A note on the contact problem in an ultrasonic travelling wave motor

In this paper we discuss the non-linear contact problem between the stator and the rotor of an ultrasonic travelling were motor. For a first simplified mathematical model the problem is formulated for a linear motor in which the stator is modelled as a Bernoulli-Euler beam and the slider (rotor) is assumed to be rigid. A thin layer of visco-elastic material is assumed to exist between stator and slider. Expressions are obtained for the contact pressure between the two parts. The frictional forces both in the sticking and in the sliding zone can then be easily obtained assuming Coulomb friction.     

超声马达转子摩擦材料厚度对驱动性能的影响研究

制备了一系列不同厚度的摩擦材料 ,利用超声马达摩擦特性模拟试验装置 ,研究了摩擦材料厚度对超声马达空载转速和堵转力矩的影响 .基于一个简化的行波超声马达定子和转子接触模型 ,用有限元法计算了定子和转子接触变形随摩擦材料厚度的变化规律 ,提出了定子和转子具有合理接触变形的摩擦材料厚度范围 .根据试验和理论计算结果确定了摩擦材料最佳厚度 ,为超声马达摩擦材料厚度设计提供了理论依据     

摩擦材料应用方式对超声波电机驱动特性的影响

摩擦材料是超声波电机的关键零件,其应用方式直接影响超声波电机的驱动特性.以行波超声波电机为研究对象,将摩擦材料分别应用到转子和定子上,与相应的定子和转子组合,模拟超声波电机的接触方式,研究了超声波电机的负载和磨损特性随摩擦材料应用方式的变化规律.借助于阻抗仪测试了摩擦材料应用到定子齿面前后的阻抗特性,采用精密粗糙度仪和金相显微镜评价了超声波电机定子和转子接触界面磨损前后的形貌变化及其磨损模式.结果表明:当摩擦材料应用到定子齿面时,定子的谐振频率略微降低;当2台超声波电机空载转速相同时,摩擦材料应用到定子齿面与金属转子配副时可获得较大的堵转力矩,定子摩擦材料表面呈现抛光的磨损特征,而当摩擦材料应用到转子表面与金属定子配副时,转子摩擦材料表面呈现较严重的犁沟磨损.     

Optimization of travelling wave ultrasonic motors using a three-dimensional analysis of the contact mechanism at the stator–rotor interface

The present paper investigates optimization rules and new design methodologies dealing with the contact mechanics in rotative travelling wave ultrasonic motors (TWUM). The proposed approaches focus on the design of the rotor, including the friction layer that is usually deposited onto its lower surface, while the stator is supposed to be preliminary designed. Contact aspects such as the transmission of mechanical power as well as the wear mechanism of the friction layer are investigated, according to the analysis of the stator–rotor contact mechanics in both hoop and radial directions. Considering a classical wear criterion in a preliminary step, a contact ratio, that allows the mechanical power to be optimized, is pointed out in the hoop direction. In a further step, the contact conditions in the radial direction are improved through the elastic fitting of the stator and rotor radial deflexions, therefore allowing the material's wear to be decreased. Some experimental tests, that have been recently performed, give a comparison of wear marks, which occur onto optimal and non-optimal rotor geometries. A first mechanism synthesis is finally proposed in such a way to allow the mechanical architecture of the rotor (including the friction layer) to be automatically designed according to a given set of mechanical constraints.     

A Model of Contact Forces in Pneumatic Motor Vanes

The paper presents an investigation on the dynamic equilibrium of a pneumatic motor vane. The investigation was based on an analysis of the vane's free body diagram. In particular, a model was formulated for determining the contact forces between vane, rotor and stator and the contact configuration from the known motor geometry, friction coefficients and chamber pressures. In addition, the paper presents experimental measurements of friction coefficients in vane-rotor and vane-stator contact together with a validation of the model through comparison with a FEM model.     

面内行波超声电机定子表面质点运动轨迹与电机转矩

提出了面内行波超声电机的摩擦模型 ,研究了面内行波超声电机的动力传递机理 ,得出了电机的理想工作点 ,同时将电机的转矩和效率与定子表面质点的法向位移、切向位移及预应力相结合 ,提出为了实现电机大转矩和高效率 ,表面质点的法向位移应与转子接触区域质点的周向运动方向相同 .在满足上述条件的基础上 ,定子表面质点的切向位移和法向位移之比应尽量大 ,最佳比值应在考虑定子和转子之间的预紧力的条件下 ,使得电机工作于最大静摩擦力下 .最后采用有限元计算进行了验证     

杆状弯曲行波型超声电机运动机理研究

为了深入研究杆状弯曲行波型超声电机的运动机理，本文分析了定子表面质点椭圆运动轨迹的形成，并将椭圆运动分解为产生驱动力的有效椭圆运动与使定、转子产生径向滑动的径向直线运动；然后基于有效椭圆运动变化情况，分析了在两相振幅不平衡和任意相位差情况下对转子运动平稳性的影响，为这类电机的设计和性能控制提供理论依据。     

考虑定子质量和碰摩面刚度的转子/定子系统碰摩响应的全局动力学特性研究

对考虑定子质量和碰撞面刚度的四自由度转子/定子模型的全局响应特性进行了研究。首先,通过解析方法确定了无碰摩响应的边界,然后,求解了同频全周碰摩解并进行了稳定性分析得到了同频全周碰摩响应的区域。在此基础上,利用非线性动力学分析的数值方法,确定了准周期局部碰摩与反向涡动失稳的边界,由此得出了参数平面内的不同碰摩响应的稳定区域图。进而研究了定子与转子质量比和碰撞面刚度对碰摩全局响应特性的影响,得到了不同碰摩响应共存及随系统参数变化的典型全局响应分岔图。     

超声波电机用摩擦材料的研究进展

归纳并探讨超声波电机摩擦材料的基本要求与国内外研究进展.基于行波型超声波电机驱动特点及运行规律,从摩擦学、接触力学和材料学3个方面对超声波电机用摩擦材料的特殊要求进行探讨,初步得出超声波电机摩擦材料应具有优良的摩擦学、一定的接触变形和一定的结构特性3个方面的特殊要求.最后,针对超声波电机摩擦材料研究中存在的问题,提出一些超声波电机摩擦材料值得重视的研究方向,即建立更为完善的接触模型、研制针对多种环境下使用的多种系列摩擦材料、开发考察摩擦材料性能的专门试验设备与测试技术方法和寿命预测技术方法等.     

Mechanical energy transductions in standing wave ultrasonic motors: Analytical modelling and experimental investigations

The present work deals with experimental and theoretical analyses of mechanical energy transductions in standing wave ultrasonic motors. A piezoelectric translator prototype previously developed is tested with regard to both out-of-plane and tangential mechanical behaviours. Influences of the vibration amplitude, the normal pre-load and the dynamic friction coefficient at the stator/frame interface are pointed out through the acquisition of speed-driving force characteristics. In the main part of the article, theoretical approaches assuming the decoupling of the out-of-plane and tangential behaviours are proposed: the `complete' model takes into account transient phenomena and tangential inertia effects, and the `simplified' model supposes that the steady state is achieved. In both models, equivalent mass-spring systems allow the intermittent stator/frame contact to be characterized with regard to the vibration amplitude and the normal pre-load. Successive contact and flight periods are clearly shown. During contact periods, the sequences of stick-slip phases are at the origin of the driving mechanism. They are theoretically discriminated through the study of their behaviour equations. Finally, experimental and theoretical data fitting proves the validation of analytical analyses and allows the future optimization of standing wave ultrasonic motors to be envisaged.     

Nonlinear lateral-torsional coupled motion of a rotor contacting a viscoelastically suspended stator

Interaction of a rotor with a stationary part is a kind of serious malfunction that could result in a catastrophic failure if remained undetected. Past analytical and numerical simulation work on rotor?Cstator interactions mainly focus on the vibrations along the lateral directions. The torsional degree of freedom (dof) is usually ignored. The present work is aimed to study the influence of a rotor to stator contact on the lateral-torsional coupled vibrations. A mathematical model consisting of interacting vibratory systems of rotor and stator is presented. The contact is modeled using contact stiffness, damping and Coulomb friction. Equations derived for kinetic, potential and dissipation energies and non-conservative external forces are used in the Langrange??s equations for deriving the motion equations for the rotor?Cstator system. Equations revealed that the lateral-torsional motion coupling exists twofold for the rotor. The unbalance couples lateral-torsional motion of rotor through inertia and damping matrices. Coupling due to the rotor?Cstator friction occurs through a force vector. The nonlinear equations are solved using a Runge?CKutta fourth-order numerical integration scheme using relatively small time step. Results obtained through the proposed model are compared with the identical rotor?Cstator system without torsional dof and differences are identified. Effect of several parameters such as speed, relative inertia, coefficient of friction and contact damping on the bifurcation behavior of the rotor?Cstator motion has been investigated. Vibration motions presented in the forms of spectrum cascade of the coast-up response, and orbit and Poincaré plots of the steady-state response are exhibiting rich dynamic behavior of the system.     

单相旋转型驻波超声电机的数学模型及仿真

尽管单相驱动的旋转型驻波超声电机的原理样机早巳研制成功，但对这类电机的运动机理的研究却一直局限在定性分析上。本文将从能量角度，根据Hamilton变分原理，定、转子摩擦界面采用纯滑动模型建立了该种电机的数学模型；并根据此模型，用MATLAB语言作了计算机仿真，得到了该种电机的开、关过程动态响应。     

Improvement of rotor performance under rubbing conditions through active auxiliary bearings

This paper develops a new concept to enhance the adaptive capability of rotating machinery to the rubbing conditions through active auxiliary bearings. To demonstrate the feasibility of this idea, a model with a Jeffcott rotor and an active auxiliary bearing, which accounts for both the dynamics of the auxiliary bearing and the deformation on the contact surface, is investigated. The dynamics and the stability of the non-linear piecewise-smooth passive rotor/stator (auxiliary bearing) system are first studied. Then, two control approaches are proposed with the aim to reduce the rubbing severity during the rotor/stator rubbing. It is shown that by using an optimal controller, the harmful heavy rubbing between the rotor and the stator can be well stabilized to the mild light rub through the active auxiliary bearing, and the already established rotor-to-stator rubbing can even be released by using PD-controllers.     

Frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane

The frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study. The layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions. Friction between the component couples of layer–stamp and layer–half plane is taken into account. The problem is reduced to a system of singular integral equations, in which the contact pressures and the contact areas are the unknowns, and it is treated using Fourier transforms and the boundary conditions for the problem. The system of singular integral equations is solved numerically using the Gauss–Jacobi integration formula with equilibrium and consistency conditions. Numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases. This work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas.     

Contact analysis of a flexible bladed-rotor

This paper presents a model of fully flexible bladed rotor developed in the rotating frame. An energetic method is used to obtain the matrix equations of the dynamic behaviour of the system. The gyroscopic effects as well as the spin softening effects and the centrifugal stiffening effects, taken into account through a pre-stressed potential, are included in the model. In the rotating frame, the eigenvalues' imaginary parts of the latter matrix equation give the Campbell diagram of the system and its stability can be analysed through its associated eigenvalues' real parts. The turbo machine casing is also modelled by an elastic ring in the rotating frame through an energetic method. Thus, in some rotational speed ranges the contact problem between the rotor and the stator can be treated as a static problem since both structures are stationary to each other. Prior to the study of the complete problem of contact between the flexible blades of the rotor and the flexible casing, a simple model of an elastic ring having only one mode shape, excited by rotating loads is developed in the rotating frame too, in order to underline divergence instabilities and mode couplings. Then, the complete problem of frictionless sliding contact between the blades and the casing, without rubbing, is studied. The stable balanced static contact configurations of the structure are found as function of the rotational speed of the rotor. Finally, the results are compared to these of the simple model of rotating spring-masses on an elastic ring, showing good adequacy. The present model of rotor appears thus particularly adapted to the study of blades-casing contacts and highlighted an unstable phenomenon near the stator critical speed even in case of frictionless sliding.     

数控机床电机散热温度场的数值模拟研究

电机作为数控机床的核心部件,其性能影响着机床主轴系统的精度、电机效率和使用寿命．因此,合理设计高速电机的结构使其处于最佳的温度场,了解电机在运行过程中各空气区域内的速度及温度分布非常重要．本文以某机床的电机定转子作为研究对象,利用CFD软件对转子通风道的设计方案进行数值模拟,通过数值模拟分析电机内部的流场温度场及流场分布．根据模拟结果进行优化设计,在转子和定子之间进行单排孔和双排孔的优化方案设计,通过温度分布确定最佳设计方案,为电机转子通风道的散热优化设计提供有意义的参考．     

A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate

This paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space, when they are pressed against each other. The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson’s ratio. A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction. The entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction. It is assumed that the contact region is under sliding contact conditions with the Coulomb’s law used to relate the tangential traction to the normal component. Employing Fourier integral transforms and applying the necessary boundary conditions, the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem. The Gauss–Chebyshev quadrature-collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations. This system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously. The main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region.     

Nonlinear dynamics of a Jeffcott rotor with torsional deformations and rotor-stator contact

The dynamics of a modified Jeffcott rotor is studied, including rotor torsional deformation and rotor-stator contact. Conditions are studied under which the rotor undergoes either forward synchronous whirling or self-excited backward whirling motions with continuous stator contact. For forward whirling, the effect on the response is investigated for two commonly used rotor-stator friction models, namely, the simple Coulomb friction and a generalized Coulomb law with cubic dependence on the relative slip velocity. For cases with and without the rotor torsional degree of freedom, analytical estimates and numerical bifurcation analyses are used to map out regions in the space of drive speed and a friction parameter, where rotor-stator contact exists. The nature of the bifurcations in which stability is lost are highlighted. For forward synchronous whirling fold, Hopf, lift-off, and period-doubling bifurcations are encountered. Additionally, for backward whirling, regions of transitions from pure sticking to stick-slip oscillations are numerically delineated.     

Frictional contact problem of a rigid stamp and an elastic layer bonded to a homogeneous substrate

In this study, the frictional contact problem for a layer bonded to a homogeneous substrate is considered according to the theory of elasticity. The layer is indented by a rigid cylindrical stamp which is subjected to concentrated normal and tangential forces. The friction between the layer and the stamp is taken into account. The problem is reduced to a singular integral equation of the second kind in which the contact pressure function and the contact area are the unknown by using integral transform technique and the boundary conditions of the problem. The singular integral equation is solved numerically using both the Jacobi polynomials and the Gauss?CJacobi integration formula, considering equilibrium and consistency conditions. Numerical results for the contact pressures, the contact areas, the normal stresses, and the shear stresses are given, for both the frictional and the frictionless contacts.