| It is a leading and hot issue in the studying field of the rotary machine system to investigate the effect of more than one parameter varying synchronously on the dynamics of the rotary machine system and explore the incidence relation of parameter as well as the proper matching rules of parameters.At present,the mainly researches about the influence of dynamics belonging to the rotary machine system are based on the discussion of single-parameter bifurcation,however,some relevant studies in connection to the dynamic distribution in parameter space and the incidence relation of parameter are limited due to the visual means and the limitation of the large computation.The GPU parallel computation comes up in this paper in order to track the dynamic behavior of parameter space and realize the trace of the dynamics by means of CUDA programming technology,moreover,the stable phrase diagrams that are complementary are designed,and a variety of dynamic features and the transition rules are presented by choosing the representative two-parameter space.Some novel fractal structures are discovered,such as the hierarchical organization of Farey tree and Stern-Broot tree,the loop structure of"eye" of chaos and the comb structure of "fountains" of chaos and so on.According to self-similarity theory of fractal in terms of these structures,the relationships of partial and partial along with partial and whole are disclosed.Besides,some deep dynamic features are also found,including the mixed-mode oscillation of chaotic harmonic and non-chaotic harmonic,the shrimp structures covered with three numbers of peak and the free form of oscillation with mosaic phrase of peak.Based on these results,the universal property and regularity concealing behind the rotary machine system are revealed,which helps us to deeply understand the nature of the dynamics of the rotary machine system,meanwhile,can provide the dynamic bases of parameter choice for the optimization design of parameters,failure detection and vibration control of the rotary machine system.The major researches of this paper as following:According to the research ideas from simpleness to complication,two kinds of simple rotor systems are studied firstly.Based on a great deal of dynamical information,it is showed that the hexagonal centrifugal governor mainly relates to the instability caused by Hopf bifurcation and the parameter space consisting of frequency,amplitude and damp,and the structure of mode locking of the hexagonal centrifugal governor is arranged in terms of Farey sequence,which are universal structures of the centrifugal governor in quasi-periodic motion region.On the other hand,to the rhombic centrifugal governor,the intermittent chaos is the primary factor resulting in the unstable motion of the system,and a lot of special fractal structures in the shape of comb called "fountains" of chaos are formed in the main parameter planes of it.What's more,the structure of mode locking for rhombic centrifugal governor is arranged according to Stern-Broot sequence containing Farey tree.By discovering the matching rules of damp and other parameters about the above rotor systems,it is found that relatively larger damp is beneficial to the stable motion of the system.Next,the dynamics and the matching rules about parameters in connection to single-spencer,three-axis,motor-triaxial gyroscope systems are studied respectively in parameter space and a great deal of dynamical information is attained by GPU parallel computation.Results show that the intermittent chaos is the main factor for the gyroscope rotor system leading to the failure,and"fountains" of chaos is presented by combining the parameter plane where the amplitude is dominant as well as it is discovered that relatively larger momentum and angular help with the stability of the system.To our amazement,there is a route from period-doubling bifurcation to chaos for three-axis and motor-triaxial gyroscope rotor system,at the same time,the looping structure of"eye" of chaos comes into being by the utmost,accumulation of forward and reverse period-doubling bifurcations.Moreover,this paper highlights the connection between the mixed-mode oscillation and the combinations of parameters,discovering that the law of oscillation for the vibration of some dynamical variables is the same as the centrifugal governor,and the distribution of the number of peaks is equidifferent.Some variables take on a kind of complicated pattern of the mixed-mode oscillation,one that is in the free form of oscillation with mosaic phrase of peak.At last,conduct a comprehensive investigation about the dynamical behavior and the matching rule of parameters about the complex rotor system with some faults based on relevant researches of two kinds of simple rotor systems mentioned above.When the rotate speed is less than the critical speed,all kind of faulted elements(the depth of crack,cracked angle,mass eccentricity,rubbing clearance,the viscosity of oil film and so on)with regard to cracked rotor,rub-impact rotor and rub-impact rotor coupled the crack have little effect on the dynamics of the faulted rotor system and period-1 motion occupies the behavior of the system,while the rotate speed ranges from the critical speed to double critical speed,forward and reverse sequences of period-doubling bifurcation are presented,on the contrary,the quasi-periodic motion takes up the region with high rotate speed.As for the cracked rotor system,the subharmonic resonance with higher periodicity embeds inside of the quasi-periodic region,however,its structure is different from the regular structures of the centrifugal governor.In the rub-impact rotor system,widespread period-3 motion is discovered in the quasi-periodic region.In terms of the mass eccentricity,larger mass eccentricity gets close to the cracked rotor and smaller mass eccentricity is similar to the rub-impact rotor for the rub-impact rotor coupled the crack.Besides,for the above faulted rotor systems,the degree of the effect of parameters on dynamics is various,that is to say,the effect of mass eccentricity on the cracked rotor tops and the stiffness of stator has the most important effect on the rub-impact rotor and rub-impact rotor with the crack,followed by the effect of mass eccentricity,in the meantime,the effect of other parameters is identical.Three kinds of faulted rotor systems produce the mixed model oscillation in local parameter regions belonging to free oscillation,which is different from the regularities generated by gyroscope rotor system and centrifugal governor system. |
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