Film‐forming additives ‐ direct and indirect ways to reduce friction

This paper reviews the current understanding of lubricated contacts and the origins of friction in terms of the Stribeck curve. It discusses the various ways that lubricant additives can modify friction in thin‐film lubricated contacts, examining both the nature and properties of the films formed by these additives, as revealed by film thickness measurements, and their consequent effect on the Stribeck friction curve.     

基于Stribeck曲线的液压缸劣化趋势评价

为了评估液压系统的工作状态,提出了基于Stribeck摩擦模型的劣化程度评估方法。通过机理解析建立液压缸动力学模型,将实际系统可测量位移数据以及利用位移信号差分处理得到速度信号和加速度信号作为系统输入,其他测量数据和已知参数组成系统输出,设计双时间尺度最小二乘法辨识未知参数。将辨识的摩擦系数用于刻画Stribeck曲线,通过比较不同时间段的Stribeck曲线建立劣化指标,并分析相应缸体劣化程度。通过数值仿真验证理论的合理性和有效性。     

二次调节主动升沉补偿实验平台的摩擦辨识与补偿控制

以二次调节主动升沉补偿实验平台为研究对象,针对系统中存在的非线性摩擦转矩,提出摩擦辨识及补偿方案。首先,选用Stribeck模型描述系统摩擦,建立了包含非线性摩擦转矩的平台数学模型;其次,根据平台特点设计摩擦辨识策略,使用最小二乘算法辨识得到未知系统参数,在此基础上拟合Stribeck曲线获取摩擦模型参数;然后,通过摩擦前馈和非线性PID实现摩擦补偿控制,提高升沉补偿精度;最终,实验验证了所提方案的有效性。     

基于区间分析理论的摩擦补偿研究

本文采用新型Stribeck模型和区间辨识方法对伺服系统中的摩擦补偿进行了研究。首先,针对Stribeck摩擦模型存在非线性、控制计算量大和不利于控制器设计等缺点,本文对其进行了线性化,并提出一种线性化的Stribeck模型;然后介绍了区间理论的参数辨识方法,并对方法的有效性进行了仿真验证研究;利用所提出的新模型进行了摩擦实验,结果显示该模型可以辨识出摩擦参数,接着设计了前馈摩擦补偿控制器。最后,分别采用阶跃和正弦输入信号进行实验,结果显示采用所设计摩擦补偿器补偿后,两种信号的稳态精度分别提高了26.8%和83.63%,验证了新模型和方法的有效性。本文提出的新型Stribeck模型易于工程应用,所用区间分析理论适用于参数辨识。     

Non-conventional inverse-Stribeck-curve behaviour and other characteristics of DLC coatings in all lubrication regimes

Due to the specific surface properties of diamond-like-carbon (DLC) coatings their interactions with base oils and additives differ from those of conventional ferrous engineering materials such as steel. This relates not only to their reactions with additives, which were frequently investigated in the past, but also to the effects of base oils and the physical properties of these oils. In order to better understand the physical phenomena of base oils, in this study we analyse the influence of velocity and viscosity (through the Stribeck parameter) on the friction in DLC/DLC contacts for all lubrication regimes. The tribological tests were performed with various non-polar base oils and the behaviour of the DLC/DLC contacts was compared with the steel/steel contacts, where the lubrication mechanisms are well known. Several differences were found for all the lubrication regimes. However, the most surprising is that in the boundary-lubrication regime the Stribeck curve of the DLC contacts has the opposite, i.e., an “inverse”, shape to that of the steel contacts. Namely, the friction of the DLC contacts decreases at low Stribeck-parameter values, rather than showing an increase, as is known from the classical Stribeck-curve theory. This new finding shows that Stribeck curve shape depends strongly on the type of materials in contacts—not only on classical Stribeck parameters (velocity, viscosity, load).     

Tribological Performance of Silver Nanoparticle–Enhanced Polyethylene Glycol Lubricants

This article introduces a new type of nanoparticle additive for tribological purposes. A nanolubricant was synthesized and studied that consists of metallic silver nanoparticles suspended in polyethylene glycol (PEG). Silver nanoparticles were prepared directly in liquid PEG by introducing aqueous silver nitrate and subsequent reduction by PEG. The nanolubricant exhibits excellent stability due to poly(vinyl pyrollidone) used as the coating agent. Thorough tribological analysis was performed on the nanolubricant, including rheology, friction, wear, and Stribeck curve analysis. Results show that the nanoparticle additives are capable of reducing both friction and wear at low concentrations. Stribeck curve analysis also revealed that the particles are effective in reducing friction in both the boundary and mixed lubrication regimes. The possible friction and wear reduction mechanism of silver nanoparticles is also discussed in the current work.     

Modelling of kinetic friction in V-bending of ultra-high-strength steel sheets

The Stribeck friction model was investigated in this study to predict springback of high-strength steel sheets. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. The influence of forming speed, over-pressing and holding time on springback behaviour of sheets was studied numerically. By plotting the variation of bending angle with punch stroke, we found that the loading curve of finite element analysis showed similar results to the experiments. The unloading curves of FE analysis with friction models based on Stribeck curve and Coulomb law showed good agreement with experiments with error less than 1.5%. Forming speed of up to 50 mm/s does not have significant effect on springback. The effect of holding time on reducing springback is small, but over-press has large effect on reducing springback. The results showed that Stribeck model is suitable for sheet metal forming simulations, especially at higher forming speeds and pressures.     

Friction and wear of copper samples in the steady friction state

The effect of sliding velocity and load on the friction and wear of Cu-steel pairs was studied. Elasto-hydrodynamic (EHL), mixed (ML) and boundary lubrication (BL) regions were analyzed using the Stribeck curve. The lubrication number of Schipper, Z, was used in the analysis of the Stribeck curve. Steady friction states were observed in the mixed EHL and BL regions, however two types of the ML region are revealed. The first type is the stable ML range. The second one is the range of unstable friction and wear when a decrease of the lubricant film leads to abrupt change of all controlled parameters. It was found that a transition to the unstable ML region occurs within a narrow range of Z parameter. Wear modes in the lubrication regions were studied. Deformation hardening in the lubricant regimes is discussed.     

Stribeck Curve Under Friction of Copper Samples in the Steady Friction State

The friction and wear of a pure copper block (99.98 wt% Cu) against a hardened steel disc were studied. The effect of sliding velocity and load on the friction coefficient and wear rate of Cu samples during steady tests was studied. Elasto-hydrodynamic (EHL), mixed (ML) and boundary lubrication (BL) regions were analyzed using the Stribeck curve. The lubrication number of Schipper, Z, was used in the analysis of the Stribeck curve. The transitions from one lubrication region to another are discussed. The mixed EHL region is characterized by stable low values of the friction coefficient, wear rate and temperature. Straight asperity contact is the dominant mechanism under friction of Cu–steel pair in the BL region. High-friction coefficients and wear rates, thin lubricant films and large wear grooves indicate straight asperity contact between rubbed surfaces in the BL region. Although the dominant mechanisms in the mixed EHL and BL regions are different in principle, a steady friction state is preserved in both cases. It is expected that the steady friction state in the BL and mixed EHL regions is associated with deformation and fracture of surface layers but these process occur at different scale levels. It was shown that under friction of Cu–steel pair, two types of ML regions are observed. The first is the stable steady friction of mixed EHL with low values of the friction coefficient and wear rate. The second type of the ML region is the region of unstable friction and wear when a decrease of lubricant film leads to a change of external (roughness, temperature, friction and wear) and internal (strain and stress) parameters. It was found out that a transition to the unstable ML region occurs within a narrow range of Z parameter under definite values of the load and sliding velocity.     

飞机主动侧杆摩擦补偿研究

针对飞机主动侧杆系统中存在非线性摩擦因素,导致在飞机主动侧杆伺服系统中位置跟踪不精确,侧杆跟随性能下降的现象,在三环控制的基础上研究了Stribeck摩擦补偿方法。对Stribeck摩擦模型开展研究,并通过实验辨识其参数,将摩擦模型引入到飞机主动侧杆伺服系统中设计摩擦补偿方法,通过前馈补偿的方式在三环控制的基础上实现摩擦补偿。通过仿真和实验,对侧杆伺服系统摩擦补偿的可行性进行了验证。实验结果表明,所研究的摩擦补偿方法,提高了系统的稳态跟踪精度,具有较好的动态响应性能。     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

精密定位系统的摩擦力建模与补偿

为了提高由直线电机驱动的精密定位系统的定位精度,建立了优化Stribeck摩擦模型,对摩擦力这一影响定位精度的主要因素进行补偿。首先,对于传统的Stribeck摩擦模型进行优化,采用改进的最小二乘算法对模型参数进行辨识。然后,对所建立的摩擦模型补偿算法进行仿真并与扰动观测器的补偿算法进行比较,发现前者速度比后者速度在补偿后提高了4.33%,对摩擦力具有更好的补偿效果。最后,在大行程二维精密定位平台上进行验证,根据平台能够达到的最大速度定义0.005 m/s为低速运动,0.05 m/s为高速运动,在这两种速度下进行实验,并与基于库仑摩擦前馈补偿模型比较。实验结果表明：精密定位平台在速度为0.005 m/s的低速运动时,优化模型的跟随误差减小了67.67%;在速度为0.05 m/s的高速运动时,优化模型的跟随误差减小了51.63%,验证了优化Stribeck摩擦模型补偿算法的有效性。本文提出的优化Stribeck摩擦模型可用于提高由直线电机驱动的精密定位系统的定位精度。     

润滑点接触粗糙表面滑动摩擦因数的实验研究

利用多功能微摩擦试验机,在轻载荷条件下测量了具有横向纹理圆盘表面的摩擦因数,得到了包括流体润滑、混合润滑和边界润滑完整的Stribeck曲线。考虑了载荷和时间对实验结果的影响,对不同粗糙度表面的Stribeck曲线进行了比较。实验的初步结果表明:增加载荷与实验时间,会获得更加稳定的实验结果;表面越粗糙,从混合润滑向流体润滑转换的临界速度越大;表面越光滑,Stribeck曲线的“谷底”越明显。     

Contact Mechanics and Friction on Dry and Wet Human Skin

The surface topography of the human wrist skin is studied using an optical method and the surface roughness power spectrum is obtained. The Persson contact mechanics theory is used to calculate the contact area for different magnifications, for both dry and wet condition of the skin. For dry skin, plastic yielding becomes important and will determine the area of contact observed at the highest magnification. The measured friction coefficient [M.J. Adams et al., Tribol Lett 26:239, 2007] on both dry and wet skin can be explained assuming that a frictional shear stress σ_f ≈ 15 MPa acts in the area of real contact during sliding. This frictional shear stress is typical for sliding on polymer surfaces, and for thin (nanometer) confined fluid films. The big increase in the friction, which has been observed for glass sliding on wet skin as the skin dries up, can be explained as resulting from the increase in the contact area arising from the attraction of capillary bridges. This effect is predicted to operate as long as the water layer is thinner than ～14 μm, which is in good agreement with the time period (of order 100 s) over which the enhanced friction is observed (it takes about 100 s for ～14 μm water to evaporate at 50% relative humidity and at room temperature). We calculate the dependency of the sliding friction coefficient on the sliding speed on lubricated surfaces (Stribeck curve). We show that sliding of a sphere and of a cylinder gives very similar results if the radius and load on the sphere and cylinder are appropriately related. When applied to skin the calculated Stribeck curve is in good agreement with experiment, except that the curve is shifted by one velocity-decade to higher velocities than observed experimentally. We explain this by the role of the skin and underlying tissues viscoelasticity on the contact mechanics.     

A friction model evaluated with results from a bending-under-tension test

The friction in stamping is an important process parameter to control the flow of material in the tool. Consequently, it is also an important parameter in the design process of new stamping tools when numerical simulations of the forming operations are performed. In this work an advanced friction model is evaluated, which considers properties of surface topography, lubricant, sheet material, and process parameters such as sliding speed and pressure. The evaluation is made by comparing theoretical results with experimental ones obtained in a bending-under-tension friction test. The results show conformance in behaviour between the friction model and the experimental work. Furthermore, a model, which considers the influence of bulk plastic strains on the real area of contact, is investigated. The developed model predicts that the effective hardness of a surface is reduced by the presence of underlying plastic flow. It is found that when the strain rates are increased, the Stribeck curve becomes flatter and mixed lubrication is introduced at lower Hersey values. The friction model clearly shows the potential of improving the FE simulations of sheet metal forming operations, in comparison to the use of the classical Coulomb's friction model.     

基于Stribeck摩擦模型的盘式摩擦副稳定性分析

为了分析摩擦副滑动摩擦状态下的稳定性,分析系统的失稳条件,以Stribeck摩擦模型为基础,建立了速度相关的多自由度摩擦副滑动稳定性分析模型。建立了盘式摩擦副的系统动力学微分方程,进行了基于库仑摩擦定律摩擦力计算公式的级数展开,随后依据李雅普诺夫稳定性判据进行了系统稳定性求解,并分析了系统关键参数对系统稳定性的影响。研究结果表明,采用减小Stribeck系数和摩擦因数静动比、减小外载荷和增大系统阻尼等方法,能提高系统的稳定性。     

数控机床伺服系统摩擦的非线性参数辨识研究

针对常用的Stribeck摩擦指数模型,提出用泰勒高次展开的方法达到非线性摩擦模型的线性化,利用最小二乘拟合的方法得到摩擦模型参数。通过对数控机床控制系统的电动机电流和转速等信号的采集,得到了进给系统中摩擦力矩与转速的对应关系,利用提出的方法进行了辨识实验,实验结果表明,该方法能对Stribeck摩擦模型的参数进行精确的辨识。该方法在工程实际中具有应用价值。     

在不同润滑油下齿轮锻造材料摩擦特性研究

采用销-盘摩擦副接触方式在不同流体润滑及载荷下,对齿轮锻造用SCr420H合金结构钢进行摩擦试验.采用齿轮油、石蜡油以及加工润滑油润滑.利用在不同润滑及载荷下随速度变化的摩擦因数变化曲线图分析摩擦材料表面摩擦特性.利用Stribeck曲线和摩擦表面形貌SEM照片分析在不同润滑油及载荷下的摩擦状态和摩擦行为.结果表明:SCr420H合金结构钢在最低动黏度的石蜡油润滑下摩擦因数最高,且随速度增大而减少;在齿轮油和加工润滑油润滑下,最低载荷时具有最高的摩擦因数,但摩擦因数随载荷增大而减少,速度对摩擦因数影响不大;在齿轮油和加工润滑油润滑下摩擦副处于流体润滑状态,在石蜡油润滑下显示临界润滑摩擦状态.     

基于THK-SHS35V型号的滚动直线导轨副预紧力精确计算方法研究

针对目前只能通过滚动体过盈量粗略判定滚动直线导轨副预压等级(轻、中、重)的现状,首先基于Hertz接触理论建立了载荷和预紧拖动力关系模型,然后创新性构建了一种载荷和预紧拖动力同步在线测量系统,测量了不同载荷、运动速度下THK-SHS35V型号的滚动直线导轨副的动态摩擦因数,进而得到其Stribeck曲线。将摩擦因数与载荷-预紧拖动力关系模型相结合,最终建立了一种滚动直线导轨副预紧力精确计算模型。试验结果表明,所建立的预紧力计算模型能有效预测被测样件的预紧力,其最大相对误差为18.91%。提出利用Stribeck曲线得到动态摩擦因数经验公式建立预紧力计算模型的方法,可进一步扩展应用于其他型号的滚动直线导轨副。     

Theory of viscoelastic lubrication

We study the lubricated (wet) contact mechanics of a smooth hard cylinder sliding on a randomly rough nominally flat surface of a linear viscoelastic solid. We calculate the rolling and sliding friction, and study the transition from the boundary lubrication to the elasto-hydrodynamic lubrication regime. For the viscoelastic contact the minimum (average) separation does not monotonically increase with the sliding velocity, and the Stribeck curve exhibits new structures not shown for elastic solids.