An Analytical Circuit Model of Switched Reluctance Motors

We have developed a dynamic analytical circuit model to simulate the performance of switched reluctance motors (SRMs). Our model expresses flux linkages as multiple decoupled one-argument functions, either current dependent or rotor position dependent, instead of one two-argument function dependent on both current and rotor position. We propose a novel approach for the computation of the air gap permeance at various rotor positions. By using this analytical model, the performance of a SRM can be simulated very efficiently and with improved accuracy. As an application example, we present a simulation of an 8/6 pole SRM in the system domain, and compare the results with transient finite element analysis (FEA) solutions.      

Measurement and Real-Time Modeling of Inductance and Flux Linkage in Switched Reluctance Motors

This paper presents a real-time model to identify the inductance and the flux linkage of switched reluctance motors (SRMs). A dynamic measurement method is used for the real-time modeling. An artificial neural network (ANN), designed in accordance with the inductance and the flux linkage data obtained from the dynamic measurement method, is used to make the real-time model. Experimental studies are realized to prove the applicability of the dynamic measurement method and the ANN-based model. The experiments are performed by using a TMS320F2812 digital signal processor (DSP). The results show that the dynamic measurement method and the ANN-based model ensure real values in all the positions and load conditions of the motor.      

Analytical Prediction of Cogging Torque in Surface-Mounted Permanent-Magnet Motors

We present a new approach to computing cogging torque based on only one analytical field solution in surface-mounted permanent-magnet (PM) motors. We use conformal transformation to compute the magnetic field created by the permanent magnets in the air gap with a single slot. Then, we derive the cogging torque due to the single-slot effect at different rotor positions directly from the 2-D analytical field solution. The total cogging torque is synthesized from the contribution of each slot. We have applied our approach to predicting the cogging torque of two surface-mounted PM motors, one with 4 poles, 24 slots and the other with 42 poles, 36 slots. The predicted cogging torques for both applications agree well with those obtained from 2-D finite-element analysis.      

Design of Electrical Rotating Machines by Associating Deterministic Global Optimization Algorithm With Combinatorial Analytical and Numerical Models

This paper presents a new methodology of design of electrical rotating machines. The methodology is an extension of previous works of the second author. Indeed, associating combinatorial analytical models with exact global optimization algorithms leads to rational solutions of predesign. These solutions need to be validated by a numerical tool (using a finite-element method) before the expansive phase of hand-making a prototype. Such an automatic numerical tool for computing some characteristic values, such as the torque, was previously developed. The idea of this paper is to extend the exact global optimization algorithm by inserting the direct use of this automatic numerical tool. This new methodology makes it possible to solve design problems more rationally. Some numerical examples validate the usefulness of this new approach.     

Performance Analysis of Linear Permanent-Magnet Motors With Finite-Element Analysis

This paper presents models for finite-element analyses and design of linear permanent-magnet motors (LPMMs) with surface-mounted or interior-buried permanent magnets (PMs). Several different models are studied in order to compare and discuss different LPMM structures. Using an analytical model of LPMMs, equations for thrust are derived. Then, we used 2-D finite-element analysis to illustrate the performance variation of LPMMs caused by the variation of structure parameters. Computer simulation results show that the characteristics and dimensions of the PMs, the shapes and dimensions of the armature, and the exciting current all have significant effects on motor performance. Several design examples based on the effects of these parameters demonstrate the design of the LPMMs. The design consideration presented in this paper can be used to determine preliminary LPMM mechanical structures before hardware implementation.     

Analytical Interpretation and Quantification of Rotational Losses in Stator Cores of Induction Motors

We propose an approach to allocate and delimit a region in which the rotational losses are of most importance in the stator core of induction motors. The delimitation is based on the analysis of points at which the minimum flux density is not null. The analysis of flux paths and values of flux density over a number of motors allows a model of flux density to be proposed for the chosen rotational region. We conducted the process by post-processing finite-element results. A comparison with bench test results shows that the approach can confine the effects of rotational losses within a region allocated in the tooth roots without significant loss of accuracy. We give analytical expressions based on geometrical data. The approach provides a quick method to evaluate the rotational losses by analytical means, bypassing the use of numerical methods at those design stages at which is preferable to reduce the accuracy in favor of computational speed.     

Analytical Models for the Performance of von Neumann Multiplexing

As conventional silicon CMOS technology continues to shrink, logic circuits are increasingly subject to errors induced by electrical noise. In addition, device reliability will become a problem, and circuits will be subject to permanent faults. Rather than requiring the circuit to be defect-free, fault-tolerance techniques can be incorporated to allow the continued operation of these devices in the presence of defects. We present an improved model for the reliability of nand multiplexing, a fault-tolerance technique typically requiring large levels of redundancy. It extends previous models to account for dependence between the inputs and derives the distribution of the outputs of each stage when subject to errors. The Markov chain approach used in earlier models is shown to be correct in modeling the effect of multiple stages. Our new model produces more accurate results for moderate levels of redundancy. An example shows the required hardware redundancy is reduced by 50% versus the previous binomial model. In addition, three new types of errors are modeled: the output stuck-at-one, output stuck-at-zero, and input stuck-at-zero faults     

Analytical Solutions to Models of Local Nonequilibrium Heat Transfer

High Temperature - A series of boundary-value problems of local nonequilibrium heat transfer is considered in terms of the theory of transient heat conduction for hyperbolic-type equations (wave...     

Emulation of Numerical Models With Over-Specified Basis Functions

Mathematical models are frequently used to explore physical systems, but can be computationally expensive to evaluate. In such settings, an emulator is used as a surrogate. In this work, we propose a basis-function approach for computer model emulation. To combine field observations with a collection of runs from the numerical model, we use the proposed emulator within the Kennedy-O’Hagan framework of model calibration. A novel feature of the approach is the use of an over-specified set of basis functions where number of bases used and their inclusion probabilities are treated as unknown quantities. The new approach is found to have smaller predictive uncertainty and computational efficiency than the standard Gaussian process approach to emulation and calibration. Along with several simulation examples focusing on different model characteristics, we also use the method to analyze a dataset on laboratory experiments related to astrophysics.     

Numerical Simulation of Photothermal Lens Spectrometry Models Relevant for Analytical Chemistry

Three numerical models (radial symmetry two-dimensional and three-dimensional with cw and pulsed excitation) that correspond to the samples and schematics of dual-beam thermal lens measurements in solution most commonly used in chemical analysis are implemented by finite element analysis using COMSOL Multiphysics and geometry simulations using MATLAB. The comparison of the results obtained using the implemented models with the existing infinite two-dimensional model by Shen and Snook (J Appl Phys 73(10):5286, 1993.  https://doi.org/10.1063/1.353761) under the same conditions showed their good agreement. The models were used to study the influence of the basic geometric and physical parameters of the sample. Conditions are found under which the boundary conditions for heat transfer and the geometrical parameters of the cell have the strongest and weakest effects on the signal.     

Construction of Differential Material Matrices for the Orthogonal Finite-Integration Technique With Nonlinear Materials

The linearization of an electromagnetic formulation by the Newton method can be expressed similarly as for the linear case, by introducing differential material matrices. For the case of the finite-integration technique applied to an orthogonal grid, the chord material matrix is diagonal whereas the differential material matrices includes off-diagonal bands, representing the cross-directional coupling introduced by the nonlinearity. An approximative Newton method based on a unidirectional differential material matrix yields a diagonal matrix, which has a higher computational efficiency but may lead to a degenerated convergence.     

Error Correction of Rainfall-Runoff Models With the ARMAsel Program

Improved predictions can be based on recent observed differences or errors between the best available model predictions and the actual measured data. This is possible in the predicted amount of supplies, services, sewage, transportation, power, water, heat, or gas, as well as in the predicted level of rivers. As an example, physical modeling of the dynamics of a catchment area produces models with a limited forecasting accuracy for the discharge of rivers. The discrepancies between the model and the actually observed past discharges can be used as information for error correction. With a time-series model of the error signal, an improved discharge forecast can be made for the next few days. The best type and order of the forecasting time-series model can be automatically selected. Adaptive modeling in data assimilation calculates updates of the time-series model estimated from the error data of only the last few weeks. The use of variable updated models has advantages in periods with the largest discharges, which are most important in flood forecasting.     

Programmable Design of Magnet Shape for Permanent-Magnet Synchronous Motors With Sinusoidal Back EMF Waveforms

The characteristics of a permanent-magnet synchronous motor (PMSM) are influenced greatly by the back-electromotive force waveforms in the motor, which are directly related to the magnet shape. We assume that the outer surface of a magnet in a PMSM can be modeled as one part of a cylinder. Using an ANSOFT model, we optimized the radius of the magnet with respect to number of poles, rotor size, and magnet thickness when the total harmonic distortion is below 1%. We then set up a lookup table using the optimization results so that the desired outer radius of a magnet of any new PMSM motor could be derived, subject to the parameter limits. We applied this method to some PMSM prototypes, and confirmed that the calculation results are substantially accurate.      

Analytical Solution of Air-Gap Field in Permanent-Magnet Motors Taking Into Account the Effect of Pole Transition Over Slots

We present an analytical method to study magnetic fields in permanent-magnet brushless motors, taking into consideration the effect of stator slotting. Our attention concentrates particularly on the instantaneous field distribution in the slot regions where the magnet pole transition passes over the slot opening. The accuracy in the flux density vector distribution in such regions plays a critical role in the prediction of the magnetic forces, i.e., the cogging torque and unbalanced magnetic pull. However, the currently available analytical solutions for calculating air-gap fields in permanent magnet motors can estimate only the distribution of the flux density component in the radial direction. Magnetic field and forces computed by the new analytical method agree well with those obtained by the finite-element method. The analytical method provides a useful tool for design and optimization of permanent-magnet motors.     

Fast Analytical Determination of Aligned and Unaligned Flux Linkage in Switched Reluctance Motors Based on a Magnetic Circuit Model

The main advantages of the switched reluctance motor are high torque, wide speed range, simple structure and fault tolerance. Because a switched reluctance motor has inherently nonlinear magnetic characteristics and a doubly salient pole structure, a finite-element analysis approach (FEA) is often adopted to obtain accurate magnetic representation. However, the solution time can be large for a FEA simulation if the mesh is detailed and/or many simulations are required. We propose a rapid analytical solution for determining the aligned and unaligned flux linkage using a magnetic circuit model. We present a simple method for obtaining the air-gap permeance for unaligned linkage. The results of our method agree well with FEA solutions.      

The Simplified Analytical Models for Evaluating the Heat Transfer Performance of High-Porosity Metal Foams

The accurate evaluation of the specific surface area and the effective thermal conductivity (ETC) of high-porosity metal foams is an important prerequisite to study the mechanism of heat transfer enhancement. In this paper, the tetrakaidecahedron, concave triangular prism and equivalent tetrahedron were used to develop the geometry shapes of cell, ligament and node, respectively. The calculation model of the specific surface area characterized by porosity and pore density (PPI) was deduced by considering the shape characteristics. Based on the angle between the two-dimensional plane skeleton layer and the heat flow direction, the ETC analytical calculation model characterized by only the porosity in the three-dimensional space was deduced. Without any other fitting or experimental empirical parameters, these two models are only related to porosity and PPI, which are the most readily available parameters for the metal foams. The results of these models are consistent with the experimental and empirical data in other literature, indicating that these models are both versatile and accurate.     

Analytical Solution of Thermal Wave Models on Skin Tissue Under Arbitrary Periodic Boundary Conditions

Modeling and understanding the heat transfer in biological tissues is important in medical thermal therapeutic applications. The biothermomechanics of skin involves interdisciplinary features, such as bioheat transfer, biomechanics, and burn damage. The hyperbolic thermal wave model of bioheat transfer and the parabolic Pennes bioheat transfer equations with blood perfusion and metabolic heat generation are applied for the skin tissue as a finite and semi-infinite domain when the skin surface temperature is suddenly exposed to a source of an arbitrary periodic temperature. These equations are solved analytically by Laplace transform methods. The thermal wave model results indicate that a non-Fourier model has predicted the thermal behavior correctly, compared to that of previous experiments. The results of the thermal wave model show that when the first thermal wave moves from the first boundary, the temperature profiles for finite and semi-infinite domains of skin become separated for these phenomena; the discrepancy between these profiles is negligible. The accuracy of the obtained results is validated through comparisons with existing numerical results. The results demonstrate that the non-Fourier model is significant in describing the thermal behavior of skin tissue.     

Analytical Representations of Elastic Moduli Data With Simultaneous Dependence on Temperature and Porosity

An analytical model providing simultaneous, self-consistent representations of the temperature and porosity dependence of the elastic and bulk moduli of polycrystalline ceramics is applied to data compiled from the literature for 24 oxide ceramics.