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dr hab. inż. Rafał Hein
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Catalog Publications
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A DISCRETE-CONTINUOUS METHOD OF MECHANICAL SYSTEM MODELLING
PublicationThe paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described...
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HYBRID REDUCED MODEL OF ROTOR
PublicationIn the paper, the authors describe the method of model reduction of a rotor system. The proposed approach enables to obtain a low order model including e.g. nonproportional damping or the gyroscopic effect. This method is illustrated using the example of a rotor system. First, a model of the system was built without gyroscopic and damping effects by using the rigid finite element method. Next, this model was reduced. Finally, two...
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Port-based approach to distributed transfer function method
PublicationIn the paper there is presented an uniform, port-based approach to modeling of both lumped and distributed parameter systems. Port-based model of distributed system has been defined by application of distributed transfer function method (DTFM). The approach proposed combines versatility of port - based modeling and accuracy of distributed transfer function method. It enables to formulate appropriate input data for computer analysis...
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Hybrydowe modele i metody modelowania układów mechanicznych
PublicationW monografii przedstawiono metody modelowania układów mechanicznych umożliwiające uzyskanie odpowiednio dokładnych modeli niskiego rzędu. Jedną z nich jest dyskretno-ciągła metoda pryzm (DCMP). Łączy ona zalety metod modelowania układów ciągłych o parametrach rozłożonych i dyskretyzowanych przestrzennie o parametrach skupionych. Jej opis matematyczny wyprowadzono posługując się metodami sztywnych elementów skończonych i transmitancji...
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Hybrid Model of Axially Moving Continua
PublicationThe paper introduces the method of the model reduction of systems that experience a Coriolis acceleration component. It causes that system equations are non-self-adjoined. To avoid such problem modal, reduced model is built up for the system without Coriolis acceleration terms which are next included by application of any lumping technique. Hence, the final reduced model is a hybrid one, obtained by both lumping and modal methods...
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Port-Based Modelling of Distributed-Lumped Parameter Systems
PublicationThere in the paper is presented an uniform, port-based approach to modelling of both lumped and distributed parameter systems. Port-based model of the distributed system has been defined by application of bond graph methodology and distributed transfer function method (DTFM). The approach proposed combines versatility of port-based modelling and accuracy of distributed transfer function method. The concise representation of lumped-distributed...
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Modal Reduction and Analysis of Gyroscopic Systems
PublicationThe paper introduces the method of the modal reduction of systems that experience the Coriolis acceleration or gyroscopic effect component. In such cases corresponding system equations are non-self-adjoined. To solve the problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are included by application of any lumping technique. Hence, the final reduced model...
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Hybrid, Approximate Models of Distributed-Parameter Systems
PublicationThe paper introduces the method of distributed-parameter systems modelling. It enables to obtain low order modal model of the system that experiences Coriolis acceleration component and gyroscopic effect. In such cases, corresponding system equations are non-self-adjoined. To solve this problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are next included...
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Modelling of Mechatronic Systems with Distributed Parameter Components
PublicationThe paper presents an uniform, port-based approach to modelling of both lumped and distributed parameter systems. Port-based model of distributed system has been defined by application of the bond graph methodology and the distributed transfer function method (DTFM). The proposed method of modelling enables to formulate input data for computer analysis by application of the DTFM. The computational package for the analysis of complex...
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Computational algorithm for the analysis of mechatronic systems with distributed parameter elements
PublicationThe paper presents a systematic computational package for analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The algorithm is based on the transfer function method (DTFM). With this algorithm, a bond graph technique for the modelling is developed to simplify computations. Analysis of different systems requires only changing the inputs data in the form of the bond graph diagram
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Optimum Control of Gyroscopic Systems
PublicationThe problem of optimum control of transverse rotor vibrations with gyroscopic interactions has been described and solved in the paper. An integral performance index has been defined for such system in order to minimize vibration level of a chosen rotor point. For this reason, an efficient way of finding the weight coefficients of integral performance index for multi-degrees-of-freedom system with gyroscopic interactions has been...
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Application of the distributed transfer function method and the rigid finite element method for modelling of 2-D and 3-D systems
PublicationIn the paper application of the Distributed Transfer Function Method and the Rigid Finite Element Method for modelling of 2-D and 3-D systems is presented. In this method an elastic body is divided into 1-D distributed parameter elements (strips or prisms). The whole body (divided into strips or prism) is described by a set of coupled partial differential equations. Solving this equations in the state space form it is possible...
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Hybrid Reduced Model of Continuous System
PublicationThe paper introduces an alternative method of modelling and modal reduction of continuous systems. Presented method is a hybrid one. It combines the advantages of modal decomposition method and the rigid finite element method. In the proposed method continuous structure is divided into one-dimensional continuous elements. For each 1D element modal decomposition and reduction is applied. Interactions between substructures are...
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Hybrid model of moving or rotating continua
PublicationThe paper introduces the method of the model reduction of systems that experience a Coriolis acceleration or gyroscopic effect component. In such causes that corresponding system equations are non-self-adjoined. Modal reduced model is built up for the system without Coriolis or gyroscopic effect terms. These phenomena are next included by application of any lumping technique. Hence, the final reduced model is a hybrid one, obtained...
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Modelling of pipes conveying flowing liquid
PublicationThe paper introduces the method of modal reduction of system which consists of pipe with flowing liquid. The concept of hybrid model is proposed. The system model consists of two parts, the modal model and the finite elements model. The modal model represents linear, self-adjoined part of the system, while simple lumped technique is applied for modelling of Coriolis phenomena.
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Software tool for modelling of mechatronic systems with elastic continua
PublicationThe paper presents a systematic computational package for modelling and analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The constructed computer program enables the frequency domain analysis of a class of linear systems and to obtain reduced order model in the form of bond graph. Obtained modal bond graph can be directly exported into 20-Sim package to further processing including nonlinear...
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Modelling method for a class of distributed-lumped parameter systems
PublicationThe paper presents an alternative approach for modelling and order reduction of continuous system. The proposed methodology combines application of two methods: the modal decomposition method and the rigid finite element method. The given continuous structure is divided into 1D continuous substructures. For each 1D substructure modal decomposition and reduction procedure is applied. Interactions between substructures are described...
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Reduced order model of 2d system
PublicationA new method of modelling is developed for static and dynamic analysis of two-dimensional elastic bodies. In the analysis, an elastic body is divided into strips. For each one-dimensional strip the reduced modal model is build up. The modal model contains appropriate number of inputs and outputs to connect lumped interaction that occur between strips. Proposed method of modelling enables to obtain more accurate and more simple...
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Model hybrydowy układu wielowirnikowego z przekładnią
PublicationW pracy przedstawiono metodę redukcji modelu układu wielowirnikowego z przekładnią, w którym uwzględniono zmienną prędkość kątową wirników, oddziaływania żyroskopowe, nieproporcjonalne tłumienie oraz nieliniowość podatności zazębienia. Zaproponowano hybrydową metodę modelowania, w której zastosowano: dekompozycję modalną oraz dyskretyzację przestrzenną. Zredukowany model modalny zbudowano dla części rozważanego układu, w której...
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Modelling of Geared Multi-Rotor System
PublicationIn the paper the method of modelling a speed-varying geared rotor system is presented. The proposed approach enables us to obtain an accurate low-order lumped parameter representation of the investigated system. The final model consists of reduced modal models of an undamped beam/torsional shaft system as well as a spatially lumped model of other linear and nonlinear phenomena including gear mesh interaction.
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