This paper discusses how the output current of servo drives is specified. Standard industry terminology is explained. The paper concludes with examples of how to convert rms and crest ratings for sinusoidal, trapezoidal and DC servo drives.
The following is a simplified electrical drawing of a typical 3 phase servo drive system using sinusoidal commutation:
On a permanent magnet brushless AC motor that is rotating at a constant speed, the phase currents will have a sinusoidal waveform with a 120º delay between them, theoretically. For constant speed applications, the current is sometimes expressed in Root Mean Square or RMS (see detailed description below). The RMS value of those currents in that situation can be calculated as crest current / √2. For example, if your BLAC motor is rated at 17 ARMS it means the crest current will be 24 A at this rated point. However, although RMS current is commonly used in the industry for continuous power applications, it does not provide a clear answer for a detailed design of many robotics applications where the frequency is not constant and the motor can be fixed on a position. At these points, the calculation or measurement of RMS current using a typical device or multimeter could lead to non-practical results.
Because of this fact, Celera Motion’s Ingenia manuals and documentation – if not specified otherwise – show the current expressed as the crest value of the phases. The software also shows either the instantaneous value for the individual phase currents or the computed “current actual value”, which matches the crest positive value of the instantaneous currents.
To keep the explanation free of ambiguities, consider this nomenclature:
The servo drive has several current levels or limits. Some of them correspond to registers in the firmware.
Figure 3 – Servo drive current levels
Depending on the type of motor and/or the commutation method/mode, one of these current modes shall be met. In each case, the RMS current can be easily approximated:
In sinusoidal mode, the motion controller provides phase currents with the form of a sine wave (outphased 120 degrees from each), and the 3 phases conduce current during the whole electric cycle in a way that any of them is the algebraic sum of the other 2 at all time. Therefore, the resulting torque is flat (ideally). This is accomplished by a control algorithm called Space Vector
Modulation. Whenever the currents match the shape of an ideal sine, the RMS value can be calculated as:
IRMS = ICREST / √2
In trapezoidal mode, the motion controller modulates the voltage to fit the shape of a trapezoid. In this scenario, only 2 phases are active at the same time, matching the flat sections of the trapezoid, and the 3rd is left floating. Therefore, the current is positive in the phase modulated with positive voltage, it is negative in the phase modulated with negative voltage, and there is no current at all in the phase left floating, in which the observable voltage is the BEMF changing from positive to negative or vice-versa. The resulting torque shows a characteristic ripple, which is product of the fact that each 1/6th of the cycle a DC excitation is applied over a rotating magnetic field, so the resulting torque is proportional to the sine of the angle between the rotor and the excitation.
As the current can be approximated to ideal square waves, the approximate RMS value of the current can be calculated as:
IRMS = ICREST * 2/3
With ICREST being the value of the current in DC during the flat section.
In the diagram, the BEMF of each phase is shown in dashed line. Torque and current is shown in solid line.
|(This torque response might depend on the internal construction of the motor)|
In DC mode, the current is simply proportional to voltage, therefore the controller must only modulate voltage in accordance with the required torque and direction. The RMS value of the current can be calculated as:
IRMS = IDC
In the diagram, voltage of each phase is shown in dashed line and current is shown in solid line.