20100325 BDC Motor Presentation

March 25, 2010 Slide 1

Brushless DC Motors

Basic Model and Selection

Prepared and Presented by Steven GarfinkelEllipsah LLC

Motor Sample

Stator with Rotor

Commutation Sensor

Custom Motor Prototype:Rotor

Lamination Stack

Phase Winding

Wound Stator

Lead Attach

Lead Out

Formed End Turns

Hall Effect PWA

Stator Assembly

The Pieces

• Laminations

• Magnets

• Insulation System

• Commutation System

Laminations

• Quality (M number) and thickness drive losses

• Lower M number has lower losses

• Typical: M19 0.014 thick

Magnets

• Rare Earth – Neodymium Iron and Samarium Cobalt.

• Critical characteristics for design Br, Hc, Energy Product, Operating Temperature.

• Maximum operating temperature typically defined as the temperature below which the magnet will not demagnetize when in a circuit with a permeance of 2.

• Maximum temperature can range from 85ºC for cheap NdFe magnets to 300ºC for SmCo.

Insulation System

• Critical characteristic: temperature rating

• Temperature rating typically defined as hot spot operating temperature that will give 10k hours life.

• Can be as high as 220ºC

Commutation System

• Hall Effects – limited by maximum operating range of hall effect sensor, typically 150ºC.

• Resolver – requires more complicated interface. Temperature range increased to insulation system of resolver.

The Goal

• Select the right size motor for a task

• The requirements:– Operating speed at load

– Supply Voltage

– Operating Dutycycle

– Thermal requirements

The Model

• Ignore commutation. Commutation is done in electronics and (for now) assumed correct.

• Start from the most basic model and add complexity

Model – Version 0

• Change in magnetic flux through coils produces back emf. A fixed voltage on the stator produces a fixed speed. Torque has no effect on the motor speed. The ratio of voltage to speed is the back emf constant Ke, which has units of V/kRPM or V/(radians per second)

• Quick test – attach hand drill to motor and turn motor while viewing commutation sensors and back emf on oscilloscope.

Diversion 1 – Sample Motor back emf

Diversion 1 – Prototype Motor back emf

Model – Version 1

• Torque load on the motor is matched by motor torque, producing current flow in the windings. The ratio of torque to current is called the torque constant Kt which has units of in-oz/amp or Nm/amp. Kt and Keare ratiometric, in fact:

• Ke[V/(rads/sec)] = Kt[Nm/amp]

Model – Version 1

• Model Equations

I = T/Kt

N = (V – I*Ra)/Ke

Model – Version 1Speed and Current Vs Torque

0 200 400 600 800 1000Torque

Speed [kRPM]

Current [A]

Current

Model – Version 1

• The slope of the speed – torque curve is sometimes called the speed regulation constant.

Model – Version 2

• The physical design has some inherent friction tf.

• The rotational magnetic field produces losses in the laminations which are proportional to speed. This constant is called Kd which has units of in-oz/kRPM.

Model – Version 2

• Model Equations

I0 = (T+ tf)/Kt

N0 = (V – I*Ra)/Ke

In = (T+ tf + Kd*Nn-1)/Kt

Nn = (V – I*Ra)/Ke

Model – Version 2Speed and Current Vs Torque

0 200 400 600 800 1000Torque

Speed [kRPM]

Current [A]

Current

Model – Version 3

• The stator windings have inductance. The windings are switched at the commutation frequency.

• The inductance impedes the flow of current at the leading edge. Effectively, some voltage is used to overcome the switched inductance.

• On the trailing edge, the stored energy in the winding continues the current flow, producing useful torque.

• The net effect of the leading and trailing edge produces a speed-torque slope higher then theoretical and a current-torque slope lower then theoretical.

• The resistance, when calculated based upon the decrease in speed versus torque, is typically from 2 to 4 times as high as the resistance of the stator winding and is speed dependent.

Model – Version 3

Speed and Current Vs Torque

0 200 400 600 800 1000Torque

Speed [kRPM]

Current [A]

Current

Winding Constants versus Size Constants

• Winding constants vary with the number of turns on the stator. Size constants are independent of turns.

• A small motor and a large motor can have the same Ke. The difference is that a large motor will have a lower resistance and therefore be more efficient than a small motor.

Winding Constants

• Kt, Ke, R, L are all winding constants.

• For a given motor, changing the number for turns by a factor of F gives new winding constants of:

Kt’=F* Kt

Ke’ = F * Ke

R’ = F2 * R

L’ = F2 * L

Size Constants

• Tf, Kd, Θ and Km are size constants.

• Θ is the thermal impedance from the motor hot spot to a reference point, which could be ambient or could be the temperature of a mounting surface.

• Km is called the motor constant. It has units of in-oz/√Watts.

Selecting a motor

• Since most of a motors losses are due to torque, to minimize the motor size, run it as fast as possible (high gear ratio) so that the torque is low at a given power output.

• Select from motors that can safely operate at the target speed. High speeds require a sleeved rotor.

• At the operating point, compare motors based upon Θ, Km, the maximum ambient temperatureand the insulation system maximum temperature of operation.

The data sheet doesn’t have Km!

Km = Kt [in oz/amp]/ √R

The data sheet doesn’t have Kd

• Test the motor at no load with different line voltages. Plot the motor current versus the speed. The slope of the line is Kd and the intercept is Tf.

• Since Kd is a size constant, estimate it based upon data provided for similarly sized motors.

Why don’t my Speed Torque Curves match my calculations?

• The test devices for motor inherently have high inertia.

• As the test proceeds, the winding heats up and the resistance increases, so a short test duration is desired.

Why don’t my Speed Torque Curves match my calculations?

• If the test starts at no load speed, the inertia of the test fixture causes the resulting test speed to be high and current to be low.

• The motor supplier may use similarly suspect data to obtain published Ke and Kt

values.

So I know what size motor I need, what’s next?

• Select a Ke so that the primary speed operating point is at 85 to 90 percent of the theoretical no load speed. If the speed requirement is firm, make sure you use the low line voltage and subtract any drop in the wiring and electronics. Efficiency at the operating point is approximately the ratio of the speed to theoretical no load speed.

• Obtain or calculate the remaining winding constants.

So I know what size motor I need, what’s next?

• Check to make sure the drive electronics will work with the derived motor inductance.

• Check to make sure the drive electronics can provide the desired current within its thermal envelope.

• Re-check the thermal analysis at maximum ambient temperature. Remember, the resistivity of copper increases with temperature.

• If you need help selecting a motor, a drive, or need a custom or semi-custom motor or drive call me:

Steve Garfinkel

973 432-7401

20100325 BDC Motor Presentation

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