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A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

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Acta Mechanica Sinica 2015年第3期31卷 406-415页

作者： Yilong Liu Achim Fischer peter eberhard Baohai Wu Key Laboratory of Contemporary Design and Integrated Manufacturing Technology Northwestern Polytechnical University Institute of Engineering and Computational Mechanics University of Stuttgart

A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.

关键词： Full-discretization method Time delay -Stability Chatter

A-posteriori error estimation for second order mechanical systems

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Acta Mechanica Sinica 2012年第3期28卷 854-862页

作者： Thomas Ruiner Jrg Fehr Bernard Haasdonk peter eberhard Institute of Engineering and Computational Mechanics University of StuttgartPfaffenwaldring 970569 StuttgartGermany Institute of Applied Analysis and Numerical Simulation University of StuttgartPfaffenwaldring 5770569 StuttgartGermany

One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.

关键词： A-posteriori error estimator. Flexible multibodysystems Model reduction

Stability analysis of a thin-walled cylinder in turning operation using the semi-discretization method

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Acta Mechanica Sinica 2014年第2期30卷 214-222页

作者： Arnab Chanda Achim Fischer peter eberhard Santosha Kumar Dwivedy Institute of Engineering and Computational Mechanics University of Stuttgart

In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.

关键词： Machine tools Stability Chatter

An LSTM‐based approach to precise landing of a UAV on a moving platform

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International Journal of Mechanical System Dynamics 2022年第1期2卷 99-107页

作者： Wei Luo Henrik Ebel peter eberhard Institute of Engineering and Computational Mechanics University of StuttgartStuttgartGermany

A machine learning‐based method for the precise landing of an unmanned aerial vehicle on a moving mobile platform is *** proposed approach attempts to predict the mobile platform's future trajectory based on the past states of the mobile *** that end,it combines a long short‐term memory‐based neural network with a Kalman ***,it aims at combining the advantages of a machine learning method with those of a state estimation method from established control *** on the predicted trajectory,the unmanned aerial vehicle attempts to land precisely on the moving mobile *** experiment is conducted in the Gazebo simulation platform with a quadrotor and an omni-directional mobile robot,and the proposed method is compared with the single‐method approaches of using only either the Kalman filter or the machine learning method alone.

关键词： Kalman filter long short‐term memory(LSTM) trajectory prediction unmanned aerial vehicle(UAV)

Improving the dynamic stability of a workpiece dominated turning process using an adaptronic tool holder

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Theoretical & Applied Mechanics Letters 2013年第1期3卷 63-70页

作者： Achim Fischer peter eberhard Institute of Engineering and Computational Mechanics University of Stuttgart

In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability.A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue. C 2013 The Chinese Society of Theoretical and Applie-d Mechanics. [doi：10.1063/2.1301308]

关键词： multibody dynamics vibrations stability feedback control

Parameter Identification of Rubber Isolators Using Frequency-Dependent Spring and Damper Coefficients

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Journal of Donghua University(English Edition) 2011年第2期28卷 134-138页

作者：孙德伟 eberhard peter 张广玉 School of Mechatronics Engineering Harbin Institute of Technology Institute of Engineering and Computational Mechanics University of Stuttgart

A model to describe the hysteresis damper character of rubber material is presented in this paper. It consists of a parallel spring and damper, whose coefficients change with vibration frequencies. In order to acquire these relations, the force decomposition is carried out according to some sine vibration measurement data about nonlinear forces changing with deformations of the rubber material. The nonlinear force is decomposed into a spring force and a damper force, which are represented by a frcquency-dependent spring and damper coefficient, respectively. Repeating this step for different measurements will give different coefficients corresponding to different frequencies. Then, application of a parameter identification method will provide the requested functions over frequency. Using those formulae, as an example, the dynamic character of a hollow shaft system supported by rubber rings is analyzed and the acceleration response curve in the centroid position is calculated. Comparisons with sine vibration experiments of the real system show a maximal inaccuracy of 8. 8 %. Application of this model and procedure can simplify the modeling and analysis of mechanical systems including rubber materials.

关键词： rubber isolator parameter identification hysteresis damper virtual mass method dynamic analysis

An approach for the coupled simulation of machining processes using multibody system and smoothed particle hydrodynamics algorithms

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Theoretical & Applied Mechanics Letters 2013年第1期3卷 44-50页

作者： Fabian Spreng peter eberhard Florian Fleissner Institute of Engineering and Computational Mechanics University of Stuttgart

The prediction accuracy of a simulation method is limited by its theoretical background. This fact can lead to disadvantages regarding the simulation quality when investigating systems of high complexity, e.g. containing components showing a fairly different behavior. To overcome this limitation, co-simulation approaches are used more and more, combining the advantages of different simulation disciplines. That is why we propose a new strategy for the dynamic simulation of cutting processes. The method couples Lagrangian particle methods, such as the smoothed particle hydrodynamics （SPH） method, and multibody system （MBS） tools using co-simulations. We demonstrate the capability of the new approach by providing simulation results of an orthogonal cutting process and comparing them with experimental data. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301305]

关键词： multibody dynamics smoothed particle hydrodynamics co-simulation machining contact modeling

IJMSD: A novel journal devoting to promote the progress of modern science, technology and industry by enhancing the capabilities of mechanical system dynamics

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International Journal of Mechanical System Dynamics 2021年第1期1卷 3-4页

作者： Xiaoting Rui Marco Amabili peter eberhard Yonggang Huang Nanjing University of Science and Technology NanjingChina McGill University MontrealCanada University of Stuttgart StuttgartGermany Northwestern University EvanstonUSA

From the Stone Age to modern industry,the development of me-chanical systems has driven human civilization and the progress of science and *** dynamic performances related to manufacturing precision,mobility,comfort,reliability,and safety have become the bottlenecks restricting the development of con-temporary industrial products,which can be regarded as complex and integrated mechatronical systems composed of many subsystems with highly coupled dynamical *** the advent of the fourth industrial revolution and the widely used complicated and integrated products,it has been found clearly that quasi‐static or local dynamics study can no longer capture the critical features of contemporary mechanical systems.

关键词： dynamics journal restrict

Simplified modeling of electromagnets for dynamic simulation of transient effects for a synchronous electric motor

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International Journal of Mechanical System Dynamics 2021年第1期1卷 89-95页

作者： Florian Bechler Julius Kesten Florian Wittemann Frank Henning Martin Doppelbauer peter eberhard Institute of Engineering and Computational Mechanics University of StuttgartStuttgartGermany Institute of Electrical Engineering Karlsruhe Institute of Technology(KIT)KarlsruheGermany Institute of Vehicle System Technology Karlsruhe Institute of Technology(KIT)KarlsruheGermany

This study aims to show an approach for the dynamic simulation of a synchro-nous *** magnetic forces in the air gap are calculated efficiently using simplified approaches without neglecting important *** the modeling of the magnetic forces,an equivalent magnetic circuit is constructed in which the magnetic saturation and the leakage flux are taken into account and coupled with the electrical circuit at the *** calculated magnetic forces are then passed to a mechanical model of the *** with a predefinable load torque,the resulting motor rotation and the forces in the bearings are *** presented model is then investigated in a small *** novel ap-proach is intended to provide a method of calculating dynamically the forces transmitted from the shaft to the motor housing and to create the basis for evaluating electric motors for vibrations,noise,and harshness under varying loads and input voltages.

关键词： dynamic simulation electromagnet electromagnet modeling magnetomotive forces