Algorithm to find out how much Torque is necessary by a DC motor to rotate a rotor...

[erikl]

... the Mi of the shaft was calculated including the blades right? how can i calculate the Mi of the blade again???

Seems this was a misunderstanding on my side about the shaft: I thought with shaft you thought of the axis of the motor. I don't think you have to recalculate the M_i value.

also i understood all those calculation parts but i was wondering what formula or how did you derive this expression angle = (α/2)*t²
can you direct me what expression or formula is it?

i sense it is a expression to know how much amount of radians/degree has the object rotated with the given angular acceleration in given time t.

Right. It's just analog to the equation for the covered distance of linear movement (s) of a mass (m) accelerated by the acceleration (a) during a time (t):
s = (a/2)*t² , where a = F/m (F=force [N])

If you need a more exact explanation, I'd recommend to study thoroughly this Wiki explanation - which I've linked already in my first answer to you.

 

[abhi@eda]

Sorry,im back after some gap,

Another simple doubt was raised,the SI unit of Moment of Inertia is kg.m² not Nm² right??

[original post] In that case,each blade weighs 1.5kg and length is 1.5meter each..

hence the Moment of Inertia = (mL²)/3 = (1.5kg X (1.5 meter)²)/3 = 1.125 kg.meter² of Moment of Inertia

as there are 3 Blades,so the total Mi is 1.125 * 3 = 3.375 kg.meter² (or 33Nm²).


so i want to accelerate this shaft with 3.375 kg.m² of Mi to 2500 RPM in 15 seconds..

2500 RPM = 262 Rads/Second

Acceleration from 0 rads/se to 262 rads/sec in 15 seconds

so 262/15 = 17.46 rads/sec² Acceleration


now T = Mi X Acc

now is the Mi unit in kg.m² or Nm²?

if i plug in kg.m²,i get T = 3.375kg.m² * 17.46 rads/sec² = 58.92 Newton Meter of Troque,which looks kinda realistic number

but if i plug in Mi in Nm² unit,then its becomes T = 33Nm² X 17.46 = 576 Newton meter of Torque,which doesnt look quite realistic...

so which unit of Mi is used in T = Mi X Acc
is it Nm² or kg.m²?

,and what is the unit of T then?...

thank you

 

[erikl]

Another simple doubt was raised, the SI unit of Moment of Inertia is kg.m² not Nm² right??

Yes, you are right: the original error was here in your very first question of this thread (and I didn't notice it either, before now):

the weight of the each blade is 1.5 kg/14.7 Newtons

It is not allowed to use the acceleration of gravity for the conversion of [kg] into [N*s²/m] (not simply [N]!), because not the gravity's acceleration will be used, but the motor's.

Hence 1kg = 1N*s²/m

So your above calculation seems correct:

T = 3.375kg.m² * 17.46 rads/sec² = 58.92 Newton Meter of Torque

[kg.m² * [rads]/s²] =[(N*s²/m)*m² * [[rads]/s²] = [Nm]

[rads] is a dimensionless unit.

Merry Christmas! - erikl