Jörg Wallaschek

PANTOGRAPH/CATENARY DYNAMICS AND CONTROL.

SUMMARY The pantograph-catenary system with its dynamic behaviour turned out to be a crucial component for new train systems required to run at higher speeds. With the present systems, operational limitations have to be accepted when running with several pantographs in the train set, when tilting trains are employed, when running on low quality catenary sections or when stricter noise reduction regulations are forcing lower noise emissions also for the pantographs. This paper gives an overview of the methods to describe the catenary and the pantograph system dynamics. Furthermore, aspects concerning the interaction between current collectors and overhead equipment, the acquisition of the model data and the verification are presented. Finally various constructions of passive pantographs and proposals for active control concepts are discussed.

Contact mechanics of piezoelectric ultrasonic motors

Piezoelectric ultrasonic motors are driven by tangential stresses in the interface between stator and rotor. These stresses are generated by the elliptical motion of the material points of the stator or rotor surface and depend on frictional processes in the contact area. The contact mechanics of piezoelectric ultrasonic motors determines the operational characteristics, like rotational speed and torque or transmitted mechanical power and efficiency. Wear properties and lifetime of piezoelectric ultrasonic motors are also determined by contact mechanics. The goal of the present paper is to summarize the state of the art in the understanding of some fundamental processes governing the contact mechanics of piezoelectric ultrasonic motors. After a short introduction, a survey of publications devoted to the subject will be given. Then, an attempt will be made to classify the mechanical models, which were developed in order to explain the contact mechanics of piezoelectric ultrasonic motors, according to the physical effects which have been taken into account in their derivation. Some results concerning the choice of proper contact materials, wear and lifetime of ultrasonic motors will be addressed in a separate section. Finally a summary and outlook will be given and open questions for future research will be formulated.

The effect of friction reduction in presence of ultrasonic vibrations and its relevance to travelling wave ultrasonic motors.

In many ultrasonic applications frictional effects play an important role (e.g. ultrasonic machining, ultrasonic motors). For optimising the applications in terms of quality, efficiency and lifetime it is important to understand the frictional coupling of the vibrating and the non-vibrating part. This contribution is devoted to give an explanation for the reduction of friction forces which is often observed when ultrasonic vibrations are superimposed to macroscopic motions. Usually adopted coefficients of friction are used for modelling such conditions suggesting special frictional mechanisms for high frequency oscillations, whereas the present paper shows that Coulombs friction law provides a very good description of the observed phenomena if the kinematics of the system is taken into account. Two systems are investigated. In the first system the ultrasonic and macroscopic movements are parallel and in the second they are perpendicular to each other but also within the plane of contact. Both systems were investigated analytically and experimentally using a specially designed test rig. The measurements confirmed the analytically derived equations and therefore the validity of Coulombs friction law even for ultrasonic conditions.

Survey of the present state of the art of piezoelectric linear motors

Piezoelectric ultrasonic motors have been investigated for several years and have already found their first practical applications. Their key feature is that they are able to produce a high thrust force related to their volume. Beside rotary drives like the travelling wave motor, linear drives have also been developed, but only a few are presently commercially available. In the present paper, we first describe the state of the art of linear piezoelectric motors. The motors are characterized with respect to their no-load velocity, maximum thrust force, efficiency and other technical properties. In the second part, we present a new motor, which is judged to be capable of surpassing the characteristics of other piezoelectric motors because of its unique design which allows the piezoelectric drive elements to be pre-stressed in the direction of their polarization. The piezoelectric elements convert energy using the longitudinal d33 effect which allows an improved reliability, large vibration amplitudes and excellent piezoelectric coupling. Energy loss by vibration damping is minimized, and the efficiency can be improved significantly. Experimental results show that the motor characteristics can be optimized for a particular task by choosing the appropriate operating parameters such as exciting voltage, exciting frequency and normal force.

Piezoelectric Ultrasonic Motors

Piezoelectric ultrasonic motors are a new type of actuator. They are characterized by high torque at low rotational speed, simple mechanical design and good controllability. They also provide a high holding torque even if no power is applied. Compared to electromagnetic actuators the torque per volume ratio of piezoelectric ultrasonic motors can be higher by an order of magnitude. Recently various types of piezoelectric ultrasonic motors have been developed for industrial applications such as cameralens drive or as actuator in the head restraint of automobile seats. This paper describes several types of piezoelectric ultrasonic motors. In the first part the working principle of the travelling wave motor is explained. In the second part other types of piezoelectric ultrasonic motors are described and classified with respect to the vibration modes and contact mechanisms used in their design. Finally some open problems in piezoelectric ultrasonic motor research are addressed.

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

Abstract In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque–speed curves as well as torque–efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.

Dynamics of non-linear automobile shock-absorbers

Abstract In this paper the methods of harmonic and stochastic linearization are discussed with respect to applications in shock-absorber dynamics. It is shown that the parameters of an equivalent linear system can be obtained directly from experimental data. In a second step an attempt is made to give a simple physical interpretation of the experimental results, which were obtained for a typical passenger cars shock-absorber.

A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems

Abstract The recently developed generalized Fourier–Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes. In order to enhance the practicability regarding the investigation of complex large-scale systems, it is proposed to provide analytical gradients and exploit sparsity of the nonlinear part of the governing algebraic equations. A novel reduced order model (ROM) is developed for those regimes where internal resonances are absent. The approach allows for an accurate approximation of the multi-harmonic content of the resonant mode and accounts for the contributions of the off-resonant modes in their linearized forms. The ROM facilitates the efficient analysis of self-excited limit cycle oscillations, frequency response functions and the direct tracing of forced resonances. The ROM is equipped with a large parameter space including parameters associated with linear damping and near-resonant harmonic forcing terms. An important objective of this paper is to demonstrate the broad applicability of the proposed overall methodology. This is achieved by selected numerical examples including finite element models of structures with strongly nonlinear, non-conservative contact constraints.

A HIGH-ORDER HARMONIC BALANCE METHOD FOR SYSTEMS WITH DISTINCT STATES

Abstract A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct states, i.e. where the ODEs involve piecewise defined functions. An event-driven scheme is used which is based on the direct calculation of the state transition time instants between these states. An analytical formulation of the governing nonlinear algebraic system of equations is developed for the case of piecewise polynomial systems. Moreover, it is shown that derivatives of the solution of up to second order can be calculated analytically, making the method especially attractive for design studies. The methodology is applied to several structural dynamical systems with conservative and dissipative nonlinearities in externally excited and autonomous configurations. Great performance and robustness of the proposed procedure was ascertained.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort.In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using a Complex Nonlinear Modal Analysis technique based on the work of Laxalde and Thouverez [1]. The methodology in [1] was refined by an exact condensation approach as well as analytical calculation of gradients in order to efficiently study localized nonlinearities in large-scale systems. Moreover, a continuation method was employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the Single Nonlinear Resonant Mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for re-computation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system.The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. In contrast to [1], the contact constraints account for variable normal load and lift-off in addition to dry friction. Forced response functions, backbone curves for varying normal preload and excitation level as well as flutter-induced limit cycle oscillations are analysed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.Copyright