DC Motor amps-to-torque transfer function - Figure of merit?

[37pw56gy]

I’m in search of a simple answer to a complex issue – an expression of the transfer function that describes conversion of amps to torque in a DC motor.

As background information, I am comparing the performance of two types of 1-HP DC motors that operate at a nominal 24 VDC. The wound field motor was previously used and had two very desirable properties in this particular application. First, torque produced is at a maximum when the load is heaviest. The mechanism driven by this motor may be obstructed in its normal course of operation and a mechanical clutch protects the motor and mechanism by limiting both torque and current. Secondly, the WF motor’s RPM is relatively high when the mechanism lightly loaded. This allows the machine to complete its operating cycle in the shortest possible time.

Manufacturing cost prompted adoption of PM motors 20+ years ago. The PM motor has proven itself capable of doing the job, but not with the same efficiency as its WF predecessor. To develop the necessary low-speed torque, current fed to the PM motor must be increased (i.e. terminal voltage must be raised). Another drawback of the PM motor is its lower peak RPM when lightly loaded. The machine’s cycle time increases by a noticeable amount of time when a PM motor is substituted for its WF predecessor.

What is the proper term for expressing the performance of a motor in converting amps to torque? Going one step further, how would this figure be evaluated against differing speed-torque curves? Is there a figure of merit that can be developed to compare these qualities against the baseline established by the original WF motor?

 

[DougMSOE]

How about using watt*hours per completed cycle. Or watt*hours per ft*lb?

 

[cbarn24050]

Hi,the key to this problem is field strengh. Motors with strong field gives high torque/low speed, motors with weak field gives high speed/low torque. You could liken it to a gearbox,so if you have a PM motor you have a fixed gear ratio determined by the magnet strengh so you allways have to compromise. With a wound field you can change the field strengh to change the ratio at different places in the machine cycle to get the best result.

 

[jbartos]

Suggestion: Visit

http://www.globe-motors.com/dc_motor.pdf

http://www.informatics.bangor.ac.uk/~dewi/modules/cs/dc_motor.PDF

http://lancet.mit.edu/motors/motors3.html#torque

etc. for more info
Also, please clarify "transfer function". These are often related to transforms, e.g. Laplace Transform

 

[37pw56gy]

Doug: Determining net energy consumption was not the primary objective, however, this may be exactly the type of ‘figure of merit’ I’m looking for. In this particular case, the appropriate units would watt-seconds. With an operating time of 3-8 seconds, values would probably fall within the 600-1800 W-S range. In making a practical test or evaluation, I’m thinking that amp-seconds may be easier to work with (people working with batteries invariable speak in terms of amps*time). What about RPM as the analogous term of voltage? Additional thoughts?

Cbarn: The geartrain analogy might be useful if I could independently evaluate the forces produced by armature and WF or PM field fluxes. Does anyone have a practical means of measuring real-time field strengths at the air gap?

Jbartos: Ideally, the transfer function would represent energy input (E*I) to work output (t*w). Alternately, we could set aside the voltage and RPM terms and just consider the amps-to-torque relationship. What’s needed is a number that gives a comparison of the each motor’s ability to perform its function while consuming the least amount of energy and in the shortest amount of time.

 

[DougMSOE]

I believe that to consider the total energy input to the motor per ft*lb would be the wat to go. I do understand that (e.g.) amp*seconds certainly would be good but dollars can be tied to watt*seconds quickly, at least in my world. If you wish to stay with amps then go with amps^2*time*resistance. This way you still have energy.
Sometimes one has to make up their own "figure of merit" with units that may not exist outside of the application.
To use RPM analogus to volts might lead to trouble in the real world. From the theory you are correct. But here it could lead to trouble.
I think that you are on the right track, keep going.

 

[jbartos]

Suggestion to 37pw56gy (Electrical) Jun 6, 2003 marked ///\\
Jbartos: Ideally, the transfer function would represent energy input (E*I) to work output (t*w).
///The energy input E*I is missing time variable t. It should be E*I*t to be commeasurable with t*w work output dimension wise, which is basic engineering necessity of well posed engineering relationships. Once this is done, output/input=E*I*t/(t*w)=E*I/w under an assumption that the E and I are independent of t, else E(t) and I(t) would be variables of t. The w would be considered independent of t.\\ Alternately, we could set aside the voltage and RPM terms and just consider the amps-to-torque relationship. What’s needed is a number that gives a comparison of the each motor’s ability to perform its function while consuming the least amount of energy and in the shortest amount of time.
///It appears that transients might be neglected. Then, the problem becomes a minimization problem in Extremal Calculus. Visit

http://www.math.nps.navy.mil/~bneta/4311.pdf

etc. for more info on minimization problems.\\

 

[RadarRay]

What is the proper term for expressing the performance of a motor in converting amps to torque?

*** the Proper term is Kt (that is K sub t). This should be obtainable from the motor manufacturer. ***

Going one step further, how would this figure be evaluated against differing speed-torque curves?

*** Evaluated for efficiency? If it is net efficiency you are after you should know that no matter what motor you chose, the load is still the same load so it will have the same torque reguirement and if the speed is the same the same HP requirement. So it appears you are asking motor efficiency. Also, you never mention the kind of control on the motor ( fixed power supply, DC drive, etc) which would really have to be figured into your efficiency equation. It sound like it is operated off a fixed supply to me.

*** I would also be interested in why you think the PM motors are not at the same efficiency as the WF motors. Are you talking about the ability of the motor to accelerate a load? So you really are not talking about energy consumption but how efficient the motor is at performing your application? ***

Is there a figure of merit that can be developed to compare these qualities against the baseline established by the original WF motor?
*** I am not familiar with the term "Wound field." Is it Shunt Wound? Series Wound? Or Compound Wound? ***

 

[cbarn24050]

Hi 37pw56gy, it seems you missed the point i was trying to make. Your original motor has a series field winding, this means that the field strength rises with armature current. When the load is high the arm current is high and therefore the field strength is high, so the motor has a low speed/high torque charcteristic. When the load is low the arm current is low so the field strength is low, so the motor has a high speed/low torque characteristic. Is that clearer? or do I have to type slower

 

[UKpete]

37pw56gy - considering only at electrical efficiency, the PM motor generally wins as the wound field motor has extra copper loss due to the R*I^2 in the field winding.

However, perhaps in your original post when you used the word efficiency (3rd para) you were not refering to electrical efficiency? I like cbarn's gearbox analogy, and I also agree that it appears to be a series motor. This was the classic choice of machine in traction applications, it gave very high torque at starting. In effect, as motor speed increased a "gearchange" was implemented by field-weakening stages (using field taps). The next development in traction applications was separately excited, where the field is controlled independently of the armature circuit.

It is a well recognized limitation of PM motors (including brushless dc) that the speed range is not so good as field weakening isn't possible. This doesn't answer your original question, but I'm not sure how a mathematical model can usefully compare the two motor types you describe.

 

[etom]

sounds like you are trying to describe a series or a compound motor.
Kt is the constant you want, and a PM motor is analogous to a shunt wound motor.
A shunt wound motor will have better speed regulation, work better with a DC drive, but for heavy loads, the compund motor is the way to go.
You will heat the term :% compund,i.e....the percentage of flux coming from the series field vs the shunt field...50% means it is fairly heavily compounded.

 

[37pw56gy]

Thanks to everyone for the many useful comments and suggestions. The WF motor in question is a simple series motor; armature polarity is transposed when reversal is required. The controller is a simple on/off contactor. The power supply is steady or full-wave DC.

Kt, aka Motor Torque Sensitivity or Torque Constant (lb-in/amp), is exactly the type of figure of merit that I've been looking for. A related parameter is the Motor Constant (lb-in/sqrtWatts). Searching, I find an especially readable, useful link at

http://www.polysci.com/Documents/moapp.pdf

(by strange coincidence, I once worked for a branch of this organization - at the time I wasn't paying much attention to the finer points of mini motor math

Next problem: How do I make a determine Kt? (let's suppose that the OEM’s info is not available, accurate or applicable). My first instinct is to resort to the old-fashioned prony brake. Simply apply a reduced voltage sufficient to develop the full-load amps while the rotor is locked, then measure the torque produced at the end of a lever connected to the shaft. This approach surely has serious limitations, especially if Kt is somehow proportional to RPM or is otherwise non-linear. Comments?

PS: I always assumed that the series WF motor was overall more efficient in converting watts-to-work than its PM counterpart, however, UKPete's mention of copper losses in the field winding has me thinking this may not be so. As compared with the PM, resistance losses in the WF's field winding are obviously wasted heat. Comments?

 

[RadarRay]

Seems like I've done this before here. Excuse the English units.

The rated torque can be determined by the equation TQ=(HP*52550)/base speed.
For a 1HP, 1750RPM motor (1*5250)/1750 =3 LB-FT

You know rated current, you know rated TQ.
Rated Kt=3lb-ft/ rated current.

This approximation has worked very well with PM and Shunt wound motors. At the rated conditions is should work for a series wound motor. So now the only problem is that when supplying a series wound motor, you are exiting the field and the armature with the same current. But the Torque of a DC motor is porportional to If*Ia. But in this case If=Ia, so the torque curve should be close to Ia squared.
Tq=Ia^2

I would think this should be close enough for your analysis. I have never worked with a Pure Series motor, to say I have hands on experience but I believe all the theory should hold up.