Optimal Design of Tapered Roller Bearings Based on Multi⁃Physics Objectives Using Evolutionary Algorithms

Rolling element bearing is the most common machine element in rotating machinery.An extended life is among the foremost imperative standards in the optimal design of rolling element bearings,which confide on the fatigue failure,wear,and thermal conditions of bearings.To fill the gap,in the current work,all three objectives of a tapered roller bearing have been innovatively considered respectively,which are the dynamic capacity,elasto-hydrodynamic lubrication(EHL)minimum film⁃thickness,and maximum bearing temperature.These objective function formulations are presented,associated design variables are identified,and constraints are discussed.To solve complex non⁃linear constrained optimization formulations,a best⁃practice design procedure was investigated using the Artificial Bee Colony(ABC)algorithms.A sensitivity analysis of several geometric design variables was conducted to observe the difference in all three objectives.An excellent enhancement was found in the bearing designs that have been optimized as compared with bearing standards and previously published works.The present study will definitely add to the present experience based design followed in bearing industries to save time and obtain assessment of bearing performance before manufacturing.To verify the improvement,an experimental investigation is worthwhile conducting.

Elastohydrodynamic Lubrication Studies on Effects of Crowning Value in Roller Bearings

The purpose of this paper is to present a comparison of numerical calculations and experiment results of optical interferometry in finite line contact for the elastohydrodynamic lubrication(EHL) problem of Lundberg's profiled cylindrical roller under the conditions of flooded state, moderate load and material parameter. It shows clearly the effects of crowning value on the variations of oil film shape and thickness. The agreement between numerical analysis and experiment results is very good. The results indicate there must be an optimum crowning value that will induce the thickest and most even oil film in EHL state for a given working condition, and this value is larger than the design value in dry contact state for the same working conditions.

A Method for Incipient Fault Diagnosis of Roller Bearings Based on the Wavelet Transform Correlation Filter and Hilbert Transform

Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.

FAULT DIAGNOSIS APPROACH FOR ROLLER BEARINGS BASED ON EMPIRICAL MODE DECOMPOSITION METHOD AND HILBERT TRANSFORM

Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.

Temperature Distribution and Scuffing of Tapered Roller Bearing

In the field of aerospace, high-speed trains and automobile, etc, analysis of temperature filed and scuffing failure of tapered roller bearings are more important than ever, and the scuffing failure of elements of such rolling bearings under heavy load and high speed still cannot be effectively predicted yet. A simplified model of tapered roller bearings consisted of one inner raceway, one outer raceway and a tapered roller was established, in which the interaction of several heat sources is ignored. The contact mechanics model, temperature model and model of scuffing failure are synthesized, and the corresponding computer programs are developed to analyze the effects of bearings parameters, different material and operational conditions on thermal performance of bearings, and temperature distribution and the possibility of surface scuffing are obtained. The results show that load, speed, thermal conductivity and tapered roller materials influence temperature rise and scuffing failure of bearings. Ceramic material of tapered roller results in the decrease of scuffing possibility of bearings to a high extent than the conventional rolling bearing steel. Compared with bulk temperature, flash temperature on the surfaces of bearing elements has a little influence on maximum temperature rise of bearing elements. For the rolling bearings operated under high speed and heavy load, this paper proposes a method which can accurately calculate the possibility of scuffing failure of rolling bearings.

Running Temperature and Mechanical Stability of Grease as Maintenance Parameters of Railway Bearings

Spherical roller bearings in railway car wheels are critical components whose failure may have catastrophic consequences. The present study aims to analyse the mechanical stability of greases and temperature of bearings as indicators for condition-based bearing maintenance. The performed case study includes nine fully-formulated commercial greases examined in the wheel bearings of five ore cars operated in northern Scandinavia. The studied ore cars travelled a distance of about 300 000 km during a period of three years. Small samples of the greases were taken on eight occasions to test their mechanical stability. In addition, the temperatures of the bearings were continuously recorded. After the test period, the wear, electrical damage, and corrosion of the bearings were examined. One of the findings is that the shear stress of the grease at a certain shear velocity （the certain yieldstress （CEY） value） is a good maintenance indicator and is highly dependent on the grease type. The bearing＇s wear, electrical damage and corrosion also depend on the grease type. However, no oxidation of the greases was identified. The paper also outlines a systematic methodology to determine an overall maintenance indicator for railway roller bearings which is based on the field measurements.

THE 3-D BOUNDARY ELEMENT METHOD OF ROLLER BEARING BY PLATE ELEMENT ANALOGUE

The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM without friction, and using the structuralcharacteristics of roller bearings, middle rolls are de- scribed byelastic plate units of different shapes, which is placed on theinternal ring.

A research on the contact stress of roller bearing based on crowning analysis

According to elastic contact theory, contact model between roller and race is established. Compared with the Hertz results, the results are proved, based on which contact stress distribution of different crowning and initial contact length is given, then the appropriate value is derived. On the basis, inertia force and different radial force is given into consideration. Via analysis, it con- cludes that under balanced pure radial load condition the largest contact stress between roller and race increases along with crowning value increasing. With the same crowning value, the largest contact stress between roller and race decreases in the first and increases at the end along with initial contact length increasing. Contact stress between roller and outer race increases along with revolution speed increasing.

Profiled Cylindrical Roller Design in Consideration of Grinding Undercut Effect

In this paper, the effect of the grinding undercut of the raceways on the longitudinal pressure distribution of the profiled rollers, which are the most popular axial profile employed by the bearing manufacturers, was discussed. Based on the profiled roller geometrical equations and numerical calculation of three dimensional elastic contact problems of finite length, a new numerical method for calculating the crown drop evaluation considering the effect of grinding undercut was used. The analyses of two structure case, that roller length is greater or less than raceway width, were carried out and compared with each other. The Results show that the width of grinding undercut must be considered in determining the crown drop of rollers.

Condition Monitoring of Roller Bearing by K-star Classifier andK-nearest Neighborhood Classifier Using Sound Signal

Most of the machineries in small or large-scale industry have rotating elementsupported by bearings for rigid support and accurate movement. For proper functioning ofmachinery, condition monitoring of the bearing is very important. In present study soundsignal is used to continuously monitor bearing health as sound signals of rotatingmachineries carry dynamic information of components. There are numerous studies inliterature that are reporting superiority of vibration signal of bearing fault diagnosis.However, there are very few studies done using sound signal. The cost associated withcondition monitoring using sound signal (Microphone) is less than the cost of transducerused to acquire vibration signal (Accelerometer). This paper employs sound signal forcondition monitoring of roller bearing by K-star classifier and k-nearest neighborhoodclassifier. The statistical feature extraction is performed from acquired sound signals. Thentwo-layer feature selection is done using J48 decision tree algorithm and random treealgorithm. These selected features were classified using K-star classifier and k-nearestneighborhood classifier and parametric optimization is performed to achieve the maximumclassification accuracy. The classification results for both K-star classifier and k-nearestneighborhood classifier for condition monitoring of roller bearing using sound signals werecompared.

Robust Optimization Method of Cylindrical Roller Bearing by Maximizing Dynamic Capacity Using Evolutionary Algorithms

Optimization of cylindrical roller bearings(CRBs)has been performed using a robust design.It ensures that the changes in the objective function,even in the case of variations in design variables during manufacturing,have a minimum possible value and do not exceed the upper limit of a desired range of percentage variation.Also,it checks the feasibility of design outcome in presence of manufacturing tolerances in design variables.For any rolling element bearing,a long life indicates a satisfactory performance.In the present study,the dynamic load carrying capacity C,which relates to fatigue life,has been optimized using the robust design.In roller bearings,boundary dimensions(i.e.,bearing outer diameter,bore diameter and width)are standard.Hence,the performance is mainly affected by the internal dimensions and not the bearing boundary dimensions mentioned formerly.In spite of this,besides internal dimensions and their tolerances,the tolerances in boundary dimensions have also been taken into consideration for the robust optimization.The problem has been solved with the elitist non-dominating sorting genetic algorithm(NSGA-II).Finally,for the visualization and to ensure manufacturability of CRB using obtained values,radial dimensions drawing of one of the optimized CRB has been made.To check the robustness of obtained design after optimization,a sensitivity analysis has also been carried out to find out how much the variation in the objective function will be in case of variation in optimized value of design variables.Optimized bearings have been found to have improved life as compared with standard ones.

Post-testing measurement of freely movable and diffusible hydrogen in context of WEC formation at cylindrical roller thrust bearings from 100Cr6

Sub-surface crack networks in areas of altered microstructure are a common cause for bearing failures.Due to its appearance under light microscopy,the damage pattern is referred to as White Etching Cracks(WEC).The root causes leading to the formation of WEC are still under debate.Nevertheless,it has already been shown that atomic hydrogen can have an accelerating effect on the formation and propagation of WEC.In addition to hydrogen pre-charging,hydrogen can be released and absorbed during rolling/sliding due to the decomposing of the lubricant and water.The current work focuses on the analysis of the hydrogen content of cylindrical roller thrust bearings after testing in a FE8 type test rig using two different lubricants.Within the framework of this work,two different hydrogen analysis methods were used and assessed regarding their applicability.The results show that the so-called Hydrogen Collecting Analysis(HCA)is more suitable to investigate the correlation between lubricant chemistry and hydrogen content in the test bearings than the Local Hydrogen Analysis(LHA).The measurements with the HCA show a continuously increasing freely movable and diffusible hydrogen content under tribological conditions,which leads to the formation of WEC.Comparative tests with an oil without hydrogen showed that the tendency of the system to fail as a result of WEC can be reduced by using a lubricant without hydride compounds.

A combined experimental and analytical method to determine the EHL friction force distribution between rollers and outer raceway in a cylindrical roller bearing

Friction force is a crucial factor causing power loss and fatigue spalling of rolling element bearings.A combined experimental and analytical method is proposed to quantitatively determine the elastohydrodynamic lubrication(EHL)friction force distribution between rollers and outer raceway in a cylindrical roller bearing(CRB).An experimental system with the instrumented bearing and housing was developed for measuring radial load distribution and friction torque of bearings.A simplified model of friction force expressed by dimensionless speed,load,and material parameters was given.An inequality constrained optimization problem was established and solved by using an experimental data-driven learning algorithm for determining the uncertain parameters in the model.The effect of speed,load,and lubricant property on friction force and friction coefficient was discussed.

Experimental study on impact of roller imbalance on cage stability

This study presents a method for measuring the imbalance in a small-sized cylindrical roller.The roller imbalance was calibrated on the built static-pressure-air flotation measurement machine.The impact of the roller imbalance on the dynamic characteristics of a cage were then studied on the aero-bearing test rig.The displacement spectrums with different roller imbalance of the obtained cage orbits under various bearing speed and radial load were used to evaluate the cage stability.The results show that the cage cannot form a stable operating state at a lower bearing speed with or without the unbalanced rollers.The cage with balanced rollers gradually develops stable motion with the increase of the bearing speed.The existence of a small roller imbalance causes the stability of the cage to deteriorate.With an increase in the bearing speed and radial load,the cage with the unbalanced rollers runs unsteadily accompanied by a high-frequency vibration when the roller imbalance is large enough.The vibration amplitude of the cage in the horizontal direction is greater than that in the vertical direction during an unstable operation,which is similar in the stable status.

TEHL analysis of high-speed and heavy-load roller bearing with quasi-dynamic characteristics

In this paper, the aero-engine mainshaft roller bearing D1842926 under typical operating conditions is taken as a case study, a new integrated numerical algorithm of quasi-dynamics and thermal elastohydrodynamic lubrication（TEHL） is put forward, which can complete the bearing lubricated analysis from global dynamic performance to local TEHL state and break out of the traditional analysis way carried out independently in their own field.The 3-D film thickness distributions with different cases are given through integrated numerical algorithm, meanwhile the minimum film thickness of quasi-dynamic analysis, integrated numerical algorithm and testing are compared, which show that integrated numerical results have good agreements with the testing data, so the algorithm is demonstrated available and can judge the lubrication state more accurately.The parameter effects of operating and structure on pv value, cage sliding rate, TEHL film pressure, thickness and temperature are researched, which will provide an important theoretical basis for the structure design and optimization of aero-engine mainshaft roller bearing.

Modeling the frictional torque of a dry-lubricated tapered roller bearing considering the roller skewing

In this paper, an equation for the calculation of the frictional torque of a dry-lubricated tapered roller bearing(TRB) is provided in which the effect of the roller skewing is emphasized. Calculations were performed to investigate the effect of the roller skewing on the torque of dry-lubricated TRB for two representative preload methods, that is, axial force preload and axial displacement preload. The results show that a proper roller skewing angle under axial force preload benefits the reduction of the TRB torque. However, the roller skewing angle should not exceed a certain critical value;otherwise, it will cause a steep rise in the TRB torque. Finally, the critical value of the roller skewing angle as a function of the friction coefficient and cage pocket clearance is presented. The developed torque model provides a tool for the internal design and torque optimization of dry-lubricated TRBs.

Mechanical performance analysis of hollow cylindrical roller bearing of cone bit by FEM

Bearings are key components of cone bit,thus its rapid failure is a major cause of leading to lower life of the bit.To improve the bearing performance and prolong working life,contact mechanics of hollow cylindrical roller bearing of cone bit was simulated.Effects of hollow size,drilling pressure,friction coefficient and fitting clearance on mechanics performance of the bearing were studied.The results show that the maximum equivalent stress of the hollow cylindrical roller bearing appears on the claw journal,and the maximum contact stress appears on the contact pair of the hollow roller.Besides,hollow sizes have a greater impact on the equivalent stress and contact stress of the cylindrical roller,while the influence on the stress of the cone and claw journal is relatively small.With the increasing of the drilling pressure and fitting clearance,equivalent stress and contact stress of bearing parts increase.The friction coefficient has little impact on mechanical performance of the bearing.As the 121/4SWPI517 type hollow cylindrical roller bearing of cone bit an example,the optimal hollow size is 55%,the drilling pressure is 140 kN and the fitting clearance is 0e0.02 mm.

Effect of pulsed magnetic field pre-treatment of AISI 52100 steel on the coefficient of sliding friction and wear in pin-on-disk tests

Disc specimens manufactured from commercial bearing rollers(AISI 52100 steel,62−63 HRC)in initial state and after pre‐treatment by pulsed magnetic field(PMF)with a magnetic field strength of 1−7 MA/m were tested with sunflower oil using pin‐on‐disk apparatus.According to the obtained results the treatment causes a reduction in the coefficient of friction and wear.To explain the results,nano‐and microhardness tests as well as optical and atomic force microscopy were used.Reasons of the effect of PMF on the friction and wear were discussed.