Cogging torque

Abstract: Permanent magnet AC (PMAC) motor drives are finding expanded use in high-performance applications where torque smoothness is essential. This paper reviews a wide range of motor- and controller-based design techniques that have been described in the literature for minimizing the generation of cogging and ripple torques in both sinusoidal and trapezoidal PMAC motor drives. Sinusoidal PMAC drives generally show the greatest potential for pulsating torque minimization using well-known motor design techniques such as skewing and fractional slot pitch windings. In contrast, trapezoidal PMAC drives pose more difficult trade-offs in both the motor and controller design which may require compromises in drive simplicity: and cost to improve torque smoothness. Controller-based techniques for minimizing pulsating torque typically involve the use of active cancellation algorithms which depend on either accurate tuning or adaptive control schemes for effectiveness. In the end, successful suppression of pulsating torque ultimately relies on an orchestrated systems approach to all aspects of the PMAC machine and controller design which often requires a carefully selected combination of minimization techniques.

Abstract: The influence of various design parameters on the cogging torque developed by permanent magnet machines is investigated. It is shown that the slot and pole number combination has a significant effect on the cogging torque, and influences the optimal value of both skew angle and magnet arc, as well as determining the optimal number of auxiliary teeth/slots. A simple factor, which is proportional to the slot number and the pole number and inversely proportional to their smallest common multiple, has been introduced to indicate the "goodness"/spl beta/ of the slot and pole number combination. In general, the higher the "goodness" factor the larger the cogging torque.

Abstract: Several techniques may be adopted in designing surface-mounted permanent-magnet motors in order to reduce the cogging torque. This paper describes various classical and innovative techniques, giving a theoretical justification for each of them. To this aim, a simple original model of the cogging torque mechanism and a Fourier analysis are introduced. As a result, it is highlighted that some techniques are not always utilizable, and some of them may even be deprecatory when not used correctly. In addition, effects of cogging torque elimination on back electromotive force are discussed.

Abstract: GENERATION AND RADIATION OF NOISE IN ELECTRICAL MACHINES Vibration, Sound, and Noise Sound Waves Sources of Noise in Electrical Machines Energy Conversion Process Noise Limits and Measurement Procedures for Electrical Machines Deterministic and Statistical Methods of Noise Prediction Economical Aspects Accuracy of Noise Prediction MAGNETIC FIELDS AND RADIAL FORCES IN POLYPHASE MOTORS FED WITH SINUSOIDAL CURRENTS Construction of Induction Motors Construction of Permanent Magnet Synchronous Brushless Motors A.C. Stator Windings Stator Winding MMF Rotor Magnetic Field Calculation of Air Gap Magnetic Field Radial Forces Other Sources of Electromagnetic Vibration and Noise INVERTER-FED MOTORS Generation of Higher Time Harmonics Analysis of Radial Forces for Nonsinusoidal Currents Higher Time Harmonic Torques in Induction Machines Higher Time Harmonic Torques in Permanent Magnet (PM) Brushless Machines Influence of the Switching Frequency of an Inverter Noise Reduction of Inverter-Fed Motors TORQUE PULSATIONS Analytical Methods of Instantaneous Torque Calculation Numerical Methods of Instantaneous Torque Calculation Electromagnetic Torque Components Sources of Torque Pulsations Higher Harmonic Torques of Induction Motors Cogging Torque in Permanent Magnet (PM) Brushless Motors Torque Ripple Due to Distortion of EMF and Current Waveforms in Permanent Magnet (PM) Brushless Motors Tangential Forces vs. Radial Forces Minimization of Torque Ripple in PM Brushless Motors STATOR SYSTEM VIBRATION ANALYSIS Forced Vibration Simplified Calculation of Natural Frequencies of the Stator System Improved Analytical Method of Calculation of Natural Frequencies Numerical Verification ACOUSTIC CALCULATIONS Sound Radiation Efficiency Plane Radiator Infinitely Long Cylindrical Radiator Finite Length Cylindrical Radiator Calculations of Sound Power Level NOISE AND VIBRATION OF MECHANICAL AND AERODYNAMIC ORIGIN Mechanical Noise Due to Shaft and Rotor Irregularities Bearing Noise Noise Due to Toothed Gear Trains Aerodynamic Noise Mechanical Noise Generated by the Load ACOUSTIC AND VIBRATION INSTRUMENTATION Measuring System and Transducers Measurement of Sound Pressure Acoustic Measurement Procedure Vibration Measurements Frequency Analyzers Sound Power and Sound Pressure Indirect Methods of Sound Power Measurement Direct Method of Sound Power Measurement: Sound Intensity Technique Standard for Testing Acoustic Performance of Rotating Electrical Machines NUMERICAL ANALYSIS Introduction FEM Model for Radial Magnetic Pressure FEM for Structural Modeling BEM for Acoustic Radiation Discussion STATISTICAL ENERGY ANALYSIS Introduction Power Flow Between Linearly Coupled Oscillators Coupled Multimodal Systems Experimental SEA Application to Electrical Motors NOISE CONTROL Mounting Standard Methods of Noise Reduction Active Noise and Vibration Control APPENDIX A: BASICS OF ACOUSTICS Sound Field Variables and Wave Equations Sound Radiation from a Point Source Decibel Levels and Their Calculations Spectrum Analysis APPENDIX B: PERMEANCE OF NONUNIFORM AIR GAP Permeance Calculation Eccentricity Effect APPENDIX C: MAGNETIC SATURATION APPENDIX D: BASICS OF VIBRATION A Mass-Spring-Damper Oscillator Lumped Parameter Systems Continuous Systems SYMBOLS AND ABBREVIATIONS BIBLIOGRAPHY INDEX