53
La * i / t = 0.001 * 500 / 0.01 = 50 V
For stationary state of the motor: i = 0,
In this case, only the voltage drop due to the resistance of the armature resistor of the motor
has an effect.
EMF (electromotive force):
This is the internal motor voltage which is induced as a function of the speed n and flux of
the motor.
EMF = k1 * * n,
The EMF is thus proportional to the flux and the speed n.
Contant k1 depends on the number of pole pairs and the number of armature windings of the
motor.
During nominal operation with rated motor speed and nominal flow, a nominal EMF is
established, on speed zero the EMF is zero and the required motor voltage is I * Ra.
Motor flux :
Flux is applied to the field winding via the field current. As the result of saturation occurring
in the magnetic circuit of the motor, the relationship between the field current and the flux
resulting from it is non-linear, i.e. as the excitation current increases the flow increases less
than proportionally due to the saturation of the iron core. This relationship is determined by
the field characteristic recording with p50051 = 27 in the SINAMICS DCM.
Field current:
The field supply unit in the SINAMICS DCM regulates to a constant field current
irrespectively of the temperature-dependent field resistance and the line voltage (assumed to
be sufficiently high), the required direct voltage sets itself automatically.
The motor torque:
Motor flux and armature current I determine the torque M of the motor,
M = k2 * * I, M = motor torque in [Nm]
The motor torque is thus proportional to the product of flux and armature current I.
Constant k2 is dependent on the number of armature windings and the dimensions of the
machine.
Accelerating torque M
B
:
M
B
= J * d / dt,
with moment of inertia J in [kgm
2
], = 2 * * f, f = n / 60,
n in revolutions per minute [RPM]
M
B
= J * (2 * / 60) * dn / dt.
M is constant for a constant dn/dt, so differential quantities are to be expected. For example,
a speed change of 0 to 1500 RPM results in a n of 1500; used in the formula above, it can
be used to determine the acceleration time t.
The motor torque M required for acceleration is the sum of the load torque M
L
to be
surmounted and acceleration torque M
B
:
M = M
L
+ M
B
Relationship between torque and power:
M[Nm] = P[kW] * 9550 / n[RPM]
The rated motor power P acc. to the motor rating plate and the rated motor speed equals
rated motor torque M.
The electrical/mechanical power:
P
el
= Ud * I is the electrical power of the motor. Multiplied with efficiency of the motor it
yields mechanical motor power P
mech
, which is stated on the rating plate of the motor.
P
mech
= P
el
*
