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  • 1.
    Amouzgar, Kaveh
    et al.
    Department of Mechanical Engineering, School of Engineering, Jönköping University, Jönköping, Sweden.
    Rashid, Asim
    Department of Mechanical Engineering, School of Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, School of Engineering, Jönköping University, Jönköping, Sweden.
    Multi-objective optimization of a disc brake system by using SPEA2 and RBFN2013Inngår i: ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 3B: 39th Design Automation Conference, New York: ASME Press, 2013Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objective optimization (EMO) methods based on surrogate modeling is one approach of solving this class of problems. In this paper, multi-objective optimization of a disc brake system to a heavy truck by using EMO and radial basis function networks (RBFN) is presented. Three conflicting objectives are considered. These are: 1) minimizing the maximum temperature of the disc brake, 2) maximizing the brake energy of the system and 3) minimizing the mass of the back plate of the brake pad. An iterative Latin hypercube sampling method is used to construct the design of experiments (DoE) for the design variables. Next, thermo-mechanical finite element analysis of the disc brake, including frictional heating between the pad and the disc, is performed in order to determine the values of the first two objectives for the DoE. Surrogate models for the maximum temperature and the brake energy are created using RBFN with polynomial biases. Different radial basis functions are compared using statistical errors and cross validation errors (PRESS) to evaluate the accuracy of the surrogate models and to select the most accurate radial basis function. The multi-objective optimization problem is then solved by employing EMO using the strength Pareto evolutionary algorithm (SPEA2). Finally, the Pareto fronts generated by the proposed methodology are presented and discussed.

  • 2.
    Amouzgar, Kaveh
    et al.
    Department of Mechanical Engineering, School of Engineering, Jönköping University, Jönköping, Sweden .
    Strömberg, Niclas
    Department of Engineering Science, University West, Trollhättan, Sweden.
    An approach towards generating surrogate models by using RBFN with a priori bias2014Inngår i: Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2014, Vol. 2B, New York, USA: ASME Press, 2014, artikkel-id V02BT03A024Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, an approach to generate surrogate modelsconstructed by radial basis function networks (RBFN) with a prioribias is presented. RBFN as a weighted combination of radialbasis functions only, might become singular and no interpolationis found. The standard approach to avoid this is to add a polynomialbias, where the bias is defined by imposing orthogonalityconditions between the weights of the radial basis functionsand the polynomial basis functions. Here, in the proposed a prioriapproach, the regression coefficients of the polynomial biasare simply calculated by using the normal equation without anyneed of the extra orthogonality prerequisite. In addition to thesimplicity of this approach, the method has also proven to predictthe actual functions more accurately compared to the RBFNwith a posteriori bias. Several test functions, including Rosenbrock,Branin-Hoo, Goldstein-Price functions and two mathematicalfunctions (one large scale), are used to evaluate the performanceof the proposed method by conducting a comparisonstudy and error analysis between the RBFN with a priori and aposteriori known biases. Furthermore, the aforementioned approachesare applied to an engineering design problem, that ismodeling of the material properties of a three phase sphericalgraphite iron (SGI) . The corresponding surrogate models arepresented and compared

  • 3.
    Amouzgar, Kaveh
    et al.
    Product Development Department, School of Engineering, Jönköping University, Jönköping, Sweden; School of Engineering Science, University of Skövde, Skövde, Sweden.
    Strömberg, Niclas
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Mechanical Engineering.
    Radial Basis Functions as Surrogate Models with A Priori Bias in Comparison with a Posteriori Bias2017Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, nr 4, s. 1453-1469Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.

  • 4.
    Asnafi, Nader
    Volvo Car Components Corporation/Industrial Development Centre, Olofström, Sweden.
    Analytical modelling of tube hydroforming1999Inngår i: Thin-walled structures, ISSN 0263-8231, E-ISSN 1879-3223, Vol. 34, nr 4, s. 295-330Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The automotive industry has shown a growing interest in tube hydroforming during the past years. The advantages of hydroforming (less thinning, a more efficient manufacturing process etc.) can, for instance, be combined with the high strength of extra high strength steels, which are usually less formable, to produce structural automotive components which exhibit lower weight and improved service performance. Design and production of tubular components require knowledge about tube material behaviour and tribological effects during hydroforming and how the hydroforming operation itself should be controlled. These issues are studied analytically in the present paper. Hydroforming consists of free forming and calibration. Only the so-called free forming is treated here. The analytical models constructed in this paper are used to show what the limits are during the free forming, how different material and process parameters influence the loading path and the forming result, and what an experimental investigation into hydroforming should focus on. The present study was a part of a larger investigation, in which finite-element simulations and experiments were also conducted. The results of these simulations and experiments will be accounted for in coming papers.

  • 5.
    Asnafi, Nader
    Gränges Technology, Finspång, Sweden.
    On springback of double-curved autobody panels2001Inngår i: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 43, nr 1, s. 5-37Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The springback of double curved autobody panels is studied theoretically and experimentally. Both steel and aluminum sheets are included in this investigation. The obtained results show that the springback is decreased with increasing binder force, increasing curvature, increasing sheet thickness and decreasing yield strength. This paper comprises also a discussion on the plastic strains and their influence on the springback.

  • 6.
    Asnafi, Nader
    Industrial Development Center/Volvo Cars Body Components, Olofström, Sweden .
    On Springback of Double-Curved Autobody Panels1998Inngår i: Proceedings, working groups meeting - IDDRG, International Deep Drawing Research Group: Genval, Benelux, June 15 - 16, 1998, 1998Konferansepaper (Annet vitenskapelig)
  • 7.
    Asnafi, Nader
    Swedish Institute for Metals Research, Stockholm, Sweden.
    On Springback of Double-Curved Autobody Panels, Part I: Theoretical Treatment1996Rapport (Annet vitenskapelig)
  • 8.
    Asnafi, Nader
    Swedish Institute for Metals Research, Stockholm, Sweden.
    On Springback of Double-Curved Autobody Panels, Part II: Experimental Analysis1996Rapport (Annet vitenskapelig)
  • 9.
    Asnafi, Nader
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Proceedings of the International Conference on Mechanical, Electric and Industrial Engineering (MEIE2018)2018Konferanseproceedings (Fagfellevurdert)
  • 10.
    Asnafi, Nader
    et al.
    Sapa Profiles/Sapa Technology, Finspång, Sweden.
    Nilsson, T.
    Sapa Profiles/Sapa Technology, Finspång, Sweden.
    Lassl, G.
    Volvo Car Corp..
    Automotive tube bending and tubular hydroforming with extruded aluminium profiles2000Inngår i: SAE technical paper series, ISSN 0148-7191, artikkel-id 2670Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Side Member Left and Side Member Right, which go from bumper to bumper, were at the focus in the present study. These side members were produced using straight round (hollow with a circular cross-section) extruded aluminium profiles as tube material. The tubes were bent and hydroformed. Rotary-draw bending yielded the best result. A spread within 8 mm after bending was found to be acceptable provided that the bent tube was hydroformed with a high maximum internal pressure (1300 bars in this study). Pressure-assisted tool (hydroforming tool) closure should be preferred. Such a tool closure prevents formation of buckles, which may be difficult to straighten out completely during hydroforming. Planeness and parallelity of the press tables and adapters play a significant role, as far as the spread and inplaneness of hydroformed components are concerned. The hydroforming tool must be matched in the press that actually will be used. Proper evacuation (of particularly air) is essential, especially in long hydroforming tools. All cross sections must be deformed at least 2% (average perimeter enlargement), if the hydroformed components are to exhibit a reasonable spread. The critical (fracture) cross-sections predicted by finite-element simulation correspond to those found in practical tests. However, the finite-element simulation was not able to predict formation of wrinkles at the tube ends caused by excessively large strokes. Such wrinkles were obtained in practice.

  • 11.
    Christensen, P. W.
    et al.
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Pang, Jong Shi
    Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD, USA.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Formulation and comparison of algorithms for frictional contact problems1998Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 42, nr 1, s. 145-173Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code.

  • 12.
    Eriksson, Daniel
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Tactile sensing of carton quality2016Inngår i: Product Developments with New forest Based Materials, KTH Royal Institute of Technology, 2016, s. 45-47Konferansepaper (Annet (populærvitenskap, debatt, mm))
  • 13.
    Eriksson, Daniel
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Korin, Christer
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Thuvander, Fredrik
    Department of Engineering and Physics, Karlstad University, Karlstad, Sweden.
    Damage to Carton Board Packages Subjected to Concentrated Loads2014Inngår i: Responsible Packaging for A Global Market: Proceedings of the 19th IAPRI World Conference on Packaging / [ed] M.A. Sek, V. Rouillard and S.W. Bigger, Melbourne: Victoria University , 2014, s. 172-182Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Carton board packages subjected to concentrated loads near the edges are damaged in a characteristic way. This paper reports an attempt to simulate the damage process in the lab and Package Collapse Loads measured for this load case.

    Packages were compressed by a concentrated load. The position of load application was varied along a line parallel to a crease and the package was rotated in order to test the influence of the height of the load carrying panel. Force and displacement were recorded and the damage evolution during the test was studied. The damage produced was examined using x-ray tomography. The nature of damage at different stages of damage evolution was studied.

    Both the visual appearance of the damage and the force-displacement curve were similar in all tests. The Package Collapse Load has little dependence on where along a line parallel to a crease of the package the point load is applied. Damage started developing at the crease and a yield line perpendicular to the crease and parallel to the direction of the load developed. When the displacement increased further, a parabolic yield line, symmetric around the previous one, developed. The start of the damage development was associated with at peak in the force-displacement curve. Stiffness was more geometry dependent than strength. On macro scale, the visual appearance of the damage due to concentrated loads shows no significant dependence on geometry.

  • 14.
    Gustafsson, Erik
    et al.
    Väderstad-Verken AB, Väderstad, Sweden.
    Hofwing, Magnus
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Residual stresses in a stress lattice: experiments and finite element simulations2009Inngår i: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 209, nr 9, s. 4320-4328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work residual stresses in a stress lattice are studied. The residual stresses are both measured and simulated. The stress lattice is casted of low alloyed grey cast iron. In fact, nine similar lattices are casted and measured. The geometry of the lattice consists of three sections in parallel. The diameter of the two outer sections are thinner than the section in the middle. When the stress lattice cools down, this difference in geometry yields that the outer sections start to solidify and contract before the section in the middle. Finally, an equilibrium state, with tensile stresses in the middle and compressive stresses in the outer sections, is reached. The thermo-mechanical simulation of the experiments is performed by using Abaqus. The thermo-mechanical solidification is assumed to be uncoupled. First a thermal analysis, where the lattice is cooled down to room temperature, is performed. Latent heat is included in the analysis by letting the fraction of solid be a linear function of the temperature in the mushy zone. After the thermal analysis a quasi-static mechanical analysis is performed where the temperature history is considered to be the external force. A rate independent J2-plasticity model with isotropic hardening is considered, where the material data depend on the temperature. Tensile tests are performed at room temperature, 200°C, 400°C, 600°C and 800°C in order to evaluate the Young´s modulus, the yield strength and the hardening accurate. In addition, the thermal expansion coefficient is evaluated for temperatures between room temperature and 1000°C. The state of residual stresses is measured by cutting the mid section or the outer section. The corresponding elastic spring-back reveals the state of residual stresses. The measured stresses are compared to the numerical simulations. The simulations show good agreement with the results from the experiments.

  • 15.
    Gustafsson, Erik
    et al.
    Department of Management and Engineering, Linköping University, Linköping, Sweden.
    Hofwing, Magnus
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Simulation and Measurement of Residual Stresses in a Stress Lattice2007Inngår i: Proceedings of the 2nd International Conference on Simulation and Modelling of Metallurgical Processes in Steelmaking, Leoben: ASMET , 2007, s. 285-290Konferansepaper (Fagfellevurdert)
  • 16.
    Gustafsson, Erik
    et al.
    SweCast AB, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Shape optimization of castings by using successive response surface methodology2008Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 35, nr 1, s. 11-28Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, an optimization routine for a thermomechanical problem is presented. The optimization routine is based on the successive response surface methodology where the panning and zooming technique presented by Stander and Craig has been implemented and improved. The optimization routine has been applied to an optimization problem of a three-dimensional beam that undergoes a solidification process. The material in the beam is assumed to be low-alloyed gray iron. The thermomechanical solidification analysis is uncoupled where, first, a thermal analysis is performed to determine the thermal history. This thermal history is then used to calculate the residual stresses in the beam. The residual stresses are solved by using classical J(2)-plasticity with temperature-dependent material properties. The residual stresses from solidification are then carried on to the structural analysis where a mechanical load is applied. These are all linked together via scripts, and the commercial FE software Abaqus is used as the FE solver. The obtained maximum von Mises stress and mass information for every set of parameters are then exported to Matlab where general quadratic response surfaces are fitted by a least square method. Taken together, these response surfaces define a minimum of weight problem, which is solved by using sequential linear programming. To minimize the number of evaluations needed, the parameters are chosen to be D-optimally selected. The numerical results show that the residual stresses from solidification might influence the optimal shape significantly. The residual stress results have been compared with those obtained from casting simulation softwares, and the results are similar. The optimization has been compared with a commercial optimization software and shows very promising results.

  • 17.
    Gustafsson, Erik
    et al.
    Swedish Foundry Association, Jönköping, Sweden.
    Strömberg, Niclas
    School of Engineering, Jönköping University, Jönköping, Sweden.
    Structural optimization of castings by using ABAQUS and Matlab2005Inngår i: Competent Design by Castings: Improvements in a Nordic Project / [ed] Jack Samuelsson; Gary Marquis; Jussi Solin, Espoo, Finland: VTT , 2005, Vol. 237, s. 39-52Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work a general method for structural optimization of nonlinear structures is implemented using FE-analysis. The method utilizes the response surface methodology with polynomial surfaces and nonlinear programming. In such manner a method that is applicable for a large number of different classes of nonlinear problems is obtained. In this paper, the method is utilized to minimize weight of castings by including residual stresses from solidification. This is performed by first determine the residual stresses by a thermomechanical analysis of a metal structure that is cooled from a temperature above liquidus temperature down to room temperature. The thermomechanical analysis is uncoupled where the temperature distribution within the casting as a function of time is determined first and is later on used for residual stress calculations. These residual stresses are then included when the mechanical load is applied to the structure and the problem of minimum of weight is formulated. The structure shown in this paper is an example of a two dimensional geometry. The shape of the structures will of course affect the residual stress distribution during the optimization. The nonlinear models are then solved using ABAQUS/Standard. A set of solutions are generated by solving the model for a pre-defined set of parameters. In order to minimize the number of simulations and still achieve good surface approximations these parameters are taken to be D-optimal. The sets of solutions and parameters are in turn exported to Matlab where general quadratic response surfaces are fitted by the least square method. By utilizing these surfaces the problem of minimum of weight subjected to constraints on stresses is formulated. Finally, the nonlinear optimization problem is solved by sequential linear programming.

  • 18.
    Gustafsson, Erik
    et al.
    Swedish Foundry Association, Jönköping, Sweden.
    Strömberg, Niclas
    School of Engineering, Jönköping University, Jönköping, Sweden.
    Structural optimization of castings by using Abaqus and Matlab2005Inngår i: Proceedings of the Abaqus World Users' Conference, 2005Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work a general method for structural optimization of nonlinear structures is implemented using ABAQUS and Matlab. The method utilizes the response surface methodology with polynomial surfaces and nonlinear programming. In such manner a method that is applicable for a large number of different classes of nonlinear problems is obtained. For instance plasticity problems, thermomechanical problems and contact problems can be optimized using this strategy. In this paper, the method is utilized to minimize weight of castings by including residual stresses from solidification. This is performed by first determine the residual stresses by a thermomechanical analysis of a metal structure that is cooled down from a temperature above liquidus temperature down to room temperature. These residual stresses are then included when the problem of minimum of weight is formulated. The shape of the structure will of course affect the residual stress distribution during the optimization and the optimal shape will be different from the one obtained when residual stresses are not included in the analysis. The method is implemented by using a Python script and m-files. In such way a parameterized model can easily be treated in ABAQUS and Matlab during the optimization process. The parameterized geometry, loads, boundary conditions and mesh are first generated by the ABAQUS/CAE module. The nonlinear models are then solved using ABAQUS/Standard. A set of solutions are generated by solving the model for a pre-defined set of parameters. In order to minimize the number of simulations and still achieve good surface approximations these parameters are taken to be D-optimal. The sets of solutions and parameters are in turn exported to Matlab where general quadratic response surfaces are fitted by the least square method. By utilizing these surfaces the problem of minimum of weight subjected to constraints on stresses is formulated. Finally, the nonlinear optimization problem is solved by sequential linear programming where the linear part is solved using Matlab.

  • 19. Gustafsson, Erik
    et al.
    Strömberg, Niclas
    Department of Mechanical Engineering, University of Jönköping, Sweden.
    Successive Response Surface Methodology by using Neural Networks2007Inngår i: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, Seoul: WCSMO-7 Official Agency , 2007Konferansepaper (Fagfellevurdert)
  • 20.
    Hofwing, Magnus
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method2010Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, nr 1, s. 73-88Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work a hybrid method of a genetic algorithm  and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.

  • 21.
    Hofwing, Magnus
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    D-optimality of non-regular design spaces by using a Genetic Algorithm2009Inngår i: Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, International Society for Structural and Multidisciplinary Optimization , 2009Konferansepaper (Fagfellevurdert)
  • 22.
    Hofwing, Magnus
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Robustness of residual stresses in castings and an improved process window2010Inngår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009: Volume 5, Issue PART B, New York, N.Y.: ASME Press, 2010, s. 1081-1091Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work the robustness of residual stresses in finite element simulations with respect to deviations in mechanical parameters in castings is evaluated. Young's modulus, the thermal expansion coefficient and the hardening are the studied parameters. A 2D finite element model of a stress lattice is used. The robustness is evaluated by comparing purely finite element based Monte Carlo simulations and Monte Carlo simulations based on linear and quadratic response surfaces. Young's modulus, the thermal expansion coefficient and the hardening are assumed to be normal distributed with a standard deviation that is 10% of their nominal value at different temperatures. In this work an improved process window is also suggested to show the robustness graphically. By using this window it is concluded that least robustness is obtained for high hardening values in combination to deviations in Young's modulus and the thermal expansion coefficient. It is also concluded that quadratic response surface based Monte Carlo simulations substitute finite element based Monte Carlo simulations satisfactory. Furthermore, the standard deviation of the responses are evaluated analytically by using the Gauss formula, and are compared to results from Monte Carlo simulations. The analytical solutions are accurate as long as the Gauss formula is not utilized close to a stationary point.

  • 23.
    Hofwing, Magnus
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Simulation of residual stresses in stamping dies2008Inngår i: Proceedings of the IDDRG 2008 Conference: Best in class stamping, 16-18 June 2008, Olofström, Sweden / [ed] Nader Asnafi, Olofström: Industriellt utvecklingscentrum i Olofström AB , 2008, s. 765-776Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In the past stamping dies have in principle been designed by rules of thumb and intuition. As the sheet metals in the vehicle industry have got increased mechanical properties in recent years the demands on the stamping dies have increased. For instance increase in stiffness is desirable in order to better control spring-back. The most simple way to satisfy this new demand would be to make the stamping dies even more heavy in order to be able to handle the new sheet metals. Since there are restrictions of the weight of the stamping dies in the stamping machines and since the overhead cranes usually have reached the limit of what they can handle, this is not a desirable solution. Another approach, in order to increase the stiffness without increasing the weight is to use topology optimization. Recently in a master thesis at Volvo Car Corporation a conceptual design of a stamping die has been done by topology optimization. In that work no consideration is taken to the fact that the stamping die is casted. Casting implies that residual stresses possibly are produced during the solidification and cooling process. The residual stresses might affect the fatigue life and the risk of failure of the stamping die.

    In this work the residual stress state after casting is analyzed for the original stamping die as well as the optimized stamping die from the master thesis discussed above. The analyses are performed using an uncoupled approach, where one thermal analysis is followed by a quasi-static elasto-plastic analysis. The thermal analysis simulates the solidification and cooling during the casting process, while the quasi-static elasto-plastic analysis uses the temperature history, obtained from the thermal analysis, in order to build up residual stresses. The thermal analysis includes the release of latent heat. Furthermore, the material properties included in the heat equation (density, conductivity, specific heat) are given as temperature dependent properties for the mould as well as the casting. In the quasi-static elasto-plastic analysis the plasticity is described by the von Mises yield surface in combination with isotropic hardening and the mechanical properties (thermal expansion coefficient, Young's modulus, yield stress, hardening parameter, Poisson's ratio) are given as temperature dependent properties. The simulations show high levels of residual stresses.

     

  • 24.
    Hofwing, Magnus
    et al.
    Department of Mechanical Engineering, University of Jönköping, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, University of Jönköping, Jönköping, Sweden.
    Tapankov, Martin
    Department of Mechanical Engineering, University of Jönköping, Jönköping, Sweden.
    Optimal polynomial regression models by using a genetic algorithm2011Inngår i: Proceedings of the second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering / [ed] Yiannis Tsompanakis; B.H.V. Topping, Kippen, Scotland: Civil-Comp Proceedings , 2011Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a polynomial regression model where the constituents of are of arbitrary order is proposed. A genetic algorithm is used to find the optimal terms to be included in the so-called optimal polynomial regression model . The objective for the genetic algorithm is to minimize the sum of squared errors of the predicted responses. In practice the genetic algorithm generates an optimal set of exponents of the design variables in a polynomial regression model. Several example problems are presented to show the performance and accuracy of the optimal polynomial regression model. Results show a greatly improved performance for optimal polynomial regression models compared to traditional regression models.

  • 25.
    Hüllmann, Dino
    et al.
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Kohlhoff, Harald
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Erdmann, Jessica
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Neumann, Patrick P.
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Control of a spherical parallel manipulator2019Inngår i: Materials Today: Proceedings, E-ISSN 2214-7853, Vol. 12, nr 2, s. 423-430Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In mobile robot applications, some sensors such as open-path gas detectors or laser rangefinders need to be aimed at specific targets in order to get the desired measurements. To do this in a fast and elegant manner, we present a spherical parallel manipulator with three degrees of freedom. Compared to typical serial manipulators, it offers superior dynamics and structural stiffness, which are important parameters for this type of task. We present the mechanical design and derive kinematic equations both to compute set-points for the desired orientation and to estimate the current state of the system. A PID controller is used to generate control signals.

  • 26.
    Hüllmann, Dino
    et al.
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Kohlhoff, Harald
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Erdmann, Jessica
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Neumann, Patrick P.
    Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany.
    Control of a spherical parallel manipulator with three degrees of freedom2018Inngår i: 35th Danubia-Adria Symposium on Advances in Experimental Mechanics: Extended abstracts / [ed] D. Ş. Pastramă, D. M. Constantinescu, Bukarest, Romania, 2018, s. 159-160Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In robotic applications, it is often necessary to orient a sensor quickly. Spherical parallel manipulators (SPM) are well suited for this purpose since they offer superior dynamics and structural stiffness as compared to serial manipulators. To control them, however, the kinematic equations have to be known. In this paper, a SPM with three degrees of freedom and the kinematic equations describing its mechanical properties are presented.

  • 27.
    Ireman, Peter J.
    et al.
    Division of Mechanics, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Division of Mechanics, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Gradient theory of damage coupled to frictional contact and wear, and its numerical treatment2009Inngår i: CMES - Computer Modeling in Engineering & Sciences, ISSN 1526-1492, E-ISSN 1526-1506, Vol. 52, nr 2, s. 125-158Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper finite element approaches for fretting fatigue are proposed on the basis of a non-local model of continuum damage coupled to friction and wear. The model is formulated in the frame-work of a standard material. In a previous paper this was done in the spirit of Maugin, where an extra entropy flux is introduced in the second law in order to include the gradient of the internal variable in a proper manner. In this paper we follow instead the ideas of Frémond and others, where this extra entropy flux is no longer needed, but instead new non-classical balance laws associated to damage, friction and wear, respectively, are derived from the principle of virtual power. The standard material is then defined as usual by state laws based on free energies and complementary laws based on dissipation potentials. In particular, we pick free energies and dissipation potentials that correspond to a non-local continuum damage model coupled to friction and wear. In addition, the boundary conditions at the contact interface creates a coupling between damage and wear. This is a key feature of our model, which makes it very useful in studies of fretting fatigue. By starting from a variational formulation of the governing equations, two different finite element algorithms are implemented. Both algorithms are based on a Newton method for semi-smooth equations. In the first algorithm the Newton method is applied to the entire system of equations, while in the second algorithm the system of equations is split into two different parts such that an elastic wear problem is solved for fixed damage followed by the solution of the damage evolution problem for the updated displacements and contact forces in an iterative process. The latter algorithm can be viewed as a Gauss-Seidel scheme. The numerical performance of the algorithms is investigated for three twodimensional examples of increasing complexity. Based on the numerical solutions, the behavior of the model is also discussed. For instance, it is shown numerically how the initiation of damage depends on the contact geometry, the coefficient of friction and the evolution of wear.

  • 28.
    Ireman, Peter
    et al.
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    A model of damage coupled to wear2003Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 40, nr 12, s. 2957-2974Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present paper presents a model of damage coupled to wear. The damage model is based on a continuum model including the gradient of the damage variable. Such a model is non-local in the sense that the evolution of damage is governed by a boundary-value problem instead of a local evolution law. Thereby, the well-known mesh-dependency observed for local damage models is removed. Another feature is that the boundary conditions can be used to introduce couplings between bulk damage and processes at the boundary. In this work such a coupling is suggested between bulk damage and wear at the contact interface. The model is regarded as a first attempt to formulate a continuum damage model for studying crack initiation in fretting fatigue.

    The model is given within a thermodynamic framework, where it is assured that the principles of thermodynamics are satisfied. Furthermore, two variational formulations of the full. initial boundary value problem, serving as starting points for finite element discretization, are presented. Finally, preliminary numerical results for a simple one-dimensional example are presented and discussed. It is qualitatively shown how the evolution of damage may influence the wear behaviour and how damage may be initiated by the wear process.

  • 29.
    Ireman, Peter
    et al.
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Algorithms for thermoelastic wear problems2002Inngår i: Contact mechanics: proceedings of the 3rd Contact Mechanics International Symposiuum / [ed] J.A.C. Martins and Manuel D.P. Monteiro Marques, Dordrecht: Kluwer Academic , 2002, s. 363-370Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This contribution concerns the numerical treatment of discrete thermoelastic wear problems. Two different approaches, both utilizing a non-smooth Newton method as non-linear equation solver, are outlined and compared. Furthermore, a numerical example shows how the predicted wear gap is influenced by the bulk properties of the contacting bodies.

  • 30.
    Ireman, Peter
    et al.
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Finite element algorithms for thermoelastic wear problems2002Inngår i: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 21, nr 3, s. 423-440Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the present paper three algorithms are applied to a finite element model of two thermoelastic bodies in frictional wearing contact. All three algorithms utilize a modification of a Newton method for B-differentiable equations as non-linear equation solver. In the first algorithm the fully-coupled system of thermomechanical equations is solved directly using the modified method, while in the other two algorithms the equation system is decoupled in one mechanical part and another thermal part which are solved using an iterative strategy of Gauss–Seidel type. The two iterative algorithms differ in which order the parts are solved. The numerical performance of the algorithms are investigated for two two-dimensional examples. Based on these numerical results, the behaviour of the model is also discussed. It is found that the iterative approach where the thermal subproblem is solved first is slightly more efficient for both examples. Furthermore, it is shown numerically how the predicted wear gap is influenced by the bulk properties of the contacting bodies, in particular how it is influenced by thermal dilatation.

  • 31.
    Khodadad, Davood
    Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics, Luleå University of Technology, Luleå, Sweden.
    Combined Digital Holography and Speckle Correlation for Rapid Shape Evaluation2014Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In manufacturing industry there is a high demand for on line quality control to minimize the risk of incorrectly produced objects. Conventional contact measurement methods are usually slow and invasive, meaning that they cannot be used for soft materials and for complex shapes without influencing thecontrolled parts. In contrast, interferometry and digital holography in combination with computers become faster, more reliable and highly accurate as an alternative non-contact technique for industrial shape evaluation. In digital holography, access to the complex wave field and the possibility tonumerically reconstruct holograms in different planes introduce a new degree of flexibility to optical metrology. With digital holography high resolution and precise three dimensional (3D) images of the manufactured parts can be generated. This technique can also be used to capture data in a single exposure,which is important when doing measurements in a disturbed environment.The aim of this thesis is to perform online process control of free-form manufactured objects by measuring the shape and compare it to the CAD-model. To do this, a new technique to measure surface gradients and shape based on single-shot dual wavelength digital holography and image correlation of speckle displacements is demonstrated. Based on an analytical relation between phase gradients and speckle displacements it is shown that an object is retrieved uniquely to shape and position without the unwrapping problems that usually appear in dual wavelength holography. The method is firstdemonstrated using continues wave laser light from two temperature controlled laser diodes operating at 640 nm. Further a specially designed dual core diode pumped fiber laser that produces pulsed light with wavelengths close to 1030 nm is used. One significant problem when using the dual wavelength single-shot approach is that phase ambiguities are built in to the system that needs to be corrected. An automatic calibration scheme is therefore required. The intrinsic flexibility of digital holography gives a possibility to compensate these aberrations and to remove errors, fully numerically without mechanical movements. In this thesis I present a calibration method which allows single-shot online shape evaluation in a disturbed environment. It is shown that phase maps and speckle displacements can be recovered free of chromatic aberrations. This is the first time that a single-shot dual wavelength calibration is reported by defining a criteria to make an automatic procedure.By the results of the presented work, it is experimentally verified that the single-shot dual wavelength digital holography and numerically generated speckle images can be used together with digital speckle correlation to retrieve and evaluate the object shape. The proposed method is also robust to large phasegradients and large movements within the intensity patterns. The advantage of the approach is that, using speckle displacements, the shape measurement can be done even though the synthetic wavelength is out of the dynamic range of the height variation of the object.

  • 32.
    Khodadad, Davood
    Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics, Luleå University of Technology, Sweden.
    Multiplexed Digital Holography incorporating Speckle Correlation2016Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In manufacturing industry there is a high demand for on line quality control to minimize the risk of incorrectly produced objects. Conventional contact measurement methods are usually slow and invasive, meaning that they cannot be used for soft materials and for complex shapes without influencing the controlled parts. In contrast, interferometry and digital holography in combination with computers become faster, more reliable and highly accurateas an alternative non-contact technique for industrial shape evaluation. For example in digital holography, access to the complex wave field and the possibility to numerically reconstruct holograms in different planes introduce a new degree of flexibility to optical metrology. With digital holography high resolution and precise three dimensional (3D) images of the manufactured parts can be generated. This technique can also be used to capture data in asingle exposure, which is important when doing measurements in a disturbed environment. The aim of this thesis is devoted to the theoretical and experimental development of shape and deformation measurements. To perform online process control of free-form manufactured objects, the measured shape is compared with the CAD-model to obtain deviations. To do this, a new technique to measure surface gradients and shape based onsingle-shot multiplexed dual-wavelength digital holography and image correlation of speckle displacements is demonstrated. Based on an analytical relation between phase gradients and speckle displacements it is shown that an object is retrieved uniquely to shape, position and deformation without the unwrapping problems that usually appear in dual-wavelength holography. The method is first demonstrated using continues-wave laser light from twotemperature controlled laser diodes operating at 640 nm. Then a specially designed dual core diode pumped fiber laser that produces pulsed light with wavelengths close to 1030 nm is used. In addition, a Nd:YAG laser with the wavelength of 532 nm is used for 3D deformation measurements. One significant problem when using the dual-wavelength single-shot approach is that phase ambiguities are built in to the system that needs to be corrected. An automatic calibration scheme is therefore required. The intrinsic flexibility of digital holography gives a possibility to compensate these aberrations and to remove errors, fully numerically without mechanical movements. In this thesis I present a calibration method which allows multiplexed singleshotonline shape evaluation in a disturbed environment. It is shown that phase maps and speckle displacements can be recovered free of chromatic aberrations. This is the first time that a multiplexed single-shot dual-wavelength calibration is reported by defining a criteria tomake an automatic procedure. Further, Digital Speckle Photography (DSP) is used for the full field measurement of 3D deformations. In order to do 3D deformation measurement, usually multi-cameras and intricate set-up are required. In this thesis I demonstrate the use of only one single camera torecord four sets of speckle patterns recorded by illuminating the object from four different directions. In this manner, meanwhile 3D speckle displacement is calculated and used for the measurement of the 3D deformations, wrapping problems are also avoided. Further, the same scale of speckle images of the surface for all four images is guaranteed. Furthermore, a need for calibration of the 3D deformation measurement that occurs in the multi-camera methods,is removed. By the results of the presented work, it is experimentally verified that the multiplexed singleshot dual wavelength digital holography and numerically generated speckle images can be used together with digital speckle correlation to retrieve and evaluate the object shape. Usingmultidirectional illumination, the 3D deformation measurements can also be obtained. The proposed method is robust to large phase gradients and large movements within the intensity patterns. The advantage of the approach is that, using speckle displacements, shape and deformation measurements can be performed even though the synthetic wavelength is out of the dynamic range of the object deformation and/or height variation.

  • 33.
    Klarbring, Anders
    et al.
    Department of Management and Engineering, The Institute of Technology, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements2012Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 45, nr 1, s. 147-149Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present theoretical note shows how a naturalobjective function in stiffness optimization, including bothprescribed forces and non-zero prescribed displacements,is the equilibrium potential energy. It also shows how theresulting problem has a saddle point character that may beutilized when calculating sensitivities.

  • 34.
    Klarbring, Anders
    et al.
    Department of Management and Engineering, The Institute of Technology, Linköping University, Linköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Topology optimization of hyperelastic bodies including non-zero prescribed displacements2013Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 47, nr 1, s. 37-48Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff–St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings.

  • 35.
    Lundvall, Olle
    et al.
    Department of Mechanical Engineering, Division of Mechanics, Linköping, Sweden; Scania CV AB, Södertälje, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Division of Mechanics, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Division of Mechanics, Linköping, Sweden.
    A flexible multi-body approach for frictional contact in spur gears2004Inngår i: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 278, nr 3, s. 479-499Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the present paper, a large rotational approach for dynamic contact problems with friction is proposed. The approach is used for modelling a spur gear pair with shafts and bearings. The model is obtained by superposing small displacement elasticity on rigid-body motions, and postulating tribological laws on the gear flanks. The finite element method is used to model the elastic properties of the gear pair. Shafts and bearings are represented by linear springs. The tribological laws of the contact interface are Signorini's contact law and Coulomb's law of friction. An important feature of the approach is that the difficulties of impacting mass nodes are avoided. The governing equations of the model are numerically treated by use of the augmented Lagrangian approach. In such manner the geometry of the gear flanks are well represented in the numerical simulations. It is possible to study accurately the consequences of different types of profile modifications as well as flank errors. In this work, the dynamic transmission error is studied. For instance, it turns out that the effect from profile modification is less significant for the transmission error when frictional effects are included.

  • 36.
    Rashid, Asim
    et al.
    Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Jönköping University, Jönköping, Sweden.
    An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes2012Inngår i: Nordtrib 2012, 15th Nordic Symposium on Tribology, 2012, 2012Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    In this paper an efficient approach to simulate thermal stresses due to frictional heating of disc brakes is presented. Inthe approach thermal and stress analysis are performed sequentially. The frictional heat analysis is based on the Eulerianmethod, which requires significantly low computational time as compared to the Lagrangian approach. Completethree-dimensional geometries of a disc and a pad are considered for the numerical simulations. The contact forcesare computed at each time step taking the thermal deformations of the disc into account. The nodal temperaturehistory is recorded at each time step and is used in sequentially coupled stress analysis, where a temperature dependentelasto-plastic material model is used to compute the stresses in a disc brake. The results show that during hard braking,high compressive stresses are generated on the disc surface in circumferential direction which cause plastic yielding. Butwhen the disc cools down, the compressive stresses transform to tensile stresses. Such thermoplastic stress history maycause cracks on disc surface after a few braking cycles. These results are in agreement with experimental observationsavailable in the literature.

  • 37.
    Rashid, Asim
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Sequential simulation of thermal stresses in disc brakes for repeated braking2013Inngår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 227, nr 8, s. 919-929Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.

  • 38.
    Rashid, Asim
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by Adopting an Eulerian Approach2013Inngår i: Eurobrake 2013, 2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional geometries of the ventilated disc and pad are used in the simulations. A sequential approach is adopted, where the contact forces are computed at each time step taking the wear and thermal deformations of the mating parts into account. After each brake cycle, the wear profile of the pad is updated and used in subsequent analysis. The results show that when wear is considered, different distributions of the temperature on disc are obtained for each new brake cycle. After a few braking cycles two hot bands appear on the disc surface instead of only one. These results are in agreement with experimental observations.

  • 39.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    A method for structural dynamic contact problems with friction and wear2003Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 58, nr 15, s. 2371-2385Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A method for structural dynamic contact problems with friction and wear is suggested. The method is obtained by including wear in the non-smooth contact dynamics method of Moreau. A comparison of the method to the discrete energy-momentum method of Simo and Tarnow is also outlined briefly. The fully discrete equations are treated using the augmented Lagrangian approach, where a non-smooth Newton method is used as the equation solver. Two two-dimensional examples are solved by the method. It is investigated how solutions of contact, friction and wear are influenced by inertia. It is shown that the quasi-static assumption might be questionable for solving contact problems with friction and wear.

  • 40.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    A Newton method for three-dimensional fretting problems1999Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 36, nr 14, s. 2075-2090Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present paper concerns the numerical treatment of fretting problems using a finite element analysis. The governing equations resulting from a formal finite element discretization of an elastic body with a potential contact surface are considered in a quasi-static setting. The constitutive equations of the potential contact surface are Signorini's contact conditions, Coulomb's law of friction and Archard's law of wear. Using a backward Euler time discretization and an approach based on projections, the governing equations are written as an augmented Lagrangian formulation which is implemented and solved using a Newton algorithm for three-dimensional fretting problems of didactic nature. Details concerning the implementation are provided.

  • 41.
    Strömberg, Niclas
    Örebro universitet, Institutionen för naturvetenskap och teknik. Örebro University, Örebro, Sweden.
    A Virtual Test Rig for Disc Brake Systems by Adopting a Thermo-Flexible Multi-Body Approach2016Inngår i: the 34th annual SAE 2016 Brake Colloquium & Exhibition, Arizona, USA, September 25-28, SAE International , 2016, artikkel-id 2016-01-1932Konferansepaper (Fagfellevurdert)
  • 42.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    An augmented Lagrangian method for fretting problems1997Inngår i: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 16, nr 4, s. 573-593Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present work concerns the numerical treatment of fretting in the interface between a body and a rigid foundation. Starting from a variational formulation of a fretting model given in a framework of continuum thermodynamics, an augmented Lagrangian formulation is derived by introducing finite element discretizations in space and a finite difference discretization in time. The augmented Lagrangian formulation is implemented and solved by a Newton method for the two-dimensional case.

  • 43.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    An Efficient Tradeoff Approach for Topology Optimization with Manufacturing Constraints2010Inngår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 1: 36th Design Automation Conference, Parts A and B, ASME Press, 2010, s. 1171-1179Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper an efficient approach for generating tradeoff curves when performing topology optimization with manufacturing constraints is presented. By minimizing a new stiffness-volume ratio, or in-fact a new compliance-volume product, the tradeoff curve is generated by changing a new design parameter. The volume appearing in the objective is raised to the power of this new design parameter In such manner different conceptual designs can be generated By adopting a nested approach, the problem is easily solved by a simple numerical scheme. This is a nice feature of the approach which makes the numerical performance most efficient and robust. This feature makes it also easy to include manufacturing constraints by simply updating the move limits such that these constraints are satisfied The design parametrization is done by the SIMP-model and patterns of checker-boards are prevented by adopting Sigmund's filter. The efficiency of the approach is demonstrated by presenting tradeoff curves for both 2D- and 3D-problems.

  • 44.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    An Eulerian approach for simulating frictional heating in disc-pad systems2011Inngår i: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 30, nr 5, s. 673-683Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Thermal stresses as a result from frictional heating must be considered when designing disc brakes, clutches or other rotating machine components with sliding contact conditions. The rotational symmetry of the disc in these kind of applications makes it possible to model these systems using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed and implemented. The disc is formulated in an Eulerian frame where the convective terms are defined by the angular velocity. By utilizing the Eulerian framework, a node-to-node formulation of the contact interface is obtained, producing most accurate frictional heat power solutions. The energy balance of the interface is postulated by introducing an interfacial temperature. Both frictional power and contact conductances are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini’s contact conditions to an equivalent semi-smooth equation. The heat transfer in the disc is discretized by a Petrov–Galerkin approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such manner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermo-elastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained sequentially via the trapezoidal rule. In particular the parameter is set such that both the Crank–Nicolson and the Galerkin methods are utilized. The method seems very promising. This is demonstrated by solving a two-dimensional benchmark as well as a real disc brake system in three dimensions.

  • 45.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    An implicit method for frictional contact, impact and rolling2005Inngår i: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 24, nr 6, s. 1016-1029Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper an implicit method for frictional contact, impact and rolling is suggested. A nonclassical formulation of a two-dimensional hyperelastic body unilaterally constrained to rigid supports is proposed by following the ideas of Moreau and Jean. A total Lagrangian formulation of the system is given. The elastic properties are defined by coupling the second Piola–Kirchhoff stress to the Green–Lagrange strain via the Kirchhoff–St. Venant law. The equation of motion is written in the spirit of Moreau by using the mean value impulses introduced by Jean. The mean value impulses appear explicitly in the equation of motion. In such manner the treatment of nonconstant kinematic transformation matrices becomes straightforward. The rigid supports are described by smooth functions. By utilizing these functions and the mean value impulses, new contact/impact laws of Signorini and Coulomb type are formulated. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. Three two-dimensional examples are solved by the method: a contact problem, an impact problem and a rolling contact problem.

  • 46.
    Strömberg, Niclas
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines2018Inngår i: Proceedings of the ASME Design Engineering Technical Conference: Volume 2B, American Society of Mechanical Engineers (ASME) , 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The postprocessing step from the density result in topology optimization to a parametric CAD model is typically most time consuming and usually involves several hands on maneuvers by an engineer. In this paper we propose an approach in order to automate this step by using soft non-linear support vector machines (SVM). Our idea is to generate the boundaries separating regions of material (elements with densities equal to one) and no material (elements with densities equal zero) obtained from topology optimization automatically by using SVM. The hypersurface of the SVM can then in the long run be explicitly implemented in any CAD software. In this work we generate these hypersurfaces by solving the dual formulation of the SVM with soft penalization and nonlinear kernel functions using quadratic programming or the sequential minimal optimization approach. The proposed SVM-based postprocessing approach is studied on topology optimization results of orthotropic elastic design domains with mortar contact conditions studied most recently in a previous work. The potential energy of several bodies with non matching meshes is maximized. In such manner no extra adjoint equation is needed. Intermediate density values are penalized using SIMP or RAMP, and the regularization is obtained by applying sensitivity or density filters following the approaches of Sigmund and Bourdin. The study demonstrates that the SVM-based postprocessing approach automatically generates proper hypersurfaces which can be used efficiently in the CAD modelling.

  • 47.
    Strömberg, Niclas
    Department of Mechanical Engineering School of Engineering, Jönköping University, Jönköping, Sweden.
    Contact, impact and rolling of a nonlinear elastic body on rigid foundations2005Inngår i: Multibody Dynamics 2005: ECCOMAS Thematic Conference, 2005Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a method for frictional contact, impact and rolling of a two-dimensional hyperelastic body on rigid foundations is presented. A total Lagrangian formulation of the system is given. The elastic properties of the body are defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St.Venant law. The rigid supports are described by smooth functions. By introducing the mean value impulses, these functions are utilized to formulate the contact/impact laws. The support functions appear explicitly in the variational formulation of Signorini, and implicitly in the maximal dissipation principle of Coulomb. An attractive property of this approach is that no search algorithm is needed. Another attractive property is that the normal and tangential directions of the supports are well defined. The above constitutive assumptions together with the law of motion, which is written on velocity form, define the governing equations of the system. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. The method is implemented in TriLab. TriLab is a toolbox for simulating contact problems. TriLab is developed using Matlab and Visual Fortran. The Fortran code is linked to Matlab as mex-files. The code is vectorized and the sparsity is utilized. By using TriLab, the presented method will be demonstrated by solving structural dynamic contact problems, impact problems as well as rolling contact problems

  • 48.
    Strömberg, Niclas
    School of Engineering, Jönköping University, Jönköping, Sweden.
    Development and Implementation of an Eulerian Approach for Efficient Simulation of Frictional Heating in Sliding Contacts2011Inngår i: Computational methods for coupled problems in science and engineering IV: proceedings of the IV International Conference on Computational Methods for Coupled Problems in Science and Engineering / [ed] Papadrakakis, M; Onate, E; Schrefler, B, Barcelona: International Center for Numerical Methods in Engineering (CIMNE), 2011, s. 1136-1146Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Thermal stresses as a result from frictional heating must be considered when designing disc brakes. The rotational symmetry of a disc brake makes it possible to model this system using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed. The sliding object is formulated in an Eulerian frame where the convective terms are defined by the sliding velocity. A node-to-node formulation of the contact interface is utilized. The energy balance of the interface is stated by introducing an interfacial temperature. Both frictional power and contact conductance are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini's contact conditions to a system of semi-smooth equations. The heat transfer in the sliding body is discretized by a Petrov-Galerkin approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such manner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermoelastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained via the trapezoidal rule. In particular the parameter is set such that both the Crank-Nicolson and the Galerkin methods are utilized. The method seems very promising. The method is demonstrated for two-dimensional benchmarks as well as a real disc brake system in three dimension.

  • 49.
    Strömberg, Niclas
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Mechanical Engineering.
    Efficient detailed design optimization of topology optimization concepts by using support vector machines and metamodels2019Inngår i: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article, an approach for metamodel-based design optimization (MBDO) of topology optimization (TO) concepts is proposed by using support vector machines (SVMs) as geometric models of the concepts instead of traditional parametric computer aided design (CAD) models. In such a manner, an efficient approach for the MBDO-driven design of TO-based concepts is obtained. An implicit hypersurface representing the TO-based concept is generated by classifying the TO-solutions of zeros and ones by using the 1-norm SVM of Mangasarian. The implicit SVM-based hypersurfaces are then utilized to set up designs of experiments of nonlinear finite element analyses by morphing the TO-based concepts by using Boolean and blending operations. Finally, MBDO is performed by using an ensemble of metamodels consisting of quadratic regression, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression models. The proposed MBDO framework is demonstrated by minimizing the mass of a three-dimensional design domain with a constraint on the plastic limit load. The performance of the approach is most promising.

  • 50.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Finite element treatment of thermoelastic wear problems1998Inngår i: IUTAM Symposium on Unilateral Multibody Contacts: Proceedings of the IUTAM Symposium held in Munich, Germany, August 3-7, 1998 / [ed] G.M.L. Gladwell, F. Pfeiffer, Springer, 1998, s. 265-274Konferansepaper (Fagfellevurdert)
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