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Über dieses Buch

This book presents select papers presented during the 6th National Symposium on Rotor Dynamics, held at CSIR-NAL, Bangalore, and focuses on the latest trends in rotor dynamics and various challenges encountered in the design of rotating machinery. The book is of interest to researchers from mechanical, aerospace, tribology and power industries, engineering service providers and academics.

Inhaltsverzeichnis

Frontmatter

Analytical, Computational and Experimental Methods

Frontmatter

Stability Improvement for Upgraded Four-Stage Centrifugal Compressor Rotor-Bearing System

As the plant capacity is increased, the equipment in the plant also needs to be upgraded. Replacing with a new machine is not always the right economical decision when alternative options for upgrading and retrofitting the exiting machine exist. Upgrading the machine not only increases the performance thus reducing the power consumption, but it also increases the system reliability, reducing the downtime and thus helping the plant operate more efficiently. The compressor used for this work was in operation, and due to prolonged operation, the impellers had degraded primarily due to fouling caused by process contaminants. This multi-stage centrifugal compressor was subsequently upgraded to increase the inlet volume flow rate by 20% with the objective of retaining the same casing and rotor shaft. The redesigned compressor stages has better performance with reduced power consumption. The redesigned four-stage centrifugal compressor operating at design speed of ~8856 rpm may be prone to instabilities caused by aerodynamic cross-coupling and hydrodynamic bearing modification. The authors in the present study are exploring any instabilities in the rotor-bearing system that may be caused due to the upgrade of the compressor for higher volume flow rate. To meet the new operational requirements, the bearings were redesigned. The stability analysis was performed considering the destabilizing effects of the aerodynamic excitations, based on which modifications were performed on the design to stabilize the multi-stage centrifugal compressor and to conform to satisfy the API Level I stability criteria. The modifications performed on the rotor/bearing system resulted in reduced vibration amplitudes for the required level of rotor unbalance conditions. These modifications also significantly eliminated the instability that was initially observed, and the redesigned compressor not only met the requirements for the change in operating conditions but also fully complied with API 617 standards.

Vignesh Selvam, Roman Kochurov, Evgen Kashtanov, Leonid Moroz, Abdul Nassar

3D Finite Element Rotor Dynamic Analysis of Turbine Test Rig Rotor-Shaft Systems

Design of a 385 kW turbine (T385 turbine) to drive the compressor of 1 kN small gas turbine engine is carried out in Propulsion Division, CSIR-NAL. Aero-thermodynamic performance evaluation of designed turbine stage was planned through experimental testing in VTTR, Propulsion Division, CSIR-NAL. The turbine speed is 50,500 rpm at the engine design point, and the equivalent design speed in test rig conditions is 30,000 rpm. Since performance evaluation at higher speeds consists of high-speed rotating components constituting a complex dynamic system, it is of prime importance to consider rotor dynamic characteristics to operate the turbine safely. Test section is designed for the T385 turbine rotor BLISK considering rotor-shaft system with bearings. The dynamic behavior of test rig rotor systems was evaluated for vibration reliability. This paper presents the 3D FE rotor dynamic analysis of T385 turbine rotor-shaft system. The stiffness of bearing supporting structure is evaluated along the direction of stress field using FEA. T385 turbine rig rotor system is modeled in FEA using lumped mass method. All the masses of rotor shaft sytem with inertias are considered in the analysis. The Campbell and response plots are plotted using frequencies and mode shapes to predict the critical speeds and unbalance response, respectively. The critical speeds from Campbell diagram indicates that rotor system is safe to operate in the test rig. The maximum amplitude due to unbalance is within the limits of clearance at the operating conditions. The predicted natural frequencies of T385 rotor system from modal analysis are compared with impact hammer test and frequencies are matching well with analysis.

Nanjundaiah Vinod Kumar, Rajeevalochanam Prathapanayaka, Revanna Jai Maruthi, Shashidhar Swaroop

Evaluation of Dynamic Characteristics of a VMC Spindle System Through Modal and Harmonic Response. Part 1: Spindle Supported by Angular Contact Ball Bearings

Machine spindle dynamic characteristics are precisely related to the operation and stability of the machining process. The finite element analysis (FEA) has been used to find out the dynamic behavior of spindle-bearing system. The unbalance response of the vertical machining center (VMC) spindle system at the cutting tool due to thrust force is calculated to study the dynamic properties. In this paper, Ansys Workbench rotordynamic and harmonic response have been used to make the dynamic investigation of VMC spindle and estimate the final values. Results show that the obtained critical speeds are nowhere near to the spindle operating speed range; hence, the resonance would not occur, and at operating speed, the maximum unbalance response is within an acceptable limit. The effect of rotordynamic and harmonic response on same VMC spindle system supported by hybrid bearing set is analyzed in Part 2 as an extension of this work.

Gireesha R. Chalageri, Siddappa I. Bekinal, Mrityunjay Doddamani

Evaluation of Dynamic Characteristics of a VMC Spindle System Through Modal and Harmonic Response—Part 2: Spindle Supported by Hybrid Bearing Set

This paper extends the proposed dynamic analysis of spindle with conventional bearings of Part 1 and demonstrates feasibility of hybrid bearing set (HBS) usage in machine tool spindles. HBS consists of permanent magnet bearing (PMB) and conventional angular contact bearing (ACB). The rotordynamic and unbalance response of vertical machining center (VMC) spindle supported by HBS is presented. Harmonic responses are also determined using Ansys Workbench finite element tool. Results show that the system is stable at obtained frequencies, critical speeds are higher than the spindle operating speed range, and the maximum unbalance response is within acceptable limit. The comparison between the results of ACB and HBS has verified that the HBS can effectively be used in machine tool spindles with higher critical speeds and maximum amplitudes generating due to cutting forces.

Gireesha R. Chalageri, Siddappa I. Bekinal, Mrityunjay Doddamani

Dynamic Analysis of Three-Dimensional Composite Tube Shafts

Three-dimensional (3D) composites have good delamination resistance along with high specific stiffness and high specific strength. Composite tube shafts are modeled with different reinforcement architecture such as multi-axial, stitched, knitted, braided, orthogonal woven, interlock and z-pinned. The in-plane elastic properties at different fiber volume fractions of these composites are obtained from the literature. 3D composite tube shafts are modeled with length: 1 m, internal radius: 25 mm and thickness: 4 mm using modified equivalent modulus beam theory formulation. Modal analysis is carried out, and bending natural frequencies are calculated for different 3D composite tube shafts with E-glass, carbon and kevlar fibers and epoxy as matrix materials. The natural frequency reduces with through thickness reinforcement for orthogonal, knitted, z-pinned and stitched composites. Braided composites tube shafts have higher natural frequencies compared to that of other types.

Pavani Udatha, A. S. Sekhar, R. Velmurugan

Analysis of Rotor Supported in Double-Layer Porous Journal Bearing with Gyroscopic Effects

In this paper, a numerical analysis on the dynamics of a multi-degree of freedom shaft–rotor, supported on bearings, is presented. The system is a shaft with multiple rotor discs attached to it and supported on double-layer porous journal bearings. The system is modelled using finite element methods. Euler-Bernoulli beam element theory is used for modelling the shaft. The discs are considered as rigid. The support bearings are modelled based on linear spring elements for stiffness and linear damping elements for viscous damping coefficients. The rotor dynamic model of the system is analysed by incorporating the gyroscopic effects due to the precession of the offset discs and the bearing stiffness and damping anisotropy. The fluid flow in double-layer porous film is analysed using Brinkman equations to consider lubricant additives influences. The pressure gradients with respect to linearized perturbation of displacements and velocities under dynamic conditions are derived using Reynolds modified equation for Ocvirk (short) bearing. The dynamic linear and cross-coupled coefficients (stiffness and damping) dependent on speed are calculated using dynamic pressure gradients for the double-layer porous journal bearings. The system is represented in reduced order state-space form, and eigen value problem is solved to calculate its whirl frequencies. The rotor system critical speeds are obtained by plotting the Campbell diagram. This paper provides the basis for rotor system design with support bearings, representative of a multi-stage centrifugal pump. The design helps to identify and prevent rotor vibrations.

C. Shravankumar, K. Jegadeesan, T. V. V. L. N. Rao

Rotordynamic Analysis and Redesign of High-Pressure Turbine Test Rig

The high-speed test rigs pose several operational problems originating from rotordynamics, bearings, lubrication and thermal gradients. When the critical speeds exist within the design speed, it is possible to accelerate the rotor through resonant speed zones in many applications. However, in very few cases, the resonance crossovers pose serious problems resulting from operational schedules and demand major modifications to rotor-bearing system. The design modifications, driven by rotordynamic considerations, carried out for an existing high-speed test rig with serious operability issues are presented in this paper. During operation, one of the bearings supporting the rotor has failed twice causing significant damages. On both occasions, the bearing failure took place when the rotor was approaching the first critical speed. Considering the difficulty experienced to pass the first critical speed quickly, the rotor-bearing system of the rig is completely redesigned with safe separation margin away from the design speed. Designer’s challenges arising from overall layout, manufacturing, imported hardware, assembly and operation are highlighted while addressing the problem. The turbine stage could be tested successfully up to its design speed after implementing all design modifications.

C. Veera Sesha Kumar, E. K. Vivek, S. Vignesh

Thermo-Mechanical Analysis of a Rotor-Bearing System Having a Functionally Graded Shaft with Transverse Breathing Cracks

Purpose: The dynamic behavior of two-cracked functionally graded (FG) shaft system under thermal environment has been carried out. The finite element (FE)-based formulation is used to model metal-ceramic FG (SS/ZrO2) shaft using Timoshenko beam theory (TBT). Power law of material gradation is used to derive effective thermo-elastic properties of radially graded FG shaft. Methods: The governing system equations of motion are formulated using Hamilton’s principle. The local flexibility coefficients (LFCs) are derived as functions of material gradient, temperature, size and orientation of crack, for the cracked FG circular cross-sectional FG shaft, using linear elastic fracture mechanics, Castigliano’s theorem and energy method. Results: Numerical simulations are performed to analyze the effects of geometric, material and temperature gradient parameters on the natural frequencies of the cracked FG shaft system. Conclusion: LFCs are functions of material gradient and temperature besides crack size. Even though the reduction in eigenfrequencies is decided by crack parameters, material gradient and temperature, however, the reduction in eigenfrequencies is greatly influenced by gradient index and the index may be selected properly to design FG shafts for high-temperature applications.

Debabrata Gayen, Rajiv Tiwari, Debabrata Chakraborty

A Coupled Field, Circuit and Rotor Model of a BCW Induction Machine

The current trend in designing rotating machine is the integration of motor or generator into the overall machine. The use of these integrated machines is finding its applications in the development of compact drive systems in the areas, such as integrated power system for electric spacecrafts and unmanned air vehicles. These machines present great challenges and at the same time they also present great opportunities through the ability to achieve transverse actuation (in two independent directions) without any significant sacrifice. The eccentric position of the rotor with respect to the stator of electric machines makes the magnetic field distribution asymmetric and generates a force along the shortest air gap of the electrical machine. This magnetically induced force is called unbalance magnetic pull (UMP). The present work discusses the development of a coupled magnetic field, electric circuit and rotordynamic model of a 3.7 kW 4-pole induction machine with a special stator winding called bridge configured winding (BCW). This stator winding has the capability to produce torque as well as controllable transverse force. The simulation has been carried out in different eccentricity conditions. The developed model can be used for further study of vibration control or for the development of bearingless machines using BCW scheme.

Gaurav Kumar, Karuna Kalita, Kari Tammi, Seamus Garvey

Dynamic Modeling and Analysis of Propeller Shaft Supported on Rolling Element Bearings

This paper presents modeling and dynamic analysis of marine propulsion shaft supported on three radial and one thrust bearings. The motions of rotor and bearings are under the influence of each other, and therefore, such a system requires structural dynamic studies. Initially, the rotor bearing system is analyzed with finite element model to obtain the modal properties. Internal unbalance force due to mass eccentricity acts on the propeller. Unbalance response of the rotor is obtained numerically from Neumark time integration scheme. Effect of speed and bearing stiffness on the dynamic response is studied. In further case, the radial springs are replaced with three ball bearings, which are modeled by Hertz contact forces expressed in terms of the corresponding nodal displacements. The effects of disk imbalance, thrust bearing stiffness and number of propeller blades on system response are illustrated for different speeds in terms of time and frequency responses. The generalized interactive approach is useful for carrying out parametric studies.

Devendra Singh, J. Srinivas

Rotordynamic Analysis of High-Speed Rotor Used in Cryogenic Turboexpander Using Transfer Matrix Method

Cryogenic turboexpander is considered as the heart of modern gas liquefier for its high thermodynamic efficiency and high reliability. The operating speed of small- and mid-sized turboexpander is usually greater than 50,000 rpm. Such high rotational speed brings constrain in the selection of the appropriate bearings. In turboexpander, gas bearings are found suitable to use, where process gas is used as a lubricant to avoid contamination. The study of rotordynamic behaviour of such high-speed turbomachinery is essential to avoid resonant conditions and predict unbalance vibrations. In the current application, transfer matrix method (TMM) is used to predict critical speed, mode shapes and unbalance response of a rotor using gas foil journal bearings. The predicted critical speeds are compared with experiments to validate the same. The rotational speed of the designed rotor is 80,000 rpm with an unbalance of 40 mg-mm at each journal bearing.

Debanshu S. Khamari, Partha Sarathi Kar, Shantashree Jena, Jitesh Kumar, Suraj K. Behera

Clustering in Pareto Front: Application on an Aero Engine Rotor-Bearing System for Improved Design

In the aero engine rotor-bearing systems, a design modification to move the critical speed away from resonance zone and to improve the unbalance response is a practical problem for designers. The objective functions are selected as amplitude of vibration due to unbalance and second critical speed. The two selected objectives are found to be conflicting, and hence, multi-objective optimisation is used to solve this problem through numerical formulation. Diameters of the stepped shaft and stiffness of the two bearings are selected as design variables. Weight is set as a constraint, and additional constraints based on the initial design are introduced. Objectives resulting from multi-objective optimisation and corresponding design variables are clustered separately using k-means clustering algorithm. The novelty of the work is in empowering the designer to recognise the hugely diverse designs resulting in identical solutions and achieving manufacturing sovereignty in choice of design through clustering in objective and design space and their mapping.

K. Joseph Shibu, K. Shankar, Ch. Kanna Babu, Girish K. Degaonkar

Sensitivity Analysis for Unbalance Identification of Rotor Systems

Various types of rotor faults may appear in rotating machines over time. Unbalance is the most commonly occurring fault in rotating machines. This work proposes sensitivity analysis for unbalance identification in rotating machines using a model-based approach. The sensitivity for unbalance response has been computed as response per unit rotating unbalance force using the finite element method. The rotor system has been considered under various end supporting conditions, e.g. isotropic undamped, damped bearing and anisotropic bearing cases. Viscous form of damping has been considered to model bearing damping. The effect of gyroscopic forces has been included in the model. In the analysis, the response of the rotor system is recorded at various locations on the shaft when a unit unbalance is applied on any of the rotor disc/plane. The process has been repeated to find out the unbalance response sensitivity of the rotor system to unit rotating unbalance force at other disc/plane locations. The idea of the work involves applying the sensitivity analysis in proper selection of measurement points of unbalance responses in rotating machines in the process of unbalance identification.

Dinesh Kumar Pasi, Manoj Chouksey, Amit Kumar Gupta

Sommerfeld Effect Attenuation Using Switched-Stiffness Method of a Non-ideal Internally Damped Shaft–Disk System with Constant Eccentricity

Internally, damped shaft–disk system when driven by a non-ideal power source, i.e., limited power source often exhibits complex dynamics. Upon exceeding a critical power input near resonance, the system may contribute to increasing the transverse vibration severely rather than increasing the spin speed. This phenomenon is referred to as the Sommerfeld effect. This effect can cause instability in high speed rotor system and needs to be addressed carefully for safe and smooth operations. In the present study, a semi-active control scheme based on switched-stiffness method is employed to attenuate the Sommerfeld effect of a eccentric shaft–disk system driven by a brushed DC motor. Following, the equations of motion are solved numerically to obtain time response and amplitude frequency response with a specified supply voltage. It has been shown that as the value of switched-stiffness increases, the Sommerfeld effect is found to be attenuated. However, the rotor response is corrupted with spikes as a fallout of switching stiffness technique, which may destabilize the system and becomes critical when the switching time is very fast. The attenuation of Sommerfeld effect can be further verified through the time varying potential energy plot which is seen to be diminished after crossing the critical speed owing to the dissipative characteristics of non-potential switching stiffness force.

Abhishek Kumar Jha, Sovan Sundar Dasgupta

Rotor Dynamic Analysis of Rotor Assembly of a Small Liquid Metal Pump

Fast breeder reactors (FBRs) utilize liquid metal, such as liquid sodium as the main coolant in their heat transport circuits. Choice of liquid sodium as the coolant comes due to its excellent heat transfer and neutronic properties. A 500 MWe, sodium cooled, prototype fast breeder reactor (PFBR) is being commissioned with technology inputs from Indira Gandhi Centre for Atomic Research (IGCAR). This centre has test facilities to demonstrate working and the development of components related to a fast reactor. The liquid sodium needs to be propelled in the loops of heat transport circuits of reactor and hence requires the use of pumps. Use of such pumps to propel liquid sodium has been demonstrated in one of the loops present in IGCAR. Capacity of this pump is 50 m3/h with its shaft currently being supported on top by an angular contact bearing while at bottom by hydrostatic bearing. The rated speed of operation of this pump is 2900 rpm. Use of active magnetic bearings (AMB) in place of oil lubricated bearings is being actively explored to eliminate the chances of oil leakage into the sodium. To demonstrate this concept for primary pump of PFBR, a small-scale magnetic bearing was designed and tested in the 50 m3/h pump. The shaft of this pump was modified to accommodate magnetic bearings and its associated components. Estimation of the critical speed of the shaft, both before and after modification, has been carried out using commercially available finite element analysis (FEA)-based software advanced rotating machinery dynamics (ARMD). Further, unbalance response studies have been carried out to know maximum displacement responses. The details of these analyses and results are discussed in this paper.

Ashish Kumar, Y. V. Nagaraja Bhat, B. K. Sreedhar, S. I. Sundar Raj, S. Murugan, P. Selvaraj

Bearings, Dampers and Seals

Frontmatter

Rotor Dynamics of Turbine–Generator Shaft with Dampers During Subsynchronous Resonance Generated by Series Capacitors

Purpose In this paper, an electromechanical approach to study the turbine–generator shaft stability with and without dampers is made. The shaft is subjected to electrical disturbances created by series capacitors. The high power capacitors help the electric power system to improve the reactive power in high voltage transmission lines. Methods Finite element method is used to study the stability of the shaft under subsynchronous resonance when compared to the traditional methods like eigenvalue analysis, frequency scanning method and digital time simulation techniques. At the same time, it leads to subsynchronous resonance. Results Electromechanical stress in the rotating shaft arises when the resonance is created in the system. Maximum stress and strain of the shaft are calculated with other necessary parameters to prove the system instability. In order to maintain stability, dampers are installed at an optimum location. Conclusion Best location of installing damper is found using ANSYS 16.0 by modal analysis, harmonic and phase response analysis. The damper installed at the point reduces the stress caused by subsynchronous resonance and maintains the stability of the system.

P. Manikandan, Faheem Ahmed Khan

Active Control of Bridge Configured Self-bearing Motor, a Numerical Study

Vibration is a major concern of the rotating machine industry. The wear and tear of the support bearing and the eccentric motion of the rotor are among the main sources of vibration of an electrical machine. The development of a bearingless machine is a good way to address this problem. This paper mainly focuses on the development of a bearingless bridge configured winding (BBCW) induction motor. The bridge configured winding (BCW) is a specialized single set of winding scheme, which has the capability to produce the torque and the transverse force simultaneously. There are two sets of supply for this winding scheme. The three-phase main supply produces a p-pole pair of the magnetic field and is responsible for the torque-producing component. The external supply in the bridges produces a p ± 1 pole pair of the magnetic field. The interaction between these two fields produces a net radial force, which is used to neutralize the various forces acting on the rotor and the weight of the rotor. The magnitude and the direction of this magnetic force can be controlled by supplying currents or voltages at different frequencies and amplitudes through the bridge points of the BCW winding. There is no study in the literature related to the development of bearingless machine using BCW scheme. In the present work, a Simulink model of a BBCW induction motor has been developed. The convergent control scheme has been used for the control of forces of various frequencies acting on the rotor. The PID controller has been used for the levitation of the rotor. The shaft of the motor has been modeled as a Euler–Bernoulli beam, and it is supported by only one isotropic bearing at the one end. The other end of the rotor has been kept unsupported to demonstrate the levitation effect.

Gaurav Kumar, Karuna Kalita, Kari Tammi

Stability Analysis of Partial Slip Texture Journal Bearing

Stability analysis of one-dimensional (long) partial slip texture journal bearing is presented. A journal bearing (one-dimensional) is analyzed considering slip on land, recess depth and extent of partial slip texture region. A modified dynamic Reynolds equation is based on theory of narrow groove approximation considering infinite cells (land with slip and recess configuration) in partial slip texture region. Pressure under static state and pressure gradients dynamic state due to journal center perturbation are derived considering Lund’s method (infinitesimally small perturbation of displacements and velocities). Load capacity and linearized dynamic coefficients are derived from integration of pressure (under static state) and pressure gradients (under dynamic state), respectively. The performance characteristics (stiffness (nondimensional) and damping (nondimensional) coefficients, threshold (critical) speed and critical ratio of whirl frequency) are presented based on partial slip texture configuration parameters. Stability threshold increases for both configurations of slip and texture at higher partial slip texture extent (angular) for low-to-medium eccentricity ratio bearing operating conditions.

T. V. V. L. N. Rao, Ahmad Majdi Abdul Rani, Norani Muti Mohamed, Hamdan Haji Ya, Mokhtar Awang, Fakhruldin Mohd Hashim

Experimental Study of Temperature Effect on Labyrinth Seal Leakage and Vibration Characteristics of Rotor

Labyrinth seals are the most widely used non-contact-type turbine seals. The main design concern is to prevent the seal rub with the stator in the range of operating conditions and to control the system rotordynamics. This work aims at experimentally evaluating the effect of thermal growth of labyrinth seal on the leakage flow rates and effect on vibration characteristics of the system. An experimental seal test rig for teeth on rotor (TOR)-type straight labyrinth seal with four flat tip teeth has been developed. Constant clearance between seal and stator is maintained and tested at different speeds and temperatures by varying the inlet air pressure. Leakage results are compared for the seal for the range of operating conditions and for a given seal radial clearance. In addition, vibration data are measured at various locations to understand the influence of seal on the vibration characteristics of the rotor system. It is seen that flow leakage rate and vibration of system are influenced by the pressure difference and the temperature.

Vivek V. Shet, A. S. Sekhar, B. V. S. S. S. Prasad

Study of Static Performance Characteristics of Offset-Pressure Dam Bearing Considering Turbulent and Adiabatic Thermal Effects

As there is an increasing demand for high-performance turbo-machinery, hydrodynamic bearings are expected to run at high surface speed (>100 m/s) and heavy load (>4 MPa) operating conditions. Especially, high-speed and high-power gearboxes operate at such severe operating conditions for gas or steam turbine power generation applications. Conventionally, fixed profile bearings such as pressure dam or offset bearings are used in these gearboxes. However, they have design limitation on maximum surface speed due to stability requirements at no load conditions and maximum oil film temperature at heavy load and high-speed conditions. In this paper, it is attempted to combine the offset design feature “preload” with pressure dam bearings to see that if the operational design limits could be improved. The governing mathematical model includes turbulent and adiabatic thermal effects. The static performance characteristics of combined offset pressure dam bearings are compared with individual bearings. The analytical study found that combined offset pressure dam bearing delivers better performance than the other bearings. Also, the analytical model is validated with published experimental results.

Sivakumar Dakshinamurthi, Suresh Nagesh

Computational Fluid Dynamics Study of Oil Lubrication in Ball and Roller Bearings

Lubrication plays a significant role in performance of rolling element bearings. It is essential for proper functioning of bearings to reduce friction and to help avoid failure of bearings. Computational fluid dynamics (CFD) is one of the design and simulation tools, which is mainly used to identify proper lubrication for bearings. This work summarizes the CFD simulation results of oil transport within deep groove ball bearing and concave roller bearing. The volume fraction of oil has been predicted around the contacts at both outer and inner rings, all components and the gaps between the cage and rollers for both bearings. Drag losses (both pressure and shear drag) and film thickness have also been predicted. Cage design plays a significant role in determining the lubrication and the internal fluid drag losses in a bearing. The influence of cage design on the lubrication and the drag is evaluated by employing a metallic cage and a polymer cage. The simulation results show that oil content inside the bearing is dependent on the bearing free volume and operating speed. At lower speeds, both cage designs give similar performance; however, at the higher speed, it is different. Compared to metallic cage, polymer cage functions better in oil bath lubrication by splashing the oil on raceways at higher rotation speed. A linear decrease in oil content is observed with increased volume of polymer cage for concave roller bearing. In all case, cage and rollers experience maximum oil drag. An improved polymer cage is developed with the help of CFD to provide more oil to the cage and other bearing components.

Vijay Tijare, Shanmukha Nagaraj, Mehul Pandya, Jun Wang

Feasibility Studies on Newly Conceptualized Inter-shaft Squeeze Film Damper (ISSFD) Rings for Vibration Attenuation

Squeeze film dampers (SFDs) have become very essential for high-speed turbomachinery as means of vibration energy dissipating mechanism. However, SFDs are not very common for inter-shaft bearing applications and are still in the R&D phase. It is observed that the application of SFDs for inter-shaft bearing systems is not being pursued in a real practical sense, as it becomes extremely difficult to realize a compatible component facilitating the radial squeezing mechanism—where squeeze film oil could be introduced—thus resulting in squeeze film damping. The gap that could be made available between the inner spool and inner race or the outer spool and the outer race of the inter-shaft bearing also being very little further complicates the application of a conventional squeeze film damper in the inter-shaft bearing plane. In this research work, newly conceptualized inter-shaft squeeze film damper (ISSFD) rings are fabricated and tested for evaluating their damping potential characteristics in dedicated instrumented test rig/s fabricated for the purpose. Parametric experimentations are conducted in a single-spool test rig as a proof of concept in attempting to quantitatively evaluate the damping potential of ISSFD rings and hence the suitability of their applications in inter-shaft bearing plane of two-spool system. This research study very clearly indicated the damping contribution of the ISSFD rings, and the performance of the system improved in terms of substantial reduction in shaft vibration amplitudes. The study also clearly indicated that the ISSFD rings contribute toward the stiffness in the bearing plane also, and as a result, the rigid body critical speed gets shifted. Parametric experimental studies brought out the effect of different geometric parameters on the stiffness and damping contribution of ISSFD rings.

H. M. Shivaprasad, G. Giridhara, Ajit Kumar, Praveenkumar Kamanat, V. Arun Kumar

Characterization of a Squeeze Film Damper for Aircraft Engine Applications

High-speed turbomachinery designs rely on adequate damping at the bearing supports to provide smooth operation throughout the sub-idle and normal operating speed ranges. Squeeze film damper (SFD) designs employ a thin oil film between bearing and housing that softens the bearing support and provides increase damping. During operation, the dynamic motion of the damper squeezes the thin lubricant film, thus generating hydrodynamic pressures and film forces to dissipate mechanical energy. This paper discusses test results from two different sealed SFD designs: The first design uses butt-end piston rings to seal the damper film where the oil exits the damper through a small circumferential gap in the piston rings. The second design uses on overlap piston ring design which more completely seals the oil in the damper. For this design, an alternate set of exit holes is provided to allow the oil to exit the damper. Testing was done over a range of frequencies from 20 to 300 Hz, with oil supply pressures from 14 to 140 psi, with oil temperatures from 75 to 225F and with SFD eccentricity ratios from 0.05 to 0.5, encompassing both cavitated and non-cavitated regimes of operation. The damping and added mass terms for the SFD were identified through standard data reduction algorithms. Test results indicate that for the same basic damper geometry, a significant difference in measured damping coefficient was obtained between the two different damper designs. Variation in damping using the overlap piston ring damper design was much less than with the butt-end damper design due to the alternate set of exit holes at all operating conditions. No significant drop in damping observed at the cavitation regions for both the damper designs. Piston rings were observed to rotate. A discussion about the observed results is included.

Praveen Thirumalasetty, Kishore Vetcha, Mahesh Sivakumar, Tod R. Steen, Anthony M. Metz

Stability of Parametrically Excited Active Magnetic Bearing Rotor System Due to Moving Base

Active magnetic bearings (AMBs) offer contact-less functioning and active vibration control capability while supporting and levitating a rotor. This is the reason that the AMBs are being progressively researched for novel and challenging applications in the industry. In application areas, such as ships, airplanes and space crafts, the rotor is mounted on a moving base, which causes parametric excitation to the system. This, in turn, is generally known to cause stability issues in a rotor shaft system. The present work thus attempts to conduct stability analysis of a rotor shaft system supported by an AMB and is parametrically excited due to the presence of periodically varying base motion. The finite element model for a generic rotor shaft system mounted on a moving base is first presented, and the time-periodic state matrix for the system is found. The Floquet–Liapunov method of analyzing stability of a periodically varying system is used to find the stability boundaries for the system with two widely used control laws for the AMB. The analysis reveals that it is important to consider the parametric excitation caused to the system when the AMBs are being designed for applications involving large base motions.

Tukesh Soni, J. K. Dutt, A. S. Das

Experimental Investigation on the Effect of Housing Profile and Its Relative Position on the Performance of Semi-Active Journal Bearing

Demand for higher speeds, reduced noise and improved reliability along with other safety requirements necessitates an effectively controlled rotor dynamics system. The desired requirements are often not met by using conventional bearings which are passive in nature. Additional improvements can be achieved only with the aid of active or semi-active controls. A new concept adopted here is to conceptualize a semi-active journal bearing to simulate a multi-lobed journal bearing. This research work attempts to develop a semi-active journal bearing by modifying the profile of the bearing and position of the bearing with respect to the shaft. The performance is here defined in terms of attenuation of the vibration amplitude in the bearing plane. For different bearing profiles and various bearing positions, rotor responses are acquired experimentally and FE method is used to obtain extent of simulation with the experimental results. The study is predominantly experimental in nature, and a simple versatile instrumented test rig is designed and fabricated for the purpose. The results indicate a high potential toward practically realizing a semi-active control on journal bearing profile, resulting in quantitative reduction of vibration amplitudes and also benefits derived from optimally positioning the bearing.

Raghu Yogaraju, L. Ravikumar, G. Saravanakumar, V. Arun Kumar

Some Fundamental Issues in Foil Bearings

While the foil bearing technology is well established, some inherent issues must be addressed at the design stage to vastly expand its utilization. This paper highlights the need for one of the critical problems dealing with the need for accurate prediction of maximum temperature of the shaft and bearing to avoid failure due to thermoelastic instability (TEI). A brief description of the cause and consequence of TEI along with a simple prediction methodology is presented.

P. Samanta, N. C. Murmu, M. M. Khonsari

Condition Monitoring, Diagnostics and Prognostics of Rotors

Frontmatter

Study of Turbocharger Fully Floating Hydrodynamic Bearing Oil Whirl Behavior—Test and Prediction

Automotive engines are facing increased design focus toward downsizing, higher performance and lower emissions, in the process challenging turbocharger technology to their limits. The exhaust-driven turbine energy must transmit to the compressor stage with minimal losses through the bearing system. In general, two types of bearings are used in turbocharger applications, namely semi-floating rotary bearings (SFRB) and fully floating rotary bearing (RFRB) system. In the latter, bearing is suspended in the lubricant, and by virtue of its rotational speed, brings down the angular speed of the fluid in the clearances between the shaft and the bearings. The ring rotates in the range from 0.25 to 0.4 times the shaft speed, and as a result has a positive effect on lubricant drag. On the other hand, this bearing system now has two spinning oil films and has to sustain the dual self-excited oil whirl vibrations in the inner and outer clearances that have a reciprocal influence on each other. The final evaluation calls for application specific validation either on the respective engine or vehicle system, as the system peripherals could resonate at the same frequencies and amplify these waves. This work describes the oil whirl-related sub-synchronous investigations of the RFRB on turbochargers. A brief theoretical explanation followed by numerical rotor dynamic simulations on two bearing designs using AVL Excite simulation tool is discussed, and thus, obtained results are later validated through tests at the turbocharger sub-system-level evaluations on gas stand.

Lokesh Chandrasekaran, Praveen Kumar Selvaraj, Prasanth R. Vengala, Subramani D. Arthanarisamy

Rolling Element Bearing Fault Diagnosis by Different Data Fusion Techniques

Rolling element bearing is a crucial element of rotating machinery. A sudden failure of the bearing may result in a catastrophic failure. Therefore, the identification of bearing failure in the incipient stage is essential. The vibration signal generated by bearing fault is used for condition monitoring and fault diagnosis. The parameters extracted from vibration data provide the fault indication. However, a single parameter may miss useful information, resulting in less accurate fault diagnosis. The fused parameters after data fusion of individual parameters are more informative and efficient than a single parameter. Mahalanobis–Taguchi–Gram–Schmidt method, principal component analysis, and independent component analysis are the most popular data fusion techniques, and these techniques are applied to three most occurring fault data such as the outer race, the inner race, and rolling elements. The bearing vibration data, available on the NASA Web site, are used for the data analysis and extracting parameters. A comparison is made on the effectiveness of various data fused parameters obtained from different data fusion techniques. The best data fusion technique with respect to each type of defect (inner race, outer race, and ball) is identified.

Sandaram Buchaiah, Piyush Shakya

Diagnosability Index and Its Application to Bearing Fault Diagnosis

Bearings are essential component of rotating machines and are often prone to failure. Early detection of bearing faults thus becomes important for predictive maintenance strategies. Conventionally, vibration measurement is considered to be the most reliable and widely used indicator of fault signatures, which are to be extracted from the raw signal. Traditional signal processing techniques, like envelope spectrum, are employed for extraction of such features. However, selection of optimal band and center frequency remains the main objective of research in the field. Use of spectral kurtosis (kurtogram) is now a standard method for this selection. However, a benchmark study on Case Western Reserve University dataset shows several non-diagnosable cases using kurtogram method. The purpose of this study is to quantify diagnosability in the form of an index and use it as a selection criterion for getting optimal band and center frequency. The proposed method is validated using non-diagnosable cases of the benchmark study, and the results are compared with that of conventional Hilbert transform method and autogram method.

Ankush C. Jahagirdar, K. K. Gupta

Gearbox Health Condition Monitoring Using DWT Features

The gearbox is an accessory drive, used widely for power transmission in industries and vehicles. Since its invention in the twentieth century, it brought major changes in the field of mechanical engineering. At the same time as the gearbox evolution continues, people are focusing on customized operation with less maintenance cost. Instead of the traditional approach (scheduled and unscheduled maintenance), the industry is looking for condition-based preventive maintenance. Therefore, it is important to monitor the health condition of the gearbox. This paper presents three different architectures to diagnose the gearbox vibration signal between healthy and damaged condition. Fifteen wavelet features are extracted from the segmented signal and tested with infinite latent feature selection (ILFS) algorithm to find useful features based on ranking. Feature classification was done using a support vector machine (SVM) algorithm. The ideology of the round-robin technique was implemented in architecture-2. The result shows that, among the three developed architectures, the first architecture with discrete wavelet transform (DWT—1D) followed by the SVM model is providing better classification accuracy than the other two architectures. The results were presented with 100 Monte Carlo runs.

Setti Suresh, V. P. S. Naidu

Gas Turbine Engine Fan Blade Flutter Detection Using Casing Vibration Signals by Application of Recurrence Plots and Recurrence Quantification Analysis

Gas turbine aero engines are a specific class of turbomachinery wherein compression system and turbine are realized as spinning discs on an interconnecting shaft. Fan-bladed disc undergoes an unsteady aeroelastic phenomenon known as flutter during various operational regimes, which might lead to structural failure of blades. Study of this mode of flutter induced structural response by measuring casing vibration is of interest in health monitoring of aero engines. In this paper, authors present a novel application of detecting the rotating blade flutter based on the feature space constructed using statistical parameters, recurrence plots (RP) and recurrence quantification analysis (RQA) of engine casing vibration data. Feature vectors thus obtained are visualised in several 3D vector space plots to cluster the data points which separate flutter mode from the normal mode of operation. Results obtained through the proposed method have been compared with engine flutter test results obtained through dedicated rotating blade strain gauge instrumentation.

A. N. Viswanatha Rao, V. P. S. Naidu, Soumendu Jana

Condition Monitoring of Rolling Contact Bearing by Vibration Signature Analysis

Bearing condition monitoring is the useful technique for maintaining the health of the machines. A machine is similar to a human body as far as condition monitoring is concerned. The sensors act as stethoscope for machines, which provides the machine health-related information. The vibration information helps the analyst to predict the exact condition of machine. Condition monitoring plays a vital role in automation of medium to large-scale industries. Vibration signature is commonly used parameter for identification of fault in rotating machines. Hertzian contact deformation theory is used to calculate contact force. The mathematical model considers frequency as well as acceleration magnitude of bearing vibration. The model developed shows the nature of vibration for both defective and defect-free bearing. The results are presented in frequency domain for simulated defect on the raceways. The effects of defect location and rotating speed are investigated by using theoretical model. The actual rotor with defective bearing is tested at constant speed under known load. The wire cut EDM process is used for creation defects in the bearing. The results obtained in theoretical are validated through the experimentation. The model developed can be used for the signature pattern database development which will act as knowledge base for the future studies in the field.

Kashinath Munde, Ganesh Kondhalkar

Misalignment, Rotor-Bow, Crack, Rub-Imapct

Frontmatter

Dynamic Response Analysis of an Unbalanced and Misaligned Rotor Supported on Active Magnetic Bearings and Touchdown Bearings

This paper investigates a study of the simultaneous interaction between active magnetic bearing (AMB) and touchdown bearing (TDB) in an unbalanced and misaligned rotor system. Numerous practical importance of the working together of both bearings in high-speed rotating machinery, such as the turbines and pumps, can be explained by examining two cases depending upon the types of touchdown bearings. The first case is to consider a faulty rotor supported by active magnetic bearings and conventional touchdown bearings (rolling element bearings) as backup support, in which AMB is active but conventional touchdown bearing is inactive during operation. The second case is considering foil bearings as touchdown bearings, in which AMB and foil bearing both are in action during operation. The hydrodynamic principle of air in foil bearing while rotation of the rotor causes to make it in working condition. Mathematical modelling of the unbalanced and misaligned rigid rotor with a disc at middle supported on both bearings has been done for this investigation purpose. Misalignment has been considered between the rigid rotor and active magnetic bearings. The dynamic equations of motion are developed to numerically generate rotor displacement and current responses of the system. It has been found that simultaneous working of AMB and foil touchdown bearings helps in suppressing the vibration response of the rotor system, increasing the reliability of the machine and making more energy efficiently. It is also observed that current consumption is less in the second case than the first.

Prabhat Kumar, Rajiv Tiwari

Finite Element Modeling and Analysis of Coupled Rotor System Integrated with AMB in the Presence of Parallel and Angular Misalignments

Misalignment is one of the commonly encountered faults in rotor systems. The standard techniques that are used to detect misalignment are loopy orbits, multiple harmonics with predominant 2X and high axial vibration. In real rotor systems, it is caused due to improper seating of bearing housing on foundation or lack of concentricity between bearing and its housing. This chapter presents a numerical model of the coupling, which mimics the forces/moments produced due to parallel and angular misalignment. The coupling connects two rotor systems each with a centrally mounted disk and simply supported on two flexible bearings. The rotor train is modeled with two-node Timoshenko beam finite elements. An AMB is used as an auxiliary support on rotor-2. The coupling connecting the two rotor systems is modeled by a stiffness matrix, which has both static and additive components. While the static component is unchanging during operation, the additive component displays multi-harmonic behavior and exists only in the presence of misalignment. The multi-harmonic nature of coupling’s misalignment force/moment is mathematically modeled by an appropriate steering function. The development of mathematical model is followed by some response analysis, which shows lateral vibration of rotor, current signal of AMB and the orbit plots of rotor in the presence of misalignment and unbalance.

R. Siva Srinivas, Rajiv Tiwari, Ch. Kanna Babu

Detection of Fatigue Crack in the Shaft Using Time-Frequency Analysis

Rotating shafts operating under complex loading conditions are susceptible to develop fatigue cracks at the localized stress concentration points. Fatigue cracks are the prime sources for catastrophic failures. Therefore, it is vital and challenging for the early fatigue crack detection to prevent costly machinery breakdowns. A rotor test rig with a facility of introducing stochastic loads on to the rotating shaft is designed and developed to induce fatigue crack on the shaft is utilized for this study. Accelerated fatigue tests are performed, along by introducing stochastic loads, on a shaft specimen seeded with circumferential V-notch configuration. The methodology for early crack detection is based on analyzing the steady-state vibration data acquired, till the shaft specimen develops fatigue crack, from various locations of the test rig using different sensors like miniature accelerometers, wireless telemetry strain gauge, and laser vibrometer. In the present study, signal processing tools like continuous wavelet transforms (CWT), Hilbert–Huang transform (HHT), and short-time Fourier transform (STFT) are employed for the early fatigue crack detection. Wavelet packet (WP) analysis is used to decompose the experimental vibration response data into narrow frequency band signals before the processing of CWT, HHT, and STFT analyses. In addition, these techniques are compared to evaluate their detection performance when employed directly on raw data and preprocessed data using WP analysis. Finally, this paper provides a detailed description and comprehensive selection of time-frequency techniques for the early fatigue crack detection.

Sagi Rathna Prasad, A. S. Sekhar

Coupling Misalignment Detection and Condition Monitoring of a Rotor Assembly Using FEA-Based Reduced-Order Modeling Methods

Coupling misalignment is a common issue in rotating assemblies connected to driving shafts via coupling systems. Keeping the level of misalignment within safe thresholds is a major requirement for the reliable functioning of rotating systems. Coupling misalignments can result in sub- and super-synchronous excitations (displacements, velocity and acceleration, reaction forces at critical locations) that can be used to ascertain the level of misalignment for a given coupling type. Coupling misalignment happens due to frictional interaction of the coupling spider from driving and driven side. To model it in full generality, it will require nonlinear transient analysis of actual 3D CADs of the couplings with frictional contacts. Challenge to model such systems using FEA is that it requires full nonlinear FEA analysis and is very time-consuming. In the present study, a full 3D nonlinear transient analysis is first done to capture the effect of misaligned coupling and proposes various methodologies that can be employed to reduce the solution times. Component mode synthesis (CMS) is employed to model the stationary part to reduce the solve times considerably. Further effect of varying levels of misalignment on the results is studied. Result trends are studied to explore the possibility of creating reduced-order models (ROMs) from such design of experiments (DoE) study for real-time physics-based condition monitoring of rotating machinery.

Anil Kumar, Dinesh Kumar, Ravindra Masal

Vibration Control Using Active and Semi Active Methods

Frontmatter

Vibration Reduction in Indigenous Wankel Rotary Combustion Engine with Structured Layer Damping

Rotary engines are simpler in design and operation compared to the gas turbines. Rotary engines propel many monoplanes, power hang gliders, and unmanned aerial vehicles (UAV). In an indigenization effort, a 65 hp Wankel rotary combustion engine (WRCE) was successfully developed in the country for a wheeled version of Nishant UAV. As a part of the testing and certification process, three engines were required to be tested in the test bed for a stipulated number of hours. The engine was mounted in the test bed on two cantilever bolts in horizontal and two in the vertical direction with equi-frequency anti-shock mounts. During testing without the alternator, it was observed that the vibrations are higher with 1X amplitude of 24 g. To identify the source of vibration, a detailed modal analysis was carried out. Impact test data showed the existence of dominating frequency around 138 Hz. To reduce the vibrations, the engine mount is modified suitably, and structured layer damping is introduced between the engine mount and support structure. This modification resulted in increased damping leading to vibration reduction to the acceptable level. Testing of Wankel engine with alternator up to the required speed was completed successfully using the structured layer damping method.

Sadanand Kulkarni, S. Satish Kumar, S. Santhosh Kumar, Umesh Kumar Sinha, Brijeshkumar Shah, K. Satish Kumar, A. J. Steve Mithran, K. Monickavasagom Pillai

Characteristic Parameters Estimation of Active Magnetic Bearings for Varying Controlling Parameters

Online condition monitoring of rotor systems with the help of active magnetic bearings (AMBs) has been achieved more importance for the last few decades due to its ability to work in a feedback loop. Proportional-integral-derivative (PID) has three characteristic gain parameters, namely proportional (KP), integral (KI) and derivative (KD). The main purpose of the controller is to provide current for the steady operation of the system. The stability condition of the system is achieved by applying Routh–Hurwitz stability criteria. The stable responses of the system are obtained by tuning the PID controller. Ziegler–Nichols tuning method is used to acquire the least settling time for different controlling parameters. Two different sets of PID controlling parameters are considered for tuning the system against different sets of frequency range. For identifying the characteristic parameters, two different sets of PIDs are selected for the frequency range of 35–51 Hz. A total of 10 operating speeds are selected randomly between the frequency ranges to generate the independent responses that are used in identification algorithm. In this article, a numerical experiment has been performed to identify characteristic parameters of the active magnetic bearing (AMB) along with dynamic parameters of coupling misalignment. An approach is proposed to evaluate the unknown parameters for two different sets of PIDs.

Sampath Kumar Kuppa, Mohit Lal

Characterization of Digital Power Amplifier-Based Active Magnetic Bearings

Active magnetic bearings (AMB’s) are used to support rotors using magnetic forces, without any solid to solid contact. The AMB system has four main components: power amplifier, electromagnetic actuator, sensor and controller. In this work, the characterization of power amplifier for the AMB system is undertaken. The gain and phase lag of the power amplifiers over the operating frequency is obtained experimentally. Equivalent circuit models are made for the power amplifier. These characteristics of the amplifiers are used in developing the control algorithm for the AMB. The experimental results of these characterizations will help in understanding the gain of the power amplifier and also the lag between the signal input and the output signal over the desired frequency range.

Pravina R. Mali, Balaji Sankar, Gurunayk Nayak, Soumendu Jana, A. S. Sekhar

Nonlinear, Parametric Effects on Rotor

Frontmatter

Effect of Sinusoidal and Non-sinusoidal Periodic Forces on the Stability of Gas Foil Bearing

The effect of unidirectional sinusoidal and non-sinusoidal external periodic forces on the stability of gas foil bearing has been investigated using the nonlinear transient analysis. In the case of sinusoidal forces, the loading is considered to follow a sine wave. In the case of non-sinusoidal forces, the periodic forces are assumed to follow square and triangular wave. The spatial domain and time domain terms of the governing Reynolds equation have been discretized using the finite difference method and the Crank–Nicholson method, respectively. The Reynolds equation and the equation of film thickness have been coupled with the elastic deformation of the bump foil structure as the deformation of the bump foil structure is a function of hydrodynamic pressure. The stability of the bearing has been investigated for different loading frequency ratio and loading amplitude. Trajectories are obtained for different values of journal speed to ascertain if the rotor-bearing system is in the stable, unstable, or in critically stable condition. The effect of loading frequency ratio and loading amplitude on the minimum film thickness is also presented.

Kamal Kumar Basumatary, Sashindra K. Kakoty, Manash Pratim Ghosh

Modal Response of a 4-DOF Cantilever Rotor System with 2 Bearing Support Under Rotor Rub Impact with Unbalance

This paper studies the modal response of rotor systems such as turbine engines during rubbing due to unbalance. Rubbing in rotor introduces nonlinearity in the system which leads to phenomena such as rotor stiffening. Experimentation for such cases bears huge cost; hence, nowadays simulation results are widely acceptable. In this paper, a cantilever rotor with 2 bearing support model has been studied for unbalance due to rub in the rotor. Response of such system has been studied on MATLAB. The results reveal the dependence of natural frequency on additional parameter, modal amplitude, which usually is dependent on rotor spin speed in case of linear systems. Effect of parameters such as external damping, stiffness, friction coefficient between the rotor and stator on the modal response of such system has also been presented. The modal response clearly brings out the nonlinear behavior of the rotor system.

Aman K Srivastava, Mayank Tiwari, Akhilendra Singh

Dynamic Response Analysis of Rotating Shaft-Bearing System with an Open Crack

The best of effective design and practices of constructive methods in the analysis of rotor excessive vibration will yield the solutions for the dynamic problems. The extensive effusion of the finite element method (FEM) strongly induced in the area of rotordynamic studies and can give accurate results. Diagnosis of a rotor shaft with crack for its operating conditions is essential to the dynamic systems design. This paper carries the analysis of a finite element model of a flexible rotor-bearing system with a transverse open crack by accounting the various crack depths and internal damping of the shaft. The effect of transverse crack on the system instability regions was found out. It is noted that the natural whirl speeds reduce with increase in crack depths. The system unbalance response and damped natural whirl speeds are presented with undamped orthotropic bearings. The stability of the rotating shaft-bearing system with transverse open crack has also been studied for the various spin speeds and disk eccentricity with the time integration procedure. The phase-plane portraits and frequency-domain diagrams are drawn to study the dynamic behavior. Further, the study is yet to be extended to a fully levitated rotor model supported in active magnetic bearings (AMBs).

S. Bala Murugan, R. K. Behera, P. K. Parida

Rotordynamic Design Studies of Medium Thrust Class Twin Spool Engine

Rotordynamic design studies are an important part of gas turbine design and development since there is a direct influence on the structural integrity, health and fatigue life of rotating as well as static components. Rotordynamic analysis primarily involves the estimation of critical speeds, mode shapes, strain energy distribution, kinetic energy distribution and response to unbalance. The important parameters in design studies include number of bearings, location of bearings, geometric properties of rotor, bearing support design, stiffness and damping in bearing planes. The design procedure is iterative and constraints imposed by the layout should be considered during design modification. In this work, parametric study of various configurations of the rotor-bearing system of a medium thrust class turbofan engine have been presented. The modelling and analysis have been performed in DyRoBeS Rotor software using Timoshenko beam element. The chosen general arrangements are compared against each other to arrive at the optimum configuration from the point of view of overall dynamic behaviour.

R. Siva Srinivas, S. E. Muthu, Girish K. Degaonkar

Rotor Structural Dynamics

Frontmatter

Improving Structural Integrity of a Centrifugal Compressor Impeller by Blading Optimization

Three-dimensional blading features of impellers like sweep and lean improve the aerodynamic performance of centrifugal compressors, especially in terms of pressure ratio, stall margin and efficiency. But, these blade geometrical features often impose challenges on mechanical design and structural integrity of the impeller. Modern small gas turbine engines demand high-work input impellers rotating at very high speeds, making the structural design even more difficult. The present study deals with improving the structural integrity of a centrifugal impeller of a compressor stage designed for 42,000 rpm and power input of 1200 kW. The baseline design of the impeller, arrived using an advanced three-dimensional design software, met the aerodynamic performance requirements but failed to satisfy structurally. Higher backward lean present in the blade was found to be contributing to severe bending stresses and deformation. Hence, three different impellers, with modified thickness, lean angle and wrap angle distributions, were designed. These designs were subjected to 3D CFD and FEM analysis. Structural analysis was carried out to study stresses and deformations for all configurations, followed by pre-stressed modal analysis to predict their natural frequencies and corresponding mode shapes. The design with modified wrap angle distribution not only met the aerodynamic requirements but also satisfied structural requirements. This paper elaborates the design evolution of the centrifugal impeller from the baseline design to a more structurally stable one.

E. K. Vivek, Lakshya Kumar, R. Senthil Kumaran, C. Veera Sesha Kumar

3D Finite Element Vibrational Analysis of T385 Turbine Rotor BLISK Using SAFE Diagram

Integrally bladed rotors (BLISK) are most stressed part of aircraft engines due to high rotational speeds, elevated temperatures and pressures. Turbine blades fail mainly due to fatigue under alternating stresses resulting from vibration of rotor systems. Non-uniform pressure field is experienced by turbine BLISK due to interaction of stator and rotor blades which acts as a source of excitation during turbine operation. The number of stator blades dictates the occurrence of resonance in the rotor BLISK during steady-state operation. Therefore, it is necessary to design a mechanically feasible rotor with respect to stator and verify its modal and harmonic response to ensure its resonance-free operation. Design and development of T385 turbine stage for 1 kN small gas turbine engine are carried out in Propulsion Division, CSIR-NAL. The dynamic behaviour of T385 turbine rotor BLISK is evaluated for vibration reliability. This paper presents vibrational analysis of the T385 turbine rotor BLISK using finite element technique to evaluate critical nodal diameter, critical frequencies and response in engine environment. The turbine speed is 50,500 rpm at the engine design point based on the inlet temperature. Detailed vibration analysis of T385 turbine is carried out using FEA to plot Campbell and SAFE diagrams. The critical nodal diameter extracted from plotted SAFE diagram is 19, which is very well agreeing with Bertini analytical formulae. The Campbell diagram is plotted for T385 turbine at critical nodal diameter of 19. The obtained critical speed from this Campbell diagram is 33,000 rpm, which ensures the rotor is safe in the operating conditions.

Revanna Jai Maruthi, Rajeevalochanam Prathapanayaka, Nanjundaiah Vinod Kumar

Dynamic Analysis of Thermo-Mechanically Loaded Functionally Graded Disks by an Iterative Variational Method

The present study focuses on the free vibration behavior of functionally graded (FG) rotating disk under thermal and centrifugal load, up to the limit elastic state of stress. Power law variation across the radial direction is assumed for the material properties of the FG disks. Variational principles are used to obtain the governing equations, and energy principles are used for the analysis method. The solution algorithm is executed by utilizing MATLAB® computational simulation software. For various combinations of rotational speed and thermal load up to the limit elastic state as predicted by von Mises criteria, the dynamic characteristics of the FG disk are presented in a non-dimensional plane. Some parametric studies are carried out to explore the impacts of the disk geometries and material gradients on the in-plane natural and forced frequencies of the FG disks.

Priyambada Nayak, Kashinath Saha

Stationary and Rotating Frame Instrumentation for Large Scale Rotating Rig

The Large Scale Rotating Rig at NAL is designed to carry out detailed experimental investigations of the flow through compressor and turbine stages. Instrumentation and data acquisition system (DAS) for stationary and rotating frame measurements, pressure distribution measurements across the vane and the blade surface and the flow measurement was developed in-house. This enabled making pressure measurements on the vane surfaces, blade surfaces, platforms and at the vane/blade exit wake flows. There were added challenges in terms of unsteady pressure measurements, transferring of data from rotating frame and condition monitoring of the rig. The DAS is developed using state-of-the-art instruments and is coupled with a GUI data acquisition software developed using LabVIEW to tackle all these challenges. This paper presents elaborated details of the multichannel instrumentation and the DAS.

N. Poornima, R. Senthil Kumaran, Kishor Kumar

Performance of Bolted Joint Modelling Using Master Element

Energy dissipation at the interfaces of the mechanical joints is the primary source of damping in many rotor dynamics structures as well as built-up structures. In the majority of structures, micro- and macro-slips at the interfaces are the mechanisms for energy dissipation. Modelling of the dissipation using detailed finite element (FE) of the joint interfaces is computationally very expensive. Consequently, it places severe restrictions in the application of detailed FE methods to real-life structures for capturing energy dissipation at joints. In the present work, a reduced-order Masing’s model is adopted to model overlapping joint interfaces. The dynamic contact of the overlapping interface is captured using coupled normal and tangential Masing’s contact rate forms in commercial FE software through the user-defined subroutine. Masing’s parameters are established from the detailed FE model of isolated bolt structure. It is found that the reduced-order modelling is well suitable for capturing dissipation energies without the need for the detailed finite element methods.

G. Vamsi Krishna, C. Viswanath, Ashok Kumar Pandey
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