What is a Harmonic Drive? How does a Harmonic Drive work, and just how much contact is there between the teeth of the splines? Let's take a close look at how the beautiful Harmonic Drive reducer works.
There’s something about cogitating on ways to make precise, backlash-free motion actuators that’s so interesting to me. I genuinely get a small dopamine hit when I find myself stuck in a waiting room, because I realise that I have nothing else pressing to do, I’m now allowed to get lost in my thoughts. My experience and success with using Harmonic Drives has surely played a big part in installing that habit in me.
By the way, the generic name for the Harmonic Drive is the Strain Wave Reducer, but I'll continue going by Harmonic Drive because it's shorter and it's what most people know them as.
When I think I have a design that might work, I immediately get to wondering how well it would perform; I get to wondering how much force or torque the mechanism might take and remain rigid enough for serious CNC machining applications. Perhaps calculations and FEA can be used to give me a good estimate, but I’m not educated enough to know how to do any of that, I tend to go more off of an intuitive and experimental approach. To do that, I like to compare to what I know, and what I know are the Harmonic Drives that I’ve used on my DIY 5 Axis CNC router.
What I don’t know is how much of the splines on the Harmonic Drives are really engaged with each other, having a better idea of that will give me more information to judge just what’s possible with a given design of my own. So, with that personal objective in mind and the knowing that I won’t be getting part 2 of the Pascal 5 Axis CNC Conversion series out for weeks, I set out to make you all a video exploring this subject.
Back in 2015, when I was building the DIY 5 axis router, I found these units on eBay from an industrial surplus store for a great price, completely unused. I bought all three of them and kept one to either flip or use in the future. I’m glad I kept that last one because now I have about 963 ideas for it. 😄
People ask me ALL THE TIME what models I used, the exact model number is HDUC-25-80-2A-GR-IV-SP. I vaguely remember trying to find them on the Harmonic Drive Systems website and couldn’t find an exact match, so I have to wonder if they were a special order. In any case, their website is quite nice and gives specifications for each model’s static and dynamic torque ratings as well as other useful specs.
Often you’ll find Harmonic Drive units for sale online that come as a complete gearbox with a cross roller bearing at the output, which makes them easy to attach a servo or stepper (if the unit doesn’t also come with one) and simply attach the device to be driven, such as a spindle. I didn’t go that route, I bought the drives only and designed my rotary axes to inherently incorporate the drives and cross roller bearings directly.
This isn’t so much an article about my 5 axis router as it is about Harmonic Drives, so I don’t want to digress too far, but I’m sure many people will be interested to know which cross roller bearings I used. They are THK brand, measuring 90mm ID, 120mm OD, 13mm wide. They’re designed for the inner race to be the rotating part, which — from what I understand — means that the outer race is the one that splits in two for assembly and is expected to be clamped rigidly in place in a chassis. You can see the little holes on the outer race where the assembly and alignment pins go. These bearings also have rubber seals, which is nice. I think I also got these for a good price brand new on eBay at the time, they seem to be more expensive these days… maybe I’m just imagining it.
Back to the Harmonic Drives.
To be honest, I think the best way to explain to you how a Harmonic Drive works is to watch the video that this article is written in conjunction with, but I’ll try to explain it here too.
There’s three major components, below is the Circular Spline. This is a fully rigid component that gets mounted to the chassis/gearbox casing. It has a spline on the inside.
Next is the Flex Spline, this is a thin cup shape that’s flexible at the spline end. That spline has two less teeth than the Circular Spline above. The other end is thick and rigid, this end is the high torque, low speed output interface.
Last is the Wave Generator which takes high speed, low torque input. The Wave Generator has a mild elliptical shape with a bearing fitted over it such that the bearing is now elliptically shaped. The Wave Generator is inserted into the Flex Spline, causing the Flex Spline to take on the elliptical shape.
The whole package assembled looks like this:
As the input is rotated, the gap on either side of the now elliptically shaped Flex Spline causes the teeth to gradually stretch over and skip one tooth. This is very carefully controlled by the dimensions of the ellipse and the perimeter (circumference?) it produces.
Now, I haven’t counted to the teeth on each spline, but since the reduction ratio is 80:1, I suppose the Circular Spline might have 162 teeth and the Flex Spline 160. The reason I guess 162 and 160 is because there’s two points of contact at the wider ends of the ellipse, each skips one tooth as they rotate through the elliptical phase. Each half rotation of the input skips one tooth, so a full rotation would cause two teeth skipped. Knowing the ratio is 80:1, then 80 * 2 = 160. Either the Circular Spline or the Flex Spline will have 160 teeth, surely.
Everything I say here is just my assumption, but I imagine that the ideal way to adjust the drive ratio of the unit would be to adjust the size of the teeth in the splines, or put another way: to adjust the number of teeth while maintaining the same diameter. If you increase the size of the teeth, then each tooth skipped will account for a larger movement of the Flex Spline.
Because the teeth are now bigger, the difference in diameter between the Circular Spline and the Flex Spline would be larger. That is: taking two larger teeth off the Flex Spline than before would result in a comparatively smaller diameter Flex Spline. Because of this, the ellipse also has to be more aggressive to stretch the smaller diameter out further to make contact with the Circular Spline.
Following my previous logic, I suppose the 60:1 drive would have 122 teeth on the outer Circular Spline and 120 on the Flex Spline. It might actually be 120 on the outer and 118 on the inner, I’m not going to pretend like I know for sure here.
It might also be possible to keep the teeth the same size and just take four teeth off the Flex Spline, resulting in the similarly more aggressive ellipse and each full rotation of the input causing four skipped teeth instead of two.
Now knowing that the Flex Spline is doing just that: flexing, I wanted to know how much of the teeth in the splines is making contact with each other and actually doing the work of transmitting torque. Having an idea for this will help me understand better how much tooth engagement is necessary to achieve the strength that these units have.
To test this, I brushed some Prussian Blue (engineer’s blue) onto the teeth of the Circular Spline.
Then insert the Flex Spline as a complete assembly, first testing it without rotating just to see what the contact looks like static, then with one rotation of the input.
If you’ve already watched the video, you’ll know that this didn’t really come out as hoped. There was a nice large patch of blue on the Flex Spline, but I’m almost certain that this is a false reading. I think that the jarring of the Circular Spline as I slide it on and off the Flex Spline is what contributed to the large patch compared to the following test under rotation of the input.
You can, however, still see how the blue gets thinner towards the left, which indicates to me the real contact that was made under assembly, so I’d bet the contact when static is identical to when rotating. I can’t really imagine a reason for it to be any different.
Next was to reassmble the unit and rotate the input (Wave Generator) one full rotation, this enabled me to get a good reading around the Flex Spline without unintentionally interfering with the result when taking the Circular Spline off.
As you can see, there’s not heaps of contact, perhaps only 1/4 of the length of each tooth is making contact.
I didn’t think to test it while filming, but I suspect that if you push the Wave Generator further into the Flex Spline, the spline will be expanded out further along its length, causing more contact.
What have we learned? Well we looked at what a Harmonic Drive does, how it works and how the reduction ratio might be adjusted. I hope that was clear and easy to understand, and I hope you’ve taken some value from that.
We also looked closely at the contact patch between the Flex Spline and the Circular Spline, which was very interesting to me. Eventually I might make a video or even a series on some backlash-free reducer mechanisms that I have in mind. Until then, enjoy your days, reader, and don’t forget to watch the video if you haven’t already.
Subscribing to the YouTube channel would be great, but I don’t want to tell you what to do, you’re an individual. 🙂
