Electrodynamic forces in induction heating of bimetallic plates with planar circular coils

Contents The paper deals with the calculation of the electrodynamic forces acting on a planar circular coil placed over a bimetallic plate.The analysis is carried out with reference to the induction heating of plates of magnetic and non-magnetic materials.

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Elektrodynamische Kräfte bei Induktionsheizung einer Bimetallplatte durch ebene kreisförmige Spule

Übersicht Die vorliegende Arbeit beschreibt die Berechnung der elektrodynamischen Kräfte zwischen einer Bimetallplatte und einer darüber befindlichen ebenen kreisförmigen Spule.Die Analyse ist mit Bezug auf die Induktionsheizung der magnetischen und nicht magnetischen Platten durchgeführt.

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Symbols J ₀,J ₁ Zero and first order Bessel functions of the first kind - H ₀,H ₁ Zero and first order Struve functions - Legendre gamma function - r, ,z cylindrical coordinates - R _i ,R _e inner and outer radii of the inductor coil - h distance between the inductor coil and the surface of the metal plate - s _i thickness of the i-th layer of the plate - =2f angular frequency - ₀ permeability of free space - _i , _i resistivity and relative permeability of the material of the i-th layer of the plate - penetration depth of the induced currents in the i-th layer - N number of turns of the inductor coil - sinusoidal current in the inductor - magnetic potential vector - magnetic flux density - F _z time average value of the force acting on the coil - P _z (r,h) time average value of the pressure acting on the coil at radiusr. Work supported by the C.N.R. (National Research Council)     

Torque calculation between circular coils with inclined axes in air

In this paper we derive new semi‐analytical expressions for calculating the electromagnetic torque between inclined circular coils in air. The torque calculation has been obtained from the corresponding mutual inductance between inclined circular coils using the filament method. The coils of rectangular cross‐section whose centers are at the same and the different axes have been considered. From this general case it is possible to calculate the torque between all possible coil combinations either with rectangular or neglected cross‐section. Results obtained by the presented approach are in very good agreement with already published data. This method can be used for industrial electromagnetic devices such as torque sensors, transducers and torque‐measuring devices. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical calculation of circular diagram of large induction motor

The analytical calculation of a circular diagram of a large induction motor carried out based on load testing at undervoltage requires no graphic constructions and permits one to calculate the operating performances and maximal torque with acceptable accuracy.     

无线充电系统实际Litz线绕平面线圈高频电阻分析与计算

线圈高频电阻的计算对无线充电系统线圈的优化设计至关重要.实际工程一般采用Litz线来绕制线圈以减小趋肤和邻近损耗,但由于扭绞工艺的影响,实际Litz线的电阻值介于理想Litz线和平行束导线之间.本文首先详细分析Litz线电阻的组成与影响因素;其次,提出采用理想Litz线和平行束导线的电阻来拟合实际Litz线电阻的计算方...     

Inductance calculation for 3d microsolenoids with single-layer coils

Three-dimensional (3D) single-layer microcoils have always been a key element for electromagnetic systems; but they lack an easy and accurate method to calculate the inductance value for their complex 3D micro-structures. This paper employed a curve-fitting process to obtain the associated equation for the inductance value and geometric parameters based on the simulation results. The correction factors regarding helical pitch and wire diameter were reviewed, which are used for compensation in the Nagaoka formula. The simulation process numerically simulated the performance of the 3D microcoils using a FEM electro-magnetic-coupled analysis method. Comparison of the simulated inductance value and the Nagaoka formula was undertaken, which shows that the helical pitch and wire diameter contribute a main role in the calculation error. The derived formula was expressed in a concise form to precisely calculate the inductance value of 3D microsolenoids with single-layer coils.     

任意空间位置线圈的互感计算方法

磁耦合谐振式无线电能传输技术通过空间分离线圈之间的电磁耦合实现电能的无线传递,耦合线圈尺寸的不同和相对位置的变化会引起线圈间的互感变化,继而影响无线电能传输系统的特性。以常见的矩形截面空心线圈为分析对象,对任意空间位置线圈间互感的计算方法进行研究,通过纽曼公式和细分求和法推导了互感的理论计算公式,为静态和动态无线电能传输系统的设计提供支持。在耦合线圈具有不同轴向距离、径向偏距及旋转角度等空间位置情况下,公式编程计算和实验测量结果都具有一致性,证明了计算方法的正确性。     

厚金属板与任意方位圆柱线圈间的电磁力计算

针对一个交流电激励的圆柱线圈倾斜放置于金属板上方时,它们之间的电磁作用力无法以传统方法进行解析计算的问题,引入高阶矢量势求解该问题,并采用矢量分析和Struve函数化简,可得到适用于任意方位圆柱线圈的二重积分表达式。所得结果表明任意方位圆柱线圈至多受到两个方向力的作用。在线圈轴垂直或平行于导电板的特殊情形,表达式可进一步简化为单重积分,而线圈将只受垂直力的作用。随后以数值算例对给出公式的有效性进行验证。数值结果表明,对于线圈轴的某个倾角,垂直力分量周期均值可以为零,而水平力分量周期均值将在某个倾角处达到最大值。当线圈通以直流电时,仅当金属板的磁导率与空气磁导率一致时线圈才不受电磁力的作用。     

感应加热电源锁相电路分析与设计

感应加热电源在工作中由于负载谐振频率的波动,要求逆变器触发频率能同步负载谐振频率的变化,即要求锁相频率范围覆盖负载谐振频率波动的范围。分析了感应加热电源的锁相工作原理,给出了CD4046芯片为核心的锁相电路和频率参数计算。企业生产实践证明该锁相电路工作可靠,锁相频率范围较宽,能满足加热不同规格产品的需要。     

感应加热电源频率跟踪控制的研究

为减小逆变器功率器件的开关损耗,提高装置输出效率,应该控制逆变器的工作频率实时跟踪负载谐振频率,确保开关器件工作在零电压零电流开关(ZVZCS)状态。介绍了在感应加热电源中采用TMS320F2812实现超音频频率跟踪的数字锁相环(DPLL)方法,给出了实现DPLL的算法。并对基于该芯片的DPLL频率跟踪控制的原理进行了分析。最后给出了相应的仿真波形和感应加热电源样机的实验波形,验证了该方法的正确性。     

A degeneracy study in the circulant and bordered-circulant approach to birdcage and planar coils

A method for finding closed-form solutions for the normal mode frequencies of systems with circulant 2pi/2 symmetry was investigated. This method is particularly good for questions of degeneracy that arise when one considers parallel imaging techniques like SENSE and SMASH in MRI. It is applicable to systems that include birdcage coils as well as planar coils with the appropriate rotational symmetry. A proof is given that complete degeneracy of all normal mode frequencies is impossible when all mutual inductive couplings are included. We tested the method against measurements made on a planar coil array and on an 8-element birdcage coil. The inclusion of the co-rotating end-ring mode changes the fundamental symmetry of the system from circulant to "bordered circulant". Closed-form solutions for the normal mode frequencies of a bordered circulant system are also given.     

A degeneracy study in the circulant and bordered-circulant approach to birdcage and planar coils

A method for finding closed-form solutions for the normal mode frequencies of systems with circulant symmetry was investigated. This method is particularly useful for questions of degeneracy that arise when one considers parallel imaging techniques like SENSE and SMASH in MRI. It is applicable to systems that include birdcage coils as well as planar coils with the appropriate rotational symmetry. A proof is given that complete degeneracy of all normal mode frequencies is impossible when all mutual inductive couplings are included. We tested the method against measurements made on a planar coil array and on an 8-element birdcage coil. The inclusion of the co-rotating end-ring mode changes the fundamental symmetry of the system from circulant to 'bordered circulant.' Closed-form solutions for the normal mode frequencies of a bordered circulant system are also given.     

感应加热电源PDM波形的频率谱分析

脉冲密度调制(PDM)技术可用于调节感应加热电源的输出功率,其主要优点在于能够保证感应加热电源逆变器开关器件始终工作在零电压或零电流开关状态,然而PDM控制的负载电流波形含有多种谐波,分析了各种PDM波形的频率谱,得出了调制比D、负载的时间常数t和PDM序列长度T与PDM波形频率谱的关系。分析表明均匀脉冲密度调制技术控制脉冲序列对称性良好,产生的谐波最少。     

Mathematical modeling of induction heating units for moving round billets

The paper considers the question of constructing interrelated nonlinear electromagnetic and thermal models of processes arising when the moving steel round billets undergo thermal heating. The peculiarities of the effect of temperature on physical parameters are described.     

Application of the evolution strategy to optimize multistep field plates for high voltage planar pn-junctions

Contents The blocking capability of a high voltage planar pn-junction, equipped with a five-stepped field plate and a channelstopper is optimized. The breakdown voltage of the optimized structure is 92% of the bulk breakdown voltage (2000 volts). The structure without field plate reaches only 21% of the bulk breakdown voltage. It is shown, how the optimization procedure can be carried out almost automatically taking advantage of the evolution strategy. The method is demonstrated and the benefits are elaborated in comparison to the conventional optimization procedure.

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Anwendung der Evolutionsstrategie zur Optimierung mehrstufiger Feldplatten für hochsperrende planare pn-Übergänge

Übersicht Die Blockierfähigkeit eines hochsperrenden planaren pn-Übergangs mit einer fünfstufigen Feldplatte und einer Stoppzone wird optimiert. Die Durchbruchspannung der optimierten Struktur beträgt 92% der Volumendurchbruchspannung (2000 Volt). Ohne Feldplatte erreicht die Struktur nur 21% der Volumendurchbruchspannung. Es wird gezeigt, wie durch Nutzung der Evolutionsstrategie das Optimierungsverfahren nahezu selbständig durchgeführt werden kann. Die Methode wird vorgestellt und die Vorteile gegenüber dem konventionellen Optimierungsverfahren werden präsentiert.

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Dedicated to Prof. Dr.-Ing. Manfred Stiebler on the occasion of his 60th birthday     

A three-dimensional temperature field calculation for a transformer-type heating element

A mathematical model for calculating the temperature field of a transformer-type heating element with a spatial pole core using the finite element method is described. A computer simulation program of the three-dimensional temperature field is developed, and calculation results for a transformer of 25-kW capacity are given.     

无压圆形隧洞正常水深直接算法

明渠均匀流正常水深是渠道设计、运行管理的重要水力要素。圆形断面是水力最佳断面,正常水深计算需求解超越方程,计算复杂。针对目前现有计算公式存在误差大且适用范围小的问题,根据明渠均匀流基本原理,采用SAS软件的NLIN过程,给定非线性函数模型,利用Marquardt法建立圆形隧洞无压流正常水深直接水力计算公式。通过误差分析和实例计算,表明:该公式在较大工程适用范围内最大计算相对误差小于0.093%。与现有公式相比,不仅工程适用范围扩大,具有较强的通用性,且计算精度高。另外计算公式为二次多项式形式,物理概念清晰,计算便捷。研究成果可为渠道工程设计和运行管理提供可靠的理论依据和有益参考。     

Mathematical model for calculation of the heat-hydraulic modes of heating points of heat-supplying systems

The mathematical model and calculation method of the thermal-hydraulic modes of heat points, based on the theory of hydraulic circuits, being developed at the Melentiev Energy Systems Institute are presented. The redundant circuit of the heat point was developed, in which all possible connecting circuits (CC) of the heat engineering equipment and the places of possible installation of control valve were inserted. It allows simulating the operating modes both at central heat points (CHP) and individual heat points (IHP). The configuration of the desired circuit is carried out automatically by removing the unnecessary links. The following circuits connecting the heating systems (HS) are considered: the dependent circuit (direct and through mixing elevator) and independent one (through the heater). The following connecting circuits of the load of hot water supply (HWS) were considered: open CC (direct water pumping from pipelines of heat networks) and a closed CC with connecting the HWS heaters on single-level (serial and parallel) and two-level (sequential and combined) circuits. The following connecting circuits of the ventilation systems (VS) were also considered: dependent circuit and independent one through a common heat exchanger with HS load. In the heat points, water temperature regulators for the hot water supply and ventilation and flow regulators for the heating system, as well as to the inlet as a whole, are possible. According to the accepted decomposition, the model of the heat point is an integral part of the overall heat-hydraulic model of the heat-supplying system having intermediate control stages (CHP and IHP), which allows to consider the operating modes of the heat networks of different levels connected with each other through CHP as well as connected through IHP of consumers with various connecting circuits of local systems of heat consumption: heating, ventilation and hot water supply. The model is implemented in the Angara data-processing complex. An example of the multilevel calculation of the heat-hydraulic modes of main heat networks and those connected to them through central heat point distribution networks in Petropavlovsk-Kamchatskii is examined.     

Characteristics of an induction motor with reduced turns of terminal coils

The use of PWM inverters with high switching characteristics for the adjustable speed drive system causes an overvoltage with steep‐fronted waveform on the motor terminals. As this steep‐fronted transient voltage in inverter drive loads heavily on the terminal coils of motor winding, the insulation failure in the motor winding occurs mostly on the terminal coils. Therefore, it is reasonable to reduce the turns of terminal coils only and to increase the dielectric strength of interturn insulation. This paper presents a comparison of measured characteristics of normal induction motors and induction motors with reduced turns of terminal coils and also a comparison of the results measured and calculated by equivalent circuit. The appropriate rate of reduced turns of terminal coils is about 20%. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(3): 49–56, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10093     

Stochastic controlled system intended for induction heating of high-speed tubular billets

Statistical and spectral analyses of longitudinal distribution of tubular billet heating temperature caused by rolling process have been carried out. The transfer functions of the electric heating channel (EHC) of an induction pusher-type furnace (IPF) are revealed. A mathematical model is developed in Simulink environment. The processes of tubular billets heated in an IPF are analyzed for the case where the output temperature is distributed stochastically in a longitudinal direction.