Machine learning-based classification of unbalance and crack faults in a Jeffcott rotor system supported by air foil bearings

Abstract. High speed rotating machines are very useful in several industries and production plants or factories. The rotating components in these machines are usually prone to multiple types of faults. These faults can cause large and heavy amount of vibrations in the assembled rotor systems during its operation. So, there is a need for analyzing the rotor behavior in the presence of faults and their identification. This paper discusses the dynamic behavior of a rigid rotor with two discs at offset positions and mounted on air foil bearings at the ends. In this system, it is assumed that the discrete unbalance fault is present at discs only. The stiffness and damping coefficients of both foil bearings are considered to be different and anisotropic in nature. Considering the forces due to foil bearings, inertia force, discs unbalance force, inertia moment, gyroscopic couple effect, the equations of motion of the rotor system have been derived in the two-dimensional transverse directions. Further, these equations are solved using a model developed in the Simulink platform. The obtained solutions of the equations are the time domain rotor displacement in the vertical and horizontal directions. It would be very interesting to investigate and study the unbalance fault effect and displacement responses with variation in the fault parameters, rotor spin speed, and stiffness and damping parameters of foil bearings.

This paper presents a design approach of air foil bearings (AFBs) for a 120 kWe gas turbine generator, which is a single spool configuration with gas generator turbine and alternator rotor connected by a diaphragm coupling. A total of four radial AFBs support the two rotors, and one set of double acting thrust foil bearing is located inside the gas generator turbine. The rotor configuration results in eight degree of freedom (DOF) rotordynamic motions, which are two cylindrical modes and two conical modes from the two rotors. Stiffness of bump foils of candidate AFB was estimated from measured structural stiffness of the bearing, and implemented to the computational model for linear stiffness and damping coefficients of the bearing and frequency-domain modal impedances for cylindrical and conical modes. Stiffness of the diaphragm coupling was evaluated using finite element analysis and implemented to nonlinear rotordynamic analyses of the entire engine. Analyses show the conical mode of the turbine rotor is the main source of instability of the entire engine when AFB clearance is not selected properly. Optimum AFB clearance is suggested from frequency domain modal analyses and nonlinear transient analyses.

Air foil bearings are very attractive bearing systems for turbomachinery because they have several advantages over conventional bearings in terms of oil-free environment, low power loss, long life, and no maintenance. However, most of the developed machines using air foil bearings are limited to small and high-speed rotors of 60,000–120,000 rpm, since the increase in power of turbomachinery requires lower rotor speed and greater loading in bearings, which makes it difficult to use air foil bearings for large machines. In this paper, a 75 kW turboblower using air foil bearings is introduced, and the vibration characteristics of the machine have been investigated experimentally under a wide range of operating conditions, including compressor surge in the performance test. The machine is designed to be fully air lubricated and air cooled, and its operating speed is 20,000–26,000 rpm with maximum pressure ratio of 1.8. The results show that the air foil bearings offer adequate damping to ensure dynamically stable operation in the whole range.

This paper presents design approach of air foil bearings (AFBs) for 120kWe gas turbine generator, which is a single spool configuration with gas generator turbine and alternator rotor connected by a diaphragm coupling. Total four radial AFBs support the two rotors, and one set of double acting thrust foil bearing is located inside the gas generator turbine. The rotor configuration results in eight degree of freedom (DOF) rotordynamic motions, which are two cylindrical modes and two conical modes from the two rotors. Stiffness of bump foils of candidate AFB was estimated from measured structural stiffness of the bearing, and implemented to computational model for linear stiffness and damping coefficients of the bearing and frequency-domain modal impedances for cylindrical and conical modes. Stiffness of the diaphragm coupling was evaluated using finite element analysis and implemented to non-linear rotordynamic analyses of entire engine. Analyses show conical mode of turbine rotor is the main source of instability of entire engine when AFB clearance is not selected properly. Optimum AFB clearance is suggested from frequency domain modal analyses and nonlinear transient analyses.

An investigation was conducted on the suppression of subsynchronous vibrations due to aerodynamic response to surge in a two-stage centrifugal compressor with air foil bearings. Unsteady aerodynamic response to surge caused excessive subsynchronous shaft vibration which might result in reduced bearing life. Notably, subsynchronous vibrations associated with rigid mode frequencies were more severe than any other subsynchronous vibrations. The objective was to develop rotordynamic stability near the surge line in a two-stage compressor by the modification of bearings into high damping foil bearings. Viscoelastic foil bearings, which consist of a viscoelastic top foil supported by a series of bump foils, were adapted to replace bump type foil bearings in a two-stage compressor. Investigations were made in the form of a compressor operating test near the surge line with the conventional bump foil bearing and the viscoelastic foil bearing respectively. Testy results showed the effectiveness of the viscoelastic foil bearing for suppressing the subsynchronous vibrations, including subsynchronous vibrations associated with rigid mode frequencies of the shaft. Thus, rotordynamic stability was improved with a viscoelastic foil bearing, which has enhanced damping characteristics near the surge line. Scheduled for Presentation at the 58th Annual Meeting in New York City April 28–May 1, 2003

This article explores use of foil air bearings in land-based turbomachinery. A machine with foil air bearings is more reliable than one with rolling element bearings because it requires fewer parts to support the rotative assembly and needs no lubrication. Foil air bearings can handle severe environmental conditions such as the ingestion of sand and dust. A reversed pilot design at the cooling flow inlet prevents large particles from entering the bearing's flow path, and smaller particles are continually flushed out of the bearing by the cooling flow. Many applications of foil air/gas bearings other than air cycle machines have been built and successfully tested, but nothing appears to be currently in production. Foil bearings have strong potential in several applications. Among these are small general aviation gas turbine engines; oil-free cryogenic turboexpanders for gas separation plants; auxiliary power units for various aerospace and ground vehicles; and, taking advantage of automated manufacturing methods, automotive gas turbine engines, vapor-cycle centrifugal compressors, and commercial air/gas compressors.

The rotordynamic characteristics of a micro power system supported by air foil bearings were investigated. Stability analysis was performed by a finite element method with the predicted dynamic coefficients of the foil bearings. A preliminary test rig was developed to simulate the operating characteristics of the micro power system. It consisted of a rotor supported by two air foil journal bearings and two air foil thrust bearings, and an impulse driven turbine. The foil journal bearings had a diameter of 7 mm and a length of 7 mm (L/D = 1). The test rig was operated stably under various situations and speeded up to 300 000 rpm. The main portion of the rotor response was synchronous and the amplitude of synchronous vibration was about 5–20 µm. Further, theoretical and experimental results for the unbalance response were compared. From this study, we showed the possibility of stable performance for the micro power system supported by air foil bearings.

This work gives a theoretical contribution to the problem of modelling air foil bearings considering large sagging effects in the calculation of the non-linear transient and steady state response of a rigid rotor. This paper consists of two parts: the development of a miltiphysics model of the air foil bearing, and a numerical parameter study of a rigid journal supported in an air foil bearing with a partially supported top foil. The mathematical model of the air foil bearing is centred around the finite element models of both the air film and the top foil structure. These finite element models utilise two types of eight-node isoparametric elements. The rotor is modelled as a rigid body without rotational inertia, i.e. as a journal. The bump foil is included via a bilinear version of the simple elastic foundation model. This paper introduces the bilinear simple elastic foundation model, which combined with the top foil structure model, enables a separation of the top foil and the bump foil. A phenomenon associated within areas of the top foil is where the aerodynamic pressure is sub-ambient. The parameter study investigates the performance of three air foil bearings with partially supported top foils and one air foil bearing with a fully supported top foil. The steady state responses of a journal supported by these air foil bearings are investigated for varied rotational speeds and journal unbalances as well as the top foil sagging in the unsupported area. The study reveals that sub-harmonic vibrations associated with a large journal unbalance can be eliminated by a proper design layout of the bump foil, i.e. placement of the unsupported area. The positive effect is attributed to ‘equivalent shallow pockets’ formed by the sagging top foil.

Air foil bearings (AFBs) are a vital element of high-speed rotating equipment because they transfer energy efficiently and without causing friction. Because tribological assessment requires accurate mathematics and there are many parameters that interact intricately, optimising AFBs is a difficult task. Current optimisation techniques fail to strike a proper equilibrium between exploration and utilization, particularly when dealing with the complex tribological dynamics found in AFBs. In order to achieve mathematical exactness, this research employs a novel optimisation technique called Boosted Chameleon Swarm Optimisation (BCSO) for the complex domain of the AFBs. The suggested BCSO technique improves the exploration-exploitation equilibrium present in conventional swarm optimisation by incorporating the adaptable and self-organizing properties derived from chameleon behaviour. By means of exacting mathematical simulations and finely tuned tribological examination, this research endeavours to maximise AFB effectiveness throughout a range of operational scenarios. Specifically designed to tackle the complex tribological problems that arise in AFBs, the BCSO technique seeks to maximise load-carrying ability, minimise friction and improve entire performance.

This paper presents a theoretical model for the analysis of double-bumped Air Foil Bearings (AFBs). The stiffness and damping coefficients of the double bump vary depending on the external load and its friction coefficient. The double bump can be either in the single or double active region depending on vertical deflection. The equivalent stiffness and damping coefficients of the bump system are derived from the vertical and horizontal deflection of the bump, including the friction effect. The results of the performance analysis for a double bumped AFB are compared with those obtained for a single bumped AFB. This paper successfully proves that a double bumped AFB has higher load capacity, stiffness, and damping than a single bump AFB in a heavily loaded condition.

Foil air bearing load capacity tests were conducted to investigate if a solid lubricant coating applied to the surface of the bearing's top foil can function as a break-in coating. Two foil coating materials, a conventional soft polymer film (polyimide) and a hard ceramic (alumina), were independently evaluated against as-ground and worn (run-in) journals coated with NASA PS304, a high-temperature solid lubricant composite coating. The foil coatings were evaluated at journal rotational speeds of 30,000 rpm and at 25 °C. Tests were also performed on a foil bearing with a bare (uncoated) nickel-based superalloy top foil to establish a baseline for comparison. The test results indicate that the presence of a top foil solid lubricant coating is effective at increasing the load capacity performance of the foil bearing. Compared to the uncoated baseline, the addition of the soft polymer coating on the top foil increased the bearing load coefficient by 120 percent when operating against an as-ground journal surface and 85% against a run-in journal surface. The alumina coating increased the load coefficient by 40 percent against the as-ground journal but did not have any effect when the bearing was operated with the run-in journal. The results suggest that the addition of solid lubricant films provide added lubrication when the air film is marginal, indicating that as the load capacity is approached foil air bearings transition from hydrodynamic to mixed and boundary lubrication. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

Aerodynamic foil bearings are used in various industrial applications, e.g. in cooling turbines, small gas turbines or exhaust gas turbochargers, to support light, high-speed rotors under extreme operating conditions. Air (or another gas) is used as a lubricant in these bearings. In addition, the possible thermal deformations and production errors can be compensated by a flexible foil structure between the lubricant film and the bearing housing in air foil bearings. Since many static and dynamic properties of the lubricant are strongly dependent on the inner contour of the bearing, the idea of an adaptive air foil bearing (AAFB) is developed to optimize the performance of the bearing at different operating points. This paper focuses on a semi-analytical approach based on plate theory and the Ritz method for approximating the static shape control of a piezoelectrically actuatable AAFB. The main objective of this study is to consider adaptive bearing shells in calculating the behavior of an AAFB, as they provide additional degrees of freedom to a passive air foil bearing without adaptivity. Before the final step is taken, the model presented in this analysis is used for the shape optimization of the adaptive frame of AAFB in order to achieve the most efficient shape adaption with regard to target shapes.

Vibration characteristics control of hybrid radial gas foil bearing-rotor system: Simulation and experiment

PS304 self-lubricating composite coatings were successfully deposited on steel substrates at various plasma spray facilities using mixtures blended from commercially obtained constituent particles. Coatings were evaluated in thrust-washer tests against Inconel X-750 at low contact pressures to 40kPa, sliding speed of 5Amis, and either ambient temperature or 500 °C chosen to simulate conditions in airfoil bearings during startup and shutdown contact. Wear factors for all PS304 coatings tested, regardless of contact pressure and temperature, ranged from 1–3*10−4 mm3/Nm while coefficients of friction of approximately μ =0.5 were measured in all cases. While wear and friction behavior of PS304 in air foil bearings appear to have been simulated, surface roughening was observed in these thrust-washer tests which used continuous sliding contact, as opposed to the evolution of smoother surfaces observed in high-temperature foil bearings experiencing cyclic startup/shutdown. Wear-induced surface smoothening of PS304 was additionally simulated in thrust-washer tests with sliding contact instead imposed intermittently.

The present paper analyses the vibrational behaviour of an unbalanced and cracked Jeffcott rotor supported by foil bearings. Foil bearings have numerous advantages over rolling element bearings due to their significant operational limitations as well as suitable for only lower speed mechanical and other applications. Incorporating the equivalent stiffness concept of shaft and foil bearing and considering the forces due to inertia, unbalance and crack faults, the dynamic equations for the vibration of an unbalanced Jeffcott rotor with a crack nearby disc at the middle mounted on foil bearings have been derived. The mechanism of a switching crack has been utilized to analyse the crack fault effect which manifests multiple harmonics in the vibrational nature of the system. The displacement responses in transverse directions have been obtained using the Simulink block diagram. Full spectrum data analysis has also been performed to transform the time domain response into the frequency domain, which gives rise to both the forward and backward rotor whirls. The main emphasis of this paper would be to exhibit the interplay between unbalance and crack faults in a Jeffcott rotor system supported by foil bearings.KeywordsVibrationFoil bearingUnbalanceSwitching crack