Raceway Groove Research Articles

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Investigation on collaborative regulation shape, fibrous macrostructure and microstructure of raceway groove in BG801 steel bearing ring with mounted edge

Whether the macro- and micro-structure of bearing ring forging is desired or not greatly decides the property of ring parts. An unreasonable forging design or processing easily leads to the fibrous macrostructure outcrop in the raceway damaging service life. In this study, a novel forging design method of symmetry design on raceway groove (RG) and mounted edge for ball bearing ring with mounted edge structure was proposed. Meanwhile, the height diameter ratio (HDR) of the billet was adjusted to achieve metal fibers distributed along the RG shape in both forging and parts, which was verified by experiments. Fibrous macrostructures of BG801 steel are mainly dominated by primary carbides M23C6/I-M6C and assisted by precipitated carbides II-M6C along matrix shear regions. The microstructure on the RG can be regulated by deformation temperature, in which the texture transforms from Cube to Rotated-Cube than to {332} 〈120〉, the size and content of retained austenite (RA) increase and twin substructure appear within lath martensite with temperature. By optimizing parameters HDR = 1.1 and deformation at 1050 °C, the high strength and hardness of RG were achieved that yield strength (YS), ultimate tensile strength (UTS), and hardness were 671 MPa, 1560 MPa, and 419.9 HV, respectively. The strengthening effect is not only attributed to the desired microstructure of thin film-like RA, dislocation martensite and carbides, but also fine grain strengthening of the prior austenite grain (PAG) that induces almost half of strengthen contribution.

Calculation method for the static carrying curve of double-row different-diameter ball slewing bearings.

A method for calculating the static carrying curve of a double-row different-diameter ball slewing bearing was proposed. The relationship between the internal maximum rolling element load of each row and the combined external axial load and tilting moment load of the slewing bearing was established using the deformation compatibility and force equilibrium conditions. The rolling element load distribution range parameters of the main and auxiliary raceways of the double-row different-diameter ball slewing bearing were used as input invariables, and the corresponding external load combinations of the axial and tilting moment loads of the slewing bearing were obtained. These external load combinations were plotted in the coordinate system to obtain the static carrying curve of the slewing bearing. The obtained static carrying curve was compared with that calculated using the finite element method for verification. Finally, the influences of detailed design parameters such as the raceway groove radius coefficient, raceway contact angle, and rolling element diameter on the carrying capacity of the double-row different-diameter ball slewing bearing were analyzed based on the carrying curves. As the groove radius coefficient increases from 0.515 to 0.530, or the contact angle increases from 50° to 65°, the carrying capacity of the slewing bearing decreases. As the rolling element diameter increases from 0.90 times the initial diameter to 1.05 times the initial diameter, the carrying capacity of the slewing bearing increases.

Multi-Objective Robust Optimization of Deep Groove Ball Bearings Considering Manufacturing Tolerances Based on Fatigue and Wear Considerations

Abstract In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein, deep-groove ball bearings have been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have a minimum effect on the objective function, i.e., its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, manufacturing accuracy, and material quality, and thus, the dynamic capacity and elasto-hydrodynamic minimum film thickness have been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter, and bearing width for the case of deep-groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients, and the number of rolling elements. These five internal geometrical parameters are taken as design variables; moreover, five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometry and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). Nondominated sorting genetic algorithm (NSGA-II) has been used as the optimization tool. Pareto-optimal fronts are obtained for one of the bearings. Of many points on the Pareto-front, only the knee solutions have been presented . This paper shows that geometrically feasible bearings can be designed by optimizing multiple-objective functions simultaneously and by also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

Research on the effect of structural and material parameters on vibrations based on quasi-static model of bearings

Variable compliance vibration is an inevitable source of the parametrically excited factors of rolling bearing–rotor system under the effect of only a limited number of rolling elements to carry the loads. Based on the quasi-static model of ball bearing, the mechanism of time-varying stiffness is studied and the effects of external load, rotational speed, geometric structure of the bearing and material parameters on the time-varying stiffness and relative variation of stiffness are analyzed quantitatively. Results show that load redistribution in bearing caused by the change of ball spatial position is the direct cause of the time-varying stiffness. Rotational speed, the number of balls and diameter have great effect on varying compliance vibration compared with external load and material parameters. In order to reduce the vibration, axial preload, contact angle, ball diameter and density should be appropriately increased, raceway groove curvature radius and radial load should be reduced, and the optimal number balls and rotational speed can be obtained according to the single-variable optimization method. The results provide theoretical basis for the structural design, material and manufacturing process selection.

Accurate prediction method of initial value of high-speed ball bearing model and gyroscopic torque analysis

An accurate prediction method of initial value of high-speed ball bearing model is studyed and its gyroscopic torque is analyzed. First, a new iterative algorithm for high-speed ball bearings is proposed, in which the effects of gyroscopic torque and centrifugal force are considered. Then, to accurately predict the initial values for the proposed iterative algorithm, the combined displacements of bearings are calculated as the initial values according to the deformation superposition principle. The general applicability of this new iterative algorithm for high-speed ball bearings is demonstrated. Subsequently, the effects of combined loads, rotational speed, moment, and raceway groove curvature radius on the gyroscopic torque are discussed in detail. The results provide valuable guidelines for the reasonable selection of combined loads, rotational speed, and raceway groove curvature radii.

Numerical analysis of loaded stress and central displacement of deep groove ball bearing

The aim of this work is to develop a three-dimensional model of deep groove ball bearing to investigate the loaded stresses and central displacements of bearing rings. The equivalent stresses and central displacements of bearing rings are obtained based on the simulated analysis. Moreover, several parameters, such as load magnitude, raceway groove curvature radius (RGCR), thicknesses of outer and inner rings, are varied to investigate their effects on the equivalent stresses and central displacements of bearing rings. Research results provide useful guidelines for determining the design parameters.

Investigation on contact angle of ball bearings

As an important structure parameter, contact angle is also a judgement factor for the working performance of ball bearings. However, under some conditions, the ball may roll over the raceway shoulder, and contact angle is not enough for estimating this phenomenon. Thus, edge angle and edge distance are proposed as compensatory judgement factors in the current study. A six-degree dynamic model with time-varying contact stiffness was developed for investigating effects of initial contact angle, raceway groove curvature factors, number of balls, axial load, shaft speed, friction coefficient and raceway misalignment on contact angle, contact stiffness, edge angle and edge distance. Inapposite initial contact angle may make the ball roller over the raceway shoulder, inner raceway misalignment have significant influences on the stable motion of ball bearings, and more harmonics frequencies about contact angle appear. Comparison of contact angle from presented model with Jones–Harris model under axial load shows reasonable qualitative agreement.

Design and Development of Reliable Integral Shaft Bearing for Water Pump in Automotive Engine to Reduce Assemble Time and Increase Production

Background/Objectives : The prime objective of this work is modifying of water pump which is used for cooling the engine in automotives. Methods/Statistical Analysis: In the existing pump ball, bearing is used in which the assembly and maintenance is difficult. In order to overcome these problems integral bearing is proposed. So it is planned to modify the existing pump to accommodate integral bearing with the purpose of reduce the assembly time and increase production. Findings: The proposed integral shaft bearing has compact in size which is developed by eminence material and have one or two rows contains with balls as well as one row of roller. It has high reliability through a newly developed water resistant seal. This reliable bearing is three time better durability when comparing with existing ball bearing. It has high load durability, high resistant to heat load and water. Application/Improvements: The bearing with integral shaft has no inner rings, while having the raceway groove directly on the shaft.

OS0610 転動体の接触状態が転がり案内の減衰に及ぼす影響

Rolling guideways are widely used in machine tools. In rolling guideways, rolling elements move raceway groove between rail and carriage. Commonly, rolling guideways have two or four rows, eight rows' are getting a lot of attention as high rigidity and damping. Eight-row guydeways have more and smaller rolling elements than others. However, the influence of the number and diameter of balls on its damping has not been clarified. Thus, this paper describes the influence of number and diameter of balls on its damping using damping measurement apparatus. In this apparatus, it is possible to measure the influence of design variable of rolling guideways respectively. In consequence, the number of balls is more relevant to dynamic characteristics of rolling guideways than diameter of balls.

A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects

Ball passing frequencies (BPFs) are very important features for condition monitoring and fault diagnosis of rolling ball bearings. The ball passing frequency on outer raceway (BPFO) and the ball passing frequency on inner raceway (BPFI) are usually calculated by two well-known kinematics equations. In this paper, a systematic study of BPFs of rolling ball bearings is carried out. A novel method for accurately calculating BPFs based on a complete dynamic model of rolling ball bearings with localized surface defects is proposed. In the used dynamic model, three-dimensional motions, relative slippage, cage effects and localized surface defects are all considered. Moreover, localized surface defects are modeled accurately with consideration of the finite size of the ball, the additional clearance due to material absence, and changes of contact force directions. The reasonability of the proposed method for the prediction of dynamic behaviors of actual ball bearings with localized surface defects and for the calculation of BPFs is discussed by investigating the motion characteristics of a ball when it rolls through a defect. Parametric investigation shows that the shaft speed, external loads, the friction coefficient, raceway groove curvature factors, the initial contact angle, and defect sizes have great effects on BPFs. For a loaded ball bearing, the combination of rolling and sliding in contact region occurs, and the BPFs calculated by simple kinematical relationships are inaccurate, especially for high speed, low external load, and large initial contact angle conditions where severe skidding occurs. The hypothesis that the percentage variation of the spacing between impulses in a defective ball bearing was about 1–2% reported in previous investigations can be satisfied only for the conditions where the skidding effect in a bearing is slight. Finally, the proposed method is verified with two experiments.

Determination of the precise static load-carrying capacity of pitch bearings based on static models considering clearance

Static models for a single row and a double row four-point contact pitch bearing, taking into account the clearances therein, were presented. A precise computation method was proposed for the static load-carrying capacity curves of such pitch bearings, which can be used to pre-select pitch bearings and slewing bearings supposing rigid bearing rings. The effects on the static load-carrying capacity induced by changing the clearance, the raceway groove radius of curvature, and initial contact angle were analysed. The clearance has a significant effect on the static load-carrying capacity of the bearing only in load cases with a rather small axial force and a large tilting moment. When the coefficient of raceway groove curvature radius increases, the static load-carrying capacity decreases. The smaller the radial load, the more significant the effect of the coefficient of raceway groove curvature radius on the static load-carrying capacity of the bearing. When radial loads range from 0 to 800kN, the load-carrying capacity increases with increasing initial contact angle. When the radial loads are above 800kN, the load-carrying capacity decreases with increasing initial contact angle.

Numerical Study on Effect of Narrow Groove On Hot Bearing Ring Rolling Process

Ball-section raceway groove and narrow groove ring (BGNGR) is a complex part of bearing rings. The mandrel for the forming of the narrow groove will push and press the metal and lead to instability of the rolling process. Therefore, the effect of the narrow groove on the metal flow is investigated. Two methods for BGNGR rolling are presented, and by deducing the dimensional relationship between rectangular blank and deformed ring, the finite element models for both methods are established and simulated in Forge3D software. Method I is proved to be a failure through the finite element analyses of the effect of the narrow groove on the metal flow. Based on the analysis result in Method I, the Method II with appropriate mandrel profile for the going up metal is proposed. The simulated result shows that the BGNGR whose geometry size meets the requirement can be rolled by Method II.

Dynamic Carrying Capacity Analysis of Double-Row Four-Point Contact Ball Slewing Bearing

Carrying capacity is the most important performance index for slewing bearings. Maximizing the carrying capacity of slewing bearing is one pursuing goal for the bearing designer; this is usually realized by optimizing the design parameters. A method of analyzing the carrying capacity of double-row four-point contact ball slewing bearing by using dynamic carrying capacity surfaces was proposed in this paper. Based on the dynamic load carrying capacity surface of the slewing bearing, the effect of changes of the bearing design parameters, such as axial clearance, raceway groove radius coefficient, and contact angle, on the dynamic carrying capacity of the slewing bearing was researched; the trend and the degree of the effect of the micro changes of the bearing design parameters on the dynamic load carrying capacity of the bearing were discussed, and the results provide the basis for optimizing the design parameter of this type of slewing bearing.

Design Method of the Coefficient of Raceway Groove Curvature Radius of Large–size Four–point–contact Ball Bearings

Design Method of the Coefficient of Raceway Groove Curvature Radius of Large–size Four–point–contact Ball Bearings

Contact Force Distribution and Static Load-carrying Capacity of Large Size Double Row Four-point Contact Ball Bearing

Abstract Clearance not only affects the startup torque, rotation precision and stiffness of bearing, but also affects the load distribution, load-carrying capacity and life of bearing. A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial, axial and overturning moment loadings. The relation between the negative axial clearance and the contact force distribution is analyzed. The static load-carrying capacity curves are established, and the effects of the changes in negative axial clearance, curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed. The results show that, with the increase in the absolute value of negative clearance, the maximum contact load decreases first and then increases. The clearance values in the range of −0.2 mm–0 mm have little effect on the static load-carrying capacity of bearing. With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle, the static load capacity of bearing decreases.

Effect of material defects on crack initiation under rolling contact fatigue in a bearing ring

The effects of material defects such as pores on the crack initiation under rolling contact fatigue (RCF) in a bearing ring are investigated here. First, the main contact position between the ball and the raceway surface is investigated, and the effect of the depth of the pore on the crack initiation is analyzed. Second, several parameters, such as radial load, surface traction and raceway groove curvature radius (RGCR), are varied to evaluate stress intensity factors (SIFs), crack growth rates and crack growth angles. The results provide valuable guidelines for enhanced understanding of RCF in bearings.

Static load-carrying capacity and fatigue life of a double row pitch bearing with radial interference

A computational model taking into account the radial interference was first presented for determining the distribution of contact forces, static load-carrying capacity and fatigue life of a double row pitch bearing, which was subjected to the combined radial, axial and tilting moment loadings. The relation between the radial interference and the contact force distribution was analyzed. The static load-carrying capacity curves were established and the effect on the static load-carrying capacity by the change of the radial interference, coefficient of raceway groove curvature radius and initial contact angle was analyzed. The results show that with the increase in the radial interference, the maximum contact load decreases first then increases, and the basic rating fatigue life of the bearing increases first and then decreases. The radial interference value in the range of 0–0.05 mm has little effect on the static load-carrying capacity of the bearing. With the increase in the coefficient of raceway groove curvature radius and the decrease in the initial contact angle, the static load capacity of the bearing decreases.

Finite element analysis of fatigue life for deep groove ball bearing

The aim of this article is to develop an accurate three-dimensional finite element model of deep groove ball bearing to analyze fatigue lives for outer race and inner race. By the finite element analysis, the stress and strain datasets for outer race and inner race are obtained and used to calculate the fatigue lives. Based on a reliable fatigue criterion, the effect of various applied loads on the fatigue lives of outer race and inner race is investigated. Several parameters, namely the raceway groove curvature radii of outer race and inner race and the thicknesses of outer race and inner race are varied to investigate their effect on the fatigue lives. Research results provide useful guidelines for determining the design parameters.

ボールねじの玉挙動とロストモーション（第２報）―ダブルナットあるいはオーバサイズ球予圧方式による荷重の影響―

It is well known that preloaded ball screws with double nut produced hysteretic motion between the rotary motion of the screw shaft and the linear motion of the nut, which is called “lost motion”, affects positioning accuracies of ball screws.Preloaded ball screws with a double nut have the characteristic that loaded balls wedge into a right angle direction to a ball rolling direction because the directions of screw shaft and nut raceways differ from the ball rolling direction. Loaded balls of preloaded ball screws with a double nut have two contact points geometrically. When the ball screw is operated under the condition of screw shaft turning and nut stationary, the balls have the velocity component perpendicular to the load line of action due to the helical raceway groove. Therefore the balls wedge into nut grooves. In the case of a ball screws with a circular-arc groove profile, “ball wedging” phenomenon is saturated when the force of resistance to ball wedging exceeds a frictional force between the ball and the raceway groove.In the present study, the authors experimentally investigated the lost motion of the X-table which is composed of a preloaded precision ball screw and a couple of linear air bearings, and the ball wedging behaviors under the condition of varied preload with double nut or over-sized balls have also measured.