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The actual radial clearance and runout of the bearing are different from design ones, because of the unavoidable raceway roundness and roller diameter errors of a cylindrical roller bearing. However, there is little knowledge about how the raceway roundness and roller diameter errors affect the radial clearance due to the lack of the analysis metho...
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... method of radial clearance and runout Figure 1 shows the sectional view of a cylindrical roller bearing. The rollers are equally spaced in the bearing. ...
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... only the diameter errors of the rollers at the lower half of the bearing are considered. The diameter error distribu- tion of the rollers in the bearing are listed in Table 2. Figure 3(a) and Figure 3(b) show the displacements x 1 and x 2 of the center of the inner ring (Figure 1) in cases 1 and 17, respectively. Although there are no diameter errors of the rollers in case 1, the displace- ments x 1 and x 2 periodically vary with the azimuth angles because the rollers pass through the lowest and highest positions of the bearing at intervals. ...
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... the effects of the phase angle of the inner raceway on the radial clearance and runout are analyzed. Figure 10 shows the radial clearances and runouts corresponding with the phase angle 0 and 135 . The inner raceway is a ellipse with two flaps. ...
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... inner raceway is a ellipse with two flaps. Figure 10 shows that the phase angle of the inner raceway which is fixed hardly changes the periods and values of the radial clearance and runout in this No diameter error (case 1 in Table 2) Diameter errors and random positions (case 17 in Table 2 No diameter error (case 1 in Table 2) Diameter errors and random positions (case 17 in Table 2) Flap number of outer raceway case. The phase angle of the outer raceway does not affect the radial clearance and runout because the outer raceway is turned one revolution. ...
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... effects of the raceways with regular shapes (Figure 5), which is described by one harmonic, on the radial clearance and runout have been analyzed above. Figure 11 shows the effects of the outer raceways with irregular shapes on the radial clearance and runout of a cylin- drical roller bearing. The outer raceways with irregu- lar shapes are described by two harmonics. ...
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... parameters j of the first harmonic are 5, 30 and 50, respectively. The parameters j of the second harmonic vary from 1 to 50 ( Figure 12). All in all, the radial clearance and runout periodically vary with the increase of the parameters j of the second harmonic. ...
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... in all, the radial clearance and runout periodically vary with the increase of the parameters j of the second harmonic. The period, which is determined by the relation between the numbers of rollers and the parameter j, is the same to that affected by the raceways with regu- lar shapes ( Figure 6,8-10). When the parameter j of the first harmonic equals that (j ¼ 5, 30, 50) of the second harmonic, the radial clearances rapidly decrease and reach the minimum. ...
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Citations
... A cylindrical roller with a straight generatrix is the most common and simple type and is widely used in the manufacturing industry. Generally, the roundness (Chen et al., 2013), surface roughness, and variation of roller gauge lot diameter in a bearing have a significant impact on the mechanical performance of bearings, including the rotation accuracy, rotation speed, working life and reliability. Rollers with high geometrical accuracy, surface quality and waviness can improve the stress distribution between rollers and raceways (Liu et al., 2022b). ...
... Terefore, tolerance analysis around the optimal design would be signifcant in predicting the life of the bearing. Studies [7][8][9][10][11][12][13][14][15] investigating the efect of manufaturing error on bearing performance have been widely conducted. Chen et al. [7,8] analyzed the efect of of-sized roller and its arrayed order on load distribution in a cylindrical roller bearing (CRB). ...
... Studies [7][8][9][10][11][12][13][14][15] investigating the efect of manufaturing error on bearing performance have been widely conducted. Chen et al. [7,8] analyzed the efect of of-sized roller and its arrayed order on load distribution in a cylindrical roller bearing (CRB). It was shown that one of-sized roller has a signifcant infuence on load distribution. ...
In order to analyze the influence of tolerance values of key parameters for cylindrical roller bearings under combined axial and radial loads, a coupled model, incorporating a dynamic model of cylindrical roller bearings, contact model, and fatigue life model, is developed to investigate the effect of flange angle, roller-end radius, interval of roller length gauge, and roller profile on contact performance and fatigue life. The results show that the grouping design of flange angle and roller-end radius in the tolerance range was helpful for reducing contact ellipse truncation. The difference of the roller length would change the axial load distribution of the bearings. For the longest roller located in the bottom position, the bigger the difference, the bigger the roller tilt angle and carried-axial load. The (0, +2.5 μm) tolerance range of the crown drop can limit the difference of the fatigue life within 20% in the current analysis.
... The cylindrical roller, as the rolling element of rolling bearing, has a large advantage of being loaded under high pressure, due to its line contact with the bearing raceway, which is widely used in the rotational machinery, e.g., spindle of machine tool, aircraft engine, wind-driven generator, and high-speed railway. The geometrical accuracy of cylindrical roller, especially in terms of roundness, plays a key role in the kinematic accuracy, working life, and reliability of rolling bearing [1][2][3][4]. The centerless grinding process, which was born in 1918 [5,6], has been developed and widely applied as a fine machining method of cylindrical parts in various fields of industry, especially automotive and bearings, providing high precision and high efficiency in mass production [6,7]. ...
In this paper, the centerless finishing process of bearing cylindrical roller made of AISI 52100 steel using free abrasives and soft pad was investigated by the Taguchi method in the experiments and simulation, with the aim of improving the roundness. The rounding and material removal process was simulated based on the improved model. The test runs of experiments and simulation were designed according to a standard orthogonal array in which four factors included loading force, abrasives concentration, particle size, and error, and each factor had three levels, as well as the total number of parameter combinations was nine. The signal-to-noise (S/N) ratio was applied in experimental data processing, representing both the average (mean) and the variation (scatter). According to the analysis of variance (ANOVA) by S/N ratio, it is indicated that the loading force makes the largest contributions respectively accounting for 72% in roundness and 54% in material removal rate (MRR), the abrasive concentration almost has no contribution in roundness but has one accounting for 24% in MRR, and the particle size has contributions respectively accounting for 21% in roundness and 13% in MRR. Through the analysis of level average response, the optimal parameter combination was chosen as loading force of 60 N, abrasives concentration of 10 wt%, and particle size of 127 μm. In the centerless finishing experiments under the optimal conditions, the roundness was improved from an initial 0.71 to a final 0.32 μm after 12 min of processing at the MRR of 0.44 μm/min.
... In recent years, many researchers have been studying how to improving the kinematic accuracy from various aspects, example as force, structure, assembly, lubrication and etc. There were many paper reported about the dependent connection between the parts precision and the bearings kinematic accuracy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. But, very few scholars studied the bearing kinematic accuracy from a statistical standpoint. ...
The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the size and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy. The copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.
... There were many works about the dependent connection between the parts precision accuracy and the bearings kinematic accuracy reported. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. But, very few scholars studied the bearing kinematic accuracy from statistical standpoint. ...
The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the dimensional and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy, the copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.
... Bhateja et al. [4] proposed a method for calculating the run-out of hollow roller bearings and studied the resultant components of the run-out from the geometric and dimensional errors in the rollers and raceways. Chen et al. [5][6] proposed a method for calculating the radial run-out and static load distribution of cylindrical roller bearings and analyzed the effects of the roundness errors in the raceways and diameter differences of the rollers on the radial run-out and load distribution. ...
Understanding the influence of bearing component manufacturing errors and roller number on the rotational accuracy of rolling bearings is crucial in the design of high precision bearings. The rotational accuracy of an assembled bearing is dependent upon roller number and manufacturing error of the bearing components. We propose a model for calculating the rotational accuracy of a cylindrical roller bearing; we experimentally verified the effectiveness of the model in predicting the radial run-out of the inner ring proposed in the previous paper in this series. We sought to define the key contributing factors to the rotational accuracy by studying both the influence of the coupling effect of the roller number and the influence of the manufacturing errors in the inner raceway, outer raceway, and rollers on the motion error. The model and results will help engineers choose reasonable manufacturing tolerances for bearing components to achieve the required rotational accuracy.
... Chen et al. [236] introduced an analytical model with algebraic equations to study the rolling element diameter errors and race roundness on the radial internal clearance. The Fourier series was used to formulate the race curves. ...
Rolling element bearings (REBs) play a most critical role in various industrial machinery. A clearly and in-depth understanding of vibration characteristics of REBs is very helpful for condition monitoring and diagnosis applications for the machinery. This work presented a comprehensive review of dynamic modelling and analysis methods for predicting the vibration characteristics of REBs with and without localized and distributed faults. Main capabilities and limitations of those methods for both the localized and distributed faults have been described. Explanations for the generations of the bearing vibrations were also reviewed. A summary of the literature was given followed by the recommendations of current and future research works. Moreover, recent challenges, directions and implications in research works on the dynamic modelling and analysis methods of the localized and distributed faults in REBs have also been conducted.
... However, the statistical aspect of the dimensional error and fatigue life was not discussed. A number of studies on bearing geometric imperfection were restricted to investigating several rolling elements with dimensional error [10,11], and certain dimensional error magnitudes [12][13][14][15]. In practice, the bearing rolling elements may involve dimensional errors of different magnitudes that might be induced due to various uncertainty factors during the manufacturing process. ...
This study examined the effect of distributed roller diameter error on the fatigue life of a Tapered roller bearing (TRB). To this end, a comprehensive analysis procedure to perform a statistical analysis of the fatigue life with respect to dimensional error was presented. The roller diameter error was assumed as normally distributed, with a designated mean value and a varying standard deviation. Simulations were conducted to investigate the effects of roller diameter deviation on the fatigue life of the TRB. The numerical results showed that the normally distributed roller diameter error did not necessarily result in a normally distributed bearing fatigue life. The adequate distribution function for the bearing fatigue life with respect to the roller diameter error was explored and found to be dependent on the amount of standard deviation of roller diameter error. The Weibull distribution is appropriate for a small standard deviation, while the gamma distribution and normal distributions are appropriate for large and in-between standard deviations, respectively.
... The vibration behaviors of the rotor roller bearing system were investigated. Chen et al. 21,22 developed a one-dimensional model for calculating the radial runout considering roundness error of raceways and diameter error of the rollers and presented a static model for the load performance in a cylindrical roller bearing based on diameter error of the rollers. The effects of diameter differences among the rollers on the load performance and the radial runout in a cylindrical roller bearing are investigated. ...
... where b ej is the angle between the line o rj D and the line o rj O, which is calculated by equation (21). c j is the acute angle between the line o rj O and x e -axis, which is computed by equation (22) b ej = arccos ...
For the rotary motion of a rolling bearing implemented by bearing components under geometric constraints, the rotational accuracy of assembled bearing should also be the result of interaction among geometric errors of bearing components. Therefore, it is significant to research the relationship between geometric errors of bearing components and rotational accuracy of assembled bearing for the design and prediction of bearing accuracy. An accuracy prediction method is proposed to study how the geometric errors of bearing components affect the radial runout of outer ring of cylindrical roller bearings in this article. Furthermore, the calculation model for the orbit of outer ring center is established from which the radial runout of outer ring can be predicted while dimension and roundness errors of raceways and rollers are given arbitrarily. Theoretical algorithms with two typical shapes of outer raceway are deduced to verify the prediction method. In addition, a test on the radial runout of outer ring in a cylindrical roller bearing is performed. The results indicate that prediction results are in good agreement with experimental and analytical results.
... Yang et al. [10][11][12] established a mathematical model and a five-degree-of-freedom model to research the influences of geometric error on the NRRO of an angular contact ball bearing. Chen et al. [13,14] developed a one-dimensional mathematical model with algebraic equation considering roundness error of the raceways and diameter error of the rollers. The influence of diameter differences among the rollers on the load performance in a cylindrical roller bearing was investigated. ...
... When the th roller is located in the fourth quadrant and point is located below the line , the geometric relationship between the inner raceway and the th roller is shown in Figure 3(d), = − + . In (13), when the angle Δ varies in a certain range, there is a point on the inner raceway and a point on the surface of the th roller, which make the distance between point and point reach a minimum value, namely, the shortest distance between the inner raceway and the surface of the th roller. When the shortest distance is more than given tolerance, the h roller is separate from the inner raceway. ...
The motion error of assembled bearing depends on the geometric profile of bearing components. Therefore, it is crucial to establish the relationship between geometric error of bearing components and motion error of assembled bearing, which contributes to improving the rotational accuracy of assembled bearing in the design and machining of the bearing. The main purpose of this research is to propose an accurate method for predicting the radial runout of inner ring based on the geometrical constraint model of cylindrical roller bearings. In the geometrical constraint model, dimension and form errors in the inner raceway, the outer raceway, and rollers are considered, and the change of contact positions between the raceways and rollers caused by geometric errors of bearing components is taken into account. This method could predict the radial runout of inner ring after bearing components with geometric error are assembled. In order to testify the validity of the proposed prediction method, two particular cases in which the profiles of the inner raceway are circle and ellipse are selected, and the analysis algorithms for the radial runout of inner ring are derived. Two analytical results obtained from the analysis algorithms validate accuracy and effectiveness of the proposed prediction method.
