{"title":"Parallel Co-Simulation Approach With Macro-Step Size and Order Control Algorithm","authors":"J. Kraft, T. Meyer, B. Schweizer","doi":"10.1115/detc2019-97781","DOIUrl":"https://doi.org/10.1115/detc2019-97781","url":null,"abstract":"\u0000 This contribution deals with the parallelization of multibody systems by making use of co-simulation techniques. The overall model is split into a user-defined number of subsystems, which are coupled and computed by means of a co-simulation approach. The co-simulation methods considered here are weak coupling approaches, which implies that each subsystem is solved independently from the other subsystems within a macro-time step. Information (i.e. coupling variables) is only exchanged between the subsystems at certain communication-time points (macro-time points). Within each macro-time step, the unknown coupling variables are approximated by extrapolation polynomials. The separate integration of the subsystems is the crucial point for a parallelized computation. A main drawback of many co-simulation implementations is that they are based on a constant macro-step size. Using an equidistant communication-time grid may in many practical applications be not very efficient with respect to computation time, especially in connection with highly nonlinear models or in context with models with strongly varying quantities. Here, a co-simulation approach is presented which incorporates a macro-step size and order control algorithm. Numerical examples show the benefit of this implementation and the significant reduction in computation time compared to an implementation with an equidistant communication-time grid.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122837001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Matteo Scapolan, Valentin Sonneville, A. Callejo, O. Bauchau
{"title":"Component-Based Modeling and Sensitivity Analysis of Composite Beam Cross-Sections","authors":"Matteo Scapolan, Valentin Sonneville, A. Callejo, O. Bauchau","doi":"10.1115/detc2019-98065","DOIUrl":"https://doi.org/10.1115/detc2019-98065","url":null,"abstract":"\u0000 Flexible multibody systems often include slender bodies that can be modeled as beams. In contrast with their three-dimensional counterparts, beam formulations are much more efficient and produce models that are more intuitive from engineering and design standpoints. This paper presents a modular approach for the analysis and design of complex beam cross-sections made of heterogeneous and isotropic materials. This approach builds on previous research by the authors, namely research that dealt with cross-sectional analysis and adjoint sensitivity analysis. In addition to the theoretical and software developments, a number of practical examples are shown and verified. The results show that this parametric approach facilitates the definition, analysis and design of complex beam cross-sections, all of which are necessary components in real-life design and manufacturing.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121247017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vibration Characteristics Analysis of Multibody Systems With Random Parameters Based on MSTMM","authors":"Guoping Wang, Y. Miao, X. Rui, T. Tu, X. Rui","doi":"10.1115/detc2019-97244","DOIUrl":"https://doi.org/10.1115/detc2019-97244","url":null,"abstract":"\u0000 Dynamics characteristics of linear multibidy systems are governed by the eigenfrequencies and the eigenvectors. The study of probabilistic characterization of the eigensolutions is now an important research topic in the field of multibody systems with random parameters. In this paper, by combining transfer matrix method for multibody system (MSTMM) and perturbation approach, a new method named as perturbation MSTMM is presented for random eigenvalue problems of multibody systems. This method has the advantages of, such as low memory storage requirement, high computational efficiency and high computational stability, etc., for dynamic design of multibody systems with random parameters. By using the proposed method, the rapid computation of random eigenvalue problems of general systems with random parameters can be realized, and the problem of repeated eigenvalues can be solved simply and conveniently. Formulations of the proposed method as well as some numerical examples are given to validate the proposed method. The simulation results of the eigenfrequencies are validated by experiment results. All the numerical applications show the merits and efficacy of the proposed method.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121396829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamics Simulation and Control Design of Gun Adjustment for Nonlinear Multibody System of Multiple Launch Rocket System","authors":"Y. Miao, Guoping Wang, X. Rui, T. Tu, L. Gu","doi":"10.1115/detc2019-97790","DOIUrl":"https://doi.org/10.1115/detc2019-97790","url":null,"abstract":"\u0000 The dynamics simulation of the processing of the gun adjustment for multiple launch rocket system (MLRS) as a complex nonlinear multibody system is studied. Based on the new version of transfer matrix method for multibody system (MSTMM), the nonlinear multibody system dynamics model of MLRS is established, and the overall transfer equation of the nonlinear multibody system is deduced. The launch dynamics simulation of MLRS is carried out by combining the general kinematics equations of rocket and Monte Carlo method, and the simulated results are verified by experiments. On this basis, the control design and dynamics simulation of the gun adjustment of MLRS has been preliminary studied by combing MSTMM with PD control method. The results show that the proposed control method has a good stability and can realize the automatic control of gun adjustment of MLRS quickly and accurately.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130593554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimization of Edge Geometry of Cylindrical Milling Tools to Enhance Dynamic Stability","authors":"Z. Dombovari, D. Bachrathy, G. Stépán","doi":"10.1115/detc2019-97761","DOIUrl":"https://doi.org/10.1115/detc2019-97761","url":null,"abstract":"\u0000 Tool geometry directly influences the dynamic performance of milling operations. Both surface properties and stability behavior are significantly influenced by the regeneration effect. The regeneration phenomenon is modelled by delay differential equations with delays originated from the time passed between consecutive flute passes. This work presents the implementation study of a constrained general optimization scheme for cutting edges of cylindrical milling cutters based on functional minimization principle. Mathematically, this leads to the determination of the corresponding weight function of a distributed delay differential equation. The presented semi-analytical methodology is based on the general milling model implemented in the semidiscretization framework.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121091183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effects of Cut Boundary Location on Finite Element Submodels With Contacts","authors":"William J. Elke, M. W. Sracic","doi":"10.1115/detc2019-98132","DOIUrl":"https://doi.org/10.1115/detc2019-98132","url":null,"abstract":"\u0000 Submodeling is a method used in Finite Element Modeling in order to evaluate features of interest, such as fillets or contact interfaces at a reduced cost. Submodeling can be done by creating a full-structure, coarse-mesh, “global” model and solving it. Once the solutions for this model are solved, a model just of the feature of interest, or “submodel”, can be solved using boundary conditions estimated based on global model results. The location of the submodel boundary has large effects on the accuracy of the solution and has been examined by the authors previously, but not for models with contact interfaces. This work uses the submodeling procedure on a model with two cantilever beams sandwiched together with a bolt close to the free end (dubbed “sandwich beam”). Numerous models are produced with different submodel boundary locations in order to better understand how those locations affect the solutions of a model with contact interfaces. The maximum contact pressure was the main metric used to examine the effects and the feature of interest was the bolt.\u0000 In previous works, it was determined that the global model mesh size and submodel boundary locations are the main sources of error in submodeling [15]. From this work, it was concluded that the inaccuracies of the global model mesh size are magnified when the submodel mesh is too close to the feature of interest. Furthermore, contact pressure tends to be overestimated as the submodel is refined, but it tends to converge as the global model is converged. This work also demonstrated that errors in global model solution (due to meshing) are mitigated when the entire feature of interest is included in the submodel and the submodel boundary locations are far enough away from that feature.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114809566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Computation of Approximate Lyapunov-Perron Transformations","authors":"Ashu Sharma, S. Sinha","doi":"10.1115/detc2019-97702","DOIUrl":"https://doi.org/10.1115/detc2019-97702","url":null,"abstract":"\u0000 Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with quasi-periodic coefficients. Application of Lyapunov-Perron (L-P) transformations to such systems produce dynamically equivalent systems in which the linear parts are time-invariant. In this work, a technique for the computation of approximate L-P transformations is suggested. First, a quasi-periodic system is replaced by a periodic system with a ‘suitable’ large principal period to which Floquet theory can be applied. Then, the state transition matrix (STM) of the periodic system is computed in the symbolic form using shifted Chebyshev polynomials and Picard iteration method. Finally, since the STM can be expressed in terms of a periodic matrix and a time-invariant matrix (Lyapunov-Floquet theorem), this factorization is utilized to compute approximate L-P transformations. A two-frequency quasi-periodic system is investigated using the proposed method and approximate L-P transformations are generated for stable, unstable and critical cases. These transformations are also inverted by defining the adjoint system to the periodic system. Unlike perturbation and averaging, the proposed technique is not restricted by the existence of a generating solution and a small parameter. Approximate L-P transformations can be utilized to design controllers using time-invariant methods and may also serve as a powerful tool in bifurcation studies of nonlinear quasi-periodic systems.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128159607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lucid Analysis of Periodically Forced Nonlinear Systems via Normal Forms","authors":"Peter M. B. Waswa, S. Redkar","doi":"10.1115/detc2019-97100","DOIUrl":"https://doi.org/10.1115/detc2019-97100","url":null,"abstract":"\u0000 This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states — making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing’s equation and Mathieu-Duffing equation.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123205139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic Modelling of a Planar Parallel Robot Manipulator Using the Discrete Time Transfer Matrix Method","authors":"Mengqiu Chu, Guoning Si, Xuping Zhang, Haijie Li","doi":"10.1115/detc2019-98333","DOIUrl":"https://doi.org/10.1115/detc2019-98333","url":null,"abstract":"\u0000 This paper aims to develop a new computationally efficient method for the dynamic modelling of a Planar Parallel Manipulator (PPM) based on the Discrete Time Transfer Matrix Method (DT-TMM). In this preliminary work, we use a 3-PRR PPM as a study case to demonstrate the major procedures and principles of employing the DT-TMM for the dynamic modelling of a PPM. The major focus of this work is to present the basic principles of the DT-TMM for the dynamic modelling of a PPM: decomposing the whole parallel manipulator to the individual components, establishing the dynamics of each component/link, linearizing the component/element dynamics to obtain the transfer matrix of each component/link, and assembling the component dynamics into the system dynamics of the PPM using the transfer matrices of all components/elements. To make the work more readable, the brief introduction of the inverse kinematics and the inverse dynamics is also included. The numerical simulations are conducted based on the 3-PRR PPM with rigid links in this preliminary research effort. The simulation results are compared with those from the model using the principle virtual work method and ADAMS software. The numerical simulation results and comparison demonstrate the effectiveness of the dynamic modelling method using DT-TMM for the PPM.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"922 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123282361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Predicting Finite Element Submodel Boundary Conditions for Contact Models Using Richardson Extrapolation","authors":"M. W. Sracic, William J. Elke","doi":"10.1115/detc2019-98070","DOIUrl":"https://doi.org/10.1115/detc2019-98070","url":null,"abstract":"\u0000 This paper considers an efficient way to apply submodeling methods to finite element models using Richardson Extrapolation. A problem is considered where a rigid cylindrical indenter contacts an elastic half plane (RCEHP). A submodeling method is introduced where the errors of the displacements on the boundaries of the submodel are controlled by employing a best-fit Richardson Extrapolation curve. Specifically, the curve is fit to the convergence relationship of various estimates of submodel boundary displacements. The method is tested on the RCEHP problem, and the results of the model predictions for maximum contact pressure are compared to an analytical and converged global model result.\u0000 The submodeling method predicted the maximum contact pressure of the RCEHP contact interface to be about 7% higher than the analytical prediction and 5% higher than the converged global model prediction. The error is likely due to the selection of the global and submodel domains, the numerical algorithm used to estimate the Richardson Extrapolation Curve Fits, and the mesh refinements used for the various models. The proposed method solved in about 42.6 minutes while the converged global model solved in 11.19 hours. Future work will aim to provide best practices to reduce error and maximize computational time savings when using the method.","PeriodicalId":338372,"journal":{"name":"Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122132196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}