Baldor 23H Series Installation & Operating Manual page 140

Using these equations we arrive at:
^ ^
φ I [sin φ + sin
T = K
2
M T
^ ^
φ I x 1.5
T = K
M T
With this commutation scheme, there is no difference between the maximum and minimum torque
developed. Therefore ideally, there is no torque ripple when employing a sine controller with a
sine-EMF motor.
Equation (18) above provides an expression for torque developed in terms of torque constant as
measured from phase to neutral. However the neutral is not accessible. Therefore an equivalent
phase to phase expression is desired. The equation is developed and is:
φφ
T = 1.5 K I
T RMS RMS
This equation provides a relationship between torque developed, the RMS current (which can be
measured), and the phase to phase torque constant of the motor. However K
measured. The saving factor is that K
ing the motor's back-EMF waveform on a scope (when driving the motor by some external means)
and measuring that waveform, the value for K
KRPM. Then converting from K
K & K Relationship
T E
The relationship between the torque constant and voltage constant can be derived as follows:
φ = K φ (where K
K
T E
since in a 3-phase wye connected system:
φ = K φφ
2 x K
T T
√3 x K φ = K φφ
E E
therefore:
φφ = 2 K φφ
K
T E
√3
φφ = 1.15473 K
K
T
(N-m/amp) (v/r/s)
This is the basic equation for the relationship of torque constant versus voltage constant for a 3
phase motor when driven with a 3 phase excitation. From this the other dimension systems can be
derived.
This provides the relationship between torque developed, the RMS current, and the measurable
voltage constant of the motor. Note that current and the voltage constant are expressed in RMS
terms, i.e. RMS of a sinusoidal waveform. By simply measuring, via a scope, the motor's peak
value of K the developed torque may now be easily calculated.
E
Figure 5 summarizes the relationship of a sinusoidal-EMF motor when driven with either a DC
drive or an AC drive. By multiplying the peak value of the sine back-EMF times the factor in the
table, the "equivalent" or "RMS" value is determined. This RMS value can then be used in calcula-
Application Notes
(φ +120) + sin
(φ + 240)]
2 2
(phase to phase) is very easy to measure. Simply by observ-
E
to K , equation (19) may be used.
E T
is N-m/amp and K
T E
φφ
E
Page 20
can be determined. K
E E
is v/r/s)
(17)
(18)
(19)
cannot be easily
T
is simply volts divided by
(20)
(21)
(22)
(23)
(24)