First applications of the electromagnetic suspension principle have been in experimental physics, and suggestions to use this principle for suspending transportation vehicles for high-speed trains go back to 1937. There are various ways of designing magnetic suspensions for a contact free support, the magnetic bearing is just one of them [BCK+09]. Most bearings are used in applications involving rotation. Nowadays, the use of contact bearings solves problems in the consumer products, industrial machinery, or transportation equipment (cars, trucks, bicycles, etc). Bearings allow the transmition of power from a motor to moving parts of a rotating machine [M+92]. For a variety of rotating machines, it would be advantageous to replace the mechanical bearings for magnetic bearings, which rely on magnetic elds to perform the same functions of levitation, centering, and thrust control of the rotating parts as those performed by a mechanical bearing. An advantage of the magnetic bearings (controlled or not) against purely mechanical is that magnetic bearings are contactless [BHP12]. As a consequence these properties allow novel constructions, high speeds with the possibility of active vibration control, operation with no mechanical wear, less maintenance and therefore lower costs. On the other hand, the complexity of the active (controlled) and passive (not controlled) magnetic bearings requires more knowledge from mechanics, electronics and control [LJKA06]. The passive magnetic bearing (PMB) presents low power loss because of the absence of current, lack of active control ability and low damping sti ness [FM01, SH08]. On the other hand, active magnetic bearing (AMB) has better control ability and high sti ness, whereas it su ers from high power loss due to the biased current [JJYX09]. Scientists of the 1930s began investigating active systems using electromagnets for high-speed ultracentrifuges. However, not controlled magnetic bearings are physically unstable and controlled systems only provide proper sti ness and damping through sophisticated controllers and algorithms. This is precisely why, until the last decade, magnetic bearings did not become a practical alternative to rolling element bearings. Today, magnetic bearing technology has become viable because of advances in microprocessing controllers that allow for con dent and robust active control [CJM04]. Magnetic bearings operate contactlessly and are therefore free of lubricant and wear. They are largely immune to heat, cold and aggressive substances and are operational in vacuum. Because of their low energy losses they are suited for applications with high rotation speeds. The forces act through an air gap, which allows magnetic suspension through hermetic encapsulations [Bet00]. / Tesis

El presente trabajo de tesis forma parte de una iniciativa de investigación multidisciplinaria enfocada en estudiar los cojinetes magnéticos y sus aplicaciones, en este contexto, los objetivos planteados para este proyecto son diseñar un prototipo del sistema formado por un rotor rígido suspendido sobre cojinetes magnéticos radiales; fabricar el prototipo diseñado y caracterizar su comportamiento dinámico mediante un análisis modal teórico. El alcance contempla el desarrollo de la ingeniería conceptual, ingeniería básica, ingeniería de detalle del prototipo así como su posterior manufactura. Asimismo, se incluye la caracterización dinámica del sistema usando la teoría de sistemas de varios grados de libertad. Dentro de este alcance no se contempla la ingeniería básica y de detalle de los actuadores electromagnéticos; la ingeniería, programación, electrónica y automatización del sistema de control de los actuadores así como su respectiva instalación, ya que son tópicos que corresponden a temas de tesis paralelos. Como resultado de este trabajo de tesis se obtuvo un prototipo de fabricación local, cuyas dimensiones son 1400 mm x 505 mm x 960 mm con un rotor rígido de 6 kg de masa accionado por un motor eléctrico que puede girar entre 1800 rpm y 2340 rpm gracias a un variador de frecuencia incorporado. La carga se regula a través de masas calibradas de 1kg, 2kg y 3kg según el operador lo requiera. Para la verificación de rigidez del rotor se utilizó la teoría de vibraciones en sistemas contínuos y se validó con ayuda del método de elementos finitos arrojando una frecuencia natural de 1158,2 Hz, lo cual garantiza que a la frecuencia de giro, el rotor tendrá un comportamiento rígido. Asimismo, se realizó una verificación dinámica de la estructura de soporte y la base del motor arrojando frecuencias de 19.37 Hz y 689.22 Hz, lo cual, en base a la verificación dinámica indica que funcionará adecuadamente y no habrá frecuencias externas que dificulten el control. La última etapa del trabajo consistió en el análisis dinámico del comportamiento del rotor en el plano bidimensional, a través de un análisis modal contínuo de donde se obtuvieron frecuencias de 46.38 Hz y 62.74 Hz para cada uno de sus modos de vibración.

This thesis work begins with the revision of state of the art about active magnetic bearings (AMB), the mathematical methods used to obtain geometric and physical parameters that will influence in the mechanical, electrical design and control system proposed by this prototype. The control system will activate the magnetic bearing to center its shaft, for which it is joined a variable load in order to study the best control performance under different load over the rotor proposed by requirements. When the rotor is not controlled in its own axis even though variable load, a position error will occur that will be corrected by the program of a control system that will center the shaft (rotor). For this design was evaluated generalized AMB models [2], [3], [4] to validate the best identification for this design, furthermore as a consequence to get the best performance for the control system as it was achieved by generalized models and it was evaluated the advantage of this AMB machine through “Two hybrid electromagnet actuators” and variable load fixed to its shaft. For this reason, it was necessary to test a simple AMB with only one electromagnet actuator [4], due to compare enhancement of hybrid characteristics for the electromagnet actuators, for which, also it was evaluated how many actuators could be necessary to join to an AMB system with the target to get the control. It means, in this work there are comparisons between a simple AMB, generalized AMB models and this design, owing to show the achievements of this design. In order to show experimental results in state of the art, it is known that Siemens presented Simotics Active Magnetic Bearings technology for wear free operation in large – machine applications, regulated magnetic fields hold the rotor in suspension precisely without oil or contact, to make this task, sensors capture the position of the shaft 16000 times per second and a regulator adjusts the magnetic field to keep the rotor hovering precisely in the bearing center [1]. By other side the author [4] describes the experimental results in which is proposed that at low speed the bearing parameters are mainly determined by the controller characteristics. While at high speed, the bearing parameters are not only related to the control rule but also related to the speed. This may be due to the influence of eddying effect. [4] Furthermore, by author [3], the algorithm to get fast responses in front of disturbances, the disadvantages of these algorithms are given by not enough memory space to execute them, due to computing time is short compared with rotor displacement response time, and it is defined that it could be possible to execute the control algorithm through a real-time operating system to obtain the desired response [3]. Finally, in reference [6] it is described about filtering every noise as additive white Gaussian noise, by a predictive filter, which is obtained by analyzing Least Mean Square (LMS) and feedback/feedforward algorithm.

First applications of the electromagnetic suspension principle have been in experimental physics, and suggestions to use this principle for suspending transportation vehicles for high-speed trains go back to 1937. There are various ways of designing magnetic suspensions for a contact free support, the magnetic bearing is just one of them [BCK+09]. Most bearings are used in applications involving rotation. Nowadays, the use of contact bearings solves problems in the consumer products, industrial machinery, or transportation equipment (cars, trucks, bicycles, etc). Bearings allow the transmition of power from a motor to moving parts of a rotating machine [M+92]. For a variety of rotating machines, it would be advantageous to replace the mechanical bearings for magnetic bearings, which rely on magnetic elds to perform the same functions of levitation, centering, and thrust control of the rotating parts as those performed by a mechanical bearing. An advantage of the magnetic bearings (controlled or not) against purely mechanical is that magnetic bearings are contactless [BHP12]. As a consequence these properties allow novel constructions, high speeds with the possibility of active vibration control, operation with no mechanical wear, less maintenance and therefore lower costs. On the other hand, the complexity of the active (controlled) and passive (not controlled) magnetic bearings requires more knowledge from mechanics, electronics and control [LJKA06]. The passive magnetic bearing (PMB) presents low power loss because of the absence of current, lack of active control ability and low damping sti ness [FM01, SH08]. On the other hand, active magnetic bearing (AMB) has better control ability and high sti ness, whereas it su ers from high power loss due to the biased current [JJYX09]. Scientists of the 1930s began investigating active systems using electromagnets for high-speed ultracentrifuges. However, not controlled magnetic bearings are physically unstable and controlled systems only provide proper sti ness and damping through sophisticated controllers and algorithms. This is precisely why, until the last decade, magnetic bearings did not become a practical alternative to rolling element bearings. Today, magnetic bearing technology has become viable because of advances in microprocessing controllers that allow for con dent and robust active control [CJM04]. Magnetic bearings operate contactlessly and are therefore free of lubricant and wear. They are largely immune to heat, cold and aggressive substances and are operational in vacuum. Because of their low energy losses they are suited for applications with high rotation speeds. The forces act through an air gap, which allows magnetic suspension through hermetic encapsulations [Bet00]. / Tesis