Influence of Non-Gaussian-Distributed Surface Roughness on the Static Performance of Slider Bearings

An investigation on full fluid film lubrication assuming non-Gaussian-distributed surface roughness has been conducted. A typical slider bearing is chosen as the research object. Edgeworth expansion containing skewness and kurtosis is introduced to approximate the roughness density function. Using Christensen's stochastic roughness model, effects of roughness direction and non-Gaussian distribution properties on the working performance of slider bearings have been quantitatively analyzed. The results show that the variation range of working performance caused by skewness and kurtosis is up to 9.82%. Effects of skewness and kurtosis on the performance are nontrivial and should not be neglected. Compared to the Gaussian distribution, Edgeworth series can represent physical rough surfaces more accurately. Though the effects of skewness and kurtosis on the working performance are complicated, some laws can still be found. For example, large skewness decreases the load capacity, whereas large kurtosis reduces friction force. According to the results, we can choose certain machining processes that can produce the desired surface roughness.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

表面织构对水润滑轴承混合润滑性能的影响

为分析表面织构对水润滑轴承混合润滑性能的影响,基于平均Reynolds方程及JFO空化边界条件建立带有表面织构的水润滑轴承混合润滑模型并数值求解,获得不同织构参数下水润滑轴承的Stribeck曲线。研究结果表明:表面织构是否能改善润滑性能与其深径比及面密度参数密切相关,织构的引入并不一定能降低水润滑轴承的摩擦因数;表面织构的面密度和深径比存在最优值,能使水润滑轴承获得最大的膜厚比与最小的摩擦因数,并在较低的转速下由混合润滑状态进入流体动压润滑状态。     

Modeling the effect of skewness and kurtosis on the static friction coefficient of rough surfaces

Engineering surfaces possess roughnesses that exhibit asymmetrical height distributions. However, the Gaussian distribution is most often used to characterize the topography of surfaces, and is also used in models to predict contact and friction parameters. In this paper, the effects of kurtosis and skewness on different levels of surface roughness are investigated independently. This is accomplished by adopting the Pearson system of frequency curves and used in conjunction with a static friction model for rough surfaces to calculate the friction force and friction coefficient. This study is the first attempt to independently model the effect of kurtosis and skewness on the static friction and friction coefficient. It is predicted that surfaces with high kurtosis and positive skewness exhibit lower static friction coefficient compared to the Gaussian case. More importantly, it is predicted that, for high kurtosis values, the static friction coefficient decreases with decreasing external force rather than increasing as seen with increasing skewness. This is a very promising result for applications involving smooth lightly loaded contacts such as magnetic storage devices and microelectromechanical systems. The practical significance of the present model is specifically demonstrated on static friction predictions in magnetic storage head–disk interfaces. Such predictions can be used to determine the optimal characteristics of such devices prior to fabrication to achieve lower friction in terms of surface roughness, mechanical properties, apparent contact area, and operational environment.     

Blind equalization using combined skewness–kurtosis criterion for gearbox vibration enhancement

In this paper a method for vibration signal enhancement is presented. It incorporates an idea that the signal acquired on the machine housing is a convolution of an informative signal (cyclic pulse train) with an impulse response of the system. The impulse response corresponds to a transmission path through which the informative signal propagates. The informative signal is a signal that contains information about a local damage. The classical method that estimates the impulse response of the system is called minimum entropy deconvolution (MED) and it aims to maximize kurtosis of the deconvolved signal, i.e. kurtosis of the informative signal estimate. Recently, skewness-based deconvolution (equalization) has been proposed as an alternative method for damage detection in rotating machines. In this paper we incorporate an alternative criterion which combines advantages of both of the previously used deconvolution criteria. Kurtosis is a widely-used tool for impulsiveness detection even if they are hidden in the signal, although favouring single-spike signals is a disadvantage of kurtosis. On the other hand, skewness is more robust, since it incorporates statistical moment one order lower than kurtosis. However, signals related to local damage are not always asymmetric, thus skewness is not a suitable criterion for their extraction. Thus, it is worth to combine both kurtosis and skewness in a single deconvolution criterion. We compare properties of two previously used criteria (kurtosis and skewness) with the novel one which is based on the Jarque–Bera statistic using a simulation study. An experimental validation on a real vibration signal (two-stage gearbox from an open-pit mine) is performed as well.     

Contact Analysis of Non-Gaussian Surfaces for Minimum Static and Kinetic Friction and Wear

Most statistical contact analyses assume that surface heights and peak (summit) height distributions follow a Gaussian distribution. However, engineering surfaces are frequently non-Gaussian with a degree of non-Gaussian character dependent upon materials and surface finishing processes used. For example, magnetic rigid disk surfaces used in magnetic storage industry are highly non Gaussian. The use of a Gaussian analysis in such cases can lead to erroneous results. This study for the first time presents a method to carry out a statistical analysis of non-Gaussian surfaces. Real area of contact, number of contacts, contact pressure and meniscus force (in wet interfaces) are calculated for probability density functions having different skewness and kurtosis. From these curves, the optimum value of skewness and kurtosis can be predicted for minimum static/kinetic friction. It is found that a range of positive skewness (between 0.3–0.7) and a high kurtosis (greater than five) significantly lower the real area of contact and meniscus contribution implying low friction and wear. Also, sensitivity of film thickness to static friction goes down for a surface with a positive skewness and a high kurtosis.     

Numerical and Experimental Studies on Tribological Behaviors of Cu-Based Friction Pairs from Hydrodynamic to Boundary Lubrication

When studying the tribological behaviors of a Cu-based friction pair in different lubrication regimes, calculation of the real contact area of asperity contacts is crucial but difficult. In this work, a mixed lubrication model in plane contacts is developed, and pin-on-disc tests are carried out. The real contact area ratio, load sharing ratio, and friction coefficient are investigated. Effects of sliding velocity, temperature, and pressure are considered. The results show that when the maximum contact area ratio is about 14.6%, the load sharing ratio of asperity contacts is about 95%. The friction coefficient obviously increases from less than 0.04 to about 0.15 as the regime changes from hydrodynamic to boundary lubrication. Asperities have a significant influence on the local lubrication of a Cu-based friction pair, and the action of hydrodynamic pressure cannot be ignored.     

数字滤波法模拟粗糙表面的误差分析

计算机模拟加工表面是数值模拟研究表面形貌特征对摩擦和润滑性能影响的前提。基于低通数字滤波技术,通过比较计算机模拟表面和实测磨削表面的粗糙度、峰度、偏度、面积支承率和自相关函数,研究了低通数字滤波法模拟加工表面高度分布特征和自相关函数的精确度,并对加工表面模拟过程中产生的高度分布误差进行了具体分析和讨论。分析结果表明:低通数字滤波法在模拟非高斯粗糙表面时模拟精确度主要受目标表面高度分布特征的影响较大,而且该方法生成非高斯表面存在一定的局限性无法生成特定高度分布的粗糙表面。     

考虑表面粗糙度和热效应的线接触非牛顿混合润滑分析

为了研究表面粗糙度及热效应对非牛顿混合润滑的影响,基于平均流量模型,考虑表面粗糙度以及热效应,建立线接触非牛顿混合润滑模型。研究表面粗糙度对膜厚、膜厚比、平均摩擦因数、载荷比以及温度分布的影响,并与等温解进行比较。结果表明:随着表面粗糙度的增大,油膜温度逐渐升高,尤其是出口区与入口区的温升最为显著,且油膜温升越大,载荷比及平均摩擦因数越大,膜厚比越小;与等温解相比,热解的膜厚比及平均摩擦因数小,载荷比大;等温与热条件相比,中心膜厚与最小膜厚随表面粗糙度的变化趋势差异显著,说明热效应对混合润滑的影响不可忽略。     

A thermal analysis of strip-rolling in mixed-film lubrication with O/W emulsions

Increase of both roll and strip surface temperatures can significantly affect a rolling process, roll conditions and strip mechanical properties. A comprehensive thermal analysis in cold rolling, especially in a mixed film regime, is needed to understand how thermal fields develop in roll and strip during rolling. It requires a simultaneous solution of the mixed film model for friction in the roll bite and the thermal model for roll and strip thermal fields. This paper presents a numerical procedure to analyse strip rolling process using lubrication with oil-in-water (O/W) emulsions. The thermal model includes the effect of heat generation due to the strip deformation and frictional shear stress at the asperity contacts. The numerical analysis employs a coupled thermal model and a mixed film lubrication model for calculating the friction and the asperity deformation in the bite. The thermal model considers the initial temperatures of the roll and strip, temperature rise due to the strip plastic deformation and friction. While the O/W mixed-film lubrication model takes into account the effect of surface roughness and oil concentration (%vol) of the emulsion. The thermal effect is analysed in terms of strip surface temperature and roll temperature, which are influenced by rolling parameters such as reduction, rolling speed, oil concentration in the emulsion. The results of the parametric study indicate that the effect of oil concentration on the thermal field is relatively small compared to that of reduction ratio and rolling speed. The reduction ratio increases the maximum interface temperature in the roll bite. In the mixed film regime, rolling speed also increases the maximum interface temperature and alters the temperature field of the strip. The numerical procedure was validated against known experimental data and can readily be extended to hot rolling or used to analyse roll strip temperature subjected to different cooling system.     

轴承结构参数对曲轴主轴承润滑性能的影响

针对曲轴主轴承润滑性能的影响因素研究,建立考虑轴颈直径、轴承宽径比和轴承间隙3种轴承结构参数的曲轴主轴承热弹性流体动力润滑模型,分析不同轴承结构参数下的主轴承最大油膜压力、最小油膜厚度、最高轴承温度和最大摩擦功率损失。计算结果表明：轴承结构参数对主轴承润滑性能有很大影响;当轴颈直径和轴承宽径比变大时,主轴承最大油膜压力会出现减小的情况,最小油膜厚度变大、最高轴承温度升高和摩擦功率损失增加;内燃机主轴承的轴承间隙会随着轴颈直径和轴承宽径比的不同而有不同影响,且轴承间隙对主轴承最高温度和最大摩擦功率损失的影响较为显著。     

基于Carreau流变模型的圆柱滚子轴承热混合润滑分析*

为了研究圆柱滚子轴承接触区的混合润滑性能,建立基于Carreau非牛顿流体的热混合润滑模型,求解非牛顿流体线接触热混合润滑数值解。研究滑滚比、卷吸速度及载荷对线接触混合润滑特性的影响,并与相同工况下牛顿流体热混合润滑的结果进行对比。结果表明：随着滑滚比、卷吸速度及载荷的增大,油膜温度都会升高,Carreau非牛顿流体的温度要低于牛顿流体的温度;油膜厚度随着滑滚比、载荷的增大而减小,随着卷吸速度的增大而增大,Carreau非牛顿流体与牛顿流体膜厚相差不大;随着滑滚比的增大,2种流体的平均摩擦因数均增大,随着卷吸速度和载荷的增大,2种流体的载荷比均减小。     

Monitoring of Ball Bearing Operation under Grease Lubrication Using a New Compound Diagnostic System Detecting Vibration and Acoustic Emission

Our new compound diagnostic system comprised of a compound sensor, a signal processor, and a personal computer installed signal processing software. The compound sensor made by an advanced sensor fusion technique was able to detect simultaneously the vibration acceleration and the acoustic emission by itself. The signal processor received a signal from the sensor and separated it into the vibration acceleration signal and the acoustic emission signal. The signal processor and the personal computer processed the acceleration signal and acoustic emission signal for diagnostic information. The rolling contact fatigue process of a ball bearing under grease lubrication was monitored using the compound system. The system outputs diagnostic information, for example, the means, the variance, the skewness, and the kurtosis of the vibration acceleration signal and the acoustic emission signal. In diagnosing the rolling contact fatigue failure, the root mean square (rms) value of the vibration acceleration was most effective, and the mean of the demodulated acoustic emission was second to the rms value of the acceleration in effectiveness. From the result of the evaluation, it became clear that the system was useful for diagnosing rolling contact bearings under grease lubrication.     

The investigation of contact ratio in mixed lubrication

In order to describe the mixed lubrication in nano-scale which is constituted from dry friction, boundary lubrication, and thin film lubrication, a contact ratio between surfaces of a glass disk and a steel ball in a pure rolling process has been measured by the technique of Relative Optical Interference Intensity (ROII) with a resolution of 0.5 nm in the vertical direction and 1 μm in the horizontal direction. The relationships between the contact ratio and its influence factors have been investigated. Experimental results indicate that the contact ratio in the static state is related to the combined surface roughness, maximum Hertz pressure, and the combined elastic module of tribo-pair in an exponential function. The decrease of rolling speed or lubricant viscosity, and the increase of the pressure will enhance the dynamic contact ratio which is the contact ratio measured in the rolling process. The addition of polar additives into basic oil will reduce the contact ratio. The contact ratio between rough surfaces is larger than that between smooth surfaces in the higher speed region. However, the former becomes smaller than the later after speed decreases below a critical value. A formula for calculating the dynamic contact ratio is given in the end of the paper.     

Simulation of non-Gaussian surfaces with FFT

A numerical procedure for the simulation of non-Gaussian surfaces has been developed. Fast Fourier Transform is used to generate the surfaces. The amplitude part is constructed from given spectral density or auto-correlation function. The phase part is obtained by using Johnson translator system. By iteration, this method can simulate surfaces with given skewness and kurtosis and with spectral density or auto-correlation function.     

Economic Statistical Design of Average Control Charts for Monitoring a Process under Non-normality

When an x control chart is used to monitor a process, three parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits for the chart. Duncan presented a cost model to determine the three parameters for an x chart, which is called the economic design of the x chart. In this paper, the Burr distribution is employed to conduct the economic statistical design of the x charts for non-normal data. Duncan’s cost model is used as the objective function, and the cumulative function of the Burr distribution is applied to derive the statistical constraints of the problem. An example is presented to illustrate the solution procedure. From the results of the sensitivity analyses of this example, we find that the skewness coefficient of the underlying population has no effect on the optimal sample size; however, a larger value of skewness coefficient leads to a slightly smaller sampling interval and a narrower control limit. Also, an increase in kurtosis coefficient results in an increase in the sample size, a slight increase in sampling interval, and a wider control limit.     

Investigation of the strain distribution with lubrication during the deep drawing process

A lubrication/friction model can be implemented in FEM codes to predict the contact area ratio, friction coefficient and strain distribution in lubricated deep drawing process. In the lubrication analysis, the surface roughness effect on lubrication flow is included by using Wilson and Marsault's average Reynolds equation that is appropriated for mixed lubrication with severe asperity contact. With regard to the asperity contact theory, the well-known flattening effect is considered. Friction is expressed in terms of variables such as lubricant film thickness, sheet roughness, lubricant viscosity, interface pressure, sliding speed, and strain rate. The proposed lubrication/friction model combined with a finite element code of deep drawing process to predict the contact area ratio, friction coefficient and strain distribution. Numerical results showed that the present analysis provides a good agreement with the measured strain distributions.     

柴油机缸套表面微沟槽织构润滑性能仿真分析

针对缸套表面织构微沟槽形貌,建立了缸套-活塞环摩擦副混合润滑理论模型,并采用MATLAB编程计算来分析微沟槽形貌参数对其润滑摩擦性能的影响规律。结果表明：缸套表面微沟槽可以形成很好的油膜压力,有效地改善缸套-活塞环间的润滑状态;随着微沟槽角度的增大,最小膜厚比逐渐增大,其润滑效果也越来越好,综合考虑摩擦润滑性能和机油耗性能情况下,最佳的微沟槽角度为60°。在上止点附近,面积占有率变化Sp对量纲一摩擦力影响较大;在其他区域,面积占有率对摩擦力影响不大;综合考虑油膜厚度与摩擦力,当Sp=0.15时效果最好。随着微沟槽深宽比e的增大,量纲一摩擦力不断增大,当e从0.025增大到0.150时,平均量纲一摩擦力增大了2.3倍,但深宽比过大,润滑效果将会减弱。研究结果认为,最佳深宽比的范围为0.05~0.08。
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Influence of temperature on the friction performance of gear oils in rolling–sliding and pure sliding contacts

The friction behaviour of five different gear oils in rolling–sliding and pure sliding contacts and how temperature influences their friction properties were investigated. It is found that increasing temperature decreases boundary friction with gear oils that contain friction modifiers while not for other gear oils, at all contact pressures investigated. In mixed lubrication region, temperature decreases friction at low contact pressures while increases friction at high contact pressures. The effect of slide–roll ratio on friction is significant in boundary lubrication region especially at higher temperature while less significant in mixed lubrication region at both low and high temperatures. The ranking of gear oils for friction in boundary and mixed lubrication regimes is similar both in rolling–sliding and pure sliding contacts, regardless of temperature. Copyright © 2013 John Wiley & Sons, Ltd.     

Friction characteristics of piston ring pack with consideration of mixed lubrication: Parametric investigation

This paper reports on the friction characteristics of a piston ring pack with consideration of mixed lubrication. The analytical model is presented by using the average flow and asperity contact model. The effect of operating condition, and design parameters on the MOFT, maximum friction force, and mean frictional power loss are investigated. Piston ring pack shows mixed and hydrodynamic lubrication characteristics. From the predicted results, it was fand that the ring tension and height of surface roughness have great influence on the frictional power losses in a ring pack. Especially, ring tension is a dominant factor for the reduction of friction loss and maintenance of oil film thickness.