Academic literature on the topic 'Linear impulse electromechanical converter'

The purpose of the article is to evaluate the efficiency of an induction-type linear pulse electromechanical converter (LPEC) when operating in shock-power mode and excitation from an alternating voltage source (AVS) in comparison with excitation from a capacitive energy storage (CES). A mathematical model of an induction-type LPEC has been developed both when excited by a unipolar pulse from a CES and from an AVS using lumped parameters of the windings, which takes into account the interrelated electromagnetic, mechanical and thermal processes. It has been found that when the LPEC is excited from the AVS with a voltage frequency of 50 Hz, the electrodynamic force takes on a periodic decaying character with a significant prevalence of positive components of forces over negative ones. The maximum value of the force is much less, and the value of its impulse is much greater than in the LPEC, excited from the CES. With an increase in the frequency of the AVS voltage from 50 to 150 Hz, the highest value of the current density of the inductor winding decreases, and in the armature winding it increases. The greatest values of force and impulse of force are realized at a voltage frequency of 150 Hz. With an increase in the AVS frequency, the relative indicator of the efficiency of the LPEC increases. References 15, figures 4.

General description of the research topic. The article presents a comprehensive study of traditional induction-dynamic mechanisms (with one disk and a fixed coil) and multi-core induction-dynamic mechanisms (linear pulse induction converters) with a movable coil and two disks. Actuality of the topic. Such induction-dynamic mechanisms are widely used in various fields, in particular, in electrical apparatus industry, where speed is one of the most important characteristics. The purpose of the article is a comparative analysis and refinement of the characteristics of the traditional induction-dynamic system with one disk and a fixed coil and multi-core one with a movable coil and two disks. Research method, scientific novelty. The calculations are based on the solution of the equations of the electromagnetic field and the equations for the electric circuit of the coil. Practical significance and main conclusions. During the calculations, the values of electromagnetic force and force impulse acting on the moving disk, energy losses in the system and electromagnetic energy of the system are determined. The results of the study are presented in the form of graphs, namely, the coil current and total magnetic energy for a traditional induction-dynamic mechanism with one disk and for multi-core one with two disks, Joule losses in a fixed coil and disk (in a traditional system) and in a moving coil and two disks (in a multi-core system), force impulse and electromagnetic force of a moving coil (in a multi-core system) and a moving disk (in a traditional and a multi-core system) total impulse of the moving parts of the induction-dynamic mechanism with a multi-core system, as well as the electromagnetic force and the total force acting on the moving parts of the induction-dynamic mechanism with a multi-core system. It is shown that the induction-dynamic mechanism with two disks is less effective in terms of electromagnetic force, impulse and electromagnetic energy than the induction-dynamic mechanism of the traditional layout.

Purpose. The purpose of the article is to establish the basic laws of operation of induction-type linear electromechanical converter (LEMС) during operation in high-speed and shock-power modes and excitation from an AC source of increased frequency. Methodology. With the help of a mathematical model, the regularities of the course of processes in a LEMС, excited from an AC source, were established when working with shock-power and high-speed modes. The solutions of the equations of the mathematical model, which describe interrelated electrical, magnetic, mechanical and thermal processes, are presented in a recurrent form. Results. It was found that when the LEMC operates in the shock-power mode, the maximum value of the current in the inductor winding occurs in the first half-period, and in the inhibited armature winding in the second half-period. The electrodynamic force changes at twice the frequency, taking on both positive and negative values. Since the positive values exceed the negative ones, the magnitude of the impulse of the electrodynamic force increases with each period of the force. Depending on the initial voltage phase, the relative change in the magnitude of the force impulse is 1.5 %. It was found that when the LEMC operates in high-speed mode, the current in the inductor winding in the first half-period has the greatest value, but after several periods it takes on a steady state. The temperature rise of the inductor winding increases with the time of connection to the AC source, and the temperature rise of the armature winding has the nature of saturation. The electrodynamic force has an oscillatory character with strong damping and a significant predominance of the positive component. Depending on the initial phase of the voltage, the relative change in the maximum speed of the armature winding is 2.5 %. Originality. For the first time, a mathematical model of the LEMC, excited from an AC source, was developed, the solutions of the equations of which describe the interrelated electrical, magnetic, mechanical and thermal processes. For the first time, the regularities of the course of processes in LEMC were established when working with shock-power and high-speed modes. Practical value. The characteristics of LEMC are obtained, which determine the efficiency of work in shock-power and high-speed modes. It is shown that the initial voltage phase has no significant effect on the power, high-speed thermal performance of the converter excited from an alternating current source.

In the process of functioning working sets with electromechanical converters included in their composition, it is necessary to take into account the influence of endogenous and exogenous disturbances that cause deviations of the parameters of electric machines from the nominal values given by the manufacturer in the appropriate documentation. These deviations of the parameters, even those within the permissible range of changes, have a noticeable effect on the quality of functioning of electromechanical converters and working sets as a whole. During the life cycle of the work of electromechanical converters, their parameters change as a result of natural wear and senescence, which necessitates continuous or periodic analysis and monitoring of the state objects under study. The paper considers a method based on the calculation of the linear integral criterion Q and the formation of Q – tables, which allows monitoring the functioning of electromechanical converters with unstable parameters during operation as part of working sets. Simulink – models of linear integral criterion calculation system and system of automated monitoring of electromechanical DC converter parameters are presented, which allow estimating unstable parameters. In these models static characteristics are implemented in tabular form reflecting the dependencies between the parameters of the electromechanical converters and the linear integral criterion. The results of the study allow us to obtain estimates of changes in the unstable parameters of electromechanical DC converters with the required accuracy.

The electromechanical interaction in cage induction motors induces additional forces between the rotor and stator. Recently, a linear parametric model was presented for these forces and the model was validated experimentally. The effective identification of the model parameters is crucial, because the electromagnetic system is nonlinear. The aim of this study was to present how to apply the impulse response method to estimate the required parameters. The numerical results show that this method is very effective. In addition, the force model was combined with a mechanical rotor model and the feasibility for electromechanical rotor problems was demonstrated.

Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.09.01 "Електричні машини й апарати" (14 – Електрична інженерія) – Національний технічний університет "Харківський політехнічний інститут", м. Харків, 2020 р. Дисертаційна робота присвячена удосконаленню лінійних імпульсних електромеханічних перетворювачів за рахунок мультиякірних конфігурацій. Для досягнення цієї мети були поставлені задачі: – провести аналіз конструкцій та сфер використання лінійних імпульсних електромеханічних перетворювачів індукційного, електродинамічного і електромагнітного типів в якості ударно-силових та прискорювальних пристроїв; – реалізувати в програмному середовищі COMSOL Multiphysics математичну модель лінійного імпульсного електромеханічного перетворювача мультиякірної конфігурації, яка враховує взаємопов’язані електричні, магнітні, механічні і теплові процеси та нелінійні магнітні і теплофізичні залежності; – провести аналіз електромеханічних характеристик лінійних імпульсних електромеханічних перетворювачів мультиякірних конфігурацій та за допомогою комплексного критерію оцінити їх ефективність; – встановити вплив форми струму збудження на ефективність лінійних імпульсних електромеханічних перетворювачів мультиякірних конфігурацій; – провести експериментальні дослідження лінійних імпульсних електромеханічних перетворювачів, запропонувати та випробувати моделі електромагнітної катапульти для безпілотного літального апарату, магнітно-імпульсного пресу для керамічних порошкових матеріалів, електромеханічного пристрою для скидання ожеледних та снігових відкладень з проводу лінії електропередачі та пристрою для знищення інформації на SSD накопичувачі. Об’єкт дослідження – електромеханічні процеси та показники лінійних імпульсних електромеханічних перетворювачів мультиякірних конфігурацій. Предмет дослідження – лінійні імпульсні електромеханічні перетворювачі мультиякірних конфігурацій силового та швидкісного призначення. Методи дослідження. При розв’язанні поставлених задач використовувалось математичне моделювання електромагнітних, механічних та теплофізичних процесів в лінійних імпульсних електромеханічних перетворювачах імпульсної дії для проведення аналізу електромеханічних характеристик та встановлення впливу форми струму збудження на ефективність перетворювачів. Експериментальні дослідження лінійних імпульсних електромеханічних перетворювачів мультиякірної конфігурації проводились на експериментальних стендах, що дозволило випробувати моделі пристроїв. В роботі отримані такі наукові результати: – отримала подальший розвиток класифікація лінійних імпульсних електромеханічних перетворювачів мультиякірних конфігурацій, які включають феромагнітний, котушковий та суцільний електропровідний якоря; – удосконалено математичну модель лінійного імпульсного електромеханічного перетворювача за рахунок включення феромагнітного, котушкового та суцільного електропровідного якорів, які взаємодіють з рухомим якорем. Математична модель, яка реалізована в програмному середовищі COMSOL Multiphysics, містить взаємопов’язані електричні, магнітні, механічні та теплові процеси і враховує магнітні та теплофізичні нелінійні залежності; – вперше встановлено особливості протікання електромагнітних процесів та визначено електричні, магнітні та силові показники лінійних імпульсних електромеханічних перетворювачів мультиякірних конфігурацій силового призначення. Показано що практично всі перетворювачі мультиякірних конфігурацій забезпечують збільшення амплітуди та величини імпульсу електродинамічних зусиль у порівнянні з перетворювачем, що має один суцільний електропровідний якір; – вперше встановлено вплив геометричних параметрів рухомого і нерухомого електропровідних якорів, які взаємодіють з рухомим індуктором, що дозволило підвищити швидкісні показники лінійного імпульсного електромеханічного перетворювача; – вперше встановлено, що при збуджені коливально-загасаючою, аперіодичною та аперіодичною з підживленням формами струму в перетворювачах мультиякірних конфігурацій величина імпульсу електродинамічних зусиль збільшується у порівнянні з перетворювачем, що має один суцільний електропровідний якір. Дисертаційна робота виконана в НТУ "ХПІ" і є частиною науково-дослідних робіт кафедри загальної електротехніки. Робота виконувалися за держбюджетними темами "Розробка засобів підвищення ефективності лінійних ударних електромеханічних прискорювачів та силових пристроїв" (ДР № 0115U000522) і "Удосконалення технічних систем та пристроїв за рахунок імпульсних електромеханічних перетворювачів та електрофізичних технологій" (ДР № 0117U004881), госпдоговірної теми № 15812 "Розробка та дослідження високошвидкісного електродинамічного приводу" і ініціативної теми "Сучасні проблеми та перспективи розвитку електротехнічних пристроїв та систем" (ДР № 0119U002551), де автор був співвиконавцем.
Dissertation for Candidate of Science Degree in Specialty 05.09.01 "Electrical Machines and Apparatuses" (14 – Electrical Engineering) – National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2020. The dissertation work is devoted to the improvement of linear pulse electromechanical converters due to multi - core configurations. To achieve this goal, the following tasks were set: – to analyze the structures and areas of use of linear pulse electromechanical converters of induction, electrodynamics and electromagnetic types as shockpower and accelerating devices; – to implement in the COMSOL Multiphysics software environment a mathematical model of a linear pulse electromechanical converter of multi-core configuration, which takes into account the interconnected electrical, magnetic, mechanical and thermal processes and nonlinear magnetic and thermophysical dependences; – to analyze the electromechanical characteristics of linear pulse electromechanical converters of multicore configurations and to evaluate their efficiency with the help of a complex criterion; – to establish the influence of the shape of the excitation current on the efficiency of linear pulse electromechanical transducers of multicore configurations; – to conduct experimental studies of linear pulse electromechanical transducers, to propose and test models of electromagnetic catapult for unmanned aerial vehicle, magnetic pulse press for ceramic powder materials, electromechanical device for discharging ice and snow deposits from the transmission line wire and transmission line. Object of research – electromechanical processes and indicators of linear pulse electromechanical converters of multicore configurations. Subject of research – linear pulse electromechanical converters of multicore configurations of power and speed purpose. Research methods. Mathematical modeling of electromagnetic, mechanical and thermophysical processes in linear pulse electromechanical converters of pulse action was used to solve the tasks to analyze the electromechanical characteristics and establish the influence of the shape of the excitation current on the efficiency of the converters. Experimental studies of linear pulse electromechanical transducers of multicore configuration were performed on experimental stands, which allowed to test device models. The following scientific results are obtained in the work: – the classification of linear pulse electromechanical converters of multicore configurations, which include ferromagnetic, coil and continuous conductive armature, was further developed; – the mathematical model of the linear pulse electromechanical converter due to inclusion of the ferromagnetic, coil and continuous electrically conductive anchors which interact with a mobile anchor is improved. The mathematical model, which is implemented in the COMSOL Multiphysics software environment, contains interconnected electrical, magnetic, mechanical and thermal processes and takes into account magnetic and thermophysical nonlinear dependencies; – for the first time the peculiarities of the course of electromagnetic processes are established and the electrical, magnetic and power indicators of linear pulse electromechanical converters of multi-core configurations of power purpose are determined. It is shown that almost all converters of multi-arc configurations provide an increase in the amplitude and magnitude of the pulse of electrodynamics forces in comparison with the converter, which has one continuous conductive armature; – for the first time the influence of geometrical parameters of movable and fixed electrically conductive armatures that interact with the movable inductor was established, which allowed to increase the speed indicators of the linear pulse electromechanical converter; – for the first time it is established that when excited by oscillatingattenuating, aperiodic and aperiodic with feeding forms of current in converters of multicore configurations the magnitude of the electrodynamics force pulse increases in comparison with the converter having one continuous electrically conductive armature. The dissertation work was performed at the National Technical University "Kharkiv Polytechnic Institute" and is part of the research work of the Department of General Electrical Engineering. The work was carried out on the basis of financing by state budget topics: "Development of means of increasing the efficiency of linear shock electromechanical accelerators and power devices" (DR №0115U000522), "Improvement of technical systems and devices by means of impulse electromechanical converters. (DR № 0117U004881), the contractual theme "Development and research of high-speed electrodynamics actuator" (at the expense of LLC "TETRA, Ltd", Kharkiv), and the initiative theme "Modern problems and prospects for the development of electrotechnical devices and systems" (DR №0119U002551) where the author was a co-author.

Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.09.01 - електричні машини і апарати. - Національний технічний університет «Харківський політехнічний інститут», м . Харків, 2003. Дисертація присвячена проблемі створення електромеханічних імпульсних перетворю вачів індукційного типу з кріорезистивними обмотками, що охолоджуються рідким азотом. Розроблена методика розрахунку кріогенних ЕІПІТ, яка враховує комплекс взаємопов’язаних електричних, магнітних, теплових та механічних процесів з урахуванням нелінійності основ-них параметрів. Визначені основні закономірності функціонування силових та енергетичних ЕІПІТ, що забезпечують лінійний рух якоря при збудженні від ємнісного накопичувача та джерела постійної напруги. Запропоновані структурно геометричний, схемний і конструктив-ний підходи удосконалення одно- та багатосекційних ЕІПІП з обґрунтуванням їх параметрів. Отримано експериментальні дані, які підтверджують достовірність прийнятих математичних моделей і технічних рішень. Основні результати досліджень використані при виконанні 7 держбюджетних і хоздоговірних науково-дослідних робіт, у науково-виробничих фірмах та в навчальному процесі.
Thesis for a Doctor's degree in Engineering Sciences by specialty 05.09.01 – Electrical Machines and Apparatus. – National Technical University “Kharkov Polytechnic Institute”, Kharkov, 2003. The dissertation deals with designing electromechanical impulse induction converters (EIIC) with liquid-nitrogen-cooled cryoresistive windings. On the basis of generalization of accumulated data in impulse electromechanics, a technique for designing cryogenic EIICs has been developed which takes into account interrelated electrical, magnetic, thermal, and mechanical complex processes with nonlinear critical parameters. The basic mechanisms of power and energy EIIC functioning which result in linear motion of the armature when the converter is excited from a capacitive accumulator or a constant-voltage source have been revealed. Structure-geometry, circuit, and design approaches for perfecting single- and multi-stage EIICs with valid parameters have been suggested. Experimental data have been obtained to validate developed mathematical models and engineering solutions. The main research results have been utilized and implemented at execution of seven state and commercial research projects, in research enterprises, and for students’ training.

Šiame baigiamajame darbe išnagrinėti tiesiaeigio asinchroninio variklio ypatumai ir naudojimo sritys, padaryta dažnio keitiklių ir juose naudojamų valdymo būdų apžvalga. Išanalizuoti impulsų pločio moduliacijos realizavimo principai, apžvelgti skaliarinio ir vektorinio valdymo metodai. Remiantis išanalizuota teorija sudarytas tiesiaeigio asinchroninio variklio matematinis ir kompiuterinis modelis α-β ir x-y koordinačių sistemoje, sudaryti TAV dažninių atviros ir uždaros sistemų matematiniai bei kompiuteriniai modeliai. Sudarius atviros ir uždaros sistemos modelius: gautos TAV antrinio elemento linijinio greičio, kelio ir jėgos pereinamųjų procesų charakteristikos ir palyginti rezultatai.
The properties of linear induction motor and areas of its application are analyzed; frequency converters and their control methods are discussed in this final work. Methods to realize a pulse width modulation are analyzed, scalar and vector control principles are discussed. The principle of operation of control systems applied in frequency converters is analyzed On the base of analysis mathematical and Simulink model of linear induction motor in α-β and x-y reference frame is developed, mathematical and Simulink models of frequency variable open and closed systems are carried out. Open and closed systems are investigated: transient characteristics of secondary element linear speed, developed force and way are analyzed and results of different characteristics are compared.

Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.09.01 "Електричні машини й апарати" (14 – Електрична інженерія) – Національний технічний університет "Харківський політехнічний інститут", м. Харків, 2020 р. Дисертаційна робота присвячена удосконаленню лінійних імпульсних електромеханічних перетворювачів силового та швидкісного призначення за рахунок використання декількох якорів, що взаємодіють з обмоткою індуктора. В дисертаційній роботі проведено аналіз конструкцій та сфер використання лінійних імпульсних електромеханічних перетворювачів індукційного, електромагнітного та електродинамічного типів в якості ударно-силових та прискорювальних пристроїв. Реалізовано в програмному середовищі COMSOL Multiphysics математичну модель лінійного імпульсного електромеханічного перетворювача мультиякірної конфігурації, яка враховує взаємопов’язані електричні, магнітні, механічні і теплові процеси, нелінійні магнітні та теплофізичні залежності. Розроблено класифікацію електромеханічних перетворювачів, які включають феромагнітний, котушковий та суцільний електропровідний якоря. Встановлено особливості протікання електромагнітних процесів та визначені електричні, магнітні та силові показники електромеханічних мультиякірних конфігурацій. Запропоновано комплексний критерій оцінювання ефективності, за допомогою якого проведено порівняльний аналіз перетворювачів мультиякірних конфігурацій з перетворювачами, що мають один якір. Встановлено вплив форми струму збудження на ефективність перетворювачів мультиякірних конфігурацій. Проведено експериментальні дослідження електромеханічних перетворювачів силового та швидкісного призначення з одночасним вимірюванням електричних, магнітних механічних та теплових параметрів. На базі електромеханічних перетворювачів мультиякірних конфігурацій розроблено оригінальні конструкції та випробувано моделі електромагнітної катапульти для БПЛА, магнітно-імпульсного пресу для керамічних порошкових матеріалів, електромеханічного пристрою для скидання ожеледних і снігових відкладень з проводу лінії електропередачі та пристрою для знищення інформації на твердотільному цифровому SSD накопичувачі.
The dissertation for the degree of Candidate of Technical Sciences in the specialty 05.09.01 “Electric machines and apparatus” (14 - Electrical Engineering) - National Technical University “Kharkov Polytechnic Institute”, Kharkov, 2020. The dissertation is devoted to the improvement of linear pulsed electromechanical converters due to multi-dia configurations. In the dissertation work the analysis of designs and spheres of use of linear pulse electromechanical converters of induction, electromagnetic and electrodynamic type as shock-power and accelerating devices is carried out. Developed and implemented in the COMSOL Multiphysics software environment, a mathematical model of linear pulse electromechanical converters multi-core configuration, which takes into account the interconnected electrical, magnetic, mechanical and thermal processes, nonlinear magnetic and thermophysical dependences. The classification of electromechanical converters which includes ferromagnetic, coil and massive electrically conductive anchors is developed. The peculiarities of the course of electromagnetic processes are established and the electrical, magnetic and power indicators of electromechanical converters of multi-core configurations are determined. A complex criterion for evaluating the efficiency is proposed, by means of which a comparative analysis of electromechanical converters of multicore configurations with electromechanical converters having one anchor is carried out. The influence of the form of excitation current on the efficiency of electromechanical converters of multicore configurations is established. The method is developed and experimental researches of electromechanical converters of power and speed appointment with simultaneous measurement of electric, mechanical and thermal parameters are carried out. On the basis of electromechanical converters multi-core configurations, original designs of electromagnetic catapult models for UAVs, magnetic-pulse press for ceramic powder materials and electromechanical device for discharge of ice and snow deposits from the power line wire were developed and tested.

Abstract Linear pulse electromechanical converters (LPEC) of induction type allow providing a high speed of the actuating element in the short active section and creating powerful power impulses with its insignificant movement. One of the ways to improve the electromechanical indicators of LPEC is the formation of current excitation pulses in the inductor using electronic power supply circuits containing a capacitive energy storage device. This publication is a continuation of our previous work on the influence of different parameters and conditions on the performance of LPEC. Using the developed chain mathematical model, recurrent relations are obtained for calculating the interconnected electromagnetic, mechanical and thermal parameters of LPEC. It has been established that the speed and power electromechanical indicators of LPEC with aperiodic excitation pulse are better than those of LPEC with unipolar excitation, but worse than those of LPEC with oscillating-damped excitation pulse. LPEC with a unipolar excitation pulse, by the end of the working cycle, the smallest temperatures of the inductor and the armature are observed, while for LPEC with a oscillating-damped excitation pulse, the greatest efficiency is ensured, being 24.88%. The highest speed and power electromechanical indicators are provided at LPEC with a step-aperiodic excitation pulse. Experimental studies of LPEC were conducted when operating as an electromechanical accelerator and a shock-power device. In studies of LPEC, a piezoelectric transducer was used as a shock-power device, which converted mechanical vibrations arising from the impact of the striker on the impact plate into electrical signals. In studies of LPEC, a displacement sensor was used as an electromechanical accelerator. It was established experimentally that the movement of the armature begins with a delay relative to the moment of occurrence of the current pulse and is almost linear in the initial part of the acceleration.

The electromechanical interaction in cage induction motors induces additional forces between the rotor and stator. Recently, a linear parametric model was presented for these forces, and the corresponding model was combined with a mechanical rotor model. The electromagnetic system is usually non-linear due to the saturation of magnetic materials. Thus, the effective identification of the force parameters is crucial. Initially, the parameters were identified numerically from the response induced by the whirling rotor. Later on, a method based on the impulse response analysis was presented. The aim of this study was to present the theoretical background of this impulse method, and to present some useful additional features. The derived equations show the mathematical equivalency of this impulse method and the previous whirling method. The results show that the impulse method is numerically effective. In addition, the feasibility of thus obtained simple electromechanical rotor model was demonstrated.

The architecture of the electrical actuation module driving a magnetic-hydraulic bearing system is presented. The bearing is intended to be scaled for use in applications of all sizes in industries like shipboard for support of the engine-propeller shaft or in power-plants for the shaft through which the prime mover, e.g. steam or gas turbine, is driving the electric generator. The benefits of this new bearing is first and foremost its superb performance in terms of low down to practically no friction losses since there is no direct contact between the supporting bearing surface and the rotating shaft supported. Other benefits include the potential of active, inline, real-time balancing and alignment. To implement such concept of a magnetic-hydraulic bearing, the following tasks need to be carried out. First, identification of mechanical, electrodynamical and circuit properties of the bearing’s electromagnets in the system is necessary. Toward such identification, a series of experiments needed to be carried out. To be able to carry out these experiments, a specific power electronic converter is developed to drive each electromagnet. The power electronic drive is a quad MOSFET circuit based on full-bridge converter topology and outfitted with appropriate sensory instrumentation to collect and record measurements of all the physical variables of interest. Special care has been taken to compensate for magnetic hysteresis of the electromagnets, mitigate any induction heating effects and maintain operation within the material’s linear region i.e. without significant saturation occurring. The use of a power transistor bridge allows rapid changes to be applied on the electromagnet’s load force which could compensate disturbance or misalignment developed on the shaft supported. The data series from these experiments are useful for formulating a possibly nonlinear model of the electromagnetical and electromechanical processes involved in the bearing’s operation. Such a model can then be employed to help design a digital microcontroller system which could effectively drive the power electronics and electromagnets to perform their required tasks as part of the bearing. Besides, the model could also be used for the synthesis of the nonlinear, sampled-data (discrete-time) control law which will be programmed on the microcontroller system board.

Abstract The objective of this paper is to present an instrumentation and data analysis method developed to determine a nonlinear viscoelastic model of brain tissue using a forced vibration technique. The application of this model is mainly for studying the injury mechanisms of brain tissue resulting from impacts to the head. Since the early 1950s several attempts have been recorded to model the mechanical behavior of brain tissue. Investigators have used a variety of quasi-static and dynamic experimental techniques in their studies and there is a general agreement that brain exhibits viscoelastic characteristics (Galford and McElhaney, 1969). However, there are three major limitations associated with most of the previous studies. First is the limitation of boundary and environmental conditions. By applying small strains (less than 10%), most researchers have explained their experimental results with linear models (Shuck and Advani, 1972). However, biomechanical models show that shear strains up to 100% occur in brain in impact situations (Ueno et al., 1996). To include finite deformation, a nonlinear model is needed to characterize the biomechanics of impact and injury of the brain tissue. Although viscoelastic material properties are generally very sensitive to temperature (Haddad, 1995), the effect of temperature on brain material properties has not been investigated in the previous studies. Most in vitro tests have been performed in the room temperature and only a few in vivo studies have been reported (Fallenstein et al., 1969; Wang and Wineman, 1972). The effect of gravity has not been addressed in the previous studies. The brain sample is so soft that it creeps under its own weight, which causes pre-stress and pre-strain in the sample (Takhounts, 1998). The second limitation is with regard to the constitutive models. A few researchers, who have investigated the nonlinear behavior of the brain tissue, have presented the results of their studies in some special forms of stress-strain relationships (Donnely, 1993). These relationships are generally dependent on the type of experiment and can not be used for other types of loading and deformation. In order to develop an analytical or numerical model of brain, a three-dimensional constitutive relation is required that is independent of the type of experiment. The third limitation is the experimental methods. In the stress relaxation test method, due to hardware and inertial limitations, the jump of ideal step input is usually simulated with high-speed ramp input (Takhounts, 1998). Therefore, time constants that are shorter than the ramp time interval (about 0.04 s) can not be identified in the relaxation response. The small time constants have a significant effect in the short time response of the material, which is of primary interest in the biomechanics of impact and injury. On the other hand, due to inertial effects, the transient vibration of the system perturbs the first portion (about 400 ms) of the relaxation curve (Takhounts, 1998). In the ramp test method also, due to the initial acceleration period, the short time constants can not be measured correctly (Donnely, 1993). Previous studies based on the forced vibration technique, due to hardware limitations, have been performed in the frequency range of 5–350 Hz with strain levels of up to 35% (Shuck and Advani, 1972; Arbogast et al., 1997). These results have been used to develop linear viscoelastic models for shear with time constants in the range of 0.4 to 32 milliseconds. In the method presented in this paper, the goal was to develop a viscoelastic model of brain tissue that is free from the constraints discussed above. The samples are taken from fresh human and bovine brain tissues (maximum 24 hours after death or slaughter). Samples are cut with cylindrical metal cores (5–20 mm diameter) from different parts of the brain tissue and in transverse and vertical anatomic directions. Using the same experimental apparatus, cylindrical samples with the length of 5–30 mm are studied in both simple extension and in simple shear modes. In order to study the effect of temperature, canceling the effect of gravity and minimizing material deterioration, each sample is placed in a temperature controlled slow flow of saline solution throughout the experiment. An electromechanical vibrator with frequency response of dc-6500 Hz and maximum force of 65lb is used to apply the input displacement to one end of the specimen. The characteristics of the vibrator allow the identification of a wide range of time constants of the brain tissue (from 80 μs to 1.6 s) in a wide range of strain inputs (infinitesimal to 100%). The reaction force at the other end of the specimen is recorded via a miniature high precision load cell. As shown in figure 1, the analog signals of the load cell, an accelerometer that measures the motion of the vibrator, and a thermocouple that measures the temperature of the sample are collected via an isolated analog to digital converter in a personal computer. Via a digital to analog converter, the computer also controls the motion of the vibrator. The whole system works as a closed loop control system. The resultant forces of a simple harmonic displacement input and also the superposition of a series of simple harmonic inputs are analyzed in the frequency domain to generate linear, quasilinear and nonlinear third order Green-Rivlin viscoelastic models of the brain tissue (Fung, 1993 and Lockett, 1972). In addition, square wave and triangular wave inputs are applied to study the relaxation and hysteresis phenomena. The lateral movement of the samples is recorded with a high-speed camera and digital image analysis. The results obtained from the samples in transverse and vertical directions are used to develop three-dimensional transversely isotropic models. Preliminary experiments, as shown in figure 2, show that for low strain levels below 10%, linear viscoelastic model describes the short time behavior of brain tissue to a high degree of accuracy. For strain levels between 10% to 40% and short relaxation times below 100 ms, a quasilinear model can be used that only considers the strain nonlinearity of the material. Assuming that the effect of a single relaxation exponential function, after passing four time constants, is negligible, 100 ms relaxation time corresponds to the frequency of 6.4 Hz. For higher strain levels (up to 100%) and longer relaxation times (up to 5 s) or lower frequencies (below 6.4 Hz), a third order Green-Rivlin model, which includes both strain and time nonlinearity, should be used. The discrete spectrum approximation is used to represent the relaxation functions. It is shown that by using this form, the nonlinear models can be easily implemented in numerical algorithms that can be used in finite element programs (Puso and Weiss, 1998). A complete set of tests on a single specimen takes between 15–30 minutes. Therefore, multiple sections from a whole brain can be analyzed in a few hours, which minimizes the effect of material deterioration.