THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

The paper presents an accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect. It is derived by solving the field governing equations in each simple and regular subdomain, i.e., magnet, air-gap and stator slots, and applying the boundary conditions to the interfaces between these subdomains. The model accurately accounts for the influence of interaction between slots, radial/parallel magnetization, internal/external rotor topologies, relative recoil permeability of magnets, and odd/even periodic boundary conditions. The back-electromotive force, electromagnetic torque, cogging torque, and unbalanced magnetic force are obtained based on the field model. The relationship between this accurate subdomain model and the conventional subdomain model, which is based on the simplified one slot per pole machine model, is also discussed. The investigation shows that the proposed accurate subdomain model has better accuracy than the subdomain model based on one slot/pole machine model. The finite element and experimental results validate the analytical prediction.

An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines

This paper examines the torque ripple and cogging torque variation in surface mounted permanent magnet synchronous motors with skewed rotor. The effect of slot/pole combinations and magnet shapes on the magnitude and harmonic content of torque waveforms in a PMSM drive has been studied. Finite element analysis (FEA) and experimental results show that for certain magnet designs and configurations the skewing with steps does not necessarily reduce the ripple in the electromagnetic torque, but may cause it to increase. The electromagnetic torque waveforms including cogging torque have been analyzed for four different PMSM configurations having the same envelop dimensions and output characteristics.

Permanent Magnet Synchronous Motor Magnet Designs with Skewing for Torque Ripple and Cogging Torque Reduction

Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.

Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines

Using energy method, this paper analytically reveals that the cogging torque can be reduced by controlling N/sub L/th harmonic components of the square of airgap permeance function and flux density function, where N/sub L/ denotes the least common multiple of number of poles and number of slots. As for design tools, it introduces various design techniques to reduce cogging torque with analytical formulation and FEM examples.

Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors

The permanent magnet motor is often the most important element in many precision rotor applications and also a frequent source of vibration and acoustic noise. The eccentricity between stator and rotor is inevitably introduced during manufacturing process, such as mass unbalance, shaft bow and bearing tolerances. This paper investigates radial force density and magnetic unbalanced force for IPM and SPM motors when rotor eccentricity exists. For the magnetic field analysis, a finite element method is used to account for the magnetic saturation and rotor eccentricity. The radial force density and magnetic unbalanced force are analyzed by Maxwell stress tensor and discrete Fourier transform. An IPM BLDC motor, mostly chosen to realize high speed operation, is significantly affected by rotor eccentricity due to magnetic saturation.

Comparison of magnetic forces for IPM and SPM motor with rotor eccentricity

Tubular hydroforming has recently attracted increased attention in the automotive industry and the finite-element analysis is an effective tool for evaluation and optimisation of the design of hydroforming dies and processes. In this paper, a comparison is made of an implicit and an explicit finite-element method, widely used for the hydroforming process. The influence of time scaling and mass scaling, which have been commonly used in order to save computational time, in an explicit method, for the hydroforming simulation of an automotive lower arm, are investigated. The comparisons focus on the accuracy of the predicted geometrical shape and the stress in the explicit method with various scaling factors.

Comparison of Implicit and Explicit Finite-Element Methods for the Hydroforming Process of an Automobile Lower Arm

This paper presents methods to reduce acoustic noise in an interior permanent-magnet motor during the design stage. Mechanical and magnetic sources are considered to reduce noise of the machine, and structural and electromagnetic designs are performed. In the structural-design stage to reduce mechanical source, the structural resonances are moved to higher frequency for enhancement of stiffness. Then, in the electromagnetic-design stage to reduce exciting forces, the harmonic amplitude of magnetic forces and torque ripple are reduced by using an optimal design method, respectively. Two models are designed according to each objective function, and the validity of the design process and objective functions is confirmed by their simulated and experimental results.

Optimal Design for Noise Reduction in Interior Permanent Magnet Motor

This paper proposes design and analysis of a new linear motor called flux reversal linear synchronous motor (FRLSM), which is cost effective for long stroke applications. Passive rotor configuration of a typical flux reversal machine (FRM) can be utilized for a linear machine with less permanent magnet (PM). Three different design choices are investigated and compared both in thrust and normal force. The investigation shows extremely low force ripple and good thrust linearity through skewing and three-phase sinusoidal control. Reduced PM configuration generates about 21% higher thrust even with half amount of PM.

Sang-Moon Hwang

Papers

Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors

Comparison of magnetic forces for IPM and SPM motor with rotor eccentricity

Comparison of Implicit and Explicit Finite-Element Methods for the Hydroforming Process of an Automobile Lower Arm

Optimal Design for Noise Reduction in Interior Permanent Magnet Motor

A Novel Design of Linear Synchronous Motor Using FRM Topology