Computational model of tandem rectangular elastomeric seals for reciprocating motion

A numerical model developed by Nikas [Nikas GK. Elastohydrodynamics and mechanics of rectangular elastomeric seals for reciprocating piston rods. Trans ASME, J Tribol 2003;125(1):60–9; Nikas GK. Determination of polymeric sealing principles for end user high reliability. Technical Report DOW-08/01 (Dowty project), Mechanical Engineering Department, Tribology Section, Imperial College London, London; 2001; Nikas GK. Theoretical study of solid back-up rings for elastomeric seals in hydraulic actuators. Tribol Int 2004;37(9):689–99; Nikas GK. Analytical study of the extrusion of rectangular elastomeric seals for linear hydraulic actuators. Proc IMechE, Pt J J Eng Tribol 2003;217(5):365–73; Nikas GK. Transient elastohydrodynamic lubrication of rectangular elastomeric seals for linear hydraulic actuators. Proc IMechE, Pt J J Eng Tribol 2003;217(6):461–73; Nikas GK, Sayles RS. Nonlinear elasticity of rectangular elastomeric seals and its effect on elastohydrodynamic numerical analysis. Tribol Int 2004;37(8):651–60] to study rectangular elastomeric seals used in linear hydraulic actuators has been expanded to study the system of two identical seals in a row at some distance from each other (tandem or dual seals). The objective is to evaluate the leakage performance of this particular seal arrangement and possible problems associated with the development of a substantial interseal pressure, which have been observed in some experimental studies. The updated model involves anti-extrusion rings supporting the tandem seals. The present study covers the full typical range of operating conditions of such seals, namely sealed pressure between nearly zero and 35 MPa, stroking velocity between 0.05 and 0.5 m/s, and operating temperature from −54 to +135 °C. The leakage results are in quantitative and qualitative agreement with experimental studies and industrial experience. It is found that the tandem seal arrangement offers a significant reduction of leakage (in the order of 50% or more) compared with the single-seal configuration and that the interseal pressure remains low until the time when it rises abruptly to high value, even exceeding the sealed pressure and risking seal failure. However, by allowing a sufficiently large interseal space, the interseal pressure problem is resolved for the projected service life of the sealing system.     

Squeeze films between a rigid cylinder and an elastic layer bonded to a rigid foundation

A numerical solution to the elastohydrodynamic lubrication problem of a rigid cylinder and an elastic layer firmly bonded to a rigid substrate in normal approach and separated by a fluid of constant viscosity is presented. The rate of change of the deformation with time was neglected in the present investigation. The governing equations were solved via an iterative method in order to compute the pressure distribution and the corresponding film profile.Influences of the layer thickness, the layer compressibility and the central squeeze-film velocity on the results were investigated. In the case of the Hertzian contact, the present method was validated against the results reported in Herrebrugh [Elastohydrodynamic squeeze films between two cylinders in normal approach, Trans ASME, J Lubric Technol Ser F 1970; 92:292–302] where the results showed a very good agreement.     

The transition between fully flooded and starved regimes in EHL

Lubricant starvation of the contact can occur in high-speed oil or grease lubricated bearings resulting in reduced elastohydrodynamic (EHL) film thickness (Lubricat. Sci. 11 (1999) 227). To achieve optimum bearing performance and component life, it is obviously desirable to be able to predict when starvation will occur and the resulting level of surface protection. For both oils and greases, the transition between fully flooded and starved behaviour is determined by lubricant loss and replenishment of the track (ASME Trans. J. Tribol. 120 (1998) 126; Cann PME, Chevalier F, Lubrecht AA. Track depletion and replenishment in a grease lubricated point contact: a quantitative analysis. Proceedings of the 23rd Leeds–Lyon Symposium on Tribology. 1996. p. 405–14). The current paper develops a criterion for the fully flooded and starved transition of an oil-lubricated contact based on four primary factors controlling lubrication level; these are volume of oil, contact dimensions, oil viscosity and speed. Experiments have been carried out using an optical EHL device to investigate the effect of each of these parameters on starvation. The results show how the boundary between the fully flooded and the starved regime and the film thickness in the starved regime depend on these parameters. A single dimensionless parameter (SD), based on replenishment local to the contact, has been established between the operating parameters and the transition from the fully flooded to starved regime.In this paper, the starvation criterion has been developed for an oil-lubricated contact with a fixed volume of oil present. The next stage is to extend the analysis to grease and the prediction of lubrication failure in bearings.     

Limit transmissible torque in the traction drive of a concave and convex roller pair

This paper presents a study on the limit transmissible torque in the traction drive of a concave–convex roller pair. The transmitted torque, the specific sliding, the roller surface temperature and the oil film formation under different contact pressures and roller speeds were simultaneously measured by carrying out a concave–convex roller test. The effect of the lubricant on the limit transmissible torque of the concave–convex roller pair was investigated. Furthermore, the experimental results were compared with theoretical ones based on the thermal elastohydrodynamic lubrication theory, which takes account of the effects of viscous heating and Eyring viscosity. Close agreement between the theoretical and experimental results was obtained.     

Influence of load and elastic properties on the rolling and sliding friction of lubricated compliant contacts

Lubricated “soft” contacts, where one or both contacting solids have a low elastic modulus, are present in many practical engineering and biological applications including windscreen wipers, wet tyres, elastomeric seals, contact lenses and the tongue/palate system. In such contacts, the prevailing lubrication mode is “isoviscous EHL” (elastohydrodynamic lubrication). Unlike in steel–steel contacts, rolling friction can be considerable and this originates in part from the viscoelastic properties of the compliant surfaces.In this paper the influence on friction of both applied load and the elastic properties of the solids is studied using a mini traction machine. In this machine, the rolling and sliding friction can be separately determined. The viscoelastic properties of the polymers employed are measured using a dynamic mechanical analysis apparatus. The measured friction is compared to theoretical models for soft EHL and the viscoelastic energy losses arising from the contact deformation. Consideration of the frequency dependence of the substrate viscoelasticity enables reasonably accurate predictions of the rolling friction coefficient, especially within the mixed and boundary lubrication regimes.     

Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures

An efficient numerical method based on Lobatto quadrature analysis is adopted for a rigorous analysis of temperature in elastohydrodynamic lubrication (EHL) line contacts. Temperature distributions are calculated for maximum Hertzian pressures and rolling speeds varying between 0.5 to 2.0 GPa and 1 to 30 m/s, respectively. Significant mid-film temperature and surface temperature increases have been observed at higher rolling speeds with an increase in loads and slip ratios. Results have been compared with the results of Manton, S. M., O'Donoghue, J. P. and Cameron, A., Temperatures at lubricated rolling/sliding contacts. Proceedings of the Institution of Mechanical Engineers, 1967–68, 182(417), 813–824. An empirical equation is presented for the prediction of non-dimensional maximum mid-film temperature in the contact zone in terms of the dimensionless thermal loading parameter Q, dimensionless load W and slip S, as:

     

Compression Heating and Cooling in Elastohydrodynamic Contacts

In this study, the infrared temperature mapping technique, originally developed by Sanborn and Winer (Trans ASME J Tribol 93:262–271, 1971) and extended by Spikes et al. (Tribol Lett 17(3):593–605, 2004), has been made more sensitive and used to study the temperature rise of elastohydrodynamic contacts in pure rolling. Under such conditions lubricant shear heating within the contact is considered negligible and this allows temperature changes due to lubricant compression to be investigated. Pure rolling surface temperature distributions have been obtained for contacts lubricated with a range of lubricants, included a group I, and group II mineral oil, a polyalphaolefin (group IV), the traction fluid Santotrac 50 and 5P4E, a five-ring polyphenyl-ether. Resulting maps show the temperature rise in the contact increases in the inlet due to compression heating and then decreases and in most cases becomes negative in the exit region due to the effect of decompression. Temperature changes increase with entrainment speed but in the current tests are always very small, and less than 1 °C. Contact temperature rises from compression were compared to those from sliding contacts (where a slide-roll ratio of 0.5 was applied). Here the contribution to the contact temperature from compression is shown to decrease dramatically with entrainment speed. The lubricant 5P4E is found to behave differently from other lubricants tested in that it showed a peak in temperature at the outlet. This effect becomes more pronounced with increasing speed, and has tentatively been attributed to a phase change in the exit region. Using moving heat source theory, the measured temperature distributions have been converted to maps showing rate of heat input into each surface and the latter compared with theory. Qualitative agreement between theory and experiment is found, and a more accurate theoretical comparison is the subject of ongoing study.     

Effect of Sliding Direction on EHL Film Shape Under High Sliding Conditions

It is well known that a sliding speed influences a lubricant film thickness of elastohydrodynamic rolling–sliding contacts significantly. The effect of sliding is described quite well for unidirectional rolling and sliding; however, there are a limited number of papers dealing with sliding in different directions. This study describes how the sliding direction influences elastohydrodynamic film shape under high sliding conditions. An optical ball-on-disc tribometer together with thin-film colorimetric interferometry method is used for a film thickness measurement. The results show that the sliding direction influences lubricant film shape and the effect is connected with dimple phenomena. The temperature–viscosity wedge effect is discussed as a possible mechanism. The results are important for a film thickness prediction under high sliding conditions and provide experimental evidence for an extension of elastohydrodynamic lubrication (EHL) theory.     

Inverse approach for estimating rheological characteristics of adsorption layer in thin film EHL contacts

A modified Reynolds equation is derived for thin film elastohydrodynamic lubrication (TFEHL) by means of the viscous adsorption theory. This TFEHL theory can be used to explain the deviation between the measured film thickness and that predicted from the convenient elastohydrodynamic lubrication (EHL) theory under very thin film conditions. Results show that the thinner the film, the greater the ratio of the adsorption layer to the total film thickness becomes, and the greater the value of the pressure–viscosity index (z′). An inverse approach is proposed to estimate the pressure distribution based upon the film thickness measurement and to determine the pressure–viscosity index of oil film, and the thickness (δ) and the viscosity ratio (η^*) of the adsorption layer in TFEHL circular contacts. Based on TFEHL theory, the inverse approach can reduce z′ error, and provides a reasonably smooth curve of pressure profile by implementing the measurement error in the film thickness. This algorithm not only estimates the pressure, but also calibrates the film shape. Consequently, it predicts z′, η^*, and δ with very good accuracy. It can also be used to evaluate the lubrication performance from a film thickness map obtained from an optical EHL tester. Results show that the estimated value of z′ is in very good agreement with the experimental data.     

Thermal analysis of dry sleeve bearings — a comparison between analytical, numerical (finite element) and experimental results

Thermal analysis of a plastic sleeve bearing in dry operation was investigated experimentally by Floquet et al. [Trans. ASME, J. Lubr. Technol. 99 (1977) 277]. For a comparison with the experimental results, Kennedy [Trans. ASME, J. Tribol. 103 (1981) 90] developed a numerical approach using the finite element method (FEM) that included the development of finite element equations for the case of a moving body heat conduction. In this investigation, both the experimental results of Floquet [Docteur-Ingenier thesis, Université Claude Bernard, Lyon, 1978] and the numerical results of Kennedy were compared with the results of the analytical method developed using the classical heat source method introduced by Jaeger [Proc. Roy. Soc. NSW 76 (1942) 203] and the heat partition principles of Blok [Proc. Inst. Mech. Engrs. 2 (1937) 222], which involves matching of the temperatures on either side of the contact interface. The non-uniform distribution of heat partition (as one body is stationary and the other moving) along the interface is addressed by matching the temperatures at the interface between the stationary and the moving bodies in relative sliding contact using the functional analysis approach originally introduced by Chao and Trigger [Trans. ASME 72 (1955) 1107]. The analytical results are found to be in excellent agreement with both the experimental and the numerical results.     

界面滑移条件下点接触Stribeck曲线的实验研究

采用高黏度聚异丁烯润滑油,在光学弹流实验机上考察球-盘接触纯滑条件下的摩擦因数随卷吸速度和载荷的变化。结果表明,随着卷吸速度的增加,球-盘接触副进入弹流润滑并向流体动压润滑转变的过程中,摩擦因数并不像传统的Stribeck曲线一样,随着卷吸速度的增加而单调增加,而是呈现先上升、后下降、再上升的趋势,其中摩擦因数下降时的起始速度大致为凹陷出现的速度,摩擦因数再上升时的速度大致是润滑进入动压润滑的速度。初步论证界面滑移为产生上述波动的主要原因。     

On the thermal elastohydrodynamic lubrication in opposite sliding circular contacts

Cases of elastohydrodynamic lubrication (EHL) point contacts running under opposite sliding conditions have been studied with consideration of the thermal effect for various loads and entrainment velocities. A thermal EHL solver has been developed and proven to be able to deal even with extreme cases under an infinite slide–roll ratio. Results show that film profiles featuring a dimple can be formed in the contact zone when the slide–roll ratio exceeds a certain level. Moreover, the present study provides theoretical evidence for the lubricating film build up in the case where the two bounding surfaces run with equal but opposite velocities. An effective lubricating film under zero entrainment speeds was experimentally proven by Dyson and Wilson [1] (Proc Instn Mech Engrs, 1968–1969 183(3P) 81) in the 1960's, which, however, cannot be explained by the isothermal EHL theory.     

A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction

We present a realistic elastohydrodynamic lubrication (EHL) simulation in point contact using a Carreau-like model for the shear-thinning response and the Doolittle-Tait free-volume viscosity model for the piezoviscous response. The liquid lubricant modeled is a high-viscosity polyalphaolefin which has been shown by high-pressure viscometry to possess a relatively low threshold for shear-thinning as a single-component liquid lubricant. As a result, the measured EHL film thickness is about one-half of the Newtonian prediction. We derived and numerically solved the two-dimensional generalized Reynolds equation for the modified Carreau model based on Greenwood. In this simulation, viscosity was not treated as an adjustable parameter; the models used for the pressure and shear dependence of viscosity were obtained entirely from viscometer measurements. Truly remarkable agreement is found in the comparisons of simulation and experiment for traction coefficient and for film thickness in both pure rolling and sliding cases.     

Chain matching between hydrocarbon and fatty acid as interfacial phenomena

According to the investigations of Cameron and his coworkers^1–5 into the chain-matching phenomena between normal paraffin as a solvent and straight-chain fatty acid as an additive, the optimum condition in boundary lubrication is attained when the chain lengths of the additive and solvent are equal. A series of experiments has been conducted over the past ten years on the role of the chain-matching effect, not only on boundary lubrication but also widely on relevant interfacial phenomena. The results of the investigations are discussed.     

Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Hard Disk Drives

Slip-corrected Reynolds equations have not been widely used in the air bearing simulations for the head-disk interface in hard disk drives since Fukui and Kaneko [Trans ASME J Tribol 110:253–262, 1988] published a more accurate generalized lubrication equation (FK model) based on the linearized Boltzmann equation for molecular gas lubrication. However, new slip models and slip-corrected Reynolds equations continue to be proposed with certain improvements or with the more physical basis of kinetic theory. Here, we reanalyze those slip models and lubrication equations developed after the FK model was published. It is found that all of the slip-corrected Reynolds equations are of limited use in the air bearing simulations, and that these new slip-corrected Reynolds equations cannot replace the FK model for calculating an accurate pressure distribution of molecular gas lubrication.     

Study on Starved Lubrication Performance of a Cycloid Drive

The lubrication performance of cycloid drives affects the dynamic characteristics, mechanical efficiency, and contact fatigue behavior. Starved lubrication performance of a cycloid gear drive is studied using a numerical thermo-starved elastohydrodynamic lubrication model. The parameter of the inlet oil film thickness is chosen to represent the starvation degree. Effects of the inlet film thickness on the central film thickness, friction coefficient, frictional power loss, starting position of the effective film thickness, and lubrication efficiency are investigated. The optimum inlet film thickness is defined and is calculated under different rolling–sliding ratios, speeds, and loads. Finally, the optimum inlet film thickness during the meshing process of a cycloid drive is calculated.     

Coefficient of friction of a starved lubricated spur gear pair

The frictional power loss issue of gear pairs becomes an important concern in both industry and academia due to the requirement of the energy saving and the improvement of power density of gear drives. A thermal starved elastohydrodynamic lubrication model is developed to study the tribological performance of a spur gear pair under starved lubrication conditions. The contact pressure, the film thickness, the temperature rise, the frictional power loss, as well as the coefficient of friction are evaluated by considering the variation of the curvature radius, the sliding/rolling motion, and the load distribution of gear tooth within the meshing period. Effects of lubrication starvation condition, load and speed on the coefficient of friction are studied.

     

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.     

基于声发射技术的点接触润滑状态研究

为研究点接触在部分弹流润滑条件下的润滑状态,使用球盘式摩擦磨损试验机进行试验,利用声发射技术监测不同工况下的润滑状态,并分析在不同工况下声发射信号特征参数的变化规律。结果表明:声发射信号特征参数计数、能量、信号强度对润滑状态的改变非常敏感,都随滑动速度的增加而减小,随载荷的增加而增加且在变化规律上几乎一致;利用声发射技术能够表征边界润滑向部分弹流润滑的过渡状态。     

Failure of thin film lubrication — A detailed study of the lubricant film breakdown mechanism

The mechanism of breakdown of the lubricant film in a concentrated steel contact has been studied by examining friction-time diagrams as functions of sliding speed (ranging from 0.0007 to 0.7 m s^?1) and normal force on the contact. It was found that, even at the lower speed of 0.0007 m s^?1, the load-carrying capacity of the contact still depends strongly on lubricant viscosity. Over the whole range of speeds, lubricant film breakdown can be explained in terms of a major disturbance in the steady state condition, which is characteristic of (partial) elastohydrodynamic lubrication. In that condition, oxidation of microasperities which enter the surface zone keeps abreast of metal-to-metal junction formation.