Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

Tribological behavior of reciprocating friction drive system under lubricated contact

The dynamic friction and wear behaviors are investigated in reciprocating friction drive system using a 0.45% carbon steel pair. The effects of various operating parameters on the traction force, stick and slip time, and friction modes are examined under the lubricated contacts. Moreover, the critical operating conditions in classifying three friction modes are also established. Results show that the fluid friction induced by the shearing of lubricant dominates the variation of traction force and produces the positive slope γ at the first period of slip in the traction force–relative sliding velocity curve. The γ value decreases at higher driver speed during stick-slip motion due to the thicker fluid film and shear thinning effect. The γ value increases due to the asperity interactions as the friction region is transferred from stick-slip to sticking with normal load from 196 to 980 N. Furthermore, it is also found that the static friction force is independent of stick time for the tangential loading rate ranged from 1.12 to 16.8 s⁻¹. The transition region produces the severest wear under the different driver speeds, but the wear is insensitive to the friction regions and the severe wear only occurs at higher normal load due to the action of Hertzian contact.     

A procedure for evaluating the positioning accuracy of reciprocating friction drive systems

The dynamic characteristics of stick-slip motion in reciprocating friction drive systems are investigated under dry contact using a 0.45% carbon steel pair. Based on this dynamic analysis, the stick-slip motion can be eliminated under certain experimental conditions depending upon driver speed, normal load and spring constant. The effects of normal load, driver speed, and spring constant on the positioning accuracy of the reciprocating friction drive system are examined under harmonic oscillation without stick-slip motion. Results show that at very low spring constants, the slip increases with increasing driver speed such that higher normal load has better positioning accuracy or smaller slip than does lower normal load. However, at high spring constants and high normal loads, there exhibits severe wear or peak at two limit positions on the sliding region. As a result, smaller normal loads have a better positioning accuracy than larger normal loads due to severe wear at high normal loads.     

Stability analysis of a rotating multi-layer annular plate with a stationary frictional follower load

This paper is concerned with examining the critical rotational speeds of a annular laminated disk and instability due to the existence of a stationary frictional follower load. A refined higher order layerwise zigzag theory (RHOT) is used to derive the governing equations of motion of a laminated disk. A four-node sector finite element incorporating RHOT is developed and applied for the stability analysis of a rotating multi-layer disk. The critical rotational speeds of a laminated disk made of isotropic layers and a laminated disk made of polar—orthotropic layers are calculated using the state—space method with respect to a moving frame and an inertial frame. The effect of a frictional follower load on the system stability is investigated using the frequency—speed diagram and the state—space method. It is found that the frictional follower load makes all forward modes with nodal diameters unstable over the entire rotational speed range. Total Lagrangian kinematics with the modified Newton method is used in the solution finding procedure.     

Study on rotational fretting wear of 7075 aluminum alloy

Rotational fretting wear tests in a ball-on-flat configuration have been successfully realized on a special rotational fretting rig developed from an ultra-low-speed reciprocating rotational driver. The rotational fretting behavior of 7075 aluminum alloy against 52 100 steel was studied under different angular displacement amplitudes and normal loads. The results showed that both F_t?θ and F_t/F_n curves can be used to characterize the rotational fretting running behavior, which exhibited different curve shapes and variation trends in different fretting running regimes. The rotational fretting behavior of 7075 aluminum alloy was strongly dependent on the angular displacement amplitude, normal load and number of cycles. The wear of 7075 aluminum alloy was characterized by slight attrition in the partial slip regime, while a combination of delamination, abrasive and oxidative wear was found in the slip and mixed fretting regimes. The formation of a central bulge probably due to plastic flow was observed under gross slip condition of the rotational fretting mode.     

Analysis of the Fretting Conditions in a Contact Between an Epoxy Thermoset and a Glass Counterface

The fretting conditions in a contact between an epoxy thermoset and a glass counterface have been investigated using a specific device which allows in situ observation of the contact area. The critical displacement for transition from partial slip to gross slip conditions was investigated by the in situ detection of the micro-displacements and by the analysis of the fretting loops. Experimental results were in good relation with the theoretical predictions derived from Mindlin's approach of incipient sliding. Depending on the loading conditions, a progressive change from gross slip to partial slip conditions was found to occur during the early stages of the fretting loading, i.e., before the appearance of any macroscopic damage such as cracking or particle detachment. These fretting conditions were synthesized in a fretting map giving the boundary between various fretting regimes as a function of the normal load, the imposed displacement and the number of cycles.     

Nanofretting Behavior of Monocrystalline Silicon (100) Against SiO2 Microsphere in Vacuum

With an atomic force microscopy, the tangential nanofretting between spherical SiO₂ tips and monocrystalline Si(100) surface was carried out at various displacement amplitudes (0.5–250 nm) under vacuum condition. Similar to fretting, the nanofretting of Si(100)/SiO₂ pair could also be divided into stick regime and slip regime upon the transition criterion. However, it was found that the energy ratio corresponding to the transition between two nanofretting regimes varied between 0.32 and 0.64, which was higher than the normal value of 0.2 for the transition criterion to determine the partial slip and gross slip regimes in fretting. One of the reasons may be attributed to the effect of adhesion force, since whose magnitude is at the same scale to the value of the applied normal load in nanofretting. During the nanofretting process of Si(100)/SiO₂ pair, the adhesion force may induce the increase in the maximum static friction force and prevent the contact pair from slipping. The higher the applied load, or the higher the adhesion force, the larger will be the transition displacement amplitude between two regimes in nanofretting. Different from fretting wear, the generation of hillocks was observed on Si(100) surface under the given conditions in nanofretting process. With the increase in the displacement amplitude in slip regime of nanofretting, the height of hillocks first increased and then attained a constant value. Compared to chemical reaction, the mechanical interaction may be the main reason responsible for the formation of silicon hillocks during the nanofretting in vacuum. The results in the research may be helpful to understand the nanofretting failures of components in MEMS/NEMS.     

Relationship between the propagation of fatigue cracks and the behaviour of plastic flow under rolling/sliding contacts - effect of slip ratio

The relationship between the propagation of fatigue cracks and the behaviour of plastic flow in the surface layer was experimentally investigated under lubricated rolling-sliding contact. The test specimen material was medium carbon steel (S45C) with hardness H_v 187 after annealing. Results show that the displacement of plastic flow in the surface layer of the follower increased with increasing number of revolutions. Crack propagation occurred in the surface layer of the follower when the displacement of plastic flow on the centre of the contact reached a saturated value. On the contact surface of the follower, the propagating angle of the fatigue crack was found to be correlated to the angle of plastic flow, which was independent of the slip ratio. The rate of plastic flow increased with increasing slip ratio, resulted in a reduction of fatigue life. The displacement of plastic flow beneath the contact surface could be evaluated from the profile change of the plastic flow on the contact surface.     

Study on rotational fretting wear of bonded MoS2 solid lubricant coating prepared on medium carbon steel

The rotational fretting wear behaviors of the bonded MoS₂ solid lubricant coating and its substrate steel were comparatively studied under varied angular displacement amplitudes, constant normal load, and rotational speed. Dynamic analysis in combination with microscopic examinations was performed through SEM, EDX, XPS, optical microscope, and surface profilometer. The experimental results showed MoS₂ changed the fretting running regimes of substrate. The friction coefficients of MoS₂ were lower than those of the substrate. For MoS₂, the damage in partial slip regime was very slight. The damage mechanism of the coating in slip regime was main abrasive wear, delamination, and tribo-oxidation.     

Experimental analysis of factors influencing the cage slip in cylindrical roller bearing

This paper deals with the effect of operating parameters on cage slip in cylindrical roller bearing. A cylindrical roller bearing test rig is developed to measure the running speed of bearing elements at various operating conditions. The effect of operating parameters namely shaft speed, radial load, viscosity of lubricating oil, number of rollers, and bearing temperature on cage slip are experimentally obtained. The critical load and magnitude of cage slip for various operating conditions are obtained. The non-dimensional number is derived based on the operating parameters. The region where cage slip occurs is developed from the derived non-dimensional number and the experimental data. The temperature raise is experimentally obtained during slip condition and its effect on viscosity is included for calculations. The frictional forces are experimentally obtained and are compared with the theoretical findings. The significant effect of operating parameters on cage slip of cylindrical roller bearing is discussed based on the experimental findings.     

基于双重扩展自适应卡尔曼滤波的汽车状态和参数估计

准确实时地获取行驶过程中的状态信息是汽车动态控制系统研究的关键,为此提出了一种新的汽车状态估计器。建立了包含不准确模型参数和未知时变统计特性噪声的非线性汽车动力学模型,针对该非线性系统提出一种双重扩展自适应卡尔曼滤波算法（DEAKF）。该算法采用两个卡尔曼滤波器并行运算,状态估计和参数估计互相更新,同时将带遗忘因子的噪声统计估值器嵌入到状态校正过程和参数校正过程之间,以解决系统的噪声时变问题。基于ADAMS的虚拟试验和实车试验结果表明,该算法的状态估计精度高于EKF方法和DEKF方法的状态估计精度,同时具有良好的模型参数校正能力,对汽车动态控制系统中估计器的设计具有理论指导意义。
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Fretting behaviour of galvanised steel

The present work describes research conducted on the fretting behaviour of S 355 MC galvanised steel sheet. In order to study the influence of the normal load and the displacement effect, some of the specimens were galvanised by hot dipping and the rest were only polished before being tested. Fretting tests were carried out on a specially developed fretting rig prototype under ‘crossed-cylinders’ contact geometry. Tests were done during 0.72×10⁶ cycles in laboratory air conditions. The tangential force and the displacement were measured in order to establish the fretting cycles for each fretting condition. The fretted surfaces were analysed by means of optical and scanning electron microscopes to identify the main wear mechanisms. Three different fretting regimes were identified: the stick regime; the slip regime; and the mixed stick–slip regime, which depended mainly on the influence of the normal load and the stroke.     

Dynamic behaviour of geared systems with backlash due to stick-slip vibratory motion

Stick-slip phenomena occur with low speed rotors in fluid bearings. A typical case is the turning gear mechanism of large turbomachinery which becomes vulnerable to damage. In other cases such as rolling mills or textile machinery the stick-slip phenomenon influences product quality.An analytical investigation of a linear rotor with a complex turning gear system of many degrees of freedom is presented. Gearing backlash was included in the model. The mechanism of backlash was found to be of considerable importance for the appearance of instability. Velocity and damping were the most influential factors on the amplitude of stick-slip motion and instability.In highly unstable areas of system operation, stick-slip is not present owing to the violent nature of the unstable motion. At the onset of instability and during the transients of stable systems, stick-slip is present. Fatigue damage may result from gear backlash, even in stable systems.     

Normal displacement and dynamic friction characteristics in a stick-slip process

The dynamic friction-velocity relationship in the slip stage of stick-slip vibration was investigated with a pin-on-flat apparatus. A reasonable relationship was derived from the measured displacement and acceleration of the sliding element, using a computing technique which provided smooth, reliable curves. It was found, from an examination of the effect of data smoothing on computed friction characteristics, that the moving average method can be recommended. Variation of normal displacement of the sliding body during the slip period was examined together with tangential displacement and electrical contact resistance. The friction-velocity relationship was well explained by an assumption that the instantaneous friction variation results from the change in real area of contact resulting from normal displacement occuring in an elastic contact.     

Wear analysis of Cu–Al coating on Ti–6Al–4V substrate under fretting condition

Fretting behavior of Cu–Al coating on Ti–6Al–4V substrate was investigated with and without fatigue load. Soft and rough Cu–Al coating resulted in abrasive wear and a large amount of debris remained at the contact surface, which caused an increase in tangential force during the fretting test under gross slip condition. Fretting in the partial slip condition also showed the wear of coating. To characterize wear, dissipated energies during fretting were calculated from fretting loops and wear volumes were obtained from worn surface profiles. Energy approach of wear analysis showed a linear relationship between wear volume and accumulated dissipated energy. This relationship was independent of fatigue loading condition and extended from partial slip to gross slip regimes. As an alternate but simple approach for wear analysis, accumulated relative displacement range was correlated with the wear volume. This also resulted in a linear relationship as in the case of accumulated dissipated energy suggesting that the accumulated relative displacement range can be used as an alternative parameter for dissipated energy to characterize the wear. When the maximum wear depth was equal to the thickness of Cu–Al coating, harder Ti–6Al–4V substrate inhibited further increase in wear depth. Only when a considerable energy was supplied through a large value of the applied displacement, wear in the substrate material could occur beyond the thickness of coating.     

滑移边界对微型气浮轴承稳态性能的影响

根据气膜厚度的Knudsen数,确定滑移流为微型气浮轴承内部的润滑机制。引入二阶滑移流边界条件对连续流的状态方程进行修改,得到滑移流机制下修正的雷诺方程。利用有限差分法对雷诺方程求解,得到两种情况下的气压分布,进而得到相应的承载能力和偏位角。经过对比分析,发现在滑移流机制下气浮轴承的力学性能与连续流机制的情况有较大差异。在相同的转速和偏心率下,滑移流效应降低了气压分布的曲率,进而降低了气浮轴承所能够提供的承载能力。     

Effect of high temperature on the characterization of fretting wear regimes at Ti6Al4V interfaces

Fretting wear is a destructive phenomenon that can accelerate crack initiation in vibrating components, leading to premature catastrophic failures. Among the most important characteristics of fretting is the transition from mixed fretting wear to gross slip because of its detrimental effects on fatigue life. In this paper, a study was conducted that characterized the critical normal loads and displacements corresponding to this transition in Ti6Al4V interfaces at room temperature and 450 °C (842 °F). Experimental testing shows that there is a relationship between critical load and displacement that is temperature dependant. Tests conducted at or near the critical values of load and displacement exhibited extreme galling and evidence of cold welding. In the gross slip tests, the measured coefficient of friction also varied with applied load, which correlates with the Hertzian contact model.     

Dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force

This paper presents the dynamic stability of a cantilevered Timoshenko beam with a concentrated mass, partially attached to elastic foundations, and subjected to a follower force. Governing equations are derived from the extended Hamilton’s principle, and FEM is applied to solve the discretized equation. The influence of some parameters such as the elastic foundation parameter, the positions of partial elastic foundations, shear deformations, the rotary inertia of the beam, and the mass and the rotary inertia of the concentrated mass on the critical flutter load is investigated. Finally, the optimal attachment ratio of partial elastic foundation that maximizes the critical flutter load is presented.     

The effect of number of cycles on the critical transition boundary between fretting fatigue and fretting wear

The object of the present study was to investigate the influence of number of cycles on the critical amplitudes of tangential force and displacement, identifying the transition from a mixed stick-slip regime (fretting fatigue) to a gross slip regime (fretting wear) over a wide range of test conditions. Fretting experiments were conducted on three metal specimen combinations: copper/copper; stainless steel/stainless steel; copper/stainless steel. All experiments took place in air, at ambient temperature, using a crossed-cylinder geometry. Normal loads of 3.4 and 11.4 N were applied with frequencies ranging from 10 to 800 Hz. In most cases, n = 1.2×10⁴ and n = 6×10⁶ were adopted as the representative lower and higher number of cycles, respectively. At different numbers of cycles, critical amplitudes of tangential force and displacement were measured. The scars fretted under separately selected conditions were examined by scanning electron microscopy.

It was found that the critical amplitudes of both tangential force and displacement dropped with increasing number of cycles for all test combinations, but there was an upper limit above which the drop of critical transition values no longer occurred with further increases in the number of cycles. The micromorphology of fretting scars (in a mixed stick-slip regime) revealed that the stick zone has shrunk after a larger number of cycles under the conditions of constant amplitude of tangential force and displacement, and that the damage mechanisms vary for different combinations, although they are all characterized by a central stick zone surrounded by a slip annulus. It was suggested that the decrease of critical amplitudes after a larger number of cycles results from the shrinkage of the stick area, which may be a complex process related to plastic deformation, strain hardening, and the change of stress distribution on the contact surfaces.     

Stick–Slip and Temperature Effect in the Scratching of Materials

The stick–slip process and temperature effect in scratch testing of materials have been studied. For a poly(methyl methacrylate) (PMMA) polymer scratched by a conical diamond indenter, both the amplitude and period of the stick–slip at room temperature increase with the normal load and decrease with the driving speed. An increase in temperature leads to an increase in stick–slip amplitude and period, as well as in the average horizontal force. For bismuth metal scratched by a conical tungsten indenter, the surface temperature in the contact area reveals fluctuations related to the stick–slip motion.