Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances

The behaviour of rolling element bearings is of major importance to the vast majority of rotating machines. Due to the varying assembly compliance and the internal clearance existing in the bearing in most cases, a highly non-linear behaviour of the rotor bearing system appears. Thus, a dynamic model of a horizontal rotor supported on ball bearings with radial internal clearance is considered, taking into account contact forces between the balls and the races, as well as the effect of varying compliance and of the internal radial clearance. However, since rotational speed fluctuations of various levels practically appear in all rotating equipment, their effect is now additionally considered. Their effect is examined in two characteristic rotor bearing cases. The analysis includes all the characteristic states of the dynamic behaviour of the rotor, such as periodic, unstable periodic and chaotic responses, using methods like frequency spectra, phase spaces, higher-order Poincare maps and Lyapunov exponents. All results presented show a dominant stabilization effect of the speed fluctuations with respect to the system behaviour. From the analysis performed, it is concluded that even a minimum fluctuation of the rotor speed may result in major changes of the system dynamics, indicating that speed fluctuations of the rotor are a governing parameter for the dynamic behaviour of the system.     

A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings

A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings is presented in this paper. Detection of both localized and distributed categories of defect has been considered. An explanation for the vibration and noise generation in bearings is given. Vibration measurement in both time and frequency domains along with signal processing techniques such as the high-frequency resonance technique have been covered. Other acoustic measurement techniques such as sound pressure, sound intensity and acoustic emission have been reviewed. Recent trends in research on the detection of defects in bearings, such as the wavelet transform method and automated data processing, have also been included.     

Externally pressurized gas bearings: A comparison between two supply holes configurations

Radial vibration of a vertical rotor with externally pressurized gas bearings is analyzed. The time-dependent Reynolds equation is solved together with the journal equation of motion to obtain the response characteristics of the bearing system. The bearings are supplied with either one or two sets of supply orifices. Stiffness and flow rate are compared for both cases. Stability maps are obtained at different supply pressures and with different supply orifice diameters. The mass range from orbital stability to instability is studied as a function of supply hole downstream pressure level.     

Application of acoustic emission technique for the detection of defects in rolling element bearings

The usefulness of acoustic emission (AE) measurements for the detection of defects in roller bearings has been investigated in the present study. Defects were simulated in the roller and inner race of the bearings by the spark erosion method. AE of bearings without defect and with defects of different sizes has been measured. For small defect sizes, ringdown counts of AE signal has been found to be a very good parameter for the detection of defects both in the inner race and roller of the bearings tested. However, the counts stopped increasing after a certain defect size. Distributions of events by ringdown counts and peak amplitudes are also found to be good indicators of bearing defect detection. With a defect on a bearing element, the distributions of events tend to be over a wider range of peak amplitudes and counts.     

On the performance of dynamically loaded journal bearings lubricated with couple stress fluids

A numerical study of the performance for a dynamically loaded journal bearing lubricated with couple stress fluids is undertaken. First of all, on the basis of micro-continuum theory, the generalized Reynolds equation for dynamic loads is derived. Then it is simultaneously solved with the force balance equation of the journal, thus obtaining the transient oil film pressure, the transient position and velocity of the journal center. Results from this analysis are presented for a typical engine crankshaft bearing. It is shown, compared with Newtonian lubricants, that under a dynamic loading lubricants with couple stress yield an obvious increase in oil film pressure and oil film thickness, but a decrease in the side leakage flow. Moreover, the effects of couple stress on friction force and friction coefficient vary considerably with time.     

Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force

In this paper, a method based on the finite element vibration analysis is presented for defect detection in rolling element bearings with single or multiple defects on different components of the bearing structure using the time and frequency domain parameters. A dynamic loading model is proposed in order to create the nodal excitation functions used in the finite element vibration analysis as external loading. A computer code written in Visual Basic programming language with a graphical user interface is developed to create the nodal excitations for different cases including the outer ring, inner ring or rolling element defects. Forced vibration analysis of a bearing structure is performed using the commercial finite element package I-DEAS under the action of an unbalanced force transferred to the structure via a ball bearing. Time and frequency domain parameters such as rms, crest factor, kurtosis and band energy ratio for the frequency spectrum of the enveloped signals are used to analyse the effect of the defect location and the number of defects on the time and frequency domain parameters. The role of the receiving point for vibration measurements is also investigated. The vibration data for various defect cases including the housing structure effect can be obtained using the finite element vibration analysis in order to develop an optimum monitoring method in condition monitoring studies.     

A study of friction in worn misaligned journal bearings under severe hydrodynamic lubrication

Friction occurs in all mechanical systems such as transmissions, valves, piston rings, bearings, machines, etc. It is well known that in journal bearings, friction occurs in all lubrication regimes. However, shaft misalignment in rotating systems is one of the most common causes of wear. In this work, the bearing is assumed to operate in the hydrodynamic region, at high eccentricities, wear depths, and angular misalignment. As a result, the minimum film thickness is 5–10 times the surface finish, i.e., near the lower limit of the hydrodynamic lubrication when taking into account that in the latest technology CNC machines the bearing surface finish could be less than 1–2 μm.An analytical model is developed in order to find the relationship among the friction force, the misalignment angles, and wear depth. The Reynolds equation is solved numerically; the friction force is calculated in the equilibrium position. The friction coefficient is presented versus the misalignment angles and wear depths for different Sommerfeld numbers, thus creating friction functions dependent on misalignment and wear of the bearing. The variation in power loss of the rotor bearing system is also investigated and presented as a function of wear depth and misalignment angles.     

A comparative study of the thermal behaviour of profile bore bearings

This paper describes principally a theoretical analysis of the thermal behaviour of offset half, orthogonally displaced, three-lobe and four-lobe bearing geometries. The thermal analysis illustrates the implication of type selection with regard to the parameters of load-carrying ability, power loss, lubricant requirements and operating temperatures. The comparisons show that for all profiles considered, they have inferior load-carrying ability when compared with the cylindrical geometry along with significantly larger lubricant supply requirements. Thermal effects in profile bore bearings are less extreme than those encountered in the cylindrical profile.     

Vibration response of spalled rolling element bearings: Observations, simulations and signal processing techniques to track the spall size

Fatigue in rolling element bearings, resulting in spalling of the races and/or rolling elements, is the most common cause of bearing failure. The useful life of the bearing may extend considerably beyond the appearance of the first spall and a premature removal of the bearing from service can be very expensive, but on the other hand chances cannot be taken with safety of machines or personnel. Previous studies indicated that there might be two parts to the defect vibration signal of a spalled bearing, the first part being originating from the entry of the rolling element into the fault (de-stress) and the second part being due to the departure of the rolling element from the fault (re-stress). This is investigated in this paper using vibration signatures of seeded faults at different speeds. The acceleration signals resulting from the entry of the rolling element into the spall and exit from it were found to be of different natures. The entry into the fault can be described as a step response, with mainly low frequency content, while the impact excites a much broader frequency impulse response. The latter is the most noticeable and prominent event, especially when examining the high pass filtered response or the enveloped signal. In order to enable a clear separation of the two events, and produce an averaged estimate of the size of the fault, two approaches are proposed to enhance the entry event while keeping the impulse response. The first approach (joint treatment) utilizes pre-whitening to balance the low and high frequency energy, then octave band wavelet analysis to allow selection of the best band (or scale) to balance the two pulses with similar frequency content. In the second approach, a separate treatment is applied to the step and the impulse responses, so that they can be equally represented in the signal. Cepstrum analysis can be used to give an average estimate of the spacing between the entry and impact events, but the latter can also be assessed by an arithmetic estimation of the mean and standard deviation of the event separation for a number of realizations, in particular for the second approach. In order to determine the effects of various simulations and signal processing parameters on the estimated delay times, the entry and exit events were simulated as modified step and impulse responses with precisely known starting times. The simulation was also found useful in pointing to artefacts associated with the cepstrum calculation, which affect even the simulated signals, and have thus prompted modifications of the processing of real signals. The results presented for the two approaches give a reasonable approximation of the measured fault widths (double the spacing between the entry and impact events) under different speed conditions, but the method of separate treatment is somewhat better and is thus recommended.     

Gearbox power loss. Part I: Losses in rolling bearings

This work is devoted to the analysis, modeling and validation of gearbox power loss, considering the influence of the gears, rolling bearings and seals, the influence of the operating conditions, lubricant formulation and the lubrication method.The first part of this work a rolling bearing torque loss model is calibrated for several wind turbine gear oils and for ball and roller contacts. The results achieved clarify the importance of a rolling bearing in a gearbox power loss.In the second part of this work will be presented the same approach for gears. The final part will converge in the application of findings in two full gearboxes, a planetary and a parallel axis gearbox, both in multiplying configuration.     

On the design and development of hybrid journal bearings: a review

This paper presents a comprehensive review of developments in the design and application of hydrostatic and hybrid journal bearing systems during the last few decades. Revolutionary changes have taken place in the applications of hydrostatic and hybrid journal bearings, from very low‐speed radar to very high‐speed turbo‐machinery and ultra‐precision machine tools requiring high stiffness to improve accuracy. Hydrostatic and hybrid bearings are of interest because of their potential at very high operating speed and heavy load‐carrying capacity. This paper also outlines the analyses done of these types of journal bearings in practical application, which has led to improved bearing design. This review critically discusses the parameters that significantly affect the static and dynamic performance of a journal bearing. This review includes coverage of recent publications in the literature pertaining to hydrostatic and hybrid journal bearings focusing on the influence of parameters such as bearing geometry, supply pressure, flow control devices, fluid compressibility, fluid inertia, journal misalignment, bearing flexibility, surface roughness, and thermal effects. Copyright © 2006 John Wiley & Sons, Ltd.     

A novel approach integrating dimensional analysis and neural networks for the detection of localized faults in roller bearings

The detection of the defective/worn out bearing components used in rotating machines is one of the main concerns in various applications. To improve the computational efficiency in the nonlinear dynamic analysis for the rolling contact bearings, a new methodology based on dimensional analysis (DA) theory is proposed in this paper. The developed model is used to predict the vibration responses due to artificially spalled bearing components to quantify the level of structural damages into these components. The use of a back propagation neural network (BPNN) has been made that also predicted responses from the network trained by developed algorithm using the experimental data obtained from the defective bearing components on the developed test rig. A comparison between the responses predicted by proposed DA method and the BPNN showed a fair amount of the agreement between the two approaches and validated the proposed model and proved outstanding tool for identification of spalled/damaged bearing components.     

A computational algorithm for cavitating bearings: Requirement of boundary conditions which satisfy the principle of mass conservation

Many boundary conditions for solving lubrication problems can be found in the literature, among them the Swift-Stieber condition (film-breakdown), which is most frequently used by lubrication engineers, and the Jakobsson-Floberg condition (film-reformation), which is often not used because of the computing complexity involved. Most of these conditions, including the former, do not take proper account of mass conservation within the cavitated region and give rise to erroneous flow-rate predictions. Therefore, there is a need to develop a computational algorithm that does not violate the principle of mass conservation (like the Jakobsson-Floberg boundary condition) and yet is capable of being easily and economically accomodated into an existing bearing-program. This paper presents such a technique, and one which is generally applicable to a spectrum of liquid-film bearings, such as hydrodynamic, hydrostatic or hybrid bearings. The analysis demonstrates the importance of preserving mass conservation throughout the bearing fluid-film, especially for bearings operating at high speeds and low feed pressure-ratios. Furthermore, the necessity of a global check of the continuity requirement

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is demonstrated.     

A study of the lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing (T1516)

The lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing is studied. On the basis of the theory of micropolar fluids, the modified Reynolds equation for dynamic loads is derived. Results from the numerical analysis indicated that the effects of micropolar fluids on the performance of a dynamically loaded journal bearing depend on the size of material characteristic length and the coupling number. It is shown, compared with Newtonian lubricants, that under a dynamic loading the micropolar lubricants produce an obvious increase in the oil film pressure and oil film thickness, but a decrease in the side leakage flow. It is also shown that the friction coefficient for a dynamically loaded journal bearing with micropolar fluids is in general higher than that of Newtonian fluids, which is not the same as the results for a steadily loaded journal bearing. Furthermore, a parametric study of flow and friction for different mass parameters keeping micropolar parameters fixed is undertaken. It is indicated that, with the increase of the mass parameters, the crank angles corresponding to the maximum flow are changed and the maximum friction coefficients are obviously decreased either for the Newtonian fluids or for the micropolar fluids.     

Rolling-element bearings in China: From ancient times to the 20th century

The development of rolling-element bearings in China has spanned a long period. Based on several typical and important cases, the present article reconstructs the history of rolling-element bearings in China by dividing it into four stages according to the various characteristics of the bearings. The first stage represents the origin of rolling bearings in China, which remains controversial because of several suspected races and cages that were likely the components of bearings more than a millennium ago. At the second stage, a type of simple roller bearing was used for astronomical instruments not later than the 13th century based on clear philological and physical evidence. A similar bearing was also applied to an abridged armillary in the 17th century. Another type of spherical thrust bearings with rolling elements, which is a key component of a traditional Chinese windmill, could support a rotating shaft that moves rotationally and at an angle. At the third stage, the Chinese began studying and using the so-called Europeanstyle bearing since the 17th century. Moreover, over the last 100 years, the modern rolling bearing industry was gradually established in China, particularly because of the technology transfer from the Soviet Union in the 1950s. At the fourth stage, the Chinese government initiated the relatively rapid development of bearing technology. The government launched the “bearing movement” from the 1950s to the 1960s to establish the modern bearing industry and to promote rolling bearings as replacement for traditional sliding bearings. Furthermore, a number of large professional factories and institutions in China have continually introduced advanced technology and equipment. At present, these companies and institutions play a significant role in the international bearing industry.     

Simulating gear and bearing interactions in the presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults

This paper presents a simulation model for a gearbox test rig, in which a range of bearing faults can be implemented. Bearing faults sometimes manifest themselves by their interaction with meshing gears, and to simulate this it is necessary to model a whole system of gears and shafts supported in bearings. This has now been done for an experimental test rig through the incorporation of a time-varying, non-linear stiffness bearing model into a previously developed gear model. The incorporated bearing model is based on Hertzian contact theory, which relates the raceway displacement to the bearing load, and also accounts for the slippage between the elements. It has the capacity to model localised spalls (inner race, outer race and rolling elements), which are discussed in this part of the paper and extended inner and outer race faults (rough surfaces), which are discussed in part II. Even though the whole gearbox has not been modelled in detail, the non-linear time-varying gear-meshing operation is modelled in some detail. Both simulated and experimental localised fault signals (acceleration signals) were subjected to the same diagnostic techniques; namely spectrum comparisons, Spectral Kurtosis (SK) analysis and envelope analysis. The processed simulated signals showed a similar pattern to that observed in their measured counterparts and were found to have a characteristic, referred to in the literature as double pulses, corresponding to entry into and exit from the localised fault. The simulation model will be useful for producing typical fault signals from gearboxes to test new diagnostic algorithms, and possibly prognostic algorithms.     

On the prediction of the design criteria for modification of contact stresses due to thermal stresses in the gear mesh

The mechanism of surface failure due to temperature rise is a very important problem in gear design. Thermal considerations have received considerable attention from the gear researchers but only for scoring failures when the destruction of lubrication film occurs as a result of temperature rise. In spite of the wealth of literature on this subject, this problem is not fully analyzed.The objectives of this paper are to consider the mechanisms of thermal stresses and the thermal cycling in contact zone, during the gear mesh. This research has been conducted for the first point of contact based on consideration of transient heat transfer, elastohydrodynamic lubrications, and surface roughness and gear material.A procedure presented in this paper evaluating the stresses (thermal and mechanical) and predicting the design criteria for modifying the contact stresses due to thermal stresses. The effect of the material, oil film thickness, surface roughness and geometric operating parameters on modification parameter is illustrated. Also the effects of a load on the temperature rise and the modification parameters are evaluated.     

Simulating gear and bearing interactions in the presence of faults: Part II: Simulation of the vibrations produced by extended bearing faults

This paper presents a combined dynamic model for gears and bearings, in which an extended fault in the inner/outer race of rolling element bearings can be studied in the presence of gear interaction. A combined gear/bearing model has been made to obtain a better understanding of the interaction of the two components. The essentials of the gear/bearing model and the results of simulating the vibration of localized faults in rolling element bearings in a gearbox environment have been discussed and illustrated in the first part of this paper (part I). The simulation model has now been modified to model extended faults of the type that do not necessarily produce high frequency impact responses, but do modulate the gearmesh signals. The paper compares the simulated and actual signals from the gear/bearing test rig for inner and outer race extended faults, and in particular demonstrates that they react similarly to existing diagnostic techniques.     

Progress in terahertz nondestructive testing: A review

Terahertz (THz) waves, whose frequencies range between microwave and infrared, are part of the electromagnetic spectrum. A gap exists in THz literature because investigating THz waves is difficult due to the weak characteristics of the waves and the lack of suitable THz sources and detectors. Recently, THz nondestructive testing (NDT) technology has become an interesting topic. This review outlines several typical THz devices and systems and engineering applications of THz NDT techniques in composite materials, thermal barrier coatings, car paint films, marine protective coatings, and pharmaceutical tablet coatings. THz imaging has higher resolution but lower penetration than ultrasound imaging. This review presents the significance and advantages provided by the emerging THz NDT technique.     

切削加工表面残余应力的理论预测

对零件已加工表面的形成过程进行分析，提出表面分离法的分析模型；自行研制了求解在移动载荷作用下的二维热弹塑性力学问题的有限计算软件－ＭＴＰｌａｓｔ；对切削的已加工表面残余应力进行理论预测，并与试验结果相比较，探讨残余应力的形成机理，为控制已加工表面的残余应力提供了理论依据。