A servodrive only performs well when it is programmed in the units designated by its designer. The problem is that motordatasheet units, definitions, and conversions vary by manufacturer.
There is no unified convention for publishing servomotor data. Nor is there a standard set of units or nomenclature for entering motor data into drives. So, it’s the job of the integrator to understand and homogenize parameters. This task is most critical when setting up servocontrol loops: Inaccuracies prevent servodrive control algorithms from acting properly and reacting to the everchanging commands, loads, and feedback signals that characterize dynamic applications.
Why the inconsistencies? Many variations arose because there are two main electroniccontrol methods for permanentmagnet, threephase synchronous servomotors: Sinewave and sixstep (trapezoidal) commutation. The Motor parameters conversion table in this article maps such instances and the varied parameters’ relationships.
Motorname variations
Servomotors can be classified as brushlessdc motors (BDCMs or BLDCMs), servos, brushlessdc/ac synchronous servomotors, ac permanentmagnet (PM) servos, and more. Servo manufacturers established most of these terms in the 1980s for marketing purposes and to underscore that ac permanentmagnet (PM) motors (which are electronically commutated to create PMAC servos) can replace the servo function of permanentmagnet dcbrush motors.
Over the years, some industry sources invented explanations for the technologies’ varied naming conventions. Many such explanations relate to B_{emf} characteristics — clean sinewave sinusoidal commutation or sixstep or block commutation, also known as trapezoidal commutation, in which each electrical cycle (one electrical cycle or PM pole pair) is six commutation steps. However, the bottom line is that more than anything else, the conventions aimed to overcome false perceptions of technological barriers.
Regardless of their varied naming conventions, all of these motors are basically threephase (Φ) acPM synchronous machines.
Let us establish the typical units presented by motor manufacturers, so that engineers can convert these units for a proper comparison of one servomotor to another when applicable. This also lets us convert motor parameters to the units required by the chosen drive.
For the purpose of this article, consider a threephase wye (Y)connected motor capable of good threephase sinusoidalemf waveforms when backdriven as a generator, with electrically balanced windings, versus a delta (Δ)wound armature.
We use this example because most threephase acPM servomotors today utilize wyeconnected armatures, especially for sinusoidal commutation. (Consideration of torque angle advance algorithms and harmonic issues are beyond this article’s intent and scope.) Following is the commonly used nomenclature for such a motor.
The emfvoltage constant
The voltage (emf) constant is usually abbreviated Ke, but sometimes appears as K_{emf}, K_{E}, or K_{b}. It is the maximum linetoline voltage developed per some velocity unit, such that when the velocity unit is rad/sec and Kt is in Nm/A, then Ke (V/rad/sec) = Kt (Nm/A). This is also true for PMDC brush servomotors, for which K_{E} (V_{dc}/rad/sec) = K_{t} (Nm/A_{dc}), with no consideration for the difference between motors that are cold (at ambient temperature) or hot (at the maximum or application operating temperature.)
Two widely used Ke units are V/rad/sec and V/Krpm:
where V = V_{dc} bus for most drive systems = Maximum (crest) voltage available — Not in RMS terms.
Ke = Voltage (emf) constant, expressed in either
V/rad/sec, V/Krpm, or other equivalent — typically associated with sixstep commutation (not sinewave commutation).
For a wyewound armature, if a motor data sheet defines the voltage (emf) constant as the phase (linetoneutral) voltage developed per some velocity unit, it must be multiplied by √3 for a final result in the linetoline Ke units defined above.
The B_{emf} voltage constant
The voltage B_{emf} constant K_{b} (also listed as K_{Bemf}, K_{B}, and K_{e}) is the linetoline RMS voltage developed per some velocity unit.
Kb (Vrms/Krpm) = Ke (V/Krpm)/√2, or
Kb (Vrms/rad/sec) = Ke (V/rad/sec)/√2
where Kb (Vrms/Krpm) = Ke (V/rad/sec) · 1,000/9.55/√2.
The voltage (Bemf) constant Kb expressed in
Vrms/rad/sec, Vrms/Krpm, or other equivalent is typically associated with sinewave communication (not sixstep commutation.)
If a motor data sheet defines the Voltage (Bemf) constant as the Φ (linetoneutral) RMS voltage developed per some velocity unit, it must be multiplied by √3 for a final result in the linetoline Kb units defined above.
The torque constant
The torque constant Kt (sometimes denoted K_{T}) is the ratio of some torque T unit over either the maximum (crest) motorphase current (line to neutral), or the RMS phase current (line to neutral).
Note that the two different specifications for the term Kt arise because of the differences between sixstep and sinewave commutation. These differences prevent many engineers from deducing the relationship between the two Kt current units.
Furthermore, it’s generally assumed that the torque constant is torque developed per some unit of current through one phase of the wyewound armature. Therefore, manufacturers don’t always publish its exact definition in literature or motorspecification sheets.
In a wyewound armature, linetoline current is equal to linetoneutral current.
 The torque constant Kt (sometimes K_{T}) associated with sixstep commutation is the ratio of some torque T to the maximum (crest) phase (Φ) current (line to neutral), where Kt is in the units T/A. For this definition and a threephase servomotor, current flows through only two of the three motor coils (2ON, 1OFF) at a time.
 Torque constant Kt (sometimes K_{T}) associated with sinewave commutation is ratio of some torque T to the RMS phase (Φ) current (line to neutral), where Kt is in the units T/arms. For this definition and a threephase servomotor, current may flow through all three coils at the same time.
When manufacturers publish the torque constant for sinewave commutation in the units Nm/amp (crest of sinewave) then:
T/arms = √2 · Nm/amp (crest of sine wave).
Conversion between the two commutation methods for the torque constant is:
Kt (Nm/A) = Kt (T/arms)/√1.5
and Kt (T/arms) = Kt (Nm/A) · √1.5.
Therefore, continuous current Ic (rms) required by a given motor to reach full capacity has a lower value than if presented as an Ic (crest or dcstyle) current — just as one would expect.
We will not cover the formal derivation of √1.5 for converting between sixstep and sinewave commutation Kt and current. However, it’s verified by the equivalency of sixstep and sinewave powerloss calculations. See the Motor parameters conversion table:
The most common miscalculation between the two commutation methods is to mistakenly use the √2 RMS instead of the √1.5 conversion between the two different Kt units, or required currents. The √2 rootmeansquare conversion is not the same unit conversion as seen between the motor’s Kt units or the required current to produce a specific torque, from a sixstep unit system to a sinusoidal commutated unit system, or vice versa.
Drive selection
Let us assume that we’re selecting a drive in the form of a sinusoidalcommutation controller requiring motor parameters in the following units:
 Continuous motor current units: arms — Ic (motor), RMS value of motor’s continuous capability per Φ (lineneutral).
 Peak motorcurrentlimit units: arms — Ip (motor) is the RMS value describing the motor limit per Φ (lineneutral)
 Kt constant units: Nm/arms — Torque_unit/arms for a sinewave controller, with linetoneutral (Φ) RMS current
 Kb constant units: Vrms/Krpm — RMS voltage line to line per 1,000_rpm
 Rm (typically 20 or 25°C room temperature) units: Ohms (Ω) line to line — Two phases in series, Rm_Φ = Rm (LL)/2]
 L or Lm inductance (line to line), inductance units: milliHenry or mH — L_Φ = Lm(LL)/2
 Motor rotor inertia Jm units: Kgcm^{2}
Notes on common variations
Following are subscript notes for the Motor parameters conversion table.
 Most often the phase (Φ) current and (Φ) voltage (line to line) is defined somewhere in the manufacturer’s data. However, it commonly assumed to be understood.
 For a wyewound winding, if a data sheet states Lm = LΦ (line to neutral), multiply LΦ by two for the total motor inductance Lm (in mH, line to line).
 For a wyewound winding, if a data sheet states Rm = RΦ (line to neutral), multiply RΦ by two for the total resistance Rm (line to line). For a deltawound motor, resistance (Ω) is Rm/Φ = Rm (line to line).
 As temperature climbs from 25° ambient to a maximum of 155°C, resistance of the copper increases by a factor of approximately 1.525.

For a given motor and the scope of this article, when power for sixstep commutation is set equal to the power for sinewave commutation:
2 · V_Φ · I_Φ · cosΘ = 3 · V_Φ · I_Φ · cosΘ
The cosΘ factors out of the equation.  Conventional threephase trapezoidal commutation drives control only two motor windings at a time. Sinusoidal commutation drives can concurrently control all three windings.
 For sinewave commutation (Column F in the Motor parameters conversion table) if a drive demands that Ic (continuous) and Ip (Ipeak) be entered in the units:
Ic (crest of the sine wave)/phase (Φ)
Ip (crest of the sine wave)/phase (Φ)
Then the corresponding value in Column F must be multiplied by √2.
If the specific parameters are to be entered in the units:
Ic (crest to crest of the sine wave)/phase (Φ)
Ip (crest to crest of the sine wave)/phase (Φ)
Then the corresponding value in Column F must be multiplied by 2 · √2.
Note that “crest” is used here to minimize confusion of the myriad terms for peak motor and drive capabilities with expressions relating to sinewave peak (crest) or peaktopeak (cresttocrest) values.
The Motor parameters conversion table can be also be used as a quickcheck nomenclature reference. For example, to verify that Kt and Kb (or Ke) are in RMS units, divide what is thought to be Kb (Vrms/Krpm) by Kt (Nm/arms). If the corresponding units are correct, the resulting quotient will equal some quantity between 60 and 65, or (in a few exceptions for rounding off) just over or under that range. The method typically works regardless of the assumed motor temperature (operating or ambient) or PM servo type.
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