22N78-311P.1001【PDF 7/48 页】MOTOR BRUSHED DC 9W 12V 7300RPM

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Brush DC Working Principles

The electromechanical properties of motors with an ironless rotor :

Graphic express

“speed-torque”

with ironless rotors can be described by

means of the following equations:

U 0 =MxR M +k E x ω

(4) characteristic:

By calculating the constant k E and k T from the

1. The power supply voltage U 0 is equal to dimensions of the motor, the number of turns

n

n 0

the sum of the voltage drop produced by the per winding, the number of windings, the

U

0

I

current I in the ohmic resistance R M of the diameter of the rotor and the magnetic field

rotor winding, and the voltage U i induced in in the air gap, we find for the direct-current

the rotor :

U 0 =IxR M +U i

micromotor with an ironless rotor:

(1) M = U i = k

I ω

(5)

0

M L

M

L

I

M L

M

To overcome the friction torque M f due to

R

M

I

U

0

Which means that k = k E = k T the friction of the brushes and bearings, the

motor consumes a no-load current I 0 . This

The identity k E = k T is also apparent from the gives

following energetic considerations: M f =kxI 0

U

I

The electric power P e = U 0 x I which is supplied

and:

to the motor must be equal to the sum of the

2. The voltage U induced in the rotor is to Joule’s law) P = I x R :

i

proportional to the angular velocity ω of the P = U x I = M x ω + I x R

mechanical power P m = M x ω produced by

the rotor and the dissipated power (according

2

v M

2

e 0 M

U 0 = I 0 x R M + k x ω 0 where

ω 0 = 2π x n 0

60

hence:

rotor :

U i =k E x ω

(2)

=P m +P v

k=U 0 -I 0 xR M

ω 0

(8)

Moreover, by multiplying equation (1) by I, we

It should be noted that the following also obtain a formula for the electric power Is it therefore perfectly possible to calculate

velocity ω express in radians per second and P = U x I = I x R + U x I

relationship exists between the angular P e :

e 0 M i

the speed of rotation n express in revolutions

2

the motor constant k with the no-load speed

n 0 , the no-load current I 0 and the rotor

resistance R M .

per minute:

The equivalence of the two equations gives

ω = 2π n

60

Mx ω =U i xI

or U i = M and k E = k T = k

The starting-current I d is calculated as

follows:

ω

I

I d =U 0

3. The rotor torque M is proportional to the Quod erat demonstrandum.

rotor current I:

R M

M=k T xI

(3) Using the above relationships, we may write

It must be remembered that the R M depends

the fundamental equations (1) and (2) as

It may be mentioned here that the rotor torque follows:

to a great extent on the temperature; in other

words, the resistance of the rotor increases

M is equal to the sum of the load torque M

L

U 0 =IxR M +kx ω

(6)

with the heating of the motor due to the

supplied by the motor and the friction torque and :

dissipated power (Joule’s law):

M f of the motor :

M=M L +M f

U 0 =MxR M +kx ω

k

(7)

R M = R M0 (1 + γ x ?T)

Where γ is the temperature coefficient of

By substituting the fundamental equations (2)

and (3) into (1), we obtain the characteristics

of torque/angular velocity for the dc motor

copper ( γ = 0.004/°C).

As the copper mass of the coils is

comparatively small, it heats very quickly

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