Siddappa Iranna Bekinal

Analysis of Axially Magnetized Permanent Magnet Bearing Characteristics

The use of permanent magnets as bearings has gained attention of researchers nowadays. The characteristics of forces and moments have to be analysed thoroughly for the proper design of permanent magnet bearings. This paper presents a mathematical model of an axially magnetized permanent magnet bearing (ring magnets) using Coulombian model and a vector approach to estimate the force, moment and stifiness. A MATLAB code is developed for evaluating the parameters for flve degrees of freedom (three translational and two rotational) of the rotor. Furthermore, it is extended to analyse stacked ring magnets with alternate axial polarizations. The proposed model is validated with the available literature. Comparison of force and stifiness results of the presented model with the results of three dimensional (3D) flnite element analysis using ANSYS shows good agreement. Finally, the cross coupled stifiness values in addition to the principal stifiness values are presented for elementary structures and also for stacked structures with three ring permanent magnets.

Generalized Three-Dimensional Mathematical Models for Force and Stiffness in Axially, Radially, and Perpendicularly Magnetized Passive Magnetic Bearings With “n” Number of Ring Pairs

This work deals with generalized three-dimensional (3D) mathematical model to estimate the force and stiffness in axially, radially, and perpendicularly polarized passive magnetic bearings with “n” number of permanent magnet (PM) ring pairs. Coulombian model and vector approach are used to derive generalized equations for force and stiffness. Bearing characteristics (in three possible standard configurations) of permanent magnet bearings (PMBs) are evaluated using matlab codes. Further, results of the model are validated with finite element analysis (FEA) results for five ring pairs. Developed matlab codes are further utilized to determine only the axial force and axial stiffness in three stacked PMB configurations by varying the number of rings. Finally, the correlation between the bearing characteristics (PMB with only one and multiple ring pairs) is proposed and discussed in detail. The proposed mathematical model might be useful for the selection of suitable configuration of PMB as well as its optimization for geometrical parameters for high-speed applications.

PERMANENT MAGNET THRUST BEARING: THEO- RETICAL AND EXPERIMENTAL RESULTS

This paper presents the design and analysis of permanent magnet (PM) thrust bearing made up of three ring pairs for flve degrees of freedom of the inner rings (rotor rings). The arrangement pattern of rings in PM bearing is considered in two ways: conventional structure and Halbach structure. The simplifled three dimensional (3D) mathematical models employing Coulombian approach and vector method are used to design the bearing. MATLAB codes are written to evaluate the axial force, stifiness and moments in both the structures for flve degrees of freedom, thereby the efiect of axial, radial and angular displacements of the rotor on the aforementioned characteristics is addressed. The results of the mathematical model are validated by the results of 3D Finite Element Analysis (FEA) and experiments. It is observed that, the conventional structure seems to be more sensitive to the angular displacement, as the percentage decrease in force and stifiness is more with respect to angular displacement than the Halbach structure. The efiect of angular displacement of the rotor on the performance of bearing in both the structures is crucial.

ANALYSIS OF RADIAL MAGNETIZED PERMANENT MAGNET BEARING CHARACTERISTICS FOR FIVE DEGREES OF FREEDOM

This paper presents a simple mathematical model to determine the force, stifiness and moment parameters in Permanent Magnet (PM) bearings made of radial magnetized ring magnets using Coulombian model and vector approach for flve degrees of freedom. MATLAB codes are written to evaluate the bearing characteristics for three translational (x, y and z) and two angular (» and ∞) degrees of freedom of the rotor magnet. The results of the mathematical model are compared with the results of Finite Element Analysis (FEA) using ANSYS and experiments for a PM bearing with one ring pair, thereby the presented mathematical model is validated. Furthermore, the PM bearing with three ring pairs with alternate radial polarizations is analysed by extending the presented mathematical model and also using ANSYS. Finally, the 5£5 stifiness matrix consisting of principal and cross coupled values is presented for the elementary structure as well as for the stacked structure with three ring pairs.

A hybrid (permanent magnet and foil) bearing set for complete passive levitation of high-speed rotors

This paper presents the design and development of a hybrid bearing set for complete passive levitation of a typical rotor. A hybrid bearing set consists of permanent magnet thrust bearing and radial discrete bump foil bearings. The permanent magnet thrust bearing is made up of three pairs of ring magnets arranged in rotation magnetized direction. The mathematical model to determine the force and stiffness in rotation magnetized direction configuration is presented using Coulombian model and vector approach. Bump foil bearings are designed and developed for rotor weight to provide the radial support to the rotor system. The proposed bearing set with rotor is analysed using finite element analysis for rotor dynamic characteristics. The experiments are conducted on the fabricated rotor-bearing configuration by rotating the rotor up to the speeds of 40,000 r/min. The system response is acquired using advanced rotor-dynamic data acquisition system. The experimental results show that the rotor is completely airborne and stable at the desired speed.

Multi-objective optimization of stacked radial passive magnetic bearing

Modeling, design, and optimization for performances of passive magnetic bearings (PMBs) are indispensable, as they deliver lubrication free, friction less, zero wear, and maintenance-free operations. However, single-layer PMBs has lower load-carrying capacity and stiffness necessitating development of stacked structure PMBs for maximum load and stiffness. Present work is focused on multi-objective optimization of radial PMBs to achieve maximum load-carrying capacity and stiffness in a given volume. Three-dimensional Coulombian equations are utilized for estimating load and stiffness of stacked radial PMBs. Constraints, constants, and bounds for the optimization are extracted from the available literature. Optimization is performed for force and stiffness maximization in the obtained bounds with three PMB configurations, namely (i) mono-layer, (ii) conventional (back to back), and (iii) rotational magnetized direction. The optimum dimensions required for achieving maximum load without compromising stiffness for all three configurations is investigated. For designers ease, equations to estimate the optimized values of load, stiffness, and stacked PMB variables in terms of single-layer PMB are proposed. Finally, the effectiveness of the proposed method is demonstrated by considering the PMB dimensions from the available literature.

Generalized optimization procedure for rotational magnetized direction permanent magnet thrust bearing configuration

Optimization of rotational magnetized direction permanent magnet thrust bearing configuration is carried out using generalized three-dimensional mathematical model. The bearing features namely axial force and stiffness are maximized using in-house developed mathematical expressions solved using MATLAB. The design variables selected for the optimization are axial offset, number of ring pairs, air gap and inner radius of inner and outer rings. The maximized axial force values of the optimized configuration are validated with the finite element analysis results. To overcome the high computational cost associated with three-dimensional equations, generalized method of optimization is sucessfully demonstrated using plots representing variation of optimal design variables as a function of air gap with respect to bearing’s outer diameter. Simple and useful method of using the generalized plots for the process of optimization is presented by dimension optimization of representative bearing configuration with a particular aspect ratio. The proposed optimization using mathematical model and generalized approach assists designer in selecting optimized geometrical parameters of rotational magnetized direction thrust bearing configurations easily for variety of high-speed applications.

Hybrid Permanent Magnet and Foil Bearing System for Complete Passive Levitation of Rotor

This paper deals with the complete passive levitation for a typical Jeffcott rotor and rotation of the same at the speeds around 40,000 rpm. The passive levitation is achieved by supporting the rotor axially by a permanent magnet bearing and discrete bump foil bearings for the radial support. The permanent magnet bearing is made up of three pairs of ring magnets arranged in Halbach pattern. Bump foil bearings are designed for rotor weight to provide the radial support to the rotor system. The proposed rotor-bearing configuration is analysed using Finite Element Analysis (FEA) software (ANSYS) for rotor dynamic characteristics. The designed rotor bearing system is fabricated and tested up to the speeds of 40,000 rpm. The system response is acquired using advanced rotor-dynamic data acquisition system. The experimental results show that the rotor is completely airborne and stable at the desired speed.