| The steam turbine rotor is the key component of the steam turbine generator set,the stability of which is closely related to the safe operation of the equipment.According to statistics,the nonlinear instability has occurred to the low-voltage rotor of the 200 MW steam turbine generator set for many times,which seriously affects the normal operation of the equipment.Although a large number of theoretical achievements and operating experience have been obtained,many dynamical mechanisms still lack in-depth knowledge.Therefore,this paper takes the low-voltage rotor system of the 200 MW steam turbine generator unit as the research object.By organically combining the single-parameter bifurcation analysis tools with the GPU parallel computing method,on the basis of the numerical simulation method,the various evolutionary processes and distribution complexity of the dynamical behavior of the rotor system which is influenced by the steam-flow exciting vibration,the steam-flow exciting vibration coupling cracks,and the steam-flow exciting vibration coupling rub-impact,respectively,are shown experimentally in the parameter planes.In this paper,the global topological law of the distribution of periodic phases is extracted,and the nonlinear dynamical features and global stability of the system under the extensive parameter incidence relations are analyzed.Based on the abstract number theory,by mathematicalizing the obscure dynamical information in large rotor systems,namely,constructing a binary tree hierarchical structure with higher universality and applicability with the number of cycles,the common features exhibited by the dynamical behavior of non-autonomous large rotating mechanical systems are discovered.The research results provide a more complete visual reference for the unit design and parameter matching rules,and help to have a more accurate and in-depth grasp and understanding of the global features and failure mechanism of the system.Meanwhile,the research concerning the nonlinear dynamic characteristics of the large rotating machinery in high-dimension parameter space is pushed further.The main research work of this paper is as follows.Firstly,aiming at the difficulty of obtaining the Lyapunov exponents and the dynamical information of large rotor systems in two-dimensional parameter space,two kinds of GPU parallel computing methods are designed: one is the parallel calculation method of Lyapunov exponent spectrum,namely “clone” method,which efficiently achieves the maximal possibility of Lyapunov exponents;the other is the isoperiodic technique,which is to obtain a large number of high-definition two-dimensional parameter plane periodic stable phase diagrams through GPU parallel computing method.Isoperiodic diagrams can be used to display the evolutionary process of the dynamical behavior of large rotor systems in the two-dimensional parameter plane.Secondly,by taking the steam turbine rotor system as the research object,the distribution characteristics of the dynamical behavior are revealed in the parameter plane,and the influence of different parameter correlations on the stability of the system is analyzed.The existence of the Hopf bifurcation is proved and the occurrence conditions of the Hopf bifurcation are obtained.The evolution processes of the dynamical behavior are shown in the case of a wide range of parameter correlations,and the changes in the dynamical characteristics of the system are analyzed and compared.As a result,the single-parameter analysis is further improved,which provides more references and possibilities for practical design and application.A large number of high-definition isoperiodic diagrams with the help of GPU parallel algorithms describe how plenty of interesting periodic cascades that exist in the system unfold over a fairly wide range of parameters.The results show that if the system is influenced by the Alford force,the global topological law of the arrangement of periodic phases usually satisfies Farey tree,or two-sided Farey tree.On the contrary,the coexistence of symmetric Farey sum-tree and “eye” of chaos is a generic feature in connection to periodic cascades.The deformation and position of the periodic phases transmit complete and rich dynamical information,and the influence of different parameter incidence relations on the global stability of the system is obtained,which provides a wide range of dynamical references for practical design and parameter matching.Thirdly,by taking the steam turbine cracked rotor system as the research object,the complexity of the distribution of the dynamical behavior in the parameter plane is classified and the influence of different parameter correlations on the stability of the system is analyzed.By comparing the differences in the evolution process of the dynamical behavior in the case of extensive parameter correlations,the effects of different parameter matching on the stability of the system are summarized.Based on a large number of isoperiodic diagrams,the distribution of periodic phases due to the existence of cracks is presented to form a dense accumulation horizon of periodic cascades,thus providing classifications of various complex periodic phases.That is,these periodic cascades are arranged in overlapping doubling cascades or are distributed according to the topological regularity of highly symmetric Farey sum-tree or Stern-Brocot sum-tree.The obtained topological law is suitable for the global distribution of periodic phases in the two-dimensional parameter plane for such complex rotating mechanical systems,which provides visual and regular digital signals for fault prediction.And complex dynamical information is mathematical,which helps to further understand the dynamical nature of the cracked rotor system and better grasp the global behavior.Finally,by taking the steam turbine rub-impact rotor system as the research object,the distribution characteristics of the dynamical behavior of the rub-impact rotor system in the parameter plane are revealed,and the influence of different parameter correlations on the stability of the system is summarized.In the parameter plane,based on a wide range of parameter correlations,the distribution characteristics of the dynamical behavior of the system under the influence of rub-impact force are presented,and the differences in the global stability of the system under different parameter matching are compared.The results show that in the critical speed range,a large number of resonant structures with interesting geometric structures and the numbers of rotations satisfying the Farey sum which form“devil’s staircase” are observed.In the supercritical speed range,the dynamical horizon of the“filament-shaped” multi-period oscillations mediated by chaotic oscillations is a generic feature of the nonlinear dynamical behavior of the system.The provided charts provide a visual reference and comparison for parameter matching,nonlinear design and failure prediction of large rubbing rotor systems.The obtained results are helpful for further understanding of the mechanism of rub-impact fault.This is a more comprehensive analysis and discussion of the nonlinear dynamical behavior of the steam turbine rotor system.The numerical experiments involve parameters that are accessible or not accessible to the experiment,so the obtained dynamical information not only has a broad engineering background but also provides practical dynamic design with new possibilities. |
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