Basic Dynamic Load Research Articles

Optimizing Multi-Row Cam Roller Bearing for Long Fatigue Life of Hydraulic Motors

Cam-lobe radial-piston hydraulic motors are widely used as rotation driving units for various marine machinery owing to their ultrahigh output torque (more than 100 kN m). A multi-row cam roller bearing (MCRB) is the key component that directly determines the fatigue life of a cam-lobe radial-piston hydraulic motor. However, compact geometry and complex loads render MCRB susceptible to fatigue failure, highlighting the need for an optimized MCRB to achieve longer fatigue life and higher reliability. Therefore, this study proposes an innovative geometry optimization method for an MCRB to improve its fatigue life. In this method, a quasi-static model was developed to calculate the load distribution, with the fatigue life of the MCRB calculated using both basic dynamic loading and load distribution. Subsequently, a genetic algorithm was used to obtain the optimized geometry parameters, which significantly improved the fatigue life of the MCRB. Finally, a loading test was conducted on a hydraulic motor installed with both the initial and optimized MCRB to validate the effectiveness of the proposed optimization method. This study provides a theoretical guideline for optimizing the design of MCRB, thereby increasing the fatigue life of hydraulic motors.

The structural dimension parameter optimization method of tapered roller bearings for wind power gearbox

Taking the non-standardized internal structural dimension parameters of rolling bearings as the design variable, the constrained optimization mathematical model of tapered roller bearings under the maximum target of basic static load rating and basic dynamic load rating has been established. Optimization results of the mathematical model have been obtained by using the improved multi-objective genetic algorithm, NSGA-II. After the above-mentioned methods were used to the optimization of the tapered roller bearing on the high-speed shaft of a 750 kW wind turbine gearbox, its basic rated static load and basic rated dynamic load can be increased by 15 % and 17 % compared with its standard value. Thus, the proposed methods are feasible and reliable, and has certain application value for improving the bearing performance and prolonging its service life.

Analytical investigation of a new approach to calculation for effective length of the rolling element used in closed end needle roller bearings of driveshaft

The presence of the oscillating motion in a mechanical system, is vital in terms of the service life. Because the machine elements are under effect of fatigue due to the oscillating motion. The service life of the bearings which are in the forefront among the machine elements subjected to oscillating motion, can be calculated via an equation that depends on several variables, one of which is basic dynamic load rating (C). In this context, basic dynamic load rating (C) is one of the most important factors on estimating the service life.
 One of where bearing applications used in, is universal joint of driveshaft. A bearing on a universal joint consists of needle roller elements having larger contact area compared to the ball elements. Universal joint bearing is mounted in a bore on a component called yoke part, and so yoke part supports the bearing. In the calculation of basic dynamic load rating for universal joint bearing, effective length of the rolling element is the key factor. In this paper, a new approach to determine the effective length of rolling element used in closed end needle roller bearings of driveshaft has been investigated analytically and the effect of the said approach on the basic dynamic load rating and bearing life has been revealed in terms of ISO 281.

Linear ball guide design optimization considering stiffness, friction force, and basic dynamic load rating using particle swarm optimization

Linear-motion ball guides are one of the most common supporting elements in machine tools. Their design optimization is highly crucial for engineers and users because it can assist geometric and operating parameter selection and thereby aid in maximizing the stiffness and operating life while minimizing their friction. In this study, a multi-objective linear ball guide optimization process was performed using the particle swarm optimization (PSO). Five design parameters were selected for optimization: ball diameter, number of balls, groove curvature ratios for balls in contact with carriages and with rails, and initial contact angle. The design optimization objectives were radial stiffness, friction force, and basic dynamic load rating. The bearing stiffness and friction force were calculated using the numerical model proposed by the authors. The basic dynamic load rating was determined according to ISO 14728-1:2017. Pare-to-optimal solutions were used to support optimal design parameter selection. The final selection of an optimal point from points satisfying the Pareto optimality was performed using the cooperative equilibrium point method. The simulation results indicated a good performance of the optimized linear ball guide. Finally, the effects of parametric uncertainties in the optimal design on the performance were extensively investigated through a sensitivity analysis.

Optimal design of self-retaining full complement cylindrical roller bearings

Due to the presence of the ribs on both sides of the outer ring, the self-retaining full complement (cageless) cylindrical roller bearings have a very interesting particularity: the outer ring must be heated to create enough room between the already mounted rollers to allow the last roller to be inserted in the row. In addition, after cooling down, the rollers must support each other with a certain small clearance. For this reason, the internal geometry of the bearing as well as the precision of execution are more than critical. On the other hand, one of the most important problem in rolling bearing design is to establish the optimal set of internal dimensions in order to obtain the maximum value of the basic radial dynamic load rating. Pursuing this goal, in this paper, the optimal design of certain self-retaining cylindrical roller bearing is performed by means of the PSO (Particle Swarm Optimization) algorithm. In this approach two design variables were considered (the roller diameter and the diameter of the inner ring raceway) and both geometrical and thermal constraints were taken into account. A study referring to the sensitivity of the design to the small variation of the geometrical parameters is also presented.

Fatigue Life Assessment of Rolling Bearings Made from AISI 52100 Bearing Steel.

The rolling bearings used in various industrial applications are exposed to fatigue failure during their operation. Generally, in a practical application, the ISO 281:2007 standard is used for fatigue life assessments of rolling bearings. The application of the formula given in this standard requires knowledge concerning the basic dynamic load rating C. The natural question is raised of whether it is possible to omit the time-consuming experimental tests while still effectively calculating the fatigue load or the load capacity of the bearings. In the paper, the authors propose the application of analytical formulas for stresses in the contact area and its vicinity, and the usage of the multiaxial high-cycle fatigue hypothesis to estimate the maximal fatigue load for the rolling bearings. In the proposed methodology, only the knowledge concerning the fatigue properties of the material and geometry characteristics of the analyzed bearings are demanded. The effectiveness of the authors’ proposal is verified for arbitrarily chosen bearings. The observed discrepancy between the catalogue fatigue load (SKF catalogue) and numerically calculated fatigue load usually does not exceed 10%, which is fully acceptable from an engineering point of view and justifies the approach proposed in the paper. The proposed methodology can be used for the prediction of the fatigue life and optimization of the rolling bearings.

Design and simulation of continuous melon fruit depodding machine

Melon fruits are usually depodded in Nigeria using traditional/manual method which is not only curbersome, but equally time consuming, and poor quality of finished products obtained. In other to curb these problems, a continuous melon fruit depodding machine was designed and simulated for failure. The Melon fruit depodding machine was made up of the following main units; hopper, depodding chamber, electric motor, chain, sprocket, bearings, and frame which act as supporting base. The depodding machine has a maximum capacity of 0.185m3, and this volume can take melon fruit of 28.25 kg powered by 2.5 hp, 1440 rpm electric motor. The following parameters were design for; depodding force, torque, power, shaft diameter, bearing, density, basic dynamic load on bearing, basic dynamic life of bearing, velocity ratio, etc. The results obtained from the detail design show that a depodding force of 277.13 N and torque of 27.713 Nm was required for the operation of the machine. SolidWorks CAD was used for the simulation of the machine. The Von Mises stress obtained was less than the yield stress, thus the design is safe. The mass of melon fruit and depodded melon fruit were used to calculate the efficiency. The results obtained showed that an average efficiency of 73.55% was obtained.Keywords: Design, Simulation, Melon Fruit, Depodding Machine, SolidWorks CAD, Efficiency

BEARING'S EARLY FAULT DETECTION USING VIBRATION ANALYSIS

ABSTRACTOver recent decades, predictive maintenance's usage attracted the attention ofmaintenance specialists in some important industries. Moreover, machinery conditionmonitoring is an effective indicator for planning the maintenance schedules. Machinemonitoring or early detection of incipient fault is an important judgment tool of themachine's health at critical parts such as; gears and bearings. Furthermore, vibrationmonitoringprocess can be achieved by experienced operators using their visualinspection. However, many specialists in maintenance field recommend using thecomputerized inspection to meet increased demand for the automated monitoringapplications and helpful engineering software.This paper deals with condition monitoring of machines in addition to designingmachine monitoring assisting tool as software for time saving. This software ispresented as fast tool affording instantaneous calculations of bearing faultfrequencies for different bearing types. In addition, the presented software caninstantaneously calculate the basic dynamic load rating considering bearing ratinglife.

Design algorithm for generatrix profile of cylindrical crowned rollers

The cross-section of roller profile controls the pressure distribution in the contact area and radically affects the roller bearings basic dynamic load rating and rating lives. Today the most used roller profiles are the logarithmic profile and cylindrical-crowned (ZB) profile. The logarithmic profile has a continuous evolution with no discontinuities till the intersection with the end fillet while ZB profile has two more discontinuities at the intersections points between the crowning circle and straight line generatrix. Using a semianalytical method, a numerical study has been carried out to find the optimum ZB profile for rollers incorporated in cylindrical rollers bearings. The basic reference rating life ( L 10_r ) has been used as optimization criterion.

탄소 표면경화처리 구름베어링의 유효 경화 깊이에 대한 고찰

The effective case depth for case-hardened rolling bearing has been discussed. For this purpose, roll- ing contact fatigue tests for ball bearings built with inner race of various hardness values were conducted until L10 calculating rating life using a bearing life test machine under radial loading. Then, the distribution of residual stress below the inner raceway, which depended on the hardness value, was measured by X-ray diffraction. As a result, the linear relationship was established between the hardness value of the inner race and the theoretical shear stress evaluated at the depth where the residual stress disappeared below the inner raceway. Based on the relationship, it could be found that the factor of safety in bearing manufacturer's rules for the effective case depth of case hardened rolling bearings was set higher. However, it could be also found that the hardness values at the depth where the maximum shearing stress acted below the raceway surface in a tapered roller bearing hardened by the carburizing process, were not sufficient for preventing plastic deformation under the basic dynamic load rating. Consequently, further efforts were still required to reduce or to disperse the contact load on the material design of a rolling bearing in order to prolong its life. Keywordscase hardening (표면경화 ), rolling bearing (구름베어링 ), effective case depth (유효경화깊이 ), hardness (경도), plastic deformation (소성변형)

Cascade Analysis of a Floating Wind Turbine Rotor

Mounting a wind turbine on a floating foundation introduces more complexity to the aerodynamic loading. The floater motion contains a wide range of frequencies. To study some of the basic dynamic load effect on the blades due to these motions, a two-dimensional cascade approach, combined with a potential vortex method, is used. This is an alternative method to study the aeroelastic behavior of wind turbines that is different from the traditional blade element momentum method. The analysis tool demands little computational power relative to a full three dimensional vortex method, and can handle unsteady flows.When using the cascade plane, a "cut" is made at a section of the wind turbine blade. The flow is viewed parallel to the blade axis at this cut. The cascade model is commonly used for analysis of turbo machineries. Due to the simplicity of the code it requires little computational resources, however it has limitations in its validity. It can only handle two-dimensional potential flow, i.e. including neither three-dimensional effects, such as the tip loss effect, nor boundary layers and stall effects are modeled. The computational tool can however be valuable in the overall analysis of floating wind turbines, and evaluation of the rotor control system.A check of the validity of the vortex panel code using an airfoil profile is performed, comparing the variation of the lift force, to the theoretically derived Wagner function. To analyse the floating wind turbine, a floating structure with hub height 90 m is chosen. An axial motion of the rotor is considered.

The Simulation of Influence of Quenching Temperature on Properties of Bearing Rings

Roller bearings are a very important part of modern machineries and equipments. They have a significant impact on the smooth running, reliable performance and durability. Replacing worn or damaged roller bearings often require extensive disassembly of the machine and the costs often exceed the price of the replaced bearings. There is an influence of the correct bearing construction and dimensional accuracy on the durability, but the grade and quality of used steel and its heat treatment are very important, too. Tempering is an important chapter. Tempering has the effect to modifying the properties of martensite after quenching and transformation of residual austenite, which is related to the change of bearing rings dimensions, growth, roundness and hardness. Decrease in hardness of bearing steel is associated with a reduction in the basic dynamic load rating of rolling bearings and thus durability. In this article there is analysed the influence of quenching and tempering on their mechanical properties after heat treatment. There was also used simulation software to verify the possibility of modeling of bearing rings quenching.

E24 深溝玉軸受の寿命分布と信頼性に関する研究(OS2 最新機械要素技術(1))

The purpose of this work is to establish a database of fatigue life distribution and a reliability of rolling bearing. Fatigue life test of deep groove ball bearing #6206 lubricated by Lithium grease lubrication is carried out under pure radial loads F_r=9.14, 10.64, 12.13kN. The fatigue life distribution, the basic dynamic load rating and the load life exponent are estimated and discussed from the test results.

E26 ローラガイドの寿命と信頼性に関する研究(OS2 最新機械要素技術(1))

A study on life distribution and reliability for a roller guide with cage type is carried out with the total number of 80 test samples made up of four series and fatigue life distribution functions, such as the log-normal distribution, the two-parameter and the three-parameter Weibull distribution function are used for discussion. The basic dynamic load rating obtained ISO formula is compared with the life test data in relation to the effect of crownings of carriage raceway both end portions. As a result, the best fit for the life test series is obtained by the three-parameter Weibull distribution function introduced a minimum life with Weibull slope m=27/20 and load life exponent p=10/3, followed by the log-normal distribution as second, and the two-parameter Weibull distribution as the third.

Study on the Life Distribution and Reliability of Roller-Based Linear Bearing

A study on the life distribution and reliability for a roller guide with cage was carried out with a total number of 90 test samples in two lots (N s = 38 and 52), and different fatigue life distribution functions, such as the two and three parameter Weibull distributions, and the log-normal distribution were used for analyzing the test data. The basic dynamic load rating formula standardized by ISO in 2004 was also compared with the life test data in relation to the effect of crowning on both ends of the carriage raceway. This study revealed the following: (1) the best fit for the life test data was achieved by the three-parameter Weibull distribution with the third parameter being the minimum life γ, using a Weibull slope of m = 27/20, and a load life exponent of 10/3. The log-normal distribution came second, and the two-parameter Weibull distribution third. (2) The test data did not fit with the two-parameter Weibull distribution using a Weibull slope of 9/8, which had been used in the ISO linear bearing standard. (3) Fatigue failure on the roller guide was initiated near the starting points of the crowning on both ends of the carriage raceway. Almost 70% of the test specimens were found to have uneven and inclined contact situations with the rollers. (4) The basic dynamic load ratings evaluated theoretically fit well to the life test results, while the λ b m factors were also observed to fall within a suitable value range.

Theoretical Reevaluation of Basic Dynamic Load Rating and Rating Life for Linear Bearings

Linear motion rolling bearings, also known as linear bearings, were included as standard rolling bearings by ISO in 2004. In this standard, the basic dynamic load rating C and the rating life L10 are based on only for a standard stroke SSt defined by a linear movement with twice the raceway length 2lt for a carriage. However, if the stroke St is shorter than SSt the rating load becomes considerably smaller than the defined C value due to the effect on the probability of flaking occurrences for the rolling bodies and, conversely, if the stroke is larger than the SSt, the rating load becomes larger than the C value due to an increase in the rating load for the rail raceway surface. This article deals with the theoretical re-evaluation of the basic dynamic load rating and the rating life for linear bearings based on the Lundberg-Palmgren theory, but with a minimum life for the population as the third parameter. The rating load is defined by 100 km as unit running life (URL) mentioned in the ISO standard, and an arbitrary stroke is defined along with a stroke factor aST, which is introduced into the life formula as a life modification factor for the linear bearings. As a result, aST = 0.4–1.07 (for point contact) and aST = 0.3–1.14 (for line contact) from a very small stroke, 0.2 times of the rolling body pitch to a large stroke, St = 10lt, are obtained.

Study on Load Distribution and Life Distribution for Ball Spline (1st Report)

Ball splines were standardized by JIS in 2004 and now they are examined in ISO / TC39 as power transmitting components. In this paper the ball load distribution and basic dynamic load rating for ball spline type AII are discussed theoretically by considering the re-circulation of balls in each row including a spline shaft bending deformation with radial load and the crownings of nut raceway both end portions. The ball load distributions in case of even arrangement, condition I for the effective number of balls, Zt = Zt I = 9 and uneven arrangement, condition II for the effective number of balls, also Zt = Zt II = 8 are discussed with ball re-circulation. The results are as follows. (1) Under the application of pure torque, the ball load distributions for each condition I and II are even except the crowning portions and the shaft deformation does not occur, and maximum ball load in condition II is shown Pmax II ≤ 1.03Pmax I in accordance with ball re-circulation. (2) Under the application of pure radial load, the ball load fluctuation is Pmax II ≤ 1.19Pmax I without shaft deformation and further Pmax II ≤ 1.15Pmax I with shaft deformation. (3) Under the application of combined radial load and torque, the ball load fluctuation is Pmax II ≤ 1.07Pmax I in case of without shaft deformation and further Pmax II ≤ 1.07Pmax I with shaft deformation. (4) The basic dynamic load rating CF* for ball spline can be classified into pure torque CMx, pure radial load CFy, combined radial load and torque CFy+Mx etc. In case of pure torque, the CMx value by this report is agreed with ISO's load rating for condition I theoretically. (5) In case of combined radial load and torque, it is made clear that the load rating for CFy is remarkably decreased in accordance with the increase in load eccentricity and CFy+Mx value approaches to the basic dynamic load rating for pure torque CMx.

Re-Evaluation of Basic Dynamic Load Rating and Life Formula for a Ball Screw

The existing method of calculation for the basic dynamic load rating for a ball screw mentioned in the ISO standard is based on the method used for the angular contact ball bearing, and thus it does not align with the one used for the linear bearing. The unit for the rating life; i.e., the unit running life (URL) is defined in terms of 10 6 rev. As a result of this, the effect of the linear stroke of the nut or screw shaft, the lead, the number of starts, and the number of circulating ball circuits and their turns are not clearly reflected in the load rating formula. In this paper, the basic dynamic load rating and the life formula for the ball screw based on the method used for the linear bearing; i.e., in terms of a unit URL = 100 km is proposed and some representative calculation results for a ball screw are discussed. The results are summarized as follows: (1) Basic dynamic load rating Ca for standard stroke corresponding to the nut raceway length is defined along with a stroke factor to generalize the relationship for any stroke of the ball screw operation. (2) The Ca value for the ball screw is proportioned according to the number of ball circuits and their turns to the power of 0.7 as well as the number of starts. Any increase in the number of starts especially affects an increase in the helical raceway length of the nut and the number of balls, which results in an exceptional increase in the Ca value. Presented at the STLE Annual Meeting in Calgary, Alberta, Canada May 7-11, 2006 Review led by Dong Zhu

Life Distribution and Reliability for Linear Bearings in Case of Roller Guide

A study on life distribution and reliability for a roller guide with cage type is carried out with total number of 90 test samples of two lots (Ns=38 and 52) and fatigue life distribution functions, such as two and three parameters Weibull distribution and log-normal distribution, are used for discussion. The basic dynamic load rating formula standardized by ISO in 2004 is also compared with the life test data in relation to the effect of crownings of carriage raceway end portions. As a result, (1) the best fit for the life test series is obtained by 3-parameter Weibull distribution introduced a minimum life as a third parameter, having Weibull slope m=27/20 and load life exponent p=10/3, followed by the log-normal distribution as second, and 2-parameter Weibull distribution as the third. (2) The 2-parameter Weibull distribution with Weibull slope m=9/8 as used in ISO linear bearing standard dose not fit with the experimental results. (3) The fatigue failures of roller guide is initiated near the crowning start points of carriage raceway both end portions, and almost 70% of test specimen are uneven and inclined contact situations of rollers. (4) The basic dynamic load ratings between theory and life test result fit well each other, and λbm factors are also fallen into suitable value range.

Theoretical Analysis for Basic Dynamic Load Rating and Life Formula of Ball Screw

The existing method of calculation for the basic dynamic load rating mentioned in the ISO standard is based on the method used for the angular contact ball bearing and does not align with the one used for the linear bearing. The unit for the rating life, i.e., the Unit Running Life (URL) is defined in terms of 106 rev. As a result of this, the effect of linear stroke of the nut or screw shaft, lead, the number of starts, and the number of circulating ball circuits and their turns are not clearly reflected in the load rating formula. In this paper, the basic dynamic load rating and the life formula for the ball screw based on the method used for the linear bearing, i.e., in terms of an unit URL = 100 km is proposed and some representative calculation results for a ball screw are discussed. The results are summarized as follows: (1) Basic dynamic load rating Ca for standard stroke corresponding to the nut raceway length is defined, and a stroke factor is also defined for any stroke of the ball screw operation. (2) The Ca value for the ball screw is proportioned according to the number of ball circuits and their turns to the power of 0.7 as well as the number of starts. But, as the number of starts especially affects the nut raceway length and the number of balls, the Ca value becomes remarkably large.