 16 bolts here (red arrows). They are tapped holes, and can be used to push the HD back out of its socket or recess. (The other holes visible, outside the ring of 16, are hold-down holes used for machining the faces. They were explained earlier.)
I did forsee some potential problems in machining the hole in the front plate to a close fit. How to check the fit? Well, not so much how to check, but how to continue machining after the hole has been found to be 0.02 mm too small? The problem is, you see, that the HD sticks through the front plate some distance (previous photo). Just sticking the front plate on some 5 mm spoil board won't work.
So I used some thick old hardwood to make a very deep spoil board with a large centre hole: one able to take the HD front end. First I machined out the hole in the hardwood, then I machined the hole in the front plate. (The aluminium disk which was left over is at the front.) Then I machined the critical step. Now I could drop the HD into the hole to check the fit without moving anything. OK, I vac'ed the chips out first. In the event, by machining exactly to the specified dimension I found that the HD fitted just snugly into the hole in the first pass. So then the CNC program went on from here to drill all those mounting holes. I could then bolt the HD in place.
A typical design for a Rotary Table (RT) is a box with the chuck sticking out the front (when it is not a manual RT with a stepper motor stuck where the handle was). But I didn't have the room on the table for this, so I decided to put the front plate towards the back, 'inside' the box as it were. The actual unit was shown earlier on. Once you mount a chuck on the front of the HD, the active volume will be out the front anyhow.
In the drawing here the blue plate is the 19 mm front plate, the green plate is the 14 mm thick base, and the irregular red shape shows the two side plates which stiffen the mounting of the front plate. The multi-coloured thing in the middle is my rendering of the HD itself. The black things are obviously cap head bolts - quite a few.
This does not show the motor mount bar, which is out the back (ie at the left); nor does it show the chuck or its backplate (which will be at the right).
That is the broad design. It's all bolted together with M5 and M6 cap heads, for two reasons. The first is that welding always causes some warping, which can be hard to machine out. The second is that I decided to build the whole thing out of Fortal T651 - a very nice hard aluminium alloy rather like 7075. It is used extensively for mold-making. I bought a couple of boxes of offcuts (left over from mold making) from Scott Krezinski at www.fortal.biz in America. He was very helpful, and the price was very good (about 1/10th of what the Australian dealers wanted, except that they would only sell me whole sheets, in the $1k range).
Only aluminium? Yeah, well, Fortal is stronger and harder than 1020 steel, but it machines very nicely and faster, and since the material is extensively heat treated during manufacture it comes without much in the way of inbuilt stresses which can warp. In addition, the plates I used are 'not thin'. They build aeroplanes out of it. They also make a lot of production molds out of it these days. It's strong enough. And as i found out later, it's heavy enough too!
I mentioned using aluminium-specific cutters for this. They have a sharper cutting edge to peel the aluminium away better, and this idea does work well. However, that means the edges are thinner (of course), which means they are a bit weaker. To my mind that means that sometimes HSS-Co is better than carbide, as carbide can chip more easily when thumped. I didn't break any cutters on Fortal, but I did chip a few tiny bits off some Taiwanese carbide tips somehow, as shown here on a 6 mm end mill. I queried the vendor on this, and (so they said) their technicaal people were not sure why this happened. A rather long shank and too much vibration was all they could suggest. Dunno, not convinced. But the cutters did still work and give a nice finish, despite the chips, especially after I touched up the chips on a diamond wheel tool&cutter grinder.
I am not going to give detailed plans. For a start, I was designing around what slabs I had to hand. Yes, I had bought a selection which looked about right, but still. Second, even detailed plans don't convey the full story: you need to actually do the drawings yourself to understand them.
No, there are no beautifully rendered 3D colour projections from a CAD system. I have Alibre and Solid Edge and TurboCAD (at least), but as previously mentioned, I go faster in AutoSketch and my head. Instead you will just get photographs of the real thing.
In the next chapter I will go into a few details, especially about the motor mount. It did give me a few problems. Please don't laugh.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Weird with the end mills... On better ones, the tip has a sweeper profile that makes a nice pocket floor and strengthen the edge. It's possible that excess vibration from large stick out played a role. Also, could be defective blanks, they are sintered. I probably Would have used shorter end mills, as well as larger ones in diameter. Also you get what you pay for... I have endmills from Widia Hanita, SGS, and Onsrud that look brand new even extensive use. Try to get ZrN or TiN or PVD coating as well. It's possible you had some chip welding at the tip and broke off.
Re: The Design and Construction of a 'Backlash-Free' Rotary Table
Hi Louie
They weren't all that cheap, but they were definitely 'long' 6 mm ones. I was just testing them out.
Didn't see any welding at any stage. I use kero+olive oil pulsed misting: it's pretty effective.
I will chase up the brands you mentioned - thanks.
The coatings - are they suitable for aluminium alloy? I will have to check.
Cheers
Roger
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