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  • 1.
    Jerrelind, Jenny
    et al.
    Luleå tekniska universitet.
    Stensson, Annika
    Luleå tekniska universitet.
    Nonlinear dynamics of parts in engineering systems2000In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 11, no 15, p. 2413-2428Article in journal (Refereed)
    Abstract [en]

    By definition, chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations. In numerous engineering systems there exist nonlinearities which might affect the dynamic behaviour of the system. The objectives in this work are to summarise previous work on nonlinear dynamics of engineering parts and products and to investigate if research on how nonlinear parts can effect the total behaviour of the products have been performed. It is found that common nonlinear parts are machine elements such as gears, bearings, brakes and suspension systems. The most studied part in a product is of impact hammer type. The products are ordinary products, from sewing machines, drilling machines and printers to railway vehicles. In order to be able to design reliable products the methodology should be further developed to enable use by engineers. One can conclude that the effect of nonlinear parts on the total system behaviour is still a fairly uninvestigated area

  • 2.
    Karlberg, Magnus
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.
    Investigation of a saddle node bifurcation due to loss of contact in preloaded spherical roller thrust bearings2009In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 41, no 4, p. 1750-1759Article in journal (Refereed)
    Abstract [en]

    Spherical roller thrust bearings are used as supports in many rotating machineries. By applying an axial preload, clearance between the raceways and the rollers can be avoided. In order to increase the endurance, the preload shall be kept as low as possible. However, a bearing with low preload is sensitive of loosing full contact leading to nonlinear stiffness characteristics. The objective of this paper is to suggest a tool, which can be used to determine suitable preload and to show that a saddle node bifurcation can occur if the preload is too small.Studying the model in a rotating frame leads to an autonomous equation of motion from which stationary points and their stability can be analysed. Some set of parameters give a nonhyperbolic eigenvalue, and by investigating the corresponding central manifold it is found that a saddle node bifurcation occurs. Since explicit equations for the stationary points are derived, they can be used to choose a preload high enough to make sure that full contact always is a possible solution. It is however shown that if the preload becomes too small, the system enters an area of multiple solutions and a saddle node bifurcation can occur.

  • 3.
    Karlberg, Magnus
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Investigation of an unbalanced rotor system with bearing clearance and stabilising rods2004In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 20, no 2, p. 363-374Article in journal (Refereed)
    Abstract [en]

    The nonlinear vibrations of a rotor system with bearing clearance and stabilising rods are considered. In this paper the main objective is to evaluate effects of applying stabilising rods and from a dynamical point of view find preferable parameter ranges. A piecewise linear two degrees-of-freedom model is proposed. The system is studied and evaluated by analysis of steady state, bifurcation diagrams, Lyapunov exponents and contact force. It is shown how transition lines (which separate different categories of motion), periodicity and sensitivity to small perturbation are affected by the parameters defining the stability rods. By applying specific stabilising rods the periodicity is changed for some parameter ranges, unstable areas are reduced, the total maximum normal contact force is increased while the dynamical part is mainly reduced. The analytical expressions for the transition limits can be used as a design tool to choose suitable parameters. It is concluded that the stability rods should be applied vertically and that high preloading and stiffness prevents the system from impact motion. The stabilising rods are effective tools to avoid nonlinear behaviors but it is necessary to carefully analyse the specific application

  • 4.
    Karlberg, Magnus
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Numerical investigation of an unbalanced rotor system with bearing clearance2003In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 18, no 4, p. 653-664Article in journal (Refereed)
    Abstract [en]

    The nonlinear vibrations of a rotor system with bearing clearance are considered. The model consists of an unbalanced shaft with two d.o.f connected to a nonrotating massless housing by linear springs and dashpots. The clearance occurs when the housing (modelled as a ring) has a radius less than the stator. The behaviour of this system has been investigated with the use of time histories, Poincare maps, bifurcation diagrams, Lyapunov exponents, phase portraits, cell mapping and design space. Numerical simulations have achieved these results. The main objective was to find possible causes of failure in machines containing this type of clearance. The existence of subharmonic, quasi-periodic or even possible chaotic motion has been found. It is shown that these motions may give raise to bouncing modes, which results in high bearing forces and hence can be a possible cause of failure

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