Non-newtonian thermal analysis of an EHD contact lubricated with MIL-L-23699 oil

A thermal and non-Newtonian fluid model under elastohydrodynamic lubrication conditions is proposed, integrating some particularities, such as the separation between hydrodynamic and dissipative phenomena inside the contact. The concept of apparent viscosity is used to introduce the non-Newtonian behaviour of the lubricant and the thermal behaviour of the contact into the Reynolds equation, acting as a link element between the hydrodynamic and dissipative components of the EHD film, independently of the rheological and thermal models considered. The apparent viscosity enables the application of the rheological model better adapted to each lubricant, without appealing to special formulations of the EHD problem.The Newton–Raphson technique is used to obtain the lubricant film geometry and the pressure distribution inside the EHD contact. The shear stresses developed in the fluid film are evaluated assuming the non-linear Maxwell rheological model. The surfaces and lubricant temperature distributions are determined using the simplified Houpert's method, applied to the inlet contact zone, and the thermal method proposed by Tevaarwerk is applied in the high pressure contact zone.The non-Newtonian thermal EHD model is applied to the analysis of a contact lubricated with MIL-L-23699 oil. Significant results are obtained for the centre and minimum film thickness, for the inlet shear heating and film thickness reduction factor (φ_T), for the temperature rise of the lubricant and of the surfaces and for the friction coefficient inside the contact, considering wide ranges of the operating conditions (maximum Hertzian pressure, inlet oil temperature, rolling speed and slide-to-roll ratio).Finally, the numerical traction curves determined are compared with the corresponding experimental results, showing very good correlation.     

Influence of temperature distributions in EHL film on its thickness under high slip ratio conditions

This paper describes the influence of temperature rise of oil film in Hertzian contact area on the film thickness or profile under high slip ratio conditions. Temperatures of both surfaces of a ball and a disk as well as average temperature across the oil film were measured by means of an improved infrared. Two kinds of optical band-pass filters were used to separate the radiations from the ball surface and the oil film through an infrared transparent disk made of sapphire glass. In case of temperature measurement of the disk surface, another sapphire glass disk was coated with 300 nm chromium layer on the contact surface to radiate the infrared from the disk surface and also to intercept the radiation from the ball surface and the oil film. Temperature profiles across the oil film were estimated by assuming a parabolic profile with the measured three kinds of temperatures.For case within 200% in slip ratio, both minimum and central film thickness decreased under constant entrainment velocity as slip ratio increased. Measured film shapes were not flat at central Hertzian contact region under high-slip condition and differed from the results by the conventional EHD theory assuming constant viscosity in the direction of film thickness. The profile of Couette flow varied due to the distribution of oil film temperature in thickness direction. The viscosity wedge action, that is the variation of the profile of Couette flow causes reduction of film thickness or deformation of film profile. For case over 200% in slip ratio, the relation between central film thickness and slip ratio under constant relative slide speed had a great difference from the results calculated from the formula presented by Chittenden et al.     

Thermal point contact EHL analysis of rolling/sliding contacts with experimental comparison showing anomalous film shapes

The paper presents an experimental and numerical investigation of non-conformal lubricated contacts in which anomalous film shapes occur. The experiments were concerned with the contact between a steel ball and the plane surface of a glass disc at various slide-roll ratios. A paraffin base mineral oil was used as a lubricant and friction coefficients and film thicknesses were measured. It was found that for slide-roll ratios with the disk moving faster anomalous elastohydrodynamic lubrication (EHL) films were obtained characterized by a “dimple” in the central region of the contact. Numerical thermal-elastohydrodynamic analyses were carried out to simulate both film thickness and friction corresponding to the experimental conditions using Newtonian and Ree-Eyring rheological models. Initial results from this study suggest that neither of these lubricant models predict the correct detailed film shape and the experimental friction at the same time. An alternative lubricant model including both thermal and limiting shear stress effects (wall slippage) is currently under development.     

A Refined Solution to the Thermal-Elastohydrodynamic Lubrication of Rolling and Sliding Cylinders

In this paper, a recent solution on the thermal-elastohydrodynamic lubrication of rolling and sliding cylinders is extended to consider a more rigorous analysis of temperature by using a two-dimensional finite difference method. The effect of the local pressure-temperature dependent viscosity, the compressibility effect of the lubricant and the heat from compression of the lubricant are considered in the solution of the Reynolds and the energy equations.

Two series of results were obtained. The first is a heavily loaded series intended to correlate with Crook's experimental results, and the second is a moderately loaded series intended to correlate with experimental data (15).

These results show that temperature has a moderate influence upon the shape of the pressure and film profile, but very little effect upon the magnitude of the film thickness in the contact zone. The frictional force, however, is strongly influenced by the temperature rise in the film.

Crook's experimental film thickness data and those predicted by this report show good agreement; however, only partial agreement is shown to exist between the theoretical and experimental friction data.     

周期性载荷作用下油池形态试验观察

为了模拟轴承滚动体进入和离开接触区载荷中润滑剂的流动分布形态,采用往复结构实现球-盘接触点处载荷周期性变化,利用光干涉润滑油膜测量技术观察周期性载荷作用下接触区外围油池形态随供油量、速度和加载周期的变化规律。结果表明：低速下油池处于封闭态,载荷的增加将使量纲一入口距离和侧油池宽度减小,表明供油条件变差;速度升高后,载荷增加和加载周期减小将导致尾部油池过早破裂,载荷减小过程中将发生尾部油池合并的现象;速度较高时油池将呈现为分离态,接触区为完全乏油状态,滚道重叠作用将对润滑剂的回填和润滑状态起到一定的增强作用。     

The Film Behaviors of Grease in Point Contact During Microoscillation

Microoscillation is a typical case of transient motion, which occurs in many machine elements, including rolling or sliding element bearings, cams, and gears. Wear is easy to occur on the surface of such elements, particularly at the end point of the stroke, where the surfaces are momentarily static. In the present work, an experimental investigation is conducted to explore the grease film behavior of point contact lubrication during microoscillation in the case of pure rolling or pure sliding. The technique of relative optical interference intensity was used to monitor the variation of the grease film thickness and the motion of the grease in the contact area through analyzing the captured interferograms. Experimental results indicate that a crescent-shaped grease film can form along the motion direction in the contact area under microoscillation. The grease film is formed in the inlet region, and the film thickness remains while moving in the Hertzian contact area. In the case of pure rolling, the crescent-shaped grease film and the initial entrapped grease film are carried by a tow effect of moving interfaces in the contact area. However, in the case of pure sliding, there are relative motions in the sliding direction at the two interfaces of the grease/ball and the grease/disk in the Hertzian contact area. The shape of the entrapped grease remains almost unchanged while moving in the Hertzian contact area. During the repetition of microoscillations, the crescent-shaped grease film thickness drops gradually.     

多点接触乏油弹流润滑模型及试验研究

为探讨多点接触乏油弹流润滑机制,基于球与滚道接触区域的排油和补油平衡,建立适用于不同润滑状态的油膜厚度计算模型,可以计算从充分供油、乏油到干涸乏油的中心膜厚以及油膜不平衡时中心膜厚随滚动次数的衰减。利用自制的球-盘接触光干涉弹流试验装置,通过安装双镜筒同时获取相邻球的油膜图像,研究多点接触中相邻球的轨道重合和不重合时前球尾迹对后球油膜图像和中心膜厚的影响。结果表明:乏油润滑条件下,前后球的轨道不重合时轨道之间可相互补油;前后球的轨道重合时,在给定供油条件下,随着滚动线速度增加,入口弯液面逐渐靠近接触区域,中心油膜厚度增加,与相同工况下乏油润滑模型计算的膜厚对比吻合较好,验证了所建乏油润滑模型的正确性。     

Thermoelastohydrodynamic Analysis of Spur Gears with Consideration of Surface Roughness

Thermoelastohydrodynamic lubrication (TEHL) analysis for spur gears with consideration of surface roughness is presented. The model is based on Johnson’s load sharing concept where a portion of load is carried by fluid film and the rest by asperities. The solution algorithm consists of two parts. In the first part, the scaling factors and film thickness with consideration of thermal effect are determined. Then, simplified energy equation is solved to predict the surfaces and film temperature. Once the film temperature is known, the viscosity of the lubricant and therefore friction coefficient are calculated. The predicted results for the friction coefficient based on this algorithm are in agreement with published experimental data as well as those of EHL simulations for rough line contact. First point of contact is the point where the asperities carry a large portion of load and the lubricant has the highest temperature and the lowest thickness. Also, according to experimental investigations, the largest amount of wear in spur gears happens in the first point of contact. Effect of speed on film temperature and friction coefficient has been studied. As speed increases, more heat is generated and therefore film temperature will rise. Film temperature rise will result in reduction of lubricant viscosity and consequently decrease in friction coefficient. Surface roughness effect on friction coefficient is also studied. An increase in surface roughness will increase the asperities interaction and therefore friction coefficient will rise.     

Temperature—The Key to Lubricant Capacity

Failure of a nonreactive mineral oil can be predicted by Blok's formula for determining the maximum temperature between two bodies in rolling and sliding contact. Evaluation of many lubricants on a geared roller lest machine revealed that the lubricant failure for any particular lubricant-material combination occurs at a constant, critical contact temperature over wide ranges of load, sliding velocity, surface velocity, specimen temperature, film thickness, and viscosity grade. Coefficient of friction can be predicted by a parameter involving the unit load, inlet viscosity, sum velocity, and sliding velocity. The load capacity of a lubricant varies inversely with specimen temperature for a constant set of lest conditions. Electrical resistance measurements across the contact zone aided in identifying the lubricant failure point and in revealing the action of two deposit-forming additives.     

Experimental and numerical investigation on the behavior of transverse limited micro-grooves in EHL point contacts

This study presents experimental and numerical investigations on the effects of transverse limited micro-grooves on the behavior of film thickness and friction in EHL point contacts. The tribological performance has been compared for smooth and textured surfaces in sliding and reciprocating motion and under starvation. The measurements were conducted by using a ball-on-disk tribometer equipped with a high speed camera and torque sensor. The results show that the transverse shallow micro-grooves with a length less than the diameter of the Hertzian contact are efficiently able to enhance the film thickness under different operating conditions. The beneficial effect under starved lubrication requires a mechanism for filling the depleted micro-grooves entering the contact with fresh lubricant. This mechanism can be attributed to the capillary effect in the inlet zone under starvation. The numerical simulation of the transient behavior of transverse limited micro-grooves shows agreement with experimental results. On the other hand, introducing micro-grooves as closed texture cells on one of rubbing surfaces results in a friction reduction in the reciprocating motion. The reduction of friction is substantially attributed to the film thickness enhancement.     

冷轧铝工作区的混合润滑特性研究

为研究冷轧铝工作区的混合润滑特性,基于平均流量理论建立考虑表面粗糙度的冷轧铝工作区混合润滑模型,并通过相关文献的数据验证模型的正确性.在不同轧制速度、润滑油黏度以及前后张应力条件下对整个工作区内的润滑特性进行分析,研究轧制工艺参数对油膜厚度、接触面积比以及应力分布的影响.仿真结果表明:随着轧制速度的提高,轧制压力有一定...     

An Investigation of Lubricant Film Thickness in Sliding Compliant Contacts

An optical interferometric technique has been used to investigate fluid film thickness in sliding, isoviscous elastohydrodynamic contacts (I-EHL). Monochromatic two-beam interferometry has been employed to map lubricant film thickness across a range of applied loads and entrainment speeds. The contact was formed between an elastomer sphere and plain glass disc, illuminated under red light, λ= 630 nm. Experimental work has employed sunflower oil and glycerol/water solutions as the test lubricants, due to their similar refractive indices and varying viscosity. A black-and-white-image-intensified camera has been employed to capture interference images and a computer processing technique used to analyse these images, pixel by pixel, and create film thickness maps based on their gray-scale intensity representations. Comparison of film thickness results to theoretical models shows reasonable qualitative agreement. Experimental results show both a reduced horseshoe, which is limited to the rear of the contact, and wedge-shaped film thickness profile within the Hertzian contact region. This is unlike conventional hard EHL contacts where the horseshoe-shaped pressure constriction extends around the contact toward the inlet. Experimental results suggest that film thickness profiles take on a convergent wedge shape similar to that used in many hydrodynamic bearings. It is likely that this wedge is largely responsible for generating fluid pressure and therefore the load-carrying capacity of the contact.     

Substrate surface energy effects on a liquid lubricant film at nanometre scalesubstrate surface energy effects on a liquid lubricant film at nanometre scale

In this paper is discussed the effect of the physical characteristics of substrate surfaces on the lubrication properties of thin films at nanometre scale. Different coatings with different surface energies have been formed on the surface of a steel ball by means of plasma assisted sedimentation (PAS). The ball was put in a pure rolling system in point contact, where the lubricant film is measured by relative optical interference intensity (ROII). Experimental results show that the film thickness is closely related to the substrate surface energy when the film is in the nanometre scale, and that the combined surface roughness in the contact region is closely related to the liquid lubricant film thickness and the contact pressure. The thinner the film and the higher the contact pressure, the smaller will be the combined surface roughness. Lastly, the relationship between critical film thickness and its influencing factors is discussed.     

直齿轮传动非牛顿流体瞬态弹流润滑研究

综合考虑润滑流体的非牛顿特性以及齿轮传动的瞬态效应，采用Bair-Winer粘塑模型推导了非牛顿流体雷诺方程，建立了非牛顿流体瞬态弹流润滑模型；进行直齿轮传动非牛顿流体弹流润滑数值分析，获得了齿轮传动沿啮合线的油膜压力、油膜形状以及摩擦因数的分布。结果表明：在非牛顿流体工况下，油膜厚度、油膜压力以及轮齿表面摩擦因数均有所降低,因此在齿轮弹流润滑研究中应考虑流体的非牛顿特性的影响。     

陶瓷球轴承的热弹流润滑分析

建立陶瓷球轴承热弹流润滑的数学模型,利用多重网格法和逐列扫描法,得到陶瓷球轴承的点接触热弹性流体动力润滑完全数值解,并与普通轴承计算结果进行比较。结果表明:转速与载荷会对陶瓷轴承的接触区的压力、膜厚、温度产生影响,其中随着转速的增加,最小膜厚增加,摩擦因数减小,滚动体表面温度下降,而随着载荷的增加,最小膜厚减小,摩擦因数增大,滚动体表面温度上升;在相同的工况参数下,陶瓷球轴承的油膜压力低于普通轴承,膜厚高于普通轴承,轴承内圈、滚动体、中层油膜的温升小于钢质轴承,因而陶瓷轴承的润滑性能更好,使用寿命更长。     

A study of rolling bearing fatigue life with mineral oil lubrication

Tests on mineral oil lubricated deep groove ball bearings show that there is an optimum lubricant viscosity to ensure maximum rolling contact fatigue life. The results are explained by lubricant film thickness measurements and the application of E.H.L. theory. The optimum lubricant viscosity increases with increase of load and decreases with reduction of speed.     

Elastohydrodynamic lubrication of line contacts

Elastohydrodynamic film thickness measurements for rolling line contact under fully flooded and starved conditions have been made using optical interferometry. From the results it was found that the film shape at the end of the roller becomes more parallel as lubricant starvation increases.

Two main regions of starvation have been studied, namely progressive and catastrophic regions of lubricant starvation. Furthermore, it was found that the severity of conditions within the hertzian contact increases rapidly as m decreases and dry contact conditions are approached. It has been possible to express the dimensionless inlet distance for catastrophic and progressive lubricant starvation conditions respectively as

It has been concluded that the experimental dimensionless central and minimum film thicknesses under starvation conditions can be written respectively as      

Experimental Analysis and Modeling of the Effects of Oil–Air Lubrication Parameters on Bearings Friction Loss of High-Speed Motorized Spindle

The friction loss of an angular contact ball bearing is a key factor restricting the development of a high-speed motorized spindle. To quantitatively calculate the effects of the oil–air lubrication parameters on the friction loss of high-speed bearings, the drag resistance and the churning resistance generated by the movement of the rolling elements in the lubricant are theoretically modeled and the percentage volume of the lubricant in the bearing cavity (XCAV) is used to characterize the effects. The friction loss of bearings is tested by two novel methods: the free deceleration method and the energy-balance method. The experimental results show that the viscous resistance loss is a major component of bearing friction loss and oil–air lubrication parameters have important influence on it. A comparison of the theoretical calculations and the experimental results is used for deriving the empirical formula of XCAV with respect to the lubricant flow, gas pressure, rotating speed, and pitch diameter. The research results of this study have important significance for the measurement, prediction and reduction of the friction loss of high-speed bearings.     

Film-forming Characteristics of Grease in Point Contact under Swaying Motions

The technique of relative optical interference intensity (ROII) and simple numerical calculations were used to investigate the lubricating behavior of grease lubricant films in the rolling direction under swaying motions (acceleration/deceleration). Experimental results indicate that at a same entrainment velocity of the inlet, the central film thickness under deceleration is larger than that under acceleration. The minimum central film thickness in one swaying cycle does not occur at the moment of zero entrainment, but at the initial period of acceleration. At the moment of zero entrainment, the central film is thicker than its peripheries, and the value of the central film thickness increases with increases in the changing rate of the entrainment velocity. It is thought that the transient behaviors of the grease lubricant film deviate from those in steady state conditions. The profiles of the transient film thickness and the approximate thicknesses of elastohydrodynamic contact in the rolling direction calculated by using a simple numerical method are supported by the experimental results. The numerical method can also be used to explain the behavior of the grease lubricating film under non-steady state conditions. An erratum to this article can be found at     

The Prediction of Contact Pressure–Induced Film Thickness Decay in Starved Lubricated Rolling Bearings

Under starved conditions the thickness and distribution of the lubricant film in an elastohydrodynamically lubricated (EHL) contact is directly related to the distribution of lubricant on the track in the inlet to the contact. In starved lubricated rolling bearings this lubricant distribution is determined by many effects. The authors have developed a model to predict the oil lost from the track induced by EHL pressure with no replenishment. A complete bearing is modeled with multiple rolling element EHL contacts and with the applied load to the rolling elements varying along the circumference of the bearing. Results of the oil layer thickness on the track are presented for a ball bearing and a spherical roller bearing for different bearing loads and rotational speeds. The predicted layer thickness decay rate for a ball bearing is significantly larger than for a spherical roller bearing and the predicted effect of the bearing load on the decay rate is small compared to the effect of the rotational speed. The predicted decay periods due to the contact pressure effect are small compared to the observed (grease) life of bearings. The results show that a bearing cannot sustain an adequate layer of oil on the running track unless significant replenishment takes place.