具有非单调摩擦热弹性接触问题的有限元法

给出了一个变形体和刚性基础之间用双边摩擦表达其接触性质的、静态热弹性问题的方程式及其近似解法.以非单调、多值性表示该摩擦定律.忽略了问题的耦合效应,则问题的传热部分与弹性部分各自独立处理.位移矢量公式化为非凸的次静态问题,用局部Lipschitz连续函数来表示变形体的总势能.用有限单元法近似求解全部问题.     

基于偏最小二乘法的AMT离合器片表面温度预测

采用偏最小二乘回归方法,经交叉有效性检验建立了接合正压力的平均值、接合转速、滑摩时间与摩擦片表面最高温度的关系模型,模型对各种因变量的累计解释能力超过90%,通过该模型计算得到的拟合值与实际值的平均相对误差为3.90%,优于最小二乘支持向量机的预测效果,为AMT离合器开发、控制设计的优化及实现过温保护提供了依据.     

基于数据驱动的双离合器式自动变速器换挡过程控制

对采用双离合切换式换挡材DCT车辆而言,两个离合器的分离接合对换挡品质有重要的影响.为了实现DCT快速平顺的换挡过程控制,文章提出将换挡过程中的力矩相和惯性相作为一个整体进行优化控制,同时考虑换挡过程中发动机节气门配合的控制策略.考虑到传动系统的高度非线性和不确定性,采用数据驱动预测控制方法进行控制器设计.在进行控制器的设计时,首先针对离合器的动作设计了充分激励信号,然后根据该激励数据及在该激励数据作用下系统的输出响应利用子空间辨识的方法构造了Hankel矩阵,进而利用最小二乘法求解出被控对象的数据预测方程,依据换挡品质评价指标选取反映换挡快速性与平顺性的车辆冲击度和离合器转速差作为目标函数,考虑到换挡执行机构的响应能力的约束,进而将换挡过程闭环控制问题转化为反复开环求解使目标函数值最小的控制输入的优化问题,最后进行了离线仿真实验,验证了控制器的合理性和有效性.     

弹流润滑条件下表面形貌对摩擦噪声的影响

研究了弹流润滑状态下表面形貌对摩擦噪声的影响.通过激光微加工方法在金属圆盘试件表面上制造了两种沟槽型织构表面形貌,在双盘摩擦磨损试验机上对不同表面形貌进行了摩擦噪声和摩擦特性试验,分析了线接触弹流润滑条件下不同工况和表面形貌影响摩擦噪声的机理,并结合有限元分析对结论加以验证.结果表明:载荷和转速的变化对线接触摩擦噪声有明显影响,由于线接触副工作在部分膜弹流润滑状态下,所以摩擦噪声的特性与干摩擦时类似,摩擦因数较大的表面会辐射出更强的摩擦噪声;特定结构的表面形貌能改善表面润滑特性,有效降低摩擦噪声声压级,沟槽型织构的存在可以打断接触区域应力分布,减轻接触面微凸体碰撞作用,从而降低了表面自激振动,同时合适的表面形貌结构也有利于润滑油膜的形成,减小了系统的摩擦能量,达到降低摩擦噪声的效果.     

Casson流体作磁流体动力学流动时的Soret和Dufour效应

考虑Soret和Dufour效应,对Casson流体在可伸缩表面上,作磁流体动力学流动时的影响.首先导出相关的方程,然后用同伦法构造级数解.给出并讨论了速度、温度和浓度的场结果;在不同的物理参数下,得到并分析了表面摩擦因数、Nusselt数和Sherwood数的值;并验证了级数解的收敛性.     

具有偿付约束的衍生证券市场均衡存在性

本文通过一个简单的模型,证明了具有偿付约束的衍生证券市场均衡的存在性,由此解释了衍生证券市场的起因和衍生证券交易所的建立过程.这一结论很好地解释了市场摩擦对均衡存在性的影响,与无摩擦时均衡未必存在在形成了鲜明的对照.     

考虑铰摩擦的太阳翼展开动力学研究

研究了空间漂浮航天器太阳翼的展开动力学与控制问题.采用单项递推组集方法建立了太阳翼展开与锁定过程的动力学模型,利用虚功率原理推导了铰摩擦对系统动力学方程的贡献,通过补充含摩擦铰物体的系统动平衡方程构建了系统封闭的动力学方程.通过与ADAMS软件仿真结果的对比,验证了所建模型的正确性.研究结果显示,所建模型能够有效地对太阳翼的展开过程进行描述,铰摩擦会对系统的动力学行为产生影响,PD控制方法能够较好地抑制太阳翼展开所引起的航天器的姿态漂移.     

摩擦市场的最优消费-投资组合选择

本文研究摩擦市场中的最优消费-投资组合选择问题.当金融资产和自然状态个数为有限个以及摩擦局限于成比例的交易费时,可用原始市场或适当转换了的市场的无套利性来刻画最优消费-投资组合策略的存在性或充要条件.     

带摩擦的弹性接触问题广义变分不等原理的简化证明

在弹性摩擦接触问题中 ,从变分原理出发来研究接触问题 ,可以将摩擦力纳入问题的能量泛函 .为了得到摩擦约束弹性接触问题的能量泛函 ,日前大多是用拉格朗日乘子法 ,但拉格朗日方法用在变分不等问题中 ,要利用非线性泛函分析和凸分析来证明 ,证明复杂 .本文利用向量分析的工具及巧妙的变换 ,对带摩擦约束的弹性接触问题的广义变分不等原理进行了严格的证明 ,由于只用到向量分析 ,简化了证明 .     

摩擦市场的利率期限结构的无套利分析

本文用无套利方法分析有摩擦金融市场中利率的期限结构.对存在有限个债券和离散有限个到期日以及存在成比例的交易费、买卖差价、税赋这三种摩擦的金融市场,引入了相容期限结构的概念,给出了相容期限结构和套利机会的存在性结果或充要条件及它们的识别与计算方法.     

Modeling and simulations of the clutch dynamics using approximations of the resulting friction forces

The work presents the effectiveness of a certain class of approximate models of the resulting friction force found during simulations of a simplified model of clutch dynamics. The friction models are based on integral expressions assuming fully developed sliding and Coulomb's classical law of friction on each element of the planar contact. Special approximations of the integral model of the friction force and the moment are proposed, which are based on Padé approximants and their generalizations. The system of clutch dynamics is simplified to a friction disk on a rotating master disk. Two different configurations are investigated, including the coaxial and non-coaxial arrangement of the disks. The model based on the generalization of Padé approximants is compared with the corresponding approximants based on the Taylor series expansion and with the model using the integral expressions for the resultant friction force and torque components.     

Nonlinear dynamic effects in automotive clutches

Dynamic effects appearing in the dry friction clutches are very complex. The reason for this is the usual design of the clutches including complex two dimensional friction, unilateral contacts and nonlinear springs. The final quality of the clutch system for a customer depends among other criteria on the awareness of dynamic effects, which can affect functioning and comfort negatively. One of the usual nonlinear dynamic effects in the friction clutch is presented in this work. That is the problem of dynamic disengagement which can cause significant safety problems. First of all the global nonlinear dynamic behavior is considered roughly by means of an analytical approach. Secondly a MBS-model, which includes not only the nominal design of the clutch system but also dispersion of several parameters, is used in order to identify the influence of the asymmetry on the dynamic behavior. Analytical and numerical results are compared with measurements. Finally a possible solution of the considered problem is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controller design for uncertain dynamics of smooth shift of heavy-duty automatic transmission

Shift shock is an important index for evaluating the noise, vibration, and harshness performance of heavy-duty vehicles owing to the changeability of driving conditions. Hence, it is imperative to design a controller for a smooth shift to enhance the shift quality of automatic transmission. In this study, a novel robust control design against the uncertainties of heavy-duty vehicles is designed after dynamic modelling is performed. First, the clutch actuator model was developed by considering the uncertainty of electrohydraulic actuators, variations in friction coefficient due to clutch slip speed, and complex and volatile driving conditions of vehicles. Next, a robust control design for the inertial phase is proposed based on the clutch slip speed, including a feedforward controller, feedback controller, and disturbance controller. Finally, it is demonstrated that the control design is highly advantageous for the shift control of heavy-duty automatic transmission by comparison with a proportional-integral-derivative controller. Numerical results indicate that the proposed controller is effective in preventing shift shock, thereby improving ride comfort.     

Investigation of Damping of Vibrations in a System With Two‐Disc Inseparable Clutch

This paper presents the results of tests on free and forced harmonic torsional vibrations in a system with a two‐disc inseparable clutch, with structural friction taken into account. Nonlinear histeresis loop describing the frictional‐elastic properties of the system was introduced into the model. The mathematical model of the vibrating system containing two disks inseparable clutch was built. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude torsional displacement was determined. When vibrations were harmonically forced, the amplitude ‐ frequency characteristics of the system were determined numerically. The system was used as a nonlinear torsional vibration damper in a linear system with a harmonic force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stabilization of sliding motion by partial stiction

Rotating friction disks are utilized in many drivetrain components such as dry clutches and their actuator systems. Even the simplest pin-on-disk or disk-on-disk mechanical systems with Coulomb friction reveal a rich dynamical behavior with different types of motions. Examining the radial dynamics of minimal friction disk models, it is a prevalent assumption to have pure sliding frictional contacts. Governed by the systems' design parameters and initial conditions, stable large amplitude motions at higher rotation speeds are possible. Using a Coulomb friction model with sticking and sliding instead, gives similar motions with alternating phases of sticking and sliding. However, the amplitude can be decreased significantly by these intermittent phases of stick and slip. It is suggested to exploit such motions with partial stiction in order to reduce amplitudes and thus stabilize the systems. Similar effects can be observed in 3D-multibody simulations and measurements of double clutch actuator systems. However, for these systems analytical treatment is not feasible any more due to the number of involved degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the hydraulic fluid pipe on the dynamic stability of a shift gearbox

Shift gearboxes are used in vehicle drive trains in order to transmit the driving torque of the motor and to shift between different transmission ratios. Because of the occurrence of sliding friction forces and -torques during the shifting period, unwanted vibrations can arise. Several mechanisms which lead to a destabilization of the stationary state in shift gearboxes are conceivable: variable friction coefficient [1], wobbling clutch disc [2], or vibrations because of coupled DoFs due to the helical gearing [3]. The latter effect results in translational oscillations in axial and radial direction of the clutch disc. It was observed that damping forces influence the boundary of the region of stability in the parameter space - though it is not entirely clear where such forces originate from. For this reason, in this work the effect of the fluid of the hydraulic actuation of the clutch system is analyzed. The fluid pipe is situated in the center of the gear unit input shaft and forces the fluid to oscillate when the system becomes unstable. In return, the fluid implies shear stress and pressure on the adjacent mechanical parts (shaft, pressure plates). The analysis of the stationary state of the coupled system reveals a clear effect of fluid properties on the stability: both the mass density and the kinematic viscosity are able to change the location of the border between stable and instable regions in the parameter space. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and experimental validation of the dynamic behavior of an electromechanically actuated multiple‐disk clutch

Automated multiple‐disk clutches in automotive drivelines are at present hydraulically or electrohydraulically actuated. The electromechanical clutch actuation represents an alternative. The subject of the investigation is a functional model of an electromechanical clutch actuator which consists of a servo motor, a reduction gear and a mechanism for the realization of the force acting on the disks. For the simulation of the dynamic behavior of the electromechanically actuated multiple‐disk clutch a detailed multibody model is developed which includes models of the electromechanical actuator and the wet multiple‐disk clutch. The multiple‐disk clutch is described by coupled partial models for the rotational and translational dynamics. The coupling parameters are the relative disk distances and the forces between the disks. The results of test bench measurements are compared to simulation results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Target torque estimation for gearshift in dual clutch transmission with uncertain parameters

The target torque of engaging clutches during gearshift is a key factor that affects the dynamic response of powertrains equipped with the dual clutch transmissions (DCT). This paper investigates a method to estimate the target torque of engaging clutches under conditions where engine torque and measurement signals contain white noise and some vehicle parameters (the radius of wheel and rolling friction coefficient) are uncertain. To compute the target torque accurately, the state of system should be estimated when the uncertain parameters exist. The vehicle powertrain is modeled as the 3DOF system when one clutch is closed and the 4DOF system when two clutches are open, while the measured signals include speeds of the engine, transmission, and vehicle (rotational speed of wheels). In addition to traditional extended Kalman filter (EKF), both the joint extended Kalman filter (JEKF) and dual extended Kalman filter (DEKF) are used to estimate the target torque. The simulation results show that DEKF and JEKF provide much higher accuracy in the estimation of target torque than EKF when some parameters of the model are uncertain, so as to produce a better ride performance of the transmission during gearshift, i.e. reduction of power interruption and compressed shifting time. Furthermore, the DEKF provides higher accuracy than the JEKF in estimating uncertain parameters.     

Analysis of fluid flow and heat transfer in coolant ducts of friction clutches

This paper deals with the numerical simulation of the fluid flow in coolant ducts as wall as the calculation of temperature field in fluid and solid of a friction clutch. The simulations are carried out by means of commercial software based on a finite volume method in a relative framework, where the fluid flow is not time dependent. The results in dependence of rotation speed and slip velocity show interesting secondary flow in the ducts. Different flow pattern have distinct influence on the temperature field and the heat transfer. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The equilibrium of a rigid body on a plane with anisotropic dry friction

The problem of the conditions for the static equilibrium of a body, resting on a rough plane at one, two or three points, is considered. It is assumed that an arbitrary system of active forces is applied to the body, while the friction on the rough supporting plane is anisotropic. This model generalizes the well-known isotropic model of Coulomb dry friction. Explicit analytic formulae, which express the necessary and sufficient conditions for static equilibrium, are obtained. The investigation procedure uses the idea of an anisotropic force of static friction, which enables analytical results for the equilibrium conditions to be obtained more easily.