- Predicable design operation relies on the proper entry of servomotor parameters into a drive.
- Myriad servomotor parameters can be entered incorrectly if motor manufacturer units and drive parameters don’t match or aren’t understood.

A servodrive only performs well when it is programmed in the units designated by its designer. The problem is that motor-datasheet 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 ever-changing commands, loads, and feedback signals that characterize dynamic applications.

Why the inconsistencies? Many variations arose because there are two main electronic-control methods for permanent-magnet, three-phase synchronous servomotors: Sine-wave and six-step (trapezoidal) commutation. The **Motor parameters conversion table** in this article maps such instances and the varied parameters’ relationships.

### Motor-name variations

Servomotors can be classified as brushless-dc motors (BDCMs or BLDCMs), servos, brushless-dc/ac synchronous servomotors, ac permanent-magnet (PM) servos, and more. Servo manufacturers established most of these terms in the 1980s for marketing purposes and to underscore that ac permanent-magnet (PM) motors (which are electronically commutated to create PMAC servos) can replace the servo function of permanent-magnet dc-brush motors.

Over the years, some industry sources invented explanations for the technologies’ varied naming conventions. Many such explanations relate to B_{emf} characteristics — clean sine-wave sinusoidal commutation or six-step 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 three-phase (Φ) ac-PM 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 three-phase wye (Y)-connected motor ***capable of good three-phase sinusoidal-emf waveforms when backdriven as a generator*, **with electrically balanced windings**, versus a delta (Δ)-wound armature.

We use this example because most three-phase ac-PM servomotors today utilize wye-connected 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 emf-voltage constant

The voltage (emf) constant is usually abbreviated *Ke*, but sometimes appears as *K _{emf}*,

*K*, or

_{E}*K*. It is the maximum line-to-line voltage developed per some velocity unit, such that when the velocity unit is rad/sec and Kt is in Nm/A, then

_{b}*Ke*(V/rad/sec) =

*Kt*(Nm/A). This is also true for

**PMDC brush servomotors**, for which

*K*(V

_{E}_{dc}/rad/sec) =

*K*(Nm/A

_{t}_{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 six-step commutation* (not sine-wave commutation).

For a **wye-wound armature**, if a motor data sheet defines the voltage (emf) constant as the phase (line-to-neutral) voltage developed per some velocity unit, it must be multiplied by √3 for a final result in the line-to-line Ke units defined above.

### The B_{emf} voltage constant

The voltage *B _{emf}* constant

*K*(also listed as

_{b}*K*,

_{Bemf}*K*, and

_{B}*K*) is the line-to-line RMS voltage developed per some velocity unit.

_{e}*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 sine-wave communication (not six-step commutation.)

If a motor data sheet defines the Voltage (Bemf) constant as the Φ (line-to-neutral) RMS voltage developed per some velocity unit, it must be multiplied by √3 for a final result in the line-to-line 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) motor-phase 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 six-step and sine-wave 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 wye-wound armature. Therefore, manufacturers don’t always publish its exact definition in literature or motor-specification sheets.

In a wye-wound armature, line-to-line current is equal to line-to-neutral current.

- The torque constant
*Kt*(sometimes*K*)_{T}**associated with six-step 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 three-phase servomotor, current flows through only two of the three motor coils (2-ON, 1-OFF) at a time. - Torque constant
*Kt*(sometimes*K*)_{T}**associated with sine-wave commutation**is ratio of some torque T to the RMS phase (Φ) current (line to neutral), where*Kt*is in the units T/a-rms. For this definition and a three-phase servomotor, current may flow through all three coils at the same time.

When manufacturers publish the torque constant for sine-wave commutation in the units Nm/amp (crest of sine-wave) then:

T/a-rms = √2 · Nm/amp (crest of sine wave).

Conversion between the two commutation methods for the torque constant is:

Kt (Nm/A) = Kt (T/a-rms)/√1.5

and Kt (T/a-rms) = 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 dc-style) current — just as one would expect.

We will not cover the formal derivation of √1.5 for converting between six-step and sine-wave commutation *Kt* and current. However, it’s verified by the equivalency of six-step and sine-wave power-loss 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 root-mean-square 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 six-step 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 sinusoidal-commutation controller requiring motor parameters in the following units:

**Continuous motor current units:**a-rms —*Ic*(motor), RMS value of motor’s continuous capability per Φ (line-neutral).**Peak motor-current-limit units:**a-rms — Ip (motor) is the RMS value describing the motor limit per Φ (line-neutral)Nm/a-rms — Torque_unit/a-rms for a sine-wave controller, with line-to-neutral (Φ) RMS current*Kt*constant units:Vrms/Krpm — RMS voltage line to line per 1,000_rpm*Kb*constant units:Ohms (Ω) line to line — Two phases in series, Rm_Φ = Rm (L-L)/2]*Rm*(typically 20 or 25°C room temperature) units:milli-Henry or mH — L_Φ = Lm(L-L)/2*L*or*Lm*inductance (line to line), inductance units:**Motor rotor inertia Jm units:**Kg-cm^{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 wye-wound 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 wye-wound 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 delta-wound 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 six-step commutation is set equal to the power for sine-wave commutation:

2 · V_Φ · I_Φ · cosΘ = 3 · V_Φ · I_Φ · cosΘ

The cosΘ factors out of the equation. - Conventional three-phase trapezoidal commutation drives control only two motor windings at a time. Sinusoidal commutation drives can concurrently control all three windings.
- For sine-wave 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 sine-wave peak (crest) or peak-to-peak (crest-to-crest) values.

The Motor parameters conversion table can be also be used as a quick-check 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/a-rms). 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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