DC motor design calculations, help?

[Michael31091]

Homework Statement

Hi, well my task is to construct a DC motor. With 25w rotational mechanical output power. It cannot draw more then 5A current, and has to have 3 or more poles in rotation. The motor must be brushed/commutated. There is a max of 30v D.C. input. The motor needs to be built and tested within a few days, so ill need calculations done by tomorrow (brutally tough i know)

Homework Equations

I was not given relevant equations for the question, this is half my problem, id like some advise on which equations i should be using to caluclate the necessary parts to build the motor which will acomplish the goals stated above.

The Attempt at a Solution

My attempt came up short when i came across the term 'back emf' or 'induced emf'. i found an equation:

Vo = IR + Ve

Where:
Vo = power supply
I = current
R = terminal resistance (is this calculatable for my question or do i need to build and measure this, and what exactly is this resistance? where is it found.. i thought it was the overall resistance of the motor)
Ve = Induced EMF (Back EMF)

Further continuation of this formual suggest substituing Ve = w Ke
Where:
w = angular velocity
Ke = Induced EMF constant (how do i determine this?)


In other attempts at solving this i came up with the following:
Pi = VI
Where:
Pi = power input (i assumed motor efficiency to be 50% as someone suggested this was a good idea, how does this affect other calculations, it should have more effect then just doubling the desired output getting an input power of 50w)
V = voltage
I = Current (as no more then 5A is allowed, i set this to 3A so I am well within the boundaries)

therefore i get voltage:
V = Pi/I
V = 50/3 = 16.67 Volts

As a DC power supply is used to power the motor, this should not be a problem?

I then attempted to find the resistance of the motor, thinking i could calculate the number of coils i needed.. evidently this led me no where as i used 'V=IR'. Apparently this resistance value is the resistance of the motor when not moving, resistance changes? I know a section of my research said that the current drawn by the motor is reduced the faster it spins. I don't know how or what I am calulating from here, can someone please help?

 

[Mindscrape]

Can you reformulate your question to be a bit more clear and concise?

 

[Michael31091]

I would like to work out the number of coils i need to use in a 3 armature DC brushed motor, using AWG 24 wire, 3A ( can be up to 5 if needed), the magnets being used have B=1.25 T ( id also like to know if a stack of 4 would make 5T? ) The output of the motor must be 25W of mechanical rotational power (Power = torque x angular velocity)

 

[Michael31091]

Just updating, I've worked out how to calculate the Torque, and the Angular velocity. But to find the angular velocity i need the Back EMF, and I am still unsure as to how i can find this theoretically before i find the angular velocity? Also to find torque i need a value called 'Field density at end of pole (or armature)' and i assume this is just the field density caused by the input current in the coil of the armature, but i haven't been able to verify this yet.

so i ask, how do i work out the back emf, if i don't know angular velocity? or what other method can i use to find the angular velocity?

and when finding torque using 'T = Fr' where 'F = BIl', what is this B value and how is it calculated?

thankyou for helping!