Rear wheel drive with separate motors

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1. Sep 17, 2015

themotorman

I have built a rear wheel electric with two motors one for each rear wheel. The motors have separate controllers and both are controlled by a single throttle. This throttle sets a torque for the motors . In a straight line the torque is the same for each but when cornering the torque setting is still the same but I am trying to work out how the system works . It does corner perfectly with no dragging or slipping at the wheels, it handles as though it had a single drive via a differential.
Can anyone explain this? My thought is that because the controllers set a torque then the speed of each wheel is automatically set to make the torque equal.. Ideas anyone on this. The idea of two motors is that it avoids the weight and cost of a differential.
Thanks.
Themotorman

2. Sep 17, 2015

jim hardy

Have you ever looked at an ordinary automotive differential ? It applies equal torque to the two wheels that it drives. Just like you say your motors do.

3. Sep 17, 2015

themotorman

I agree and this would explain what happens with diff. Rear end when you lift up one wheel. I will measure the torque going to each wheel and see what happens going around a corner. I am still trying to tie the real world to the physics.

4. Sep 17, 2015

jim hardy

Lift them both and lock the driveshaft.
Rotate one by hand and the other turns reverse direction.
Observe that if you hold one and twist on the other, you'll feel that twisting moment transmitted equally to the one being held. (My little sister and i played at length while Dad had the '46 Plymouth up on blocks...)

Ordinary equal torque(open) differential versus "limited slip" differential was central to the plot of a very entertaining murder mystery movie "My Cousin Vinny" which i recommend as great fun. Good social commentary on geographic stereotyping, too.

Last edited: Sep 17, 2015
5. Sep 17, 2015

Baluncore

A differential transfers equal torque to both axles, exactly like your two motor controllers.
Power = Torque * RPM. So the wheel inside the corner will deliver less power while the outside wheel delivers proportionally more power.

6. Sep 18, 2015

cellurl

Do you have a picture or link of it. I need the same type drive...

7. Sep 19, 2015

JBA

Think of this in terms of the radii of the inside and outside driving wheels to virtual centerpoint of a turn, the torque arm length from that centerpoint to the inside wheel is less than that of the outside wheel; so, it may be that the drivng load/amperage sharing ratio between those two wheels is inversely proportional to the ratio of those two arm lengths. As a result, the inside motor is doing more work than the outside motor but there is no "solid rear axle" turning resistance effect.

8. Sep 19, 2015

Baluncore

JBA, I think you may have that backwards.

Power is Energy flow. Also Power = Torque * RPM.
A differential acts to equalise the torque to both sides.
If one side is moving slower because it is inside the turn, then torque * RPM implies lower power and a lower energy flow rate.

Also; the inside radius has a shorter track length than the outer radius, so distance moved is greater for the outer wheel with the same torque, which suggests more energy is transferred to the outer wheel.

If that is not so, then we need to re-examine the statement that; “A differential acts to equalise the torque to both sides”.

Note:
The torque of a DC motor is proportional to current. So, if you wire two DC traction motors in series you will have equal torque. They will then share the available voltage. That is a very good analogue of the mechanical differential. But is that what is really needed in a vehicle on a bend?

DC traction motors in parallel have the same voltage and so have the same maximum RPM without load. Since the torque from a DC motor on a fixed voltage is greatest at low speeds, the slower wheel will deliver more torque. While that energy flow may be different to a mechanical differential, it comes closer to the limited-slip-diff concept. With a DC motor, a fixed voltage limits the maximum RPM of a spinning wheel.

Last edited: Sep 19, 2015
9. Sep 19, 2015

JBA

I did not state that the inside wheel did more "work" than the outside motor. I haven't yet tried to do any math yet; but, it may be that the total horsepower expended through a turn may actually be the same for both motors since the outside wheel is turning at a higher rpm with lower required torque value than the inside wheel. The total work expended is obviously equal to the sum of that provided by both motors; and, what I am proposing does not violate that principal.

10. Sep 19, 2015

Baluncore

The OP specifies that the controllers regulate the motor torque to be equal. A mechanical differential also equalises the torque to the wheels.
There is no sharing of current or voltage because the controllers set the motor currents to be identical to get equal torque. They regulate current by efficiently providing sufficient voltage for the set current to flow.

But the OP specifies the torque and the controllers provide equal torque.
Power = Torque * RPM. Since the torques are equal and the RPM is determined by corner radius, the power must be different to the two wheels.

11. Sep 20, 2015

JBA

I think the last sentence "They regulate current by efficiently providing sufficient voltage for the set current to flow." in the above quote may give a clue that resolves the apparent disconnect between the actual unit operation and the Power definition.

If the controllers are actually delivering a regulated voltage, rather than current, to the motors at each throttle setting; then, due the different loading between the inside and outside wheel at their different radii from the virtual turning center, the outside motor may actually be drawing less current and power than is required by the inside wheel due to its shorter radial distance from the virtual center.

P S As a quick additional note: A simple mathematical analysis shows that for any given turning angle, the total power expended is identical for both wheels. Utilizing the power formula P = F * L / t (with F = T * wheel assembly radius), the ratio of the driving force F of the outside wheel to the inside wheel is F o = F i * r i / r o and the ratio of the circular travel distance of the outside wheel to the inside wheel travel distance is L o = L i * r o / r i. and t o = t i,
So: P o = (F i * r i / r o * D i * r o / r i) / t i = F i * D i / t. i = P i

12. Sep 20, 2015

Baluncore

You do not understand DC motors. Nor do you understand differential gears.
The "apparent disconnect" you refer to is clearly between your imperfect understanding and the established science of mechanics.

The motor controllers are set to regulate the motor torque, they do that by sensing and regulating the current to the DC motors. They regulate that motor current by continuously varying the motor voltage. Current is fixed and equal to both motors. The motor voltage must be varied to compensate for the internal resistance and the back EMF generated within the motors at different RPMs and temperatures.
You have wrongly assumed that a DC motor represents a fixed resistive load, when it is actually a dynamic generator of speed dependent back EMF and temperature dependent resistance.

A differential gear is a mechanism with two output shafts that must always have equal torque. That is true because the balanced planetary gears within the carrier freely rotate whenever a torque balance is not present.
As it is fundamental that the output shaft torques of a differential gear be equal, any analysis that considers a torque difference is a denial of mechanics. Your wrong assumptions are derived from a paralogical reasoning that is not based on mechanics.

13. Sep 21, 2015

JBA

What I poste in not way implyed "that a DC motor represents a fixed resistive load", I am well aware of the effects of back emf and load related to motor speed; and, my statement was based upon the quote "the throttle controls the voltage on the controllers" that I entered at the beginning of the post. In that case the motor speeds will vary according to the applied loading. You should understand that I am speculating because no one, not even you has given a definitive answer to how this system is operating in a similar manner to a rear differential drive.

I am totally acceptable to feedback as long as it is given in the realm of constructive infromation. You need to be aware that a forum is for the discussion of a subject, it is not intended to be a contest or battle of the wits.

14. Sep 21, 2015

Baluncore

In the OP, it specified;
Since the two controllers are regulating equal torque, by equal currents, they behave just like a differential gear that also balances the torques.

Yes I have. See post #5.

To constructively find out what is not understood here I ask you three questions that can have simple YES/NO answers.
JBA. Do you agree that;
1. The torque of a DC motor is proportional only to motor current?
2. The torque of the axle shafts from a differential gear are balanced and so must be equal ?
3. If both; (a) a differential gear; and (b) the DC motors; balance the torque, then the vehicle will handle the same ?

15. Sep 21, 2015

JBA

Simply put, my answers are: Yes, Yes, Yes

I understand what you are saying; and, I have finally resolved my conumdrum a bit, with the fact the power equation illustrates equal Hp consumed by either wheel turning the vehicle, by considering two extreme cases.
Case 1: The inside wheel is locked and the outside wheel supplies the total work of turning the vehicle.
Case 2: The outside wheel is locked and the inside wheel supplies the total work of turning the vehicle.
In each case, the required load and total travel apply and the same amount of power is consumed.

Now a question for you. In the case of both wheels driving with the same torque and each traveling their respective arc distance D i and D o during the turn mean that the power consumption ratio between the two motors/wheels is proportional to r o / r i ?

16. Sep 21, 2015

Baluncore

Yes.
For a fixed torque it gets back to the geometry of the circle and the the fundamental equation of W = Power = Torque * RPM.
For Ro > Ri > zero.
Ro / Ri = Do / Di = RPMo / RPMi = Wo / Wi

17. Sep 22, 2015

JBA

Well, I have finally resolved my issue related to the inside wheel loading vs. outside wheel more power; but, my mind had to reach back some 55 years to time that I was an engineering student and deeply interested in all elements of automobile technology.

The interesting thing about the automobile differential is that everyone tends to focus on its ability to allow one wheel to rotate at a different rate than the other; but, in that single focus they overlook the another basic function of the differential. That very important overlooked function is transfer "power" in terms of rpm from the inside wheel to the outside wheel during a turn; and, in our current evaluation of the dual motor vs. differential rear drive that becomes a very critical issue, and is where the attempted correlation between the dual motor drive we are analyzing and a standard auto differential becomes uncoupled (so to speak).

Baluncore, in your total focus on the power of the outside wheel, you have failed to ask yourself where that extra power you need on the outside wheel is go to come from. Well, in the case of the differential drive, it is sacrificed by the inside wheel, due to its increased loading and resulting rpm reduction from the moment loading imposed by the lateral force generated by the angled front wheels forcing the vehicle to turn. Based on the premise that the input power and torque are identical, but not shared on the dual electric motor drive cart; exactly where is the added power to the outside wheel going to come from, it can't be from the throttle, that will increase the current/power equally on both wheels; and, there is reportedly no electronic power transfer between the motors. Sounds like a potential problem to me. What do you think?

18. Sep 22, 2015

Baluncore

I have NOT as you say, totally focussed on power to the outside wheel. Do NOT tell me what I am thinking when you do not yet understand the subject. There is no evidence for your statement, either provide a reference quote or shut up.

If you want to turn this into a personal confrontation without evidence, then I will point out that you appear to lack the critical thinking skills necessary to reason, and that if it came to a “battle of the wits”, you would be unarmed.

Seems "like a potential problem" only because you do not yet understand differential gears and have not done the numbers.

With two DC motors, travelling in a straight line, each motor is providing 50% of the vehicle energy to it's wheel. The total vehicle power is 100%.
On a corner, one wheel will slow by say 1% while the other rises by an identical 1%. That changes the energy flow from each motor, from 50% and 50%, to 49% and 51%. The total power remains the same at 100%.

It is clear that with a mechanical differential all 100% of the energy comes from the "engine", hence the name. Since torques are equal, that energy is shared between the rear wheels in proportion to RPM. When rounding a corner, if the inner wheel slows by 1% and the outer wheel speeds up by 1% then the energy will be distributed in the ratio 49% to 51%. The total energy is still 100%. Exactly the same as when travelling in a straight line.

It can get very complex if you want a full energy analysis because you must consider both the linear kinetic energy and the rotational kinetic energy of the vehicle about it's centre of mass.

19. Sep 24, 2015

JBA

You and I are in complete agreement regarding the action of a mechanical differential in a turn and that is exactly what I was trying to convey by the "That very important overlooked function is transfer "power" in terms of rpm from the inside wheel to the outside wheel during a turn" statement the in my last post. I also have no issues with any other of its explanation, only the below lack of understanding regarding the action of the controlled electric motors under their varying loads

If you review all of my prior posts you will observe that I have never offered any actual proposed explanation to the thread inquiry. To this point, I have only been focusing on the elements, such as the unbalanced wheel loads, etc associated with it. The primary reason for my reticence has been that once I finally broke the overall problem down into its essential elements, I discovered the below unresolved issue is what has been preventing me from coming to what I consider to be a reasonable explanation of the observed turning characteristics of the cart.

The unresolved issue I have been wrestling with, in simple terms, is: How will a motor with a controller that maintains it at a constant torque react to a changing load? Based upon my limited experience in the application of electric motors, I have observed that a motor with a given applied voltage will vary its rpm accordingly, but it is unclear to me as to how a motor controlled so as to provide a constant torque will react in a similar manner to a changing load.

I hope this post will help get us back on course and I will appreciate any feedback you might have to help me resolve the above issue.

20. Sep 24, 2015

Baluncore

It appears that you project your ideas onto others. You never admit you were wrong, or apologise.
Those symptoms strongly suggest you are a Troll or have a sociopathic personality disorder.
I do not wish to waste my time entertaining you.
If you want to go back over torque*RPM again you will need to persuade someone else to reply.

21. Sep 24, 2015

jim hardy

A question well stated is half answered. That one's stated pretty well.

DC motor's external characteristics are described by two simple equations, giving numbers plenty close enough for most work.

Flux Φ, armature current current I ,counter-EMF voltage, and an emprircal constant K are all you need
For a permanent magnet motor , Φ is set by the magnet, in a wound field machine it's set by field current

(1) Counter-EMF = KΦ X RPM
where KΦ product is determined empirically by measuring open circuit voltage at some RPM.

(2) Using ft-lbs, Torque = same KΦ X I X 7.04

So a motor receiving constant current (with constant field) will deliver constant torque. It'll follow the load's speed-torque curve.

and a motor receiving constant voltage will maintain pretty constant speed.

That's the basics for a steady state solution.. Refinements for armature resistance and armature reaction effect on Φ are applied to suit the situation.

Does that help ?

22. Sep 25, 2015

JBA

Balluncore
Ironically, this morning before seeing your latest post I had already decided to apologize for wasting your time; because looking back, I realized that I committed a serious error in utilizing this forum as a personal sounding board while I was in the process of searching to find a response that I felt would allow me to describe in detail why the golf cart was logically performing as described.

In this case, in your first response you took, what I will loosely describe a global energy/work approach to what you, correctly, saw as a very simple issue.

I, on the other hand, tend to take a more microscopic and detailed approach to all problems and want to understand exactly how every element of a system works. That type of focus is, most likely, the result of, for the last 20 years of my engineering career, developing new products; and ultimately oversight of the engineering of high pressure relief valves for ASME Section VIII Pressure Vessel code. If you are familiar with that code, you are well aware of the wide range of critical services in which those valves are utilized and catastrophic consequences that can occur as a result of any malfunction in those devices.

Unfortunately, since my last post I came to the realization that my fixation upon the "The motors have separate controllers and both are controlled by a single throttle." part of the inquiry has been interfering with, and interfering with my ability to rationally analyze this problem from the very beginning. My very first post should have asked for input on exactly how the "constant torque to each individual was being achieved by the controller"; and, if not provided that information, should have simply not replied to the in the first place.

My request for feedback in my last post was a honest request, if inappropriate, and not even for the purposes of any future post to this thread, which has already endured enough of my efforts to understand how specifically each element of the system operates; but, as you stated in your last post, is not really your responsibility.

While this a terrible way to conclude an intended apology; but what I see as necessary as response to your, what I consider an inappropriate, personal attack in your last post I suggest your seriously consider the following. Since you seem to consider any position or statement that does not exactly comply with your view of a problem as a serious attack upon you personally and professionally, which is entirely in conflict with the basic concept of any forum, I suggest that you take look in the mirror, where might see exactly a bit of the traits you assigned to me.

23. Sep 25, 2015

JBA

Jim Hardy,
Thank you very much for your response to my question. It exactly answers the question as to which between voltage and current controls the torque and speed of a motor; and that is exactly what I needed.

24. Sep 25, 2015

jim hardy

Thanks ....

I've been on the periphery of some valve problems, stability in control valves,

when i get my question formulated about effect of velocity profile underneath the valve seat
and how it affects blowdown

would like to tap your experience.

I'll need a primer....

old jim

25. Sep 25, 2015

JBA

I'll be glad to help. That is something I have investigated while developing valve function simulation programs. If you are going to start your thread on the issue, then place a short note here telling me under which catagory you are placing it so I will get an email notifying me; otherwise, just post your question here and I will be glad share what I have learned.