# Electric Machine Design Course Torque vs Speed Kt

- Slides: 20

Electric Machine Design Course Torque vs. Speed & Kt vs. Ke SPM, IPM & PMSM brushless motors Lecture # 31 Mod 31 Copyright: JR Hendershot 2012 310

Performance curves for BLDC, & PMSM machines with magnets on the rotating member (Includes SPM, IPM & axial flux machines) PMDC servo motors were historically powered by batteries or SCR variable voltage drives & controllers. The motor engineer characterized each motor performance by using a ”prony brake” on the output shaft to load down the motor from noload speed. The point by point data taken was naturally a function of torque values at specific speeds. (This was called a dynamometer) The “Prony Brake” was invented in Paris in 1821 by Gaspard de Prony Mod 31 Copyright: JR Hendershot 2012 311

Modern electric motor dynamometer HORIBA Mod 31 Copyright: JR Hendershot 2012 312

Motoring & Generating (4) quadrant operation N Performance for Motor + Inverter -N Historically, (4) quadrant performance displayed as Speed vs. Torque Mod 31 Copyright: JR Hendershot 2012 313

Introduction to Speed vs. Torque curves Original PMDC commutated motors displayed Speed vs. Torque curves along with current power and efficiency vs. torque. (Constant VDC) Armature winding consists of multiple coil single phase Magnets in stator Windings in rotor Ke = V-sec/rad = Kt = Nm/A Mod 31 Copyright: JR Hendershot 2012 314

Performance analysis of machines powered by inverters The performance of interest is no longer limited to the motor capabilities alone. The system (consisting of the motor, the inverter and the controller) must be analyzed to predict the motor performance. Torque vs. RPM more useful plot Mod 31 Copyright: JR Hendershot 2012 315

Brushless PM with (6) step drive Magnets are located on rotor and phase windings are in stator Inverter & controller driven with unipolar or bipolar trapezoid or sine currents More common to display performance curves as Torque vs. Speed Torque PM DC Brushless Motor Torque vs. Speed plot No magnetic saturation Constant voltage Actual BLDC Torque vs Speed driven with 6 -step Reduce voltage limit Speed Mod 31 Copyright: JR Hendershot 2012 316

BLDC and PMSM commutation differences BLDC machines (irrespective of back emf wave shape) Related only to control system or inverter type used (6) step DC switched commutation @ 50 deg. E per step Two phases powered at a time producing torque Current in two phases for +/-120 deg. E out of possible 180 (66. 7% copper utilization) Average current/phase affected by Inductance and speed Max speed can be increased by “phase advancing” PMSM machines (usually designed for nearly sine back EMF) Two types of current control, Hysteresis or Space Vector Drive current produced in all three phases for 360 deg. E (100% copper utilization) Lowest torque ripple and lower audible noise Higher speeds possible using same motor When used with IPMs, high constant power range possible Dr. Dal Y. Ohm Mod 31 Copyright: JR Hendershot 2012 317

Block Diagram of Brushless Motor Drive System Dr. Dal Y. Ohm Mod 31 Copyright: JR Hendershot 2012 318

Torque vs. speed curve for PM-AC Synchronous Sine driven (sinusoidal or space vector controlled) PMSY-IPM REMY Mod 31 Copyright: JR Hendershot 2012 319

Kt vs. Ke definitions Kt = Torque constant Nm/amp (torque vs. current) Ke = back EMF constant V-sec/rad (EMF vs. speed) Used to match motor and drive for motion control systems (Laplace transforms of Ke & Kt for motion control) Kt & Ke varies with magnet temperature (Bm) Ferrite Nd. Fe. B Sm. Co - 0. 20 % / deg. C - 0. 12 % / deg. C - 0. 03 % / deg. C Which magnet grade yields most stable Kt & Ke with temperature? Mod 31 Copyright: JR Hendershot 2012 320

Kt & Ke vs. Flux Linkage Kt & Ke determined by linkage of the rotor flux to stator conductors Professor TJE Miller Mod 31 Copyright: JR Hendershot 2012 321

Kt vs. Ke for different pm motors Kt & Ke confusion depending upon motor back EMF Historical PMDC machines, Ke = Kt PM-DC brushless Ke = Kt, if back EMF is trapezoidal PM-AC brushless, depends upon EMF shape & definition Precise relationship requires back EMF and phase currents be defined as Peak, Mean or RMS. Precise definition of Kt & Ke proposed: “Ratio of the mean electromagnetic torque to the RMS line current in the motor” ISBN 978 -0 -9840687 -0 -8 pg. 405 Mod 31 Copyright: JR Hendershot 2012 322

Motor Constants, Ke & Kt calculations for trapezoid full wave 120 deg commutation Peak flux linkage per phase This becomes the average phase EMF during 120 deg. rotation For L-L EMF there are two phase in series and taking into account that each phase coil has two sides which are linked by the flux the equation for the peak Ke or back EMF constant is: For trapezoid emf: Peak Ke (Nm/A = Kt (Vs/rad) The above equation is for wye connected machines. If the phase windings are connected in delta, the 2/3 factor is replaced by 1/3. (See page 180, ISBN 978 -09840687 -0 -8) Mod 31 Copyright: JR Hendershot 2012 323

Kt & Ke for 3 -phase sinewave machine & drive The relationship between Ke & Kt depends upon the shape of the back emf and its definition, peak, average or mean. The back emf of sinewave machine means the peak flux linkage per phase is sinusoidal: For a wye connected sinewave machines the peak For a delta connected sinewave machine Ke constant: is omitted Z = Total conductors in machine = T/coil x 2 x number of coils = Air gap flux/pole Mod 31 Copyright: JR Hendershot 2012 324

Motor constant as a figure of merit (Km) For machine design it can be useful to compare one PMDC or Brushless DC motor to another with respect to the machine designer’s goals a figure of merit is used to: Compare peak or rated output torque capability Compare relative machine efficiencies Sometimes a motor constant value (Km) is listed as a design parameter in the machine specifications. In addition (Km) values (without units) are listed in most vendor catalogues for PMDC and BLDC servo motors & torque motors. There are more than one way this motor merit data can be presented. With all methods, for useful comparison purposes, one must know if the torque values used are peak or rated. Mod 31 Copyright: JR Hendershot 2012 325

Torque constant vs. terminal resistance figure of merit The torque constant, (Kt) is determined (by measurement or calculation) The line to line stator phase resistance, (Rt) is determined Resulting figure of merit motor constant: or (T) = rated torque (I) = rated current (Rt) = line to line resistance in ohms (Kt) is usually given in oz-in/amp by USA brushless vendors Units can be converted to Nm/Amp, oz-in/Amp or any other units Mod 31 Copyright: JR Hendershot 2012 326

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