Concepts for eBike Propulsion 2

Harmonic Drive Motor US Patent 7453176 B2

https://www.google.com/patents/US7453176

Ernie Davison

With Three Phases you can set up a push-pull scenario which should increase torque. However, it looks like you will need to advance 3 teeth per cycle rather than just 2, so effective gear ratio ends up higher.

Contact between engaged teeth goes way up, I'd guess you are getting close to 50% tooth contact at all times which means very low stress on the teeth. (meaning everything can be scaled down in weight)

Keep in mind nothing rotates here.

The only part that ends up rotating is the final output gear, but the flexispline is non-rotating... all it does is flex enough to skip teeth and advance the output gear forward.

I will get to a FEMM simulation eventually.

A flexispline motor, which is a modification of the flexispline motor of FIG. 1, is shown having a composite cup in FIG. 9. The cup is composed of a composite of magnetic powder filled polymer or a polymer bound wire or tape wound magnetic material bonded to flange, which now functions as a torque transmission agent and fulcrum (lever pivot point) for the electromagnetic deflection of flexispline.

Ernie Davison has thought this out well and sees the future where the flexispline is made of composite material that can flex more easily while being thicker. He mentions elsewhere that he would aspire to a thickness as wide as half an inch.

The logic is that a thicker flexispline can transmit more magnetic flux and that translates into more torque.

One imagines a high tech composite material being used.

The actual engagement of teeth can be with a thin metal insert, but the torque would be produced within the composite.

Ernie Davison is the "John Vranish" of Harmonic Drive Motors.

I was comparing the Harmonic Drive Motor to my previous Cycloidal Motor idea and they share similiar themes. The Cycloidal Motor would demand a rigid oscillating element which can be made thicker (solving the magnetic flux issue) but the cost is that all that mass being moved about would create vibration. With the Harmonic Drive you don't move the entire mass but instead just flex it.

Had an interesting idea...

Worm Gears have very high gear reduction, but normally suffer from really bad friction because the metal typically is forced to scrape past each other.

I did a patent search and found some ball bearing based Worm Gears but wasn't able to find anything with Cams using Roller Bearings.

So the idea would be to have a bunch of Cams that could spin freely and so when the Worm Gear interacted with these Cams there would be little friction.

Plus, for an ebike, you can angle the Cams in the direction you plan to spin the Worm Gear so as to better capture the forces involved.

Taking it a step further and the Cams might use Tapered Roller Bearings.

Using Sealed Bearings you have high strength rollers and don't need any special design effort. You could easily cut the shape for the wheel that would mount these, then drill holes and just bolt them on.

The Worm Gear would require some effort.

I'm wondering with these modern plastic printers if you could create something mathematically in software and then just print it out. Maybe create the tooth surface and leave a hollow center where you place the metal shaft in order to increase the strength. Plastic also might make it less noisy.

By spacing three turns of the Worm Gear for each Sealed Bearing and then using ten Sealed Bearings you get a 30-to-1 Gear Reduction.

This also does a 90 degree angle to the motor which means you can use a longer motor without having side-to-side clearance issues.

Ideally three Sealed Bearings are in contact at all times, but if that's impossible two might be good enough.

P.S: The Worm Gear was not drawn correctly, so just use it as a cartoon to get the idea.

Remember the idea of a direct drive left side crank motor?

Well, someone has finally created one:

http://www.gizmag.com/bimoz-bike-motor/42330/

It appears a more conventional configuration is being used (not toroidal) but the general idea is the same.

A lot of people want an electric boost while they're cycling, but don't want to replace their perfectly-good existing bicycle with a costly new e-bike. That's why several types of add-on motors exist. One of the latest, the Swiss-made bimoz, is not only a lot less obtrusive than most, but at 1.97 kg (4.3 lb) including battery, it's also claimed to be one of the lightest.

...I'd say that's "proof of concept".

It would appear that this thread and line of reasoning has reached it's logical dead end:

The limits of torque production for a given weight of motor

https://endless-sphere.com/forums/viewtopic.php?f=30&t=78923&start=75#p1168181

If you ask the question:

"How big must you make a motor if you want to eliminate all gear reduction?"

...your answer ends up:

"Huge."

This is a situation where "in theory" a direct drive makes sense because you can avoid the frictional losses of gear reduction, but the "Issues of Practicality" tend to work against actually doing things this way.

In most cases you need at least 10-to-1 gear reduction.

50-to-1 seems about the maximum because beyond that and the motor rpm becomes excessive.

If you look back at the previous post not only is the Left Side Crank Motor of a large diameter, but it's wide too. I'm not sure how they get the low weight numbers, but I'm guessing they are doing some kind of sparse design to make that inner stator as light weight as possible. They don't reveal where the copper coils are in the design. (but we know they use permanent magnets)

A direct drive hub motor typically runs 25 lbs... so how did they get 3-4 lbs?

Power = Torque * Speed

Torque = Radius * Force

Circumference = 2π * Radius

Now let's say we hold Force constant.

We also assume that magnets of the same size will pass a stator of the same size which hold copper coils of the same size.

Now we can observe:

Speed * Radius = 1

...why?

If you double the radius then it doubles the circumference which demands that you halve the speed in order to get the same conditions where magnets and stators and coils interact with each other.

Apples to apples.

So the formula becomes:

Power = Radius * Force * Speed (where we set Force = 1)

The Big Realization

Assuming you are doing a true apples-to-apples comparison where magnets are passing stators and coils that are switching at a uniform frequency the overall Power output is the SAME because motor Speed decreases such that the added Torque doesn't give you any advantage.

The entire concept suggested in the previous post (and is central to many Endless Sphere debates) is based on a flawed logic.

If you want more Power you either add weight in the form of more motor or you add gear reduction which allows increased Torque equal to that gear reduction.

The limiting factor for gear reduction is Hysteresis at high motor speed and this is intuitively obvious so people tend to see it.

What isn't obvious is that a large radius motor with many magnets and added weight spinning at moderate speed is actually running into the same Hysteresis issue as the smaller motor using gear reduction.

Electrical RPM is the best way to view things.

Higher Electrical RPM will tend to be associated with high Hysteresis no matter what form factor you use.

The relationships are very close to how planets orbit the sun:

Power-to-Weight Ratio

If the goal is reduced weight (which on a bicycle is reasonable) then the minimum weight would be found by establishing your desired Power output and working backwards to find gear reduction such that the minimum motor can be used.

This obviously has some downside as friction reduces output efficiency, but it's a tradeoff between weight and efficiency.

Maximum efficiency typically involves maximum weight.

The solar racers output about 1000 watts and use massive 25 lb Halbach Array full sized wheel motors to achieve 98% efficiency, so if pure efficiency is the goal that's the way to design the motor.

An ebike ideally would like a motor in the 2-3 lb range and with Power limitations of 250 watts the choice of gear reduction and additional multispeed gearing seems fairly certain as the preferred option. However, it's possible the Left Side Crank direct drive option could offer the compromise that would eliminate that first big gear reduction.

Another example of the Left Side Crank Motor.

6.5 kg = 14.33 lbs

http://en.pendix.de

I love this forum... an electric bearing anomaly that kind of works like a haromonic motor , except it needs a lot of amps i think and probably heats up like a mf . https://www.youtube.com/watch?v=DjKhggNJGls

Sorry I actually posted past your post and didn't see it.

I viewed the video.

Interesting.

Obviously the efficiency would be really low and the inability to lubricate the bearings make it impractical, so I can't see any way to use it for ebikes.

There are a lot of interesting simple motors.

The homopolar motor comes to mind:

https://en.wikipedia.org/wiki/Homopolar_motor

Things are heating up in the Left Side Crank Motor category.

The latest product from eRam is being introduced.

http://dienatronic.imb2b.com/introduce/

No word on pricing yet.

Remember that the founders "sold out" the rights to China, so this is the new product being built using a Chinese factory. The R&D was done in Germany or Austria somewhere.

This product uses high gear reduction with a cycloidal gear if I remember correctly. They attempted a John Vranish style compound gear reduction but abandoned it because of the noise.

Another product is the Bimoz which is direct drive.

They claim very low weight, but I'm skeptical of their numbers.

The Pendix weighs about 15 lbs which seems realistic.

I like this direction in ebike design because it's reducing the size and mess that some of the solutions require. The Left Side Crank Motor solves the problem without significant changes to a regular bike which preserves the link to ordinary bicycling.

At some point a Left Side Crank Motor using a harmonic drive needs to be attempted.

Okay... finally got around to the Harmonic Drive concept.

By using six Solenoids you can increase the Force you can apply a great deal over the standard version which attempts to pass magnetic flux through the actual Flexispline.

I could see doing this so that two pairs of Solenoids activated together which would increase the Torque even more.

Inside the Flexispline you would have a gear with two fewer teeth. (not shown)

Gear reduction equivalent to 80-to-1 would be easy to achieve.

If you go way, way back I was looking into using a Solenoid with a ratcheting gear and the Harmonic Drive does the same sort of thing in that the Flexispline only advances very slowly.

The big advantage of the Harmonic Drive with it's Flexispline is that many teeth are in contact at all times so the stress and wear will be reduced making it more durable.

Plus, with the Flexispline you eliminate the biggest problem with Solenoids which is how do you get them to return without needing a spring. This eliminates the need for a return spring in the Solenoid.

Nothing too exciting... just an upgraded Shimano Steps Mid-drive.

Looks nice, more compact.

70 Nm torque.

Here's a kind of crazy idea.

You create an ebike that is just a mid-drive... no attached battery.

Then you build a trailer that can hold a full sized solar panel, something capable of easily generating 1000 watts on a sunny day.

Finally you have a backpack battery.

The trailer also has room to store your backpack battery

So what you would do on a long trip is mostly use the solar panels to drive the motor on a sunny day. If it was cloudy or at the end of the day when the sun starts going too low to get much power you put on the battery backpack (or simply connect it) to get a few more hours at full strength. The battery backpack could even be charged if there is surplus energy.

Plus if you stop somewhere you can go on trips with just the battery backpack or maybe just ride the bike as a bicycle since it would be lightweight. (no 25 lb hub motor)

Obviously the security is an issue with leaving these solar panels out in the open with you being away, but if there was secure location to park it would be fine.

Other ebikes have done this, but typically with smaller solar panels.

A very low center of gravity and minimal vertical cross section area would reduce cross wind concerns. Smaller wheels drop everything lower, or the wheels could be pushed to the edges.

Apparently the idea wasn't all that crazy after all... there is a tour where they run these solar powered bikes already.

The SunPower Maxeon solar cells seem to be the hot item in this area of technicality. You can get about $1 a watt in solar cells these days and your only limitation is surface area and how to manage it.

It's like the somewhat more practical version of solar racing for something remotely bicycle like... there is still a lot of variability in the designs.

Essentially they are theorizing (in French) about an "in the rim" motor that could be concealed in a bicycle so as to create what they call "Mechanical Doping".

In other words... "cheating by ebike".

Some time ago I made this post:

Thu, 01/16/2014 - 10:35

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Carbon Fiber Switched Reluctance Rim Motor
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This is an idea I've been toying with for about five years but until now there was a technical problem that I couldn't seem to get past.

The idea is to "insert" thin pieces of iron into a carbon fiber rim so that you create alternating regions of either high magnetic potential or low. What had made me "stuck" in the past is that the technical problem of building it was beyond anything I could accomplish.

I had thought of the idea of using some kind of specially woven carbon fiber cloth that alternated with carbon and iron. Seems too tricky.

Another idea was to insert iron plates, but how might you assemble that so that the rim didn't fall apart under stress? Again, too unworkable.

Finally I came up with a new idea...
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When two magnets are placed outside a contained area iron filings will accumulate in the areas of highest magnetic field strength:
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So the idea would be to MIX iron filings into the RESIN as you build up a carbon fiber rim and then before the resin can set up you apply powerful magnets which draw the iron filings into alignment. Once the resin sets these iron filings create alternating regions of high and low magnetic flux potential.

This solves the problem because you can build a solid carbon fiber rim very quickly. This is the sort of technique that could be done in mass production at a low cost. The iron filings can be electrical silicon steel or some of these more high tech materials being used in transformer cores.

One thing to consider is an alternating current in those magnets because that should "shake" the iron filings and improve migration through the cloth. Ideally you want all the iron filings to accumulate in the desired regions.

Finally, you now have the basis for a switched reluctance motor because the rim will have alternating regions of high and low magnetic flux potential.

This will give torque that is roughly three times a disc motor.

Torque = Force * Radius
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Let me add a New Idea to this...

What if you ground up Neodymium Magnets into small enough bits of sand and mixed that into the RESIN?

Those Neodymium sand particles will line up under the force of a strong magnetic field during curing and produce permanent magnets inside the carbon fiber. The result might be less than pure Neodymium per volume, but this is actually part of the structural strength of the carbon wheel.

This takes the very brittle Neodymium magnet property and makes that issue dissolve. It's even possible the sand sized particles could add some strength. (it would reduce the amount of RESIN being used if the Neodymium sand is small enough to fit between the carbon fibers)

Nano-Neodymium anyone?

Just have to stand in awe of these SunPower c60 solar cells.

One hundred of them only weigh under two pounds and that can generate 320 watts of power.

These are the cells used on those solar powered airplanes that fly around the world so they are actually literally lightweight enough to fly. Amazing.

And a hundred of them run about $150 to $200 right now... a bargain.

Thanks BikeMad for the link... they are really awesome cells and solar is the kind of thing an "older guy" like me gets interested in. I'm less interested in high speed at this point than things like extended range while making that easier since I'm already 55 years old.

Anyway... to my thoughts today...

The first thing you realize about a solar cell is that the energy you get is going to depend on the angle of the sun. In the image above the parabolic shape defines the power performance of a row of five cells across and laying simply flat.

By adding "Skirts" of two cells each on either side of the flat panel rows (at a 90 degree angle downward) you now gain power on one side whenever the sun is at an angle.

Is this wasteful?

Absolutely... but the effect is to widen the powerband so that sun angles up to 43 degrees will produce the same or more energy as those flat cells alone.

This means that a solar only (no battery) option becomes more realistic without having to widen the panel or make it longer which negatively effects bike handling.

The goal is to get better AVERAGE performance rather then "peaky" power based on the sun being directly overhead.

Of critical importance is a technical breakthrough that these SunPower c60 "Maxeon" cells have achieved which is to not have current get blocked by shaded cells. That was apparently a major issue in the past and made a "Skirt" impractical because it would have blocked current flow. Other cells likely will not possess this feature.

It hadn't occurred to me just how low the sun really dips.

On average in San Jose, CA the sun peaks at just 53 degrees each day.

So the idea of using "Skirts" seems to be a necessary thing to do because the sun never is actually overhead unless you live in the tropics.

Another thing I realized is that cells mounted at 90 degrees (perpendicular) will get light that bounces off the road as well as other reflective sources.

The ideal shape would be a cube with cells on the top and the sides, but you can ignore the bottom if it's close to the ground. A Sphere shape gives no advantage because the cross section ends up the same. Plus, for a bicycle your biggest problem is width, so the sides can have cells and not increase the top.

If you go sailing you don't design a sailboat to work equally well in all directions. Instead you alter the shape and direction of the sails to match wind conditions.

Why try to create the best "average" solar position (always changing) ebike when you can use the same logic as sailing to change the position of your solar panel while riding?

There are many types of gear shifting options including twist shift, thumb shift as well as the old fashioned type that just uses a lever.

The idea would be to alter the angle of the solar panel in realtime.

Solar Sailing in a sense.

By making it possible to adapt to changing sun conditions while riding you never need to stop to make adjustments. Since roads twist and turn you would over time adjust the solar panel instinctively as your learned memory improved. Eventually you would get so that you immediately repositioned the solar panel angle as needed... "like riding a bike".

Obviously you could get all high tech and automate this (which would be awesome) but for now simply having manual realtime control would be good.

I'd figure that 30 degrees to either side left and right and maybe 10 degrees front and back since that direction is longer and more likely effected by the wind. If you are dealing with strong winds then you set everything to zero.

Another option would be to use small motors to control the solar panel angle and run them off the solar panels themselves. Buttons to control it? Hmmmm.

With solar you really don't need a battery because you get what you need from the sun. However, it might be nice to have a little buffer of energy that is there to get you started.

Often people talk about how many "watt hours per mile" they use.

Numbers vary from 10 Wh per mile to 50 Wh per mile depending on speed.

You can buy (10) 500F 2.7V Supercapacitors for about $50 making 27V/10Wh.

A typical ebike battery has about 500 Wh. (50 times the energy storage)

This means a typical ebike will have a range of from 10-50 miles.

Solar can introduce a constant of at least 100 Watts into the system which over the course of an hour is 100 Wh. (one fifth of an ebike battery) The solar panels would generate ten times the energy of the capacitor storage.

The system would look like:

Solar Panels : 100 Watts to 200 Watts @ 24 volts

Capacitors : 10 Wh capacity

DC-to-DC boost voltage converter : (10v - 30v) boost to 48v constant

Ebike Controller : Standard ebike 48 volt controller

My goal was to create a spreadsheet that could identify the direction that each individual solar cell was pointing so that I could test different designs to see how they would perform when the bike would rotate on the ground.

If the sun is at a 60 degree angle relative to the horizon then as the bike went in circles on the ground the relative position would change and the power produced per cell would change.

At first I tried a spherical coordinate system and just couldn't ever get it right so I switched to the cartesian coordinate system and it became much easier.

Assume each solar cell is a unit vector equal to one.

Position the sun based on a similiar unit vector equal to one.

Take the dot product of those two vectors and you get the relative power of the cell. If the value is negative you discard it.

Imagine an elongated cube.

Top : 4 x 10 = 40 cells

Left : 4 x 10 = 40 cells

Right : 4 x 10 = 40 cells

Front : 4 x 4 = 16 cells

Back : 4 x 4 = 16 cells

...for a total of 152 cells.

The chart above represents the power output total of those cells as you rotate relative to a specific sun elevation.

When you average those rotated numbers you get the average power.

Notice how much less power is lost as the sun gets at a lower angle when you have an elongated cube compared to just a flat solar panel.

The width is constant at 20" with the elongated cube and the length is the same at 50" so you end up with:

Better Performance

Other shapes could level out the rotational ups and downs and some will likely create a more aerodynamic result compared to the elongated cube.

Being able to be confident that under most all sunlight conditions you can get at least 100 watts out of a small space would make the solar trailer very practical. The idea of "solar sailing" (with adjustable angles) is the ideal but also a hassle. I'm not sure if anyone wants to be constantly fiddling with solar panel angles. By creating a 360 degree profile of solar cell behavior you can effectively get the ideal all the time.

40 cells * 3.2 watts = 128 watts

Using cells on the side angles can in the same space exceed perfection in the flat even when set at the perfect angle.

Same space, more power.

Still fiddling with different designs.

The Teardrop Shape has good aerodynamic properties in the forward direction. It is exposed to cross winds, but just about anything will be of that size.

Notice that the power stays fairly constant with sun elevation.

This means you can count on about 100 watts all day until the sun gets as low as about 20 degrees which is near sunrise or sunset.

Since the sun never gets above 60 degrees (unless you live in the tropics) there is little point in seeking performance there.

From 20 degrees to 60 degrees are the sun elevation angles you want to design for and in all 360 degrees of rotation. You have to assume the bicycle could be going in any direction at any time.

I've actually decreased the size by about 20% so that this fits into a space that roughly equals 4 x 8 solar cells or 20" x 40".

If you don't care about power and only torque, then you have a few options. You can make a tiny motor, and then run it through a series of mechanical toothed levers (gears) to try to simulate as though it were a motor with a larger radius, OR you can just have a motor with the appropriate radius natively, and skip the leverage stages in trade for having all the leverage you need in the motors radius. If you put the leverage you need in the motors radius itself, then for a given mass of motor, you can always achieve highest continuous power, because more of the system mass is iron and copper doing the actual conversion from the packs energy to the mechanical work output you wanted. Any portion of vehicle weight that isn't storing the electrical energy or making the electrical to mechanical power transformation is your vehicles performance burden to be minimized or removed if possible.

This argument continues to circulate on Endless-Sphere:

https://endless-sphere.com/forums/viewtopic.php?f=30&t=81074&start=25#p1195087

The main flaw in this argument is that as you increase the radius of a motor you must equally reduce it's width in order to maintain the same weight which reduces the forces proportionally balancing everything out. Just like with the copper fill question (high or low Kv) it ends up the same. (some benefit is had with hollowed out internals on big radius motors)

The reality is that when the topic centers around motor weight there is a fixed performance you can typically get for a given weight.

Small motors and gears make sense because you can create something lightweight.

Luke has no knowledge of the weight issue... it's like he has a complete blind spot to that topic and always scales his motor up so that it's 20 times bigger than needed and says:

"See... big motors are the answer."

Well, yeah, if you accept the weight penalty.

In the real world the ebike at 250 watts (which will be the most abundant) needs only a couple of pounds to satisfy that requirement.

There just is no need for a 50 hp ebike... and never will be.

The typical person generates only about 100 watts of power by casual riding.

At this point I'm drifting off into solar as my next project (likely next summer) and that subcategory is well adapted to low power situations and seems a perfect match for an ebike. These last few years I've been keeping my hands clean, but next year they should get dirty again.

I think a lot of the time people just lack a mental model of how all this stuff works and you really need an animation to really comprehend multispeed gearing. This animation does a good job (I believe) of expressing this abstract set of relationships:

You experience it intuitively on the ebike, but to see it represented visually you gain a more complete understanding. This would be roughly like a 9-speed. (gear spacing is typically closer together though)

Third gear is the best gear choice. (200%)

I've run calculations on a trailer of this size and you are looking at constant power no matter what sun angle in the range of 350 watts.

This opens up some new ideas:

Large Travel Trailer for camping that essentially powers it's own weight and a little more.

Kids Trailer for taking a child on a bike ride which adds more power than is required.

These could make actual products which are practical additions to the ebike.

It's always funny how new things appear that you didn't know about before looking.

With aerodynamic shapes I had always assumed that the "Longer the Better" meant more streamlined and a lower Coefficient of Air Drag.

But actually there are two components:

Frontal Area

Friction

...which means at some point as you stretch out the length of the shape the Friction rises and makes things worse.

This likely depends on speed which for an ebike trailer will be low. (20 mph)

So this first shape looks pretty good.

I was considering making it longer but see that's not necessary.

This was a big Disappointment.

That old style 1950's Camper Trailer has a lot going for it, but when applied to Solar Power it's a poor performer.

The performance is not much better than Flat panels.

It's better to have a flat top and sides that create the aerodynamic shape.

Good to know.

Okay now this is getting somewhere.

The rotation data is very good.

Notice how there is less variation in power despite both rotating relative to the sun 360 degrees as well as responding to different sun angles.

Ultimately the power is pretty much flat no matter what time of day and which direction you are pointed.

This should be large enough to sleep inside... a self powered solar camper.

Maybe a small air conditioning unit?

If it's hot outside you climb in and turn on the air conditioner driven by the solar power and cool off. You both get out of the sun and get cool because of the sun.

The next morning after a good nights sleep you plug in a small stove that is driven by the morning sunlight and make yourself some coffee.

No charging of batteries required... nothing to break... no Lipo fires or excess battery weight to lug around. All these solar cells weigh just two pounds.