# IVT Brushless Motor Idea - Hub Motor?



## samborambo (Aug 27, 2008)

I had this idea after reading up on the Toyota Prius' hybrid drive system. The Prius has a planetary gearbox that connects the engine to two AC motor/generators and to the output drive. Using the difference in motor/gen and engine speeds, an infinitely variable output ratio is available.

I've also seen an industrial drive IVT system that works on a similar principle - and more closely related to my idea. 

http://www.torotrak.com/IVT/works/

The above industrial drive works by having two inputs to the planetary gearbox system (PGS). The first input is connected directly to the engine and the second connects through a continuously variable transmission (CVT) from the engine spinning in the opposite direction. With the CVT at 1:1 ratio, the output from the PGS is 0 RPM, or 'geared neutral'. The engine can rev at any RPM and still have 0 RPM at the output. As the CVT deviates from 1:1 ratio, the output shaft begins to turn. The speed at the output is the sum of the two inputs. EG: Engine is 1800RPM, CVT output is -1900RPM then PGS output is -100RPM or 100 RPM in reverse. One brilliant feature of this type of drive is that it is a constant power output from 0 RPM - in other words theoretically infinite torque at 0 RPM. The torque is only limited by the combined power from both inputs and the strength of the PGS gearing.

So here's my idea: build two LRK BLDC radial motor/generators into the PGS itself. The ring gear on the outside becomes the rotor for a high torque/low speed BLDC 'inrunner'. The sun gear in the center becomes the rotor of a high speed, low torque BLDC 'outrunner'. The planetary gear carrier is the output. Efficiency should be relatively high (~95%) across the desired speed range since the BLDC motors are free to run at optimal speed. The motor system would have more torque than a tractor and high speed gearing for cruising. Direct drive hubs would be easy! Compared to a BLDC motor of similar size, the total power of the PGS motor system may be less but with more versatile torque. It's much harder designing a decent direct drive hub motor since the motor has to be capable of high torque at 0 RPM. Having 'geared neutral' also means that the rotors can efficiently hold the vehicle at a standstill without the high I^2.R losses associated with a BLDC held at 0RPM.

Motor control would be interesting. The system needs two BLDC inverters with closed loop control (hall sensors, etc.). A controller monitors the hall inputs to determine rotor speed, direction and angle and then works out the required difference in speed (delta speed) to apply to each rotor. An overall PID loop would control torque demand.

So what does everyone think?

Not sure how you'd implement the handbrake.

Sam.


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## major (Apr 4, 2008)

samborambo said:


> So what does everyone think?


You mean something like this?







The Electric Transaxle


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## samborambo (Aug 27, 2008)

Yep. Pretty much. Jeez, can't think of anything original these days.....

Anyone seen one working?

Sam.


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## Amberwolf (May 29, 2009)

I'd never heard of them before, but just reading your idea I thought how I might make one, and seeing the diagram posted I think I could do something like that if I can find a planetary drive to take apart for it. 

On a small scale, I might be able to do it with an old Sturmey-Archer internally-geared hub for a rear bike wheel. I hope you don't mind if I link this thread over at Endless-Sphere to post the idea there and see if anyone else has a contribution to try it out.

http://endless-sphere.com/forums/viewtopic.php?f=2&t=15618&start=0


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## samborambo (Aug 27, 2008)

Amberwolf said:


> I'd never heard of them before, but just reading your idea I thought how I might make one, and seeing the diagram posted I think I could do something like that if I can find a planetary drive to take apart for it.
> 
> On a small scale, I might be able to do it with an old Sturmey-Archer internally-geared hub for a rear bike wheel. I hope you don't mind if I link this thread over at Endless-Sphere to post the idea there and see if anyone else has a contribution to try it out.


Fill ya boots mate. I'm all for collaborative design. It looks like Solomon Technologies has several patents on their design though. Still doesn't hurt to make prototypes. If it were commercially viable, I think there'd be enough prior art around to challenge the patents. It's such an obvious design - hell, even I thought of it on my own!

I'd like to put some time into this but I have sooo much on - not to mention an EV conversion in progress. The diagram shows the sun gear brought out to a larger diameter rotor similar to the ring gear rotor. I'd like to develop one with the sun rotor *inside* the sun gear. It makes more sense to me. eg: take an existing PGS, cut out the center of the sun gear to make a ring and mount the magnets on the inside of the ring.

Sam.


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## Amberwolf (May 29, 2009)

samborambo said:


> The diagram shows the sun gear brought out to a larger diameter rotor similar to the ring gear rotor. I'd like to develop one with the sun rotor *inside* the sun gear. It makes more sense to me. eg: take an existing PGS, cut out the center of the sun gear to make a ring and mount the magnets on the inside of the ring.


Well, one reason to do it their way is you only have to make one kind of motor. Less tooling/etc.

Another reason is that identical motors gives same torque on either side of the planet gears, if that happens to make a difference to the system. 

Yet another reason is that identical motors means identical drives, parameters, etc, simplifying the software in the controller(s). 

At least, that's how I see it. 

For space and efficiency of the drive itself, I think your way is better, but from a cost-to-manufacture standpoint, theirs might win out if the above are reasons to do it that way.

I'd like to do it your way, if I could make the motors from scratch (probably can't, certainly not at my skill level now). But I might be able to hack one together using their way of doing it plus existing ebike motor parts (or rewound cieling fan motors plus magnets), plus existing bicycle planetary geared hubs. 

Pondering mode is running in the background, and I'm sure my brain will tell me when it's done.


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## Amberwolf (May 29, 2009)

Just had a thought. Take a bicycle hub motor and build a sun gear on it's outrunner casing.

Take an F&P washing machine motor and machine out the core of it's stator so the above would fit inside it with clearance for planetary gears and a ring gear, plus bearings for the stator to ride on (like little planetarys) between the stator and the ring.

Then the rotor would be remachined so it rides on the ring gear. 

Carrier for the planetaries gets welded or otherwise fixed to the former long axle of the F&P motor. Suitable bearings for the rest of everything to ride around these.


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## Amberwolf (May 29, 2009)

Oh, and the hub motor would need to have it's axle changed to a larger hollow tube with larger bearings for the original casing to run on, and smaller bearings inside the tube for the F&P axle to run inside of.


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## major (Apr 4, 2008)

samborambo said:


> Yep. Pretty much.


Hey Sam and Amber,

What you see is a multi port epicycloidal gear system. And if you wish to experiment with it, the easiest thing to do is get a small differential from like a powered wheelchair. The differential is a planet gear set where the sun and ring are equal. Get 2 small motors and connect one where each wheel was. The old input sprocket then becomes your output. Vary the speed and direction of the two motors and measure your output. Having the sun and ring the same makes calculations easy because of the 1 to 1 ratio.

You will find that it is not a CVT, Continuously Variable Transmission. Meaning that it is not capable of variable torque multiplication. Yes, it is a variable speed device. And has some very interesting possibilities. When a third power plant is added, it becomes a "power split" system as in the Toyota hybrids. When you add a second gear set and a couple of clutches, it becomes the GM 2-mode hybrid.

But I fail to see the value of the simple 2 motor system that Solomon has. You never get more torque out than you put in. You have variable speed, but need variable speed input from the motors to start with. You're better off just using a single motor equal to the size of the 2 and a variable speed controller.

You might want to search for the work of Dr. John Miller. He used to have some excellent notes on line from instruction it looks like he did. Ref: 


Comparative Assessment of Hybrid Vehicle Power Split Transmissions​ 

John M. Miller, P.E., PhD dated Jan. 12, 2005


Gears and motors are cool  Have fun.

major


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## Amberwolf (May 29, 2009)

Hmm. If this is the case, I guess it is not useful to me.  I wonder what purpose the Solomon unit does have, then? 

BTW, that is a good idea for the powerchair differential--I actually have someone bringing me one of those soonish, so I will be able to play with it like that. 


EDIT (added): wait--wouldn't the advantage of the Solomon unit be that even at the lowest output speed, it still can spin the input motors at their highest, most efficient, speeds? As opposed to a single-motor system that would then be forced (if used as a direct drive as that unit seems to be intended for) to run at very high current levels due to low BEMF when at very low speeds? 

If so, then that is worth having for my purposes.


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## samborambo (Aug 27, 2008)

major said:


> Hey Sam and Amber,
> You will find that it is not a CVT, Continuously Variable Transmission. Meaning that it is not capable of variable torque multiplication. Yes, it is a variable speed device. And has some very interesting possibilities. When a third power plant is added, it becomes a "power split" system as in the Toyota hybrids. When you add a second gear set and a couple of clutches, it becomes the GM 2-mode hybrid.
> 
> But I fail to see the value of the simple 2 motor system that Solomon has. You never get more torque out than you put in. You have variable speed, but need variable speed input from the motors to start with. You're better off just using a single motor equal to the size of the 2 and a variable speed controller.
> ...


I have to disagree, major. Like any gearing, altering the ratio from input to output will transform the speed and torque. With the two input PGS, you simply sum the speeds of the input motors together. Think of the power equation from input to output - it must balance (minus losses). 

EG: 
rotor one is running at 10 rad/s CW and 10Nm torque = 100W
rotor two is running at 11 rad/s CCW and 10Nm torque = 110W

planetary carrier must be 210W of load, turning at 1 rad/s CCW and therefore 210Nm.

Sam.


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## gor (Nov 25, 2009)

true, power the same, torque and rpms geared-up and can very with rpm differences


this particular design (prev.posts) - can we find and compare it to individual characteristics of each motor?

ST58 Electric Wheel™​

HP 12 HP
Nominal Voltage DC 144 Volt
Power 9 kW​Torque
MAX (SunRPM ≠ RingRPM) 150 Lb-Ft
TorqueContinuous (SunRPM ≠ RingRPM) 120 Lb-Ft
TorqueMAX (SunRPM = RingRPM) 90 Lb-Ft

TorqueContinuous (SunRPM = RingRPM) 74 Lb-Ft
RPMMAX Unloaded 1000 RPM
Duty 24 Hr
Ambient 40 °C
Service Factor 1.0
Enclosure TE
Insulation C1.H​
Weight 168 Lbs


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## major (Apr 4, 2008)

samborambo said:


> IEG:
> rotor one is running at 10 rad/s CW and 10Nm torque = 100W
> rotor two is running at 11 rad/s CCW and 10Nm torque = 110W
> 
> planetary carrier must be 210W of load, turning at 1 rad/s CCW and therefore 210Nm.


Hi Sam,

I think the correct output on the planet carrier would be 20Nm at 0.5 rad/s. 

major


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## samborambo (Aug 27, 2008)

major said:


> Hi Sam,
> 
> I think the correct output on the planet carrier would be 20Nm at 0.5 rad/s.
> 
> major


That's only 10W of output from 210W of input - only 4.8% efficient!

My mistake about the speed though. It should be 0.5 rad/s but 420Nm.

Sam.


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## major (Apr 4, 2008)

samborambo said:


> That's only 10W of output from 210W of input - only 4.8% efficient!


Sam,

We were ignoring losses for the example. It is 100%. 

110W - 100W - 10W = 0

No losses. All inputs and outputs.

major


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## samborambo (Aug 27, 2008)

In your calculation the torque for one rotor is in the wrong direction. One rotor would be motoring while the other would be in regen.

I should have included direction or sign for the torque in my example.

EG: 

Consider clockwise to be positive sign for angular velocity and torque.

rotor one is running at +10 rad/s and +10Nm torque = +100W (power source)
rotor two is running at -11 rad/s and -10Nm torque = +110W (power source)

planetary carrier must be -210W (a load), turning at -0.5 rad/s and therefore +420Nm. Input and output add to zero.


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## major (Apr 4, 2008)

samborambo said:


> In your calculation the torque for one rotor is in the wrong direction. One rotor would be motoring while the other would be in regen.
> 
> I should have included direction or sign for the torque in my example.
> 
> ...


Sam,

That is an impossible condition. It cannot happen.

Think of it like this. Rotor 2 is powering the sun. Rotor 1 is on the ring but unpowered. Rotor 2 is at 11 rad/s. Put resistance on the planet carrier and rotor 1 spins at -11 rad/sec. Planet carrier at zero. Rotor 2 is the motor and will have positive torque (in the same direction as rotation). Now how can you power rotor 1 in the negative direction as a motor (with negative torque, in the same rotation direction as rotor 1 is turning) and cause it to run at -10 rad/s? One of the rotors has to be a generator.

And the torque on the carrier is the sum of the torques on the ring and sun and will equal the load torque. There is simply nowhere else for torque to come from. 

Regards,

major


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## samborambo (Aug 27, 2008)

major said:


> Sam,
> 
> That is an impossible condition. It cannot happen.
> 
> Think of it like this. Rotor 2 is powering the sun. Rotor 1 is on the ring but unpowered.


Rotor 1 IS powered. It has torque in the same direction as its motion.



> Rotor 2 is at 11 rad/s. Put resistance on the planet carrier and rotor 1 spins at -11 rad/sec. Planet carrier at zero. Rotor 2 is the motor and will have positive torque (in the same direction as rotation). Now how can you power rotor 1 in the negative direction as a motor (with negative torque, in the same rotation direction as rotor 1 is turning) and cause it to run at -10 rad/s? One of the rotors has to be a generator.
> 
> And the torque on the carrier is the sum of the torques on the ring and sun and will equal the load torque. There is simply nowhere else for torque to come from.
> 
> ...


Apart from your assumption that rotor 1 is unpowered, you're correct about summing the input torques. However, you're missing the point that as well as summing the torques, there's a ratio from the inputs to output that transforms the speed and torque. 

I was a bit off with my ratios. Of course you need to take the number of teeth on the sun and ring gears to work out the torque ratio on the output. This page explains things well for a single input PGS:

http://science.howstuffworks.com/gear7.htm

I used the equation with the ring gear stationary and then added the ring gear speed afterwards. For speed:

PC speed = sun speed / ( 1 + sun teeth / ring teeth ) + ring speed

To verify, sun teeth = 30, ring teeth = 72, sun speed = 34, ring speed = -10 (opposite diection), planetary carrier output = 0. I made a small tool in a spreadsheet to prove it.

Total torque on both motors can be worked out once you know the speed ratios.


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## major (Apr 4, 2008)

samborambo said:


> Rotor 1 IS powered. It has torque in the same direction as its motion.
> 
> Apart from your assumption that rotor 1 is unpowered, you're correct about summing the input torques. However, you're missing the point that as well as summing the torques, there's a ratio from the inputs to output that transforms the speed and torque.
> 
> ...


Sam,

I thought we were using the 1 to 1 to 1 ratio as in the differential example I offered up. That's the way it looked from your example. You can throw in different number of teeth, it just complicates equations but doesn't change the theory. Why not keep it simple with the 1:1:1 and the 11 and 10 rad/sec and 10 Nm?



> you're correct about summing the input torques


How is the sum of 10 Nm and 10 Nm = 420 Nm?

I didn't want to get into typing equations out here, but:



> PC speed = sun speed / ( 1 + sun teeth / ring teeth ) + ring speed


This doesn't look right to me. Maybe you can manipulate the equation and get it to come out like this, I don't know. Here is how Dr. Miller has it:

k = Ring Teeth / Sun Teeth = basic ratio

Ws = Sun Gear Speed
Wr = Ring Gear Speed
Wc = Planet Carrier Speed

Ws + kWr - (k + 1)Wc = 0



> To verify, sun teeth = 30, ring teeth = 72, sun speed = 34, ring speed = -10 (opposite diection), planetary carrier output = 0.


Hmmm, I get -14.167.

Regards,

major


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## samborambo (Aug 27, 2008)

major said:


> Sam,
> 
> I thought we were using the 1 to 1 to 1 ratio as in the differential example I offered up. That's the way it looked from your example. You can throw in different number of teeth, it just complicates equations but doesn't change the theory. Why not keep it simple with the 1:1:1 and the 11 and 10 rad/sec and 10 Nm?
> 
> ...


It's not, obviously. The speed has been transformed and therefore the torque has also. 

Here's an example: A 3000RPM, 100Nm motor powering a wheel through a 3:1 gearbox has 1000RPM 300Nm at the wheel. The torque didn't "appear out of nowhere", it's transformed.



> I didn't want to get into typing equations out here, but:
> 
> 
> 
> ...


I get 2.94118 with the equation you stated. I found a problem with both my equation though. Miller's works well:

Wc = (kWr + Ws) / (k + 1)

2.94118 = (2.4 * 34 - 10) / (2.4 + 1)

So for both rotors turning in the same direction at the same speed, the carrier should turn at the same speed. If the rotors have a ratio between them of -k, carrier speed will be 0.

You're right, it does complicate things having a different ratio from 1:1 but its much more realistic. 

Sam.


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## major (Apr 4, 2008)

samborambo said:


> It's not, obviously. The speed has been transformed and therefore the torque has also.
> 
> Here's an example: A 3000RPM, 100Nm motor powering a wheel through a 3:1 gearbox has 1000RPM 300Nm at the wheel. The torque didn't "appear out of nowhere", it's transformed.


Yes, but here you have a 3 to 1 ratio. In your example, it was a 1 to 1 ratio. I didn't see any mention of a 21 to 1 ratio that would have been needed to transform 20 Nm into 420 Nm.



> I get 2.94118 with the equation you stated. I found a problem with both my equation though.


You said:


> planetary carrier output = 0


 So I solved the equation with Wc = 0. Now you change it and solve for Wc using Ws = 10. What gives? Can't we just get back to the 1 : 1 : 1 ratio and avoid confusion and talk about the point. Planet gears don't multiply torque without the difference in number of teeth (or gear pitch diameters) and then they have a fixed ratio, not a variable ratio as you claim.



> You're right, it does complicate things having a different ratio from 1:1 but its much more realistic.


Well, I beg to differ. Once you get past the ring and pinion in the automotive read end, that is exactly what you have. A 1 : 1 : 1 planet set. I think a lot of guys can identify with turning a wheel when the car is jacked up and seeing the opposite wheel spin in the opposite direction at the same speed. And seeing the wheel speed double when it is off the ground and the other wheel is held in place by the brake. And when one wheel loses traction on ice and you get no torque from the wheel on the pavement. These are all characteristic of the planetary gear set. It is a marvel. But not a CVT. 

Regards,

major


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## samborambo (Aug 27, 2008)

major said:


> Yes, but here you have a 3 to 1 ratio. In your example, it was a 1 to 1 ratio. I didn't see any mention of a 21 to 1 ratio that would have been needed to transform 20 Nm into 420 Nm.
> 
> 
> 
> ...


Major, you're missing the big point that I made right at the beginning. Aside from the tooth ratio, a variable ratio is produced by the DIFFERENCE in speed between the two inputs. Run through a few iterations of the equation and you'll get an understanding of it.

and it's not a CVT, its an IVT.......CVTs don't work down to 0 RPM.

Sam.

EDIT: Interesting that you mention a differential. A diff would work exactly the same if driven from the wheel shafts by motors and have the driveshaft as the output. The diff ratio wouldn't be practical though.


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## major (Apr 4, 2008)

samborambo said:


> EDIT: Interesting that you mention a differential. A diff would work exactly the same if driven from the wheel shafts by motors and have the driveshaft as the output. The diff ratio wouldn't be practical though.


Sam,

That is exactly what I said in post #9. It would be practical for demonstration of principle.



major said:


> And if you wish to experiment with it, the easiest thing to do is get a small differential from like a powered wheelchair. The differential is a planet gear set where the sun and ring are equal. Get 2 small motors and connect one where each wheel was. The old input sprocket then becomes your output. Vary the speed and direction of the two motors and measure your output. Having the sun and ring the same makes calculations easy because of the 1 to 1 ratio.
> 
> You will find that it is not a CVT, Continuously Variable Transmission. Meaning that it is not capable of variable torque multiplication. Yes, it is a variable speed device.





> Major, you're missing the big point that I made right at the beginning. Aside from the tooth ratio, a *variable ratio* is produced by the DIFFERENCE in speed between the two inputs.


I don't think I'm missing the point. The planet set with 2 motors as in the Solomon product gives you variable speed, not a variable transformation ratio. You can't get more torque out than what you put in, allowing for a fixed ratio which you can easily get any number of ways using a single motor drive. So what's the point of using such a device? It is just a gimmick, aside from a means to sue Toyota for infringement 

Regards,

major


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## samborambo (Aug 27, 2008)

Major,

You've shown that you don't understand how speed and torque relationships work within a multiple input or output transmission. That statement you've made that "you can't get more torque out than what you put in" is as incorrect as if you'd made the same statement referring to rotational speed instead. I suggest you study, at the very least, this page:

http://en.wikipedia.org/wiki/Transmission_(mechanics)

Especially, read the section on infinitely variable transmissions. It's stated there in plain English.

Sam.


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## major (Apr 4, 2008)

samborambo said:


> You've shown that you don't understand how speed and torque relationships work within a multiple input or output transmission. That statement you've made that "you can't get more torque out than what you put in" is as incorrect as if you'd made the same statement referring to rotational speed instead.


Sam,

I do understand this. I am (and I thought we were) talking about a planetary gear system, not CVT or IVT. I know you started the thread about IVT, but in post #9 referring to a planetary gear set with 2 motor input, I said


major said:


> You will find that it is not a CVT, Continuously Variable Transmission. Meaning that it is not capable of variable torque multiplication.


 In post #11 you disagreed with me about this. I take this to mean that you believe that a 2 motor planetary system like the Solomon unit is a CVT or IVT or otherwise has the ability for variable torque multiplication. This is further supported by your examples.

I have never said that CVTs or IVTs or spur gear sets or belts and pulleys or chains and sprockets do not multiply torque in the inverse ratio as they alter speed. And this includes planetary gear systems which have a difference in the ring and sun. CVTs and IVTs can alter the transformation ratio. The 2 motor input planetary gear system (like Solomon) cannot alter the transformation ratio. It can alter output speed, but will sum input torque, not multiply torque in an inverse ratio to the speed.



samborambo said:


> I have to disagree, major. Like any gearing, altering the ratio from input to output will transform the speed and torque. With the two input PGS, you simply sum the speeds of the input motors together. Think of the power equation from input to output - it must balance (minus losses).
> 
> EG:
> rotor one is running at 10 rad/s CW and 10Nm torque = 100W
> ...


This clearly shows you do not understand what I am saying or do not believe me. Fine. I invite you to try it and find out. A 2 motor Planetary Gear system (like Solomon) is not a CVT or IVT.

Regards,

major


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## major (Apr 4, 2008)

samborambo said:


> Like any gearing, altering the ratio from input to output will transform the speed and torque.


Hi Sam,

I've been looking for a reference to convince you that a 2 motor planetary gear system is not a CVT or IVT and it does not have a variable transformation ratio. Here are a few:



> This explains how similar a planetary or epicyclic gear ...... However, the torque multiplication effect of a true CVT is absent and it replaced by electric motor assist.


 from http://www.ecrostech.com/prius/original/Understanding/PowerSplitDevice.htm 
Also see "Torque Relationships in the PSD" further down that page.



> It acts as a continuously variable transmission (CVT) but with a fixed gear ratio.


 from http://eahart.com/prius/psd/ 



> Torque splits according to port loading (power balance)


 from Dr. Miller.



> The Prius transmission produces one of the effects of a CVT but not the other.....The Prius transmission does not, however, multiply up engine torque at low vehicle speed. This is because it has only one gear ratio. Effectively, the engine is coupled to the wheels as if the car is always in top gear.


 from http://www.ecrostech.com/prius/original/Understanding/ContinuouslyVariableTransmission.htm 

As you have agreed with me, the planetary gear system includes the familiar differential. Why do they call it "differential"? The ports can operate at "different" speeds. And those speeds are defined by the equation I posted from Dr. Miller. But the torque simply sums, or splits as he says. Torque does not multiply in the inverse ratio of the speed ratio as you think.

Regards,

major


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## samborambo (Aug 27, 2008)

Major,

Your references conclude that torque splits evenly (or according to the fixed ratio) between the sun and ring gears. This is correct ONLY when the sun and ring are turning in the same direction or the same speed (assume 1:1:1 ratio). Otherwise, torque does not split evenly. It is transformed. Here's an example:

Assume 1:1:1 ratio.

PC driving +10 rad/s, +10Nm, +100W --> Sun load +10 rad/s, -5Nm, -50W and Ring load +10 rad/s, -5Nm, -50W. 

Power splits equally between sun and ring. Input and output sum to 0W. It's not much of a gearbox really as there's no speed or torque transformation going on. I think we totally agree on this model.

Now hold the ring gear stationary:

PC driving +10 rad/s, +10Nm, +100W --> Sun load +20 rad/s, -5Nm, -100W and Ring load 0 rad/s, -5Nm, 0W. 

This is what you'd expect from a differential. Power does not split equally although torque does. Input and output power sum to 0W. We agree?

Let's leave the single-input multiple-output differential model behind. Back to the PGS with two inputs, one output: (1:1:1)

Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, +10Nm, +100W ---> PC load 0 rad/s, 0Nm, 0W.

PC isn't turning because the sun and ring are turning at the same speed in opposite directions. Input and output power DO NOT sum to 0W so the sun and ring motors must be accelerating. To keep the speed constant, either motor could apply a negative torque WRT their direction:

Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, -10Nm, -100W ---> PC load 0 rad/s, 0Nm, 0W.

Ring motor is now generating. Input to output power now adds to 0W. Speed will remain constant.

To show the difference of speed/torque transformation, hold the ring motor stationary:

Sun driving -10 rad/s, -10Nm, +100W and Ring driving 0 rad/s, +10Nm, 0W ---> PC load -5 rad/s, +20Nm, -100W.

I+O = 0W. Now at this point you'll say that the torque has been summed from the sun and ring. It hasn't. -10Nm + +10Nm does not equal +20Nm. The ring motor is opposing the sun motor's torque but since it isn't turning it isn't contributing to the power transfer at all. Since the PC is turning at half the speed of the sun, it MUST be twice the torque load.

Now look at a scenario where the sun and ring are turning at different speeds in opposite directions:

Sun driving -10 rad/s, -5Nm, +50W and Ring driving +100 rad/s, +0.5Nm, +50W ---> PC load +45 rad/s, -2.222Nm, -100W.

I+O = 0W. Motor speed will remain constant. Do you disagree?

Taking that last scenario and exaggerating the torque transformation:

Sun driving -10 rad/s, -5Nm, +50W and Ring driving +10.1 rad/s, +4.9505Nm, +50W ---> PC load +0.05 rad/s, -2000Nm, -100W.

I+O = 0W. Motor speed will remain constant. Torque is transformed from 9.95Nm to 2000Nm, a factor of 201. Speed is transformed from an average of 10.05 rad/s to 0.05 rad/s, also a factor of 201.

Like I said, when you run through enough iterations of the speed equation Dr Miller stated and apply the inverse torque equation, it makes perfect sense.


Sam.


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## major (Apr 4, 2008)

samborambo said:


> Assume 1:1:1 ratio.


Good, keep it simple.



> PC driving +10 rad/s, +10Nm, +100W --> Sun load +10 rad/s, -5Nm, -50W and Ring load +10 rad/s, -5Nm, -50W.
> 
> Power splits equally between sun and ring. Input and output sum to 0W. It's not much of a gearbox really as there's no speed or torque transformation going on. I think we totally agree on this model.


O.K.



> Now hold the ring gear stationary:
> 
> PC driving +10 rad/s, +10Nm, +100W --> Sun load +20 rad/s, -5Nm, -100W and Ring load 0 rad/s, -5Nm, 0W.
> 
> This is what you'd expect from a differential. Power does not split equally although torque does. Input and output power sum to 0W. We agree?


O.K.



> Let's leave the single-input multiple-output differential model behind. Back to the PGS with two inputs, one output: (1:1:1)
> 
> Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, +10Nm, +100W ---> PC load 0 rad/s, 0Nm, 0W.
> 
> PC isn't turning because the sun and ring are turning at the same speed in opposite directions. Input and output power DO NOT sum to 0W so the sun and ring motors must be accelerating.


Yes, this is what I called an impossible condition, speaking in terms of equilibrium.



> To keep the speed constant, either motor could apply a negative torque WRT their direction:


Yeah, that's what I said before.



> Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, -10Nm, -100W ---> PC load 0 rad/s, 0Nm, 0W.


Nope. PC would see +20Nm. 



> Ring motor is now generating. Input to output power now adds to 0W. Speed will remain constant.


Yes (noting the torque on the PC).



> To show the difference of speed/torque transformation, hold the ring motor stationary:


O.K.



> Sun driving -10 rad/s, -10Nm, +100W and Ring driving 0 rad/s, +10Nm, 0W ---> PC load -5 rad/s, +20Nm, -100W.


No. Torque on the Ring is -10Nm, not +10.



> I+O = 0W. Now at this point you'll say that the torque has been summed from the sun and ring. It hasn't. -10Nm + +10Nm does not equal +20Nm. The ring motor is opposing the sun motor's torque but since it isn't turning it isn't contributing to the power transfer at all. Since the PC is turning at half the speed of the sun, it MUST be twice the torque load.


As I pointed out, you made an error on the sign of Ring torque. The Ring will naturally want to turn in the positive direction when there is resistance on the PC, so you have to apply a negative torque to it to hold it stationary. Just the same as you had to do when the Ring was generating at +10 rad/s and the PC was stationary.



> Now look at a scenario where the sun and ring are turning at different speeds in opposite directions:
> 
> Sun driving -10 rad/s, -5Nm, +50W and Ring driving +100 rad/s, +0.5Nm, +50W ---> PC load +45 rad/s, -2.222Nm, -100W.
> 
> I+O = 0W. Motor speed will remain constant. Do you disagree?


It doesn't matter if I disagree. What you describe is an impossible condition. 


> Taking that last scenario and exaggerating the torque transformation:
> 
> Sun driving -10 rad/s, -5Nm, +50W and Ring driving +10.1 rad/s, +4.9505Nm, +50W ---> PC load +0.05 rad/s, -2000Nm, -100W.
> 
> I+O = 0W. Motor speed will remain constant. Torque is transformed from 9.95Nm to 2000Nm, a factor of 201. Speed is transformed from an average of 10.05 rad/s to 0.05 rad/s, also a factor of 201.


Another impossible condition.



> Like I said, when you run through enough iterations of the speed equation Dr Miller stated and apply the inverse torque equation, it makes perfect sense.


It only makes sense if you ignore the fact that the torque has to sum to zero. Which you obviously do.

Regards,

major


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## gor (Nov 25, 2009)

Major, can you put on chart input-output torque distriution for open diff? (and we can compare it to this isvt)


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## Amberwolf (May 29, 2009)

Hopefully I'll get that wheelchair transaxle soon and be able to verify how it works physically. Assuming that it uses a setup that inputs on the planet carrier and outputs to the wheels on the sun and ring, i can easily test this. if it's different then i'll have to describe or show how it's setup, and let you decide if it does the same thing (I won't have any idea).

I don't have torque sensors but if I have the input motors at each end set to both spin at low-torques to deliver a very slow speed at the output (former motor input) I should get a very hard to stop output drive, because it should have a lot of torque, if Sam is right. If Major is right, it will just be slow but not have any real torque and be easily stopped by hand.


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## samborambo (Aug 27, 2008)

Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, -10Nm, -100W ---> PC load 0 rad/s, 0Nm, 0W. 



major said:


> Nope. PC would see +20Nm.


Incorrect. This is a steady state condition. The PC has no torque connected to it's output. If the PC saw any torque, it'd start turning. There are opposing torques applied to either side of the planetary gears themselves, but nothing on the carrier.

Sun driving -10 rad/s, -10Nm, +100W and Ring driving 0 rad/s, +10Nm, 0W ---> PC load -5 rad/s, +20Nm, -100W. 



major said:


> No. Torque on the Ring is -10Nm, not +10.


You are correct, Major. My apologies for implying that you were ignorant about gear ratios. Less importantly, the examples I stated were not impossible conditions - just not steady state. In the latter two examples, the motors would increase in speed with no impact on the PC speed.



major said:


> As I pointed out, you made an error on the sign of Ring torque. The Ring will naturally want to turn in the positive direction when there is resistance on the PC, so you have to apply a negative torque to it to hold it stationary. Just the same as you had to do when the Ring was generating at +10 rad/s and the PC was stationary.


Thank you for persisting with the argument. Otherwise I wouldn't have seen where I went wrong in my calculations.

So there's no point in having two motor/generators on the same PGS. It would make more sense to just have either the sun or the ring stationary and use the PGS as a fixed ratio reduction drive.

Still, fixing the ring gear as stationary and driving the sun gear would make a relatively light weight hub motor since the sun rotor wouldn't need to handle that much torque. Also, the PC is just the right position for the hub studs.

Sam.


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## Amberwolf (May 29, 2009)

There *can* be sense in having the two motors on there like that, for this reason:

Even at the lowest output speed, it still can spin the input motors at their highest, most efficient, speeds.

As opposed to a single-motor system that would then be forced (if used as a direct drive as that unit seems to be intended for) to run at very high current levels due to low BEMF when at very low speeds.

At least, as I understand it, and I could certainly be wrong.


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## samborambo (Aug 27, 2008)

Amberwolf said:


> There *can* be sense in having the two motors on there like that, for this reason:
> 
> Even at the lowest output speed, it still can spin the input motors at their highest, most efficient, speeds.
> 
> ...


That was my assumption. However, the calculations show that if both motors are turning (at high speed), only a fraction of that power is delivered to the PC. The rest must be recovered by one of the motor/generators. EG: motor 1 is driving at +110W, PC output shaft is -10W and motor 2 is generating at -100W. Seems strange but that's the only way it works. Any efficiency gained by the motor 1 turning at higher speed is more than offset by the inefficiency of converting 100W from electricity to mechanical energy and back again.


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## Amberwolf (May 29, 2009)

I was actually thinking of running both motors directly as motors, at higher speeds, and using the speed differential to determine actual wheel speed (output on the PC). 

Would that not work? (Sorry if the math already covers this, i really have a hard time following even the simple stuff--I have to sort of see it in action physically in front of me to get the idea)


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## major (Apr 4, 2008)

samborambo said:


> Sun driving -10 rad/s, -10Nm, +100W and Ring driving +10 rad/s, -10Nm, -100W ---> PC load 0 rad/s, 0Nm, 0W.
> 
> 
> 
> ...


No Sam,

If the PC had no resistance (torque load) to prevent rotation, it would in fact rotate freely and therefore prevent torque being applied to the sun and ring. The torque always adds up to zero in the SS condition. -10 -10 +20 = 0.

Regards,

major


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## major (Apr 4, 2008)

samborambo said:


> the calculations show that if both motors are turning (at high speed), only a fraction of that power is delivered to the PC. The rest must be recovered by one of the motor/generators. EG: motor 1 is driving at +110W, PC output shaft is -10W and motor 2 is generating at -100W. Seems strange but that's the only way it works. Any efficiency gained by the motor 1 turning at higher speed is more than offset by the inefficiency of converting 100W from electricity to mechanical energy and back again.


I agree with you on this


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## major (Apr 4, 2008)

Amberwolf said:


> I was actually thinking of running both motors directly as motors, at higher speeds, and using the speed differential to determine actual wheel speed (output on the PC).
> 
> Would that not work?


Hey Amber,

There may actually be some value in doing such. Like using 2 equal motors but just having a speed controller on one of them. But you'd sacrifice low speed torque. Ah crap, it's late and I'm tired of thinking about stupid gears. Just get your set-up going and play around with it. You might just find a way to make something useful. Toyota did 

major


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## gor (Nov 25, 2009)

who can show torque distribution (in-output) on the chart?


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## gor (Nov 25, 2009)

btw. also interesing:
*Baldor Announces New Cooling Tower Direct Drive Motor and Variable Speed Drive*
http://www.baldor.com/news/new_products.asp?id=661

"However, the input power to the motor varies with the cube of the motor speed. For example, if a motor is run at half-speed, the power consumed by the motor is 12.5% or 1/8 [i.e. (Ѕ) 3] of the power consumed at full speed. So, if the needed airflow can be achieved by running at half-speed,
it is possible to save a large amount of energy (see energy chart below)."
http://www.baldor.com/support/literature_load.asp?LitNumber=BR411​


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