Soumendu Jana

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.

EXPERIMENTAL INVESTIGATION OF UNSTEADY FLOW IN A TRANSONIC UNI-STAGE AXIAL COMPRESSOR

Detailed steady and unsteady experimental measurements and analysis were performed on a Single stage Transonic Axial Compressor with asymmetric rotor tip clearance for studying the compressor stall phenomena. The installed compressor had asymmetric tip clearance around the rotor casing varying from about 0.65mm to 1.25mm. A calibrated 5-hole aerodynamic probe was traversed radially at exit of rotor and showed the characteristics of increased flow angle at lower mass flow rates for all the speeds. Mach number distribution and boundary layer effects were also clearly captured. Unsteady measurements for velocity were carried out to study the stall cell behavior using a single component calibrated hotwire probe oriented in axial and tangential directions for choke/free flow and near stall conditions. The hotwire probe was traversed radially across the annulus at inlet to the compressor and showed that the velocity fluctuations were dissimilar when probe was aligned axial and tangential to the flow. Averaged velocities across the annulus showed the reduction in velocity as stall was approached. Axial mean flow velocity decreased across the annulus for all the speeds investigated. Tangential velocity at free flow condition was higher at the tip region due to larger radius. At stall condition, the tangential velocity showed decreased velocities at the tip and slightly increased velocities at the hub section indicating that the flow has breakdown at the tip region of the blade and fluid is accelerated below the blockage zone. The averaged turbulent intensity in axial and tangential flow directions increased from free flow to stall condition for all compressor rated speeds. Fast Fourier Transform (FFT) of the raw signals at stall flow condition showed stall cell and its corresponding frequency of occurrence. The stalling frequency of about half of rotational speed of the rotor along with large tip clearance suggests that modal type stall inception was occurring.

Development of Foil Bearings for Small Rotors

Lubricant free high speed turbo-machineries are one of the emerging fields in the gas turbine technology. Foil bearings are the major contenders in the lubricant free bearings due to their ability to support significant loads at very high speeds. The paper deals with the various stages in the development of discrete and continuous bump foil bearings and testing of the same for designed speeds and loads. Development of bumps involves determination of bump geometry for the desired load capacity, design of special purpose dies for the fabrication of corrugated sheets, identification of suitable bump material and evolution of heat treatment process. Here Beryllium – Copper (Be-Cu) is used as a bump material because of its self-lubricating property and good mechanical strength. The clearance between the shaft and top foil can be adjusted by providing the back-up foils between the encircling foil and bump foil. The rotor system simulating the weight of a typical micro gas turbine is designed and fabricated. The foil bearings developed are tested under this simulated load conditions at speeds above 50,000 rpm. The results obtained show that the rotor is completely airborne at speed slightly above 9000 rpm and at higher speeds the rotor is stable. NOMENCLATURE D load capacity coefficient E Young’s modulus of Be-Cu G flexural stiffness per unit width L width of the bearing W load on the bearing d diameter of the shaft Ka air stiffness per unit width Kf foil stiffness per unit width Ke equivalent stiffness per unit width dc housing inner diameter lb chord of bump nb number of bumps rb radius of bump tb bump thickness ν Poisson’s ratio of Be-Cu

Aero-Thermodynamic Modelling and Gas Path Simulation for a Twin Spool Turbo Jet Engine

Engine simulation model / virtual engine building is one of the important aspects towards development of engine health management system. In the present work, an attempt has been made to develop simulation model for a typical twin spool turbo jet engine using commercially available Gas turbine Simulation Program (GSP). The engine simulation model has been used for aero-thermodynamic gas path performance analysis related to engine run at design point (ISA conditions), off design points (test-bed ambient condition) and Accelerated-Deceleration Cycles(ADC) at ISA conditions. Simulation results have been compared with sample test bed data for the purpose of validation. This document describes in detail the procedure for engine simulation model development using GSP. Predicted results show good correlation with experimental test-bed data. The engine simulation model can further be used to simulate several fault conditions leading to data generation required for engine health management system development. This work has been carried out as a part of NPMASS sponsored project entitled Aero Engine Health Management.

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.

Structural Dynamic Behavior of Axial Compressor Rotor

The vibrations involved in a typical axial compressor rotor in an aircraft engine are complex. Generally, the compressor blades are arranged in a cantilever type configuration. It is also known that the amplitude of vibration is highest near the tip section of the shroudless blade. Compressors are limited by aerodynamic instabilities such as rotating stall and surge. Rotating stall generally initiates near the tip region of the compressor. Blade vibrations coupled with aerodynamic instabilities will lead to a catastrophic scenario of flutter that is asynchronous to the rotor speed. This aeroelastic interaction is detrimental if not taken into consideration. Knowledge of vibration characteristics of the compressor rotor will help in mapping the flutter zone for safe operation. The modal characteristics of the transonic axial compressor rotor available at the Axial Flow Compressor Research (AFCR) facility of National Aerospace Laboratories (NAL) are established in this study. A cyclic-symmetric prestressed modal analysis is performed on a single sector of the compressor rotor consisting of a shroudless blade connected to the disk with a pin type dovetail arrangement for different speeds. The main diagnostic charts for turbomachinery vibration i.e., Campbell and Interference diagrams are generated for various speeds and harmonic indices/nodal diameters of the compressor rotor. The critical crossings of the engine order excitation lines over the natural frequencies of the blade are highlighted. Experimental modal investigations and analysis are carried out on the compressor rotor at the stationary condition and for two different boundary conditions. First, the blade alone modal characteristics under the free-free condition are established. Later, the complete blade-disk assembly mounted on a base test-stand is used to investigate the cantilever fixed-free boundary condition of the chosen blade. The modal characteristics are established by performing impact hammer experiments. Blade excitation is provided by a calibrated Dytran make impact hammer and the response is measured using a calibrated accelerometer. The structural dynamic data acquisition hardware and software from OROS is used for determining the natural frequencies, mode shapes and structural damping for each mode of the compressor rotor. There is a good agreement in the natural frequencies and mode shapes established using experiment and numerical methods for the first three modes investigated. Modal Assurance Criteria (MAC) analysis is carried out for two different modal identification algorithms to compare the mode shapes.