Squeak noise in lead screw systems: Self-excited vibration of continuous model

The dynamic instability of a spinning lead screw in contact with a screw nut is investigated analytically. The lead screw is modeled as a circular beam vibrating in transverse and torsion direction. The contact kinematics between the lead screw and the nut is described on the contact threads in the lead screw. The onset of squeak noise is numerically predicted with a variety of system parameters. Stability analysis shows that the transverse vibration modes can generate squeak noise in the lead screw system. It is highlighted that squeak noise can be controlled by system design parameters in such a manner that the squeak propensity is dependent on rotation speed, screw radius, axial load, contact location, and so on.     

How can automotive friction-induced noises be related to physical mechanisms?

Three main physical mechanisms are found in the literature to explain the occurrence of friction-induced noises: the stick–slip, the sprag-slip and the mode-coupling instabilities. In order to improve the understanding of the automotive friction-induced noises and regarding the variety of these noises and the systems concerned, the consideration of these three physical mechanisms in a unique model, called phenomenological model, is proposed. The relationships between the mechanisms at the origin of friction-induced noises and the different kinds of friction-induced noises that can be perceived in a vehicle are particularly investigated. First, a simple classification of automotive-friction induced noises is proposed and highlights three noise categories: squeal, squeak and creak noises. Time simulations carried out on the phenomenological model show the qualitative reproduction of the vibrational behaviors at the origin of these three noise categories. Conditions are then proposed to define the three noise categories, based on the contact states ratios encountered in the time response. In order to understand the relationships between the three physical mechanisms and the three noise categories, a fullfact design of experiments is carried out with the phenomenological model. A system with realistic dynamic properties is used and submitted to a large number of conditions of use, allowing the appearance of a wide diversity of responses. The results show that the three mechanisms as well as the three noise categories can be obtained on a same dynamic system. They also show that creak is caused by a stick–slip phenomenon, squeal is mainly due to a mode-coupling phenomenon, while squeak can be caused either by mode-coupling or stick–slip phenomena. Finally, the occurrence of each mechanism and noise category is independently analyzed for the given dynamic system, giving quite significant trends towards model parameters. These trends highlight some interesting design levers to reduce the propensity of noise for an automotive structure.     

FRICTION-INDUCED VIBRATION IN PERIODIC LINEAR ELASTIC MEDIA

For a one-dimensional finite elastic continuum with distributed contacts and periodic boundary conditions, the presence of unstable waves is investigated. The stability of the waves is evaluated and explanations for instabilities under a constant coefficient of friction are provided. A negative slope in the coefficient of friction as a function of sliding speed is not a necessary condition for the occurrence of dynamic instability. Dynamic instability occurs in the form of self-excited, unstable, travelling waves. The stabilizing effects of external and internal damping were studied. Low- and high-frequency terms of the travelling waves are stabilized by adding external and internal damping respectively. Responses corresponding to unstable eigenvalues can dominate the system response. It is presumed that this can lead to squeaking or squealing noise in applications.     

Tribological properties of silicate materials on nano and microscale

We studied the friction properties of four model silicate materials at the nanoscale and microscale. From nanotribology, we characterized the tribological properties at single asperity contact scale and from microtribology, we characterized the tribological properties at multi asperity contact scale. First, for each material we measured chemical composition by XPS, Young's modulus by acoustical microscopy and roughness σ by atomic force microscopy (AFM). Second, we measured the nanofriction coefficients with an AFM and the microfriction coefficients with a ball probe tribometer, for three hardnesses of the ball probe. We identified one friction mechanism at the nanoscale (sliding friction) and two friction mechanisms at the microscale (sliding friction and yielding friction). Comparison of the nano and microfriction coefficients at the same sliding friction regime shown, that the tribological properties of these materials didn’t depend on roughness.     

基于非连续能量耗散的滑动摩擦系数计算模型

分析了界面摩擦状态下能量非连续耗散过程,建立了简化条件下晶体材料界面摩擦滑动摩擦系数计算模型.结果表明:在弹性接触状态下,滑动摩擦系数与载荷及实际接触面积无关,当实际接触面积接近名义接触面积时,滑动摩擦系数随载荷增加而减小.在缓慢滑动时,滑动摩擦系数随滑动速度的增高而缓慢增大,相对滑动速度愈高,滑动摩擦系数增大趋势愈显著.滑动摩擦系数随晶格常数的增加而降低,而当晶格常数较大时,其变化对滑动摩擦系数影响较小.同时,滑动摩擦系数随原子的可能温升增加而增大.研究结论对工程应用及相关的理论研究具有一定的参考意义. 关键词： 滑动摩擦系数 非连续能量耗散 界面摩擦     

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.     

Experimental and numerical investigation of friction-induced vibration of a beam-on-beam in contact with friction

The vibrations generated by friction are responsible for various noises such as squealing, squeaking and chatter. Although these phenomena have been studied for a long time, it is not well-understood. In this study, an experimental and numerical study of friction-induced vibrations of a system composed of two beams in contact is proposed. The experimental system exhibits periodic steady state vibrations of different types. To model and understand this experimental vibratory phenomenon, complex eigenvalue and dynamic transient analyses are performed. In the linear complex eigenvalue analysis, flutter instability occurs via the coalescence of two eigenmodes of the system. This linear study provides an accurate value of the experimental frequency of vibration. To understand what happens physically during friction-induced instability, a dynamic transient analysis that takes account of the non-linear aspect of a frictional contact is performed. In this analysis, friction-induced instability is characterized by self-sustained vibrations and by stick, slip and separation zones occurring at the surface of the contact. The results stemming from this analysis show that good correlation between numerical and experimental vibrations can be obtained (in time and frequency domains). Moreover, time domain simulations permit understanding the physical phenomena involved in two different vibratory behaviours observed experimentally.     

ON THE DISCRETIZATION OF AN ELASTIC ROD WITH DISTRIBUTED SLIDING FRICTION

A one-dimensional elastic system with distributed contact under fixed boundary conditions is investigated in order to study dynamic behavior under sliding friction. A partial differential equation of motion is established and its exact solution is presented. Due to the friction the eigenvalue problem is non-self-adjoint. Mathematical methods for handling the non-self-adjoint system, such as the non-self-adjoint eigenvalue problem and the eigenvalue problem with a proper inner product, are reviewed and applied. The exact solution showed that the undamped elastic system under fixed boundary conditions is neutrally stable when the coefficient of friction is a constant. The assumed mode approximation and the lumped-parameter discretization method are evaluated and their solutions are compared with the exact solution. As a cautionary example the assumed modes approximation leads to false conclusions about stability. The lumped-parameter discretization algorithm generates reliable results.     

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system

The present work proposes friction coupling at the wheel-rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset-track system is studied using the finite element complex eigenvalue method. Two models for a wheelset-track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset-track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60-1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.     

Stability and transient dynamics of a propeller–shaft system as induced by nonlinear friction acting on bearing–shaft contact interface

This paper investigates the friction-induced instability and the resulting self-excited vibration of a propeller–shaft system supported by water-lubricated rubber bearing. The system under consideration is modeled with an analytical approach by involving the nonlinear interaction among torsional vibrations of the continuous shaft, tangential vibrations of the rubber bearing and the nonlinear friction acting on the bearing–shaft contact interface. A degenerative two-degree-of-freedom analytical model is also reasonably developed to characterize system dynamics. The stability and vibrational characteristics are then determined by the complex eigenvalues analysis together with the quantitative analysis based on the method of multiple scales. A parametric study is conducted to clarify the roles of friction parameters and different vibration modes on instabilities; both the graphic and analytical expressions of instability boundaries are obtained. To capture the nature of self-excited vibrations and validate the stability analysis, the nonlinear formulations are numerically solved to calculate the transient dynamics in time and frequency domains. Analytical and numerical results reveal that the nonlinear coupling significantly affects the system responses and the bearing vibration plays a dominant role in the dynamic behavior of the present system.     

分子沉积聚合物膜的制备及其摩擦学性能研究

以聚对磺酸钠苯乙烯 (PSS)为聚阴离子、聚烯丙基氯化氨 (PAH)为聚阳离子交替沉积制备了多层聚合物纳米复合膜 ,用热分析仪考察了这两种体相聚合物的热稳定性 ,采用紫外 -可见光谱仪、椭圆偏振光测厚仪、接触角测量仪等分析了复合膜的性能 ,用DF -PM型动静摩擦系数精密测定装置考察了其摩擦学性能 .结果发现 ,所制备的聚合物复合膜具有一定的减摩作用 ,原因是单晶硅表面沉积聚合物超薄膜可以降低表面的粘着力 ,对硅表面具有微观修饰作用 ,从而降低其同钢对摩时的摩擦系数 ;单晶硅表面分子沉积聚合物纳米复合膜的摩擦学特性同超薄膜的层数相关 ,沉积层数较多的超薄膜的耐磨寿命较长 ,并因加热处理而得到明显改善 .     

Thermal buckling and natural vibration of the beam with an axial stick–slip–stop boundary

As a first attempt to study the dynamics of a heated structure with complicated boundaries, this paper deals with the thermal buckling and the natural vibration of a simply supported slender beam, which is subject to a uniformly distributed heating and has a frictional sliding end within a clearance. This sliding end is initially at a stick status under the friction force, but may be slightly slipping due to the thermal expansion of the beam until the sliding end contacts a stop, i.e., the bound of the clearance. The material properties of the beam are temperature-independent for low temperature, but temperature-dependent for high temperature. For each case, the analytic solutions for the critical buckling temperature and the natural frequencies of the heated beam are derived first. Then, discussions are made to reveal the effects of beam parameters, such as the ratio of beam length to beam thickness, the ratio of clearance to beam length and the temperature-dependent material properties, on the critical buckling temperature and the fundamental natural frequency of the heated beam. The study shows that both friction force and clearance have significant influences on the critical buckling temperature and the fundamental natural frequency of the beam. When the friction force is not very large, the clearance can greatly increase the critical buckling temperature. These conclusions enable one to properly design the stick–slip–stop boundary so as to improve the mechanical performance of the beam in thermal environments.     

MODES OF CONTACT AND UNIQUENESS OF SOLUTIONS FOR SYSTEMS WITH FRICTION-AFFECTED SLIDERS

The kinetic equations of planar multi-body systems with friction-affected sliding joints are reformulated for the computation of closed-form solutions for the kinetic parameters. The state of such systems is characterized not only by the position parameters and velocities, but in addition, the modes of contact in the sliding joints must be specified. Then the cases with one or several sets of solutions, obtained for the same position parameters, velocities, active forces and friction parameters, can be related to positions of the system with different modes of contact between sliders and guiding surfaces. They are physical unequivocal states and can be interpreted as unique solutions for the kinetic problem with specified configuration of the system. If no solutions exist, then the friction parameters considered are too large and exceed limiting values, for which friction locking occurs.     

Ageing of a microscopic sliding gold contact at low temperatures

Nanometer-scale friction measurements on a Au(111) surface have been performed at temperatures between 30 and 300?K by means of atomic force microscopy. Stable stick slip with atomic periodicity is observed at all temperatures, showing only weak dependence on temperature between 300 and 170?K. Below 170?K, friction increases with time and a distortion of the stick-slip characteristic is observed. Low friction and periodic stick slip can be reestablished by pulling the tip out of contact and subsequently restoring the contact. A comparison with molecular dynamics simulations indicates that plastic deformation within a growing gold junction leads to the observed frictional behavior at low temperatures. The regular stick slip with atomic periodicity observed at room temperature is the result of a dynamic equilibrium shape of the contact, as microscopic wear damage is observed to heal in the sliding contact.     

Comparative Study of Tribological Properties of Polyphenylene Sulfide (PPS), Polyethersulfone (PES), and Polysulfone (PSU)

The tribological properties of polyphenylene sulfide (PPS), polyethersulfone (PES) and polysulfone (PSU), which have similar molecular structures, were investigated using an end-face contact tribometer and a reciprocating tribometer. The thermomechanical behavior of the polymers was analyzed using dynamic mechanical analysis (DMA). PPS exhibited a maximum friction coefficient with increasing load and sliding speed, while the friction coefficients of PES and PSU decreased only slightly. The wear rate of PPS was much lower than that of PES and PSU under high loads and speeds. It is suggested that the main factors influencing the friction and wear properties of the neat polymers are their condensed state and heat resistance. Amorphous PES and PSU showed liquid-like behavior and very low friction when the frictional surface was in the molten-flow state. The macromolecular crystals of crystallizable PPS give it some solid-like behavior and load-carrying capacity; hence PPS exhibited lower wear than PES and PSU.     

Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction

A transition from stick-slip to continuous sliding is observed for atomically modulated friction by means of a friction force microscope. When the stick-slip instabilities cease to exist, a new regime of ultralow friction is encountered. The transition is described in the framework of the Tomlinson model using a parameter eta which relates the strength of the lateral atomic surface potential and the stiffness of the contact under study. Experimentally, this parameter can be tuned by varying the normal load on the contact. We compare our results to a recently discussed concept called superlubricity.     

Friction and Wear of Polyphenylene Sulfide (PPS), Polyethersulfone (PES) and Polysulfone (PSU) Under Different Cooling Conditions

The friction and wear properties of polyphenylene sulfide (PPS), polyethersulfone (PES) and polysulfone (PSU), which have similar molecular structure, were investigated using an end-face contact tribometer in three different cooling ways: sliding without air cooling, sliding with air cooling, and sliding in water. The worn surface and wear debris were observed using a scanning electron microscope (SEM). The effect of frictional heat on the tribological properties of the polymers was comparatively studied. When sliding in air, with increasing applied load, the wear rate of PPS decreased slightly initially then increased later while the wear rate of PES and PSU increased through out. The results suggested that the friction coefficient was mainly affected by the temperature of the worn polymer that was controlled by the balance of heat flow of the whole sliding contact system. When sliding in water, the friction coefficients of the three polymers decreased compared to that sliding in air and remained relatively steady through the whole process under different load. The wear rates of the three polymers had a close value and, remarkably, increased compared to that sliding in air. The water cooling and lubrication role decreased the tribological properties difference between the polymers.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.     

Tribological Behavior of Multiply-Alkylated Cyclopentanes (MACs)-Cu Nanoparticles Composite Thin Film

Multiply-alkylated cyclopentanes (MACs) composite thin films containing Cu nanoparticles are fabricated on the octadecyltrichlorosilane (OTS)-modified substrate by a spin-coating technique. The thickness, wetting behavior, and nanoscale morphologies of the films are characterized by means of ellipsometry, contact angle measurement, and atomic force microscope (AFM). The friction and wear behaviors of the thin films sliding against Si₃N₄ ball are examined on a UMT-2MT tribometer in a ball-on-disk contact mode. The worn surfaces of the OTS-MAC-Cu composite film and the counterpart Si₃N₄ balls are investigated with a scanning electron microscope. Water contact angle on OTS-MAC-Cu composite film is higher than that of OTS-MAC film. OTS-MAC-Cu composite film exhibits higher load-carrying capacity and better friction reduction and antiwear behavior as compared with OTS-MAC film. This may be attributed to the load-carrying and self-repairing property of the Cu nanoparticles in the composite film and the formation of a transfer layer composed of OTS, MAC, and Cu on the rubbing surface of the counterpart ball.     

A method to determine dynamic loads on spur gear teeth and on bearings

A method is described which can be used to calculate dynamic gear tooth force and bearing forces. The model includes elastic bearings. The gear mesh stiffness and the path of contact are determined using the deformations of the gears and the bearings. This gives contact outside the plane-of-action and a time-varying working pressure angle. In a numerical example it is found that the only important vibration mode for the gear contact is the one where the gear tooth deformation is dominant. The bearing force variation, however, will be much more affected by the other vibration modes. The influence of the friction force is also studied. The friction has no dynamic influence on the gear contact force or on the bearing force in the gear mesh line-of-action direction. On the other hand, the changing of sliding directions in the pitch point is a source for critical oscillations of the bearings in the gear tooth frictional direction. These bearing force oscillations in the frictional direction appear unaffected by the dynamic response along the gear mesh line-of-action direction.