Stability of a Nonlinear Brake System at High Operating Speeds

The dynamics of a nonlinear car brake system is examined based on arealistic model in connection with a linearizationabout a stationary operating state. The rotating brake disc isapproximated by a rotating ring with two brake pads modeledas point masses which are in contact with the rotating ring.Each pad is visco-elastically suspended in axial and circumferential direction and loaded with a friction force. Two contact models areintroduced and incorporated in the system. The instabilitiesresponsible for brake noise evoked by internal resonances are presented.Several parameter studies are discussed,which show the sensitivity of the brake stiffness tuning and the brakeforce on the dynamic stability of the nonlinear brake system.     

Motorcycle brake squeal: experimental and numerical investigation on a case study

Since, nowadays, the NVH performance of a vehicle is one of the most important priorities for the market, the noise radiating from disc brakes is considered a source of considerable discomfort and customer dissatisfaction. Squeal is an example of noise, caused by vibrations induced by friction forces, in which the vibration modes of the brake disc are coupled to those of the friction pads or of the caliper. In this work a case study, in which the squeal phenomenon was detected after changing the supplier of the disc pads, is presented. A test bench was purposely developed to investigate the squeal phenomenon; tests at different rotating speeds and pressures in the brake circuit were carried out employing different friction pads. The experimental apparatus appeared capable of reproducing the phenomenon observed in real practice and to investigate the effect of operating parameters and different components on the onset of instability. Friction tests and geometric analysis of the friction pads were also carried out to complete the investigation. At the same time, a finite element (FE) complex eigenvalue parametric analysis was performed on the brake assembly. The different propensity of the pads to squeal was attributed to differences in their geometry and in their friction coefficients. The FE analysis, confirmed the experimental observations and indicated possible design improvements to increase the stability of the system.     

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

New method for oblique impact dynamics research of a flexible beam with large overall motion considering impact friction force

A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid mod-eling method, dynamic equations of the system, which include all states (before, during, and after the collision) are obtained. Simulation results of a concrete example are compared with the results obtained from two other models: a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.     

Variational principles for constrained systems: Theory and experiment

In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also presented from an experiment for a model system: a ball rolling without sliding on a rotating table. Both sets of equations of motion for the model system are compared with the experimental results. The effects of various forms of friction are considered in the nonholonomic equations. With appropriate friction terms, the nonholonomic equations of motion for the model system give reasonable agreement with the experimental observations.     

Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum

Lubrication oil in a rotor system guarantees the rotating components working smoothly and protects the system from being damaged due to friction. A volume of lubrication oil, however, sometimes leaks into the inner cavity of shaft and drums of rotor system and forms an oil-block during rotating operation. The oil-block usually induces abnormal vibration of the rotating machine, which is often observed in practical cases, such as in aero-engine. The work in this paper studies the nonsynchronous vibration (NSV) induced by an oil-block in a rotating drum of a Jeffcott rotor system, which consists of a shaft, a drum and two supporting isotropic bearings. The additional effect due to an oil-block rotating on the inner wall of the drum is included into rotor system differential equations considering the Coriolis acceleration and friction interaction between the oil-block and the drum. Numerical simulations are carried out under two rotating speeds conditions: a lower one and a higher one than the first critical rotor speed, which are defined as rigid rotor case and flexible rotor case. Numerical results states the transverse vibrations by bifurcation diagrams, shaft center trajectories, frequency spectra and Poincare diagrams, which reveal multi-periodic, quasi-periodic and other complex motions due to the existing of oil-block. The internal friction coefficient and mass of the oil-block are found to have a significant effect on the generation and development of NSV. As the oil-block case is very common in practice, the investigation of NSV caused by oil-block in rotor system would benefit the understanding of complex phenomena and contribute to fault detection and diagnosis of rotating machine.     

Model of the UIC link suspension for freight wagons

Summary The paper presents a model of the UIC link suspension for freight wagons with emphasis on its longitudinal and lateral characteristics, which influence the lateral dynamics of the vehicle. The functioning of the suspension in the horizontal plane is realised by a number of technical (pivoted) pendulums composing linkages. The main feature of the joints of linkages is internal rolling/sliding in the presence of dry friction. The dissipation of energy by dry friction in the joints is the only source of damping, which influences the lateral dynamics of the vehicle. After detailed modelling of the technical pendulum, phenomenological models of the suspension are built, which reproduce the characteristics of the suspension using simple elements. A three-parameter model with one dry-friction slider and two linear springs reproduces the lateral characteristic of the suspension. A nine-parameter model with four dry-friction sliders and five springs reproduces the longitudinal characteristic. The models, using a method of non-smooth mechanics, may be directly implemented to vehicle/track dynamic simulations.Professor Hans True of TU Denmark for stressing the importance of the problem of the UIC suspension modelling for successful upgrading of freight wagons.     

Dynamic characteristic analysis of spur gear system considering tooth contact state caused by shaft misalignment

The effect of gear contact state change due to shaft misalignment on meshing stiffness is usually neglected in the traditional stiffness calculation model with misalignment error, the further influence mechanism of shaft misalignment on gear dynamic characteristics is also unclear. To address these shortcomings, a new mesh stiffness calculation model with misaligned gear considering the effects of tooth contact state is proposed by combining the improved loaded tooth contact analysis (LTCA) model. Then the effects of tooth contact state changes aroused by shaft misalignment on the meshing stiffness excitation are investigated. Moreover, a dynamic model of the misaligned gear system with 8 degrees of freedom (DOF) is established, and based on which the dynamic characteristics of the gear system are investigated and verified by experiment. The study results indicate that the proposed model can be used to evaluate the stiffness excitation and dynamic characteristics of the misaligned gear system with the tooth contact state taken into consideration. This study can provide a theoretical method for evaluating and identifying shaft misalignment errors.

     

Air-cooled gas-turbine discs: a review of recent research

The flow between corotating compressor or turbine discs and the flow between a turbine disc and an adjacent stationary casing can be respectively modelled by a rotating cavity and by a rotor-stator system. This paper reviews some of the recent experimental and theoretical work on flow and heat transfer in these two classes of rotating-disc systems. Comparisons between the theoretical and measured distributions of velocity, pressure, and Nusselt numbers are made for the rotating cavity with a superimposed radial flow of cooling air. For the rotor-stator system, some recent work on the fluid dynamics is outlined, and particular mention is made of the so-called “ingress problem” and of the use of pre-swirl air to improve the blade-cooling effectiveness.     

Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics

Analytical and experimental investigations are performed in order to characterize the dynamic behaviour of a non-smooth rotational oscillator, which exhibits multiple discontinuity boundaries in the phase space. The physical system consists of a rotating body subjected to an elastic restoring force and in contact with one or two rough discs rotating with constant driving velocities. The presence of multiple discontinuity boundaries caused by frictional contacts leads to non-standard bifurcations that are studied by means of a simple mechanical model.A test set-up has then been built to investigate the correctness of modelling of the friction force and the validity of the proposed model for technical applications: the experimental measurements qualitatively and quantitatively capture the basic scenarios anticipated by the model while a strong robustness of the phenomena pointed out by the theoretical analyses has been revealed in the experiments.     

Distribution of the friction heat between two stationary pins and a rotating disc

A closed-form model for the computation of heat fluxes distribution between two motionless cylindrical pins and a fast rotating disc is investigated. Based on a finite Fourier transform technique and an asymptotic analysis, a series solution for the disc surface temperature is obtained. The solution for the pin is trivial. By matching the average temperatures over the contact areas the coefficients of the heat distribution between a pin and a disc are found. It is demonstrated that the present analysis covers the previously known case of one pin as well as new results are obtained. Received on 4 November 1996     

Superposed flow between two discs contrarotating at differential speeds

This paper describes a combined computational and experimental study of the flow between two contrarotating discs for −1 ≤ Γ ≤ 0 (where Γ is the ratio of the speed of the slower disc to that of the faster one) for the case where there is a superposed radial outflow of air. The computations were conducted using an elliptic solver and a low-Reynolds-number k-ε turbulence model, and velocity measurements were made using a laser-Doppler anenometry system. Two basic flow structures can occur: Batchelor-type flow, where there are separate boundary layers on each disc with a rotating core of fluid between, and Stewartson-type flow, where there is virtually no core rotation. The main effect of a superposed flow is to reduce the core rotation and to promote the transition from Batchelor-type flow to Stewartson-type flow. For most of the results, there is good agreement between the computed and measured velocities. Computed moment coefficients show that, for Γ = −1, superposed flow has little effect on C_m: an accepted correlation of C_m for a free disc should provide a useful estimate for design purposes.     

Response analysis of a dual-disc rotor system with multi-unbalances–multi-fixed-point rubbing faults

Rotor unbalance and rub-impact are major concerns in rotating machinery. In order to study the dynamic characteristics of these machinery faults, a dual-disc rotor system capable of describing the mechanical vibration resulting from multi-unbalances and multi-fixed-point rub-impact faults is formulated using Euler beam element. The Lankarani–Nikravesh model is used to describe the nonlinear impact forces between discs and casing convex points, and the Coulomb model is applied to simulate the frictional characteristics. To predict the moment of rub-impact happening, a linear interpolation method is carried out in the numerical simulation. The coupling equations are numerically solved using a combination of the linear interpolation method and the Runge–Kutta method. Then, the dynamic behaviours of the rotor system are analysed by the bifurcation diagram, whirl orbit, Poincaré map and spectrum plot. The effects of rotating speed, phase difference of unbalances, convex point of casing and initial clearance on the responses are investigated in detail. The numerical results reveal that a variety of motion types are found, such as periodic, multi-periodic and quasi-periodic motions. Moreover, the energy transfer between the compressor disc and the turbine disc occurs in the multi-fixed-point rubbing faults. Compared with the parameters of the turbine disc, those of the compressor disc can affect the motion of the rotor system more significantly. That is, the responses exhibit simple 1T-periodic motion in the wide range of rotating speed under the conditions of sharp convex point and larger initial clearance. These forms of dynamic characteristics can be effectively used to diagnose the fixed-point rub-impact faults.     

盘式制动器摩擦噪声特性的试验分析

盘式制动器制动时产生的摩擦噪声不仅影响车辆的驾乘舒适性,还会带来严重的环境噪声污染. 摩擦噪声具有瞬时性与不确定性的特点,至今尚未形成对制动器摩擦噪声机理的统一论断. 基于盘式制动器声振试验台,研究了摩擦系数、摩擦力波动系数和等效A声级三个参数在不同制动压力和制动初速度下的变化规律,结合对摩擦片微观特性的试验分析,从摩擦学角度揭示了盘式制动器摩擦噪声的发生规律及机理. 结果表明:摩擦噪声随制动初速度的增大而减小,随制动压力的增加而先增大后减小;制动摩擦噪声由于摩擦系统不稳定而产生,其产生原因是因为摩擦副表面的沟壑与黏着引起,沟壑与黏着程度与噪声的声压与频率呈正相关关系. 研究结果对于解释制动器摩擦噪声发生机理、控制制动器噪声污染具有重要理论意义和实际价值.      

An alternative analytic approach to the Brazilian disc test with friction at the disc-jaw interface

The role of the tangential (friction) stresses developed at the disc-jaw interface during the standardized realization of the Brazilian disc test is quantified. Sinusoidal variation of both the radial pressure and the friction stresses is considered. The pressure is maximized at the symmetry axis of the load distribution while friction is maximized at the mid-point of the contact semi-arc. Both load distributions (radial and frictional) are exerted along the actual contact length as it is developed during the loading procedure. The stress field all over the disc due to friction stresses is determined in closed form using the complex potentials technique. The solution obtained is applied for two materials both of brittle nature and of different relative deformability compared to steel (i.e. the material of the jaw). The stress field due to friction is compared for both materials with that due to radial pressure, and then, the two solutions are superimposed in order to quantify the total stress field. It is concluded that as one approaches the loading platens, non-ignorable tensile stresses are developed that could lead the disc to premature failure far from the disc’s center. The magnitude of these stresses strongly depends among others on the relative deformability of the disc’s and jaw’s materials since the latter dictates the extent of the loading rim.     

Pressure drop for flow in channels subjected to strong system rotation

A disc stack centrifuge is an industrial example of a fluid machine in which all the internal flow takes place in a rapidly rotating frame. The present report gives a survey of the experimental and theoretical work performed at Alfa-Laval in order to estimate the pressure drops in the different internal passages in the centrifuge, including both laminar and turbulent flow.For the laminar flow between the discs, a theory has been developed using the concept of a rotating Hele Shaw cell and conformal mapping. The theory is valid in the limit of very small Rossby numbers. For moderately large Rossby numbers, this model overestimates the pressure drop. The linear theory was extended by introducing advecting vortices in a computer model. The vortices cause vertical fluid transport between the Ekman and geostrophic layers by Ekman pumping, an effect which decreases the pressure drop in the disc stack. The linear model and the enhanced model have both been confirmed by experiments.The flow is turbulent in most parts of the centrifuge, except in the disc stack. The theoretical or numerical modelling for rotating turbulent flows is very difficult and no reliable models exist so far. We therefore have to rely on measurements, which show that the pressure is significantly influenced by rotation for Rossby numbers below unity.     

表面特性对纯滑弹流油膜形状和摩擦力的影响的试验研究

针对界面滑移效应可能产生较低的摩擦力,采用具有不同表面浸润性的玻璃盘,进行了纯滑弹流润滑试验.在采用SiO2镀膜玻璃盘的球-盘接触高聚物纯滑润滑试验中,从弹流到动压润滑的摩擦系数曲线呈现不同于传统Stribeck曲线的两个拐点.两个拐点分别与凹陷出现及弹性变形消失相关联.在较低载荷下,不同盘表面产生相近的干涉图像和摩擦系数曲线,高聚物的非牛顿效应产生的表观滑移可能是入口凹陷及非典型摩擦系数曲线的主因;在较高载荷下,盘滑试验中铬盘产生的摩擦系数和油膜厚度均较SiO2盘低,具有较低表面能的铬盘产生的界面滑移被认为是产生较低摩擦系数的主因.     

Flexible shaft whirl induced by dry friction and its stability

This paper is devoted to the study of the whirling phenomena of flexible rotors due to dry friction. The mechanical model used here is a two-degree-of-freedom system in which the rubbing plane is not coincident with the rotating plane of the lumped mass. The characteristic equation of whirl speeds is derived and the whirling modes are obtained. The dynamic stability of each admissible whirling motion is also discussed. The results show that the whirl speeds are always higher than the critical speed of the shaft.     

超高速微转子系统磨损特性的研究

针对高速旋转微电机中典型的转子轴衬摩擦磨损问题,以半球形轴衬为研究对象,提出了1种描述其磨损过程的线性滑动磨损模型,建立了半球形轴衬-极板接触有限元模型,分析微转子轴衬的磨损特性和轴衬-极板接触副的接触动力学特性,研究接触副几何结构参数和操作参数对微转子系统磨损特性的影响.结果表明:在MEMS微转子系统中,微转子轴衬偏心距离和转子轴衬半径影响线磨损率,以两者减至最小为较理想,但须注意设计中轴承半径的限制,并使轴衬偏心距离大于轴承内半径;在转子加工制造许可的范围内,可以通过调整转子轴衬的半径和偏心距离来减少摩擦磨损对微电机的影响,随着转子所承受载荷和转子旋转速度的增加,其磨损严重;接触区的应力分布不同于经典Hertz解,这是由于应力集中出现在不连续的曲率线上,且接触区的接触压力呈现轴对称抛物线状分布.该模型可用于预测微转子轴衬的磨损与接触状况,分析微转子系统的磨损特性.     

基于CBAM-CNN的高速列车制动闸片摩擦块偏磨状态监控

为了解决高速列车制动闸片偏磨状态特征提取困难的问题,提出了一种基于二维图像识别的多尺度卷积和卷积注意力模块(CBAM)结合的状态监控模型. CBAM分别对数据的通道和空间给予不同的关注度以提取出关键的信息,使模型能够准确的对偏磨的状态特征进行提取.模型的多尺度卷积模块则是增加模型对卷积核尺度的适应性,以提取到更加丰富的特征.此外,为了防止模型训练过程中梯度爆炸和梯度消失的现象,在模型中加入残差连接.最后,将所提方法应用于自行研制的高速列车自制试验台得到的制动闸片偏磨数据集,实验结果表明,该模型不仅能够准确有效的识别制动闸片各种偏磨状态,平均准确率达到99.89%,而且也具有较强的稳定性.