Stability and response of a self-amplified braking system under velocity-dependent actuation force

Wedge brakes, featuring self-amplification, inspire good opportunity to obtain large normal force by small actuation force. A single degree of freedom torsional model with harmonic excitation for a driveline with a wedge brake is developed to investigate the effect of velocity-dependent actuation force. The stability analysis indicates that instability can occur even with a constant friction coefficient and is greatly influenced by the slope of the actuation force. Three bifurcation points are found: one stable, one unstable, and the other one Hopf. Phase portraits, time domain responses, Poincaré maps, and frequency spectra are provided by nonlinear computation. Three motions are observed: unidirectional stick-slip, bidirectional stick-slip, and non-stick-slip. Due to the self amplification, the wedge brake leads to more stick motions and more side bands compared with the conventional brake. By varying the slope, the dynamic response of the driveline can be synchronous or irregular multi-periodic motion. The dynamics at negative slope is studied further considering three other influencing factors, i.e., the initial actuation force, excitation frequency, and wedge angle. The results are provided by the comparison with those of the driveline with a conventional brake.     

Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.     

Oscillation pattern of stick-slip vibrations

This paper studies the stick-slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick-slip limit cycle oscillations of a single degree-of-freedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.     

振动驱动移动机器人直线运动的滑移分岔

近年来,随着移动型机器人设计技术水平的不断提高,其运动形式日趋多样. 借助于仿生学的思想,模仿蚯蚓等动物的蠕动成为不少机器人设计者所追求的目标. 为了实现这一目标,学者们提出并研究了振动驱动系统. 本文研究了各向同性干摩擦下,单模块三相振动驱动系统的粘滑运动. 考虑到库伦干摩擦力的不连续性,振动驱动系统属于Filippov 系统. 基于此,运用Filippov 滑移分岔理论,分析了振动驱动系统不同的粘滑运动情况. 根据驱动参数的不同,系统运动的滑移区域被分成4 种基本情形. 对这些情形分类讨论,得到系统的6 种运动情况. 然后对这6 种运动情况进行归纳,最终得出系统一共存在4 种不同的粘滑运动,而且也解析地给出了发生这4 种粘滑运动的分岔条件. 分岔条件包含系统的3 个驱动参数,通过变化这些参数,得到了系统运动的分岔图. 借助分岔图,详细分析了随着驱动参数的变化,系统如何实现不同粘滑运动类型之间的切换,并从分岔角度给出了相应的物理解释. 最后,通过数值方法直接求解原运动方程,数值解法得到的4 种运动图像与理论分析一致,验证了系统运动分岔研究的正确性.      

Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control

Nonlinear motions of a rotary drilling mechanism are considered, and a two degree-of-freedom model is developed to study the coupled axial-torsional dynamics of this system. In the model development, state-dependent time delay and nonlinearities that arise due to dry friction and loss of contact are considered. Stability analysis is carried out by using a semi-discretization scheme, and the results are presented in terms of stability volumes in the three-dimensional parameter space of spin speed, cutting depth, and a cutting coefficient. These stability volume plots can serve as a guide for choosing parameters for rotary drilling operations. A control strategy based on state and delayed-state feedback is presented with the goal of enlargening the stability region, and the effectiveness of this strategy to suppress stick-slip oscillations is illustrated.     

Effects of damping on brake squeal coalescence patterns – application on a finite element model

Brake squeal is referred to, in most publications, as a flutter instability triggered by a mode coupling phenomenon. A lot of clues tend to prove that damping would be a key parameter in brake squeal modelling. This study aims at investigating the effects of damping on coalescence patterns, that is to say on the way the modes couple. A finite element model of the whole brake corner has been used to compute the brake modal behaviour. Then a complex eigenvalue analysis has been undertaken to assess the brake stability as a function of the friction coefficient. Different kinds of damping spreading over the modes have been studied. Two main effects have been noticed: a shifting effect and a smoothing effect. The first one always stabilize the brake, whereas this is not the case of the second one. The combination of the two effects may make the brake more unstable depending on the spreading of the additionnal damping.     

A new criterion for occurrence of strick-slip motion in drive mechanism

This paper, using Karnopp's model of friction force and phase plane method, studies the stick-slip motion of the flexble drive mechanism. It is explained that a sudden drop of friction force is the essential source of stick-slip motion when the sliding is impending. A new criterion for occurrence of stick-slip motion is established. The stick-slip region and the stable region in a parameter plane are separated by a critical parameter curve. Moreover, for the stick-slip motion of the flexible drive mechanism without viscous damping, a parameter expression is obtained. The results may be used in design of the flexible drive mechanism.     

Experimental investigation of a single-degree-of-freedom system with Coulomb friction

This paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.     

Self-excited vibration of the shell-liquid coupled system induced by dry friction

The nonlinear vibration theory and the experimental modal analysis are used in this paper to study the self-excited vibration of the shell-liquid coupled system induced by dry friction. The effect of dry friction stick-slip coefficients and rubbing velocity on self-excited vibration, and the limit cycle and Hopf bifurcation solution of the system are obtained. In particular, it is shown that the phenomenon of 4 point (or 6 point) water droplet spurting of the Chinese cultural relic Dragon Washbasin is the result of the perfect combination of the self-excited vibration induced by dry friction and its special modes, which indicates the significant scientific value of the Chinese cultural relic Dragon Washbasin.     

Stick-slip chaos detection in coupled oscillators with friction

We consider two coupled oscillators with negative Duffing type stiffness which are self (due to friction) and externally (harmonically) excited. The fundamental solutions of the homoclinic orbit are constructed. Then, the Melnikov–Gruendler approach is used to define the Melnikov’s function including smooth and stick-slip chaotic behaviour. Theoretical considerations are supported by numerical examples.     

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.     

Sensitivity analysis and Kriging based models for robust stability analysis of brake systems

This paper presents a global strategy for the prediction of brake squeal. This approach is based on the global sensitivity analysis combined with Kriging modeling. The main aim is to assess the pertinence of using this strategy to build suitable and efficient instability predictors that can be potentially associated with numerical optimization schemes and/or robustness analysis algorithms for a robust design of brake systems. Through the use of a simplified brake system, the global sensitivity analysis is, firstly, shown to be essential for obtaining great insight on how design parameters influence individually and/or collectively the stability behavior. The latter is characterized by the distance of all the systems eigenvalues from the imaginary axis. It is shown that the so-called Sobol indices help for an objective quantification of the importance of taking parameter uncertainty into account in the whole design process. Based on these conclusions, Kriging modeling is, secondly, proposed to robustly predict friction induced instabilities. Its efficiency is then demonstrated. Consequently, the global sensitivity analysis and Kriging modeling give a very promising strategy helping for squeal prediction and, more generally, for optimal and robust design of brake systems.     

一种直流力矩电机系统的滞滑摩擦补偿方法

陀螺漂移测试转台直流力矩电机系统中存在的非线性滞滑摩擦，使转台在PID控制下存在滞滑极限环。为提高转台定位精度，应用具有滞滑(stick-slip)摩擦的直流力矩电机系统模型，推导了一种补偿方法，对含有滞滑摩擦的PID控制转台直流力矩电机伺服系统进行滞滑摩擦补偿。在采用PID控制的转台电机系统定位工作状态下，这种滞滑补偿方法可以减小滞滑极限环的幅值。仿真结果证明了该补偿方法的有效性。     

蠕墨铸铁铁道车辆闸瓦摩擦磨损性能研究

随着铁路车辆向高速和重载方向发展，人们开展了抗热疲劳剥落能力优异的蠕墨铸铁在火车刹车闸盘上的应用研究，然而研究内容只涉及其耐磨性，在摩擦性能方面还很少有研究成果公开发表。因此，以含磷蠕墨铸铁为研究对象，系统地考察了石墨形态和磷含量变化对材料摩擦磨损性能的影响。并且依据研究结果制造火车闸瓦进行了实际装车使用性能的试验研究。结果表明，在给定的试验条件下于几种不同形态石墨的铸铁中，蠕墨铸铁即有优良的耐磨     

A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

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.     

Application of an explicit TVD scheme for unsteady,axisymmetric, muzzle brake flow

Operator splitting in the presence of source terms is necessary in order to apply Harten's second-order accurate, total-variation-diminishing (TVD), shock-capturing scheme to higher-dimensional problems. By employing Godunov boundary treatment at the muzzle brake, such splitting is applied to the problem of muzzle brake flow simulation for the case of blasts which are impeded, by vertical and slanted baffles, respectively. Results from numerical studies of various types of wall boundary condition treatment which are consistent with Harten's TVD scheme are indicated.     

摩擦粒子填充材料对高速列车闸片制动性能的影响

在自行研制的制动缩比试验台上,对中心孔填充不同材料的高速列车制动闸片摩擦粒子进行拖曳制动试验,并采用有限元分析方法进行制动系统复特征值和接触应力分析,探讨填充不同材料对磨损特性、振动噪声和热分布的影响. 结果表明:原始摩擦粒子中心孔填充材料后,对制动系统的摩擦系数和模态耦合特性未产生显著影响,但对界面磨损行为和系统振动噪声特性产生明显影响. 填充粉末冶金后排屑行为下降,磨损行为更为复杂,制动系统产生的噪声增大;而填充紫铜、石墨和铸铁后的制动噪声均有所降低,尤其填充铸铁后表面磨损相对均匀,其摩擦学性能相较于其他粒子得到一定的改善. 填充材料产生的磨屑及相应的界面磨损行为是影响制动摩擦振动噪声和表面热分布的关键因素,填充合理的材料有助于降低制动噪声和改善制动界面磨损行为及表面热分布.      

A damage constitutive model for sliding friction coupled to wear

Several new constitutive models are formulated for the planar interface of a soft body sliding on a rigid soil, describing stick-slip phenomena due to friction, and wear due to abrasion. Attention is focused on damage at the interface, by neglecting any interaction with damage of body and any propagation of damage inside the body. Models are formulated in the general framework of the Thermodynamics of the irreversible processes and account for suitable defined internal variables of phenomenological type, namely gap, isotropic friction hardening and wear. The main feature of the new presented models is that the formulation of the wear process at the interface is obtained in the contest of Damage Mechanics, and it is based on the formal analogy between abrasion of a soft body and ductile damage of an elastic-plastic material. By following this approach, a scalar wear field, an effective stress and appropriate state and dissipation potentials are defined, able to describe a tangential isotropic wear process due to stick-slip and to hardening mechanism. Both cases of linear and nonlinear friction hardening are formulated; moreover, wearable and no-wearable bodies are considered. Numerical results relevant to one-dimensional problems are illustrated for monotonic, forward-backward and cyclic displacement time-histories, showing evolution for stress, gap and wear. Results furnished by different models are compared and discussed.     

Analytical approximations for stick-slip vibration amplitudes

The classical “mass-on-moving-belt” model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions, the amplitudes, and the base frequencies of friction-induced stick-slip and pure-slip oscillations. For stick-slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large.