The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics cause...The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics caused by the crack rather than estimating the crack depth and position based on the obtained vibration signals.In this paper,a novel crack fault diagnosis and location method for a dual-disk hollow shaft rotor system based on the Radial basis function(RBF)network and Pattern recognition neural network(PRNN)is presented.Firstly,a rotor system model with a breathing crack suitable for a short-thick hollow shaft rotor is established based on the finite element method,where the crack's periodic opening and closing pattern and different degrees of crack depth are considered.Then,the dynamic response is obtained by the harmonic balance method.By adjusting the crack parameters,the dynamic characteristics related to the crack depth and position are analyzed through the amplitude-frequency responses and waterfall plots.The analysis results show that the first critical speed,first subcritical speed,first critical speed amplitude,and super-harmonic resonance peak at the first subcritical speed can be utilized for the crack fault diagnosis.Based on this,the RBF network and PRNN are adopted to determine the depth and approximate location of the crack respectively by taking the above dynamic characteristics as input.Test results show that the proposed method has high fault diagnosis accuracy.This research proposes a crack detection method adequate for the hollow shaft rotor system,where the crack depth and position are both unknown.展开更多
In this paper,the aero-engine test with inter-shaft bearing fault is carried out,and a dataset is proposed for the first time based on the vibration signal of rotors and casings.First,a test rig based on a real aero-e...In this paper,the aero-engine test with inter-shaft bearing fault is carried out,and a dataset is proposed for the first time based on the vibration signal of rotors and casings.First,a test rig based on a real aero-engine is established,driven by motors and equipped with a lubricating system.Then,the aero-engine is disassembled and assembled following the specification process,and the inter-shaft bearing with artificial fault is replaced.Next,the aero-engine test is conducted at 28 groups of high-and low-pressure speeds.Six measuring points are arranged,including two displacement sensors to test the displacement vibration signals of the low-pressure rotor and four acceleration sensors to test the acceleration vibration signals of the casing.The test results are integrated into an inter-shaft bearing fault dataset.Finally,based on the dataset in this paper,frequency spectrum,envelope spectrum,CNN,LSTM,and TST are used for fault diagnosis,and the results are compared with those of CWRU and XJTU datasets.The results show that the characteristic fault frequency cannot be found directly in the spectrum and envelope spectrum corresponding to this paper’s dataset but in CWRU and XJTU datasets.Using CNN,LSTM,and TST for fault diagnosis of the dataset in this paper,the accuracy is 83.13%,85.41%,and 71.07%,respectively,much lower than the diagnosis results of CWRU and XJTU datasets.It can be seen that the dataset in this paper is closer to the actual fault diagnosis situation and is a more challenging dataset.This dataset provides a new benchmark for the validation of fault diagnosis methods.Mendeley data:https://github.com/HouLeiHIT/HIT-dataset.展开更多
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.展开更多
A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to...A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.展开更多
When an aircraft is hovering or doing a dive-hike flight at a fixed speed, a constant additional inertial force will be induced to the rotor system of the aero-engine, which can be called a constant maneuver load. Tak...When an aircraft is hovering or doing a dive-hike flight at a fixed speed, a constant additional inertial force will be induced to the rotor system of the aero-engine, which can be called a constant maneuver load. Take hovering as an example. A Jeffcott rotor system with a biased rotor and several nonlinear elastic supports is modeled, and the vibration characteristics of the rotor system under a constant maneuver load are analytically studied. By using the multiple-scale method, the differential equations of the system are solved, and the bifurcation equations are obtained. Then, the bifurcations of the system are analyzed by using the singularity theory for the two variables. In the EG-plane, where E refers to the eccentricity of the rotor and G represents the constant maneuver load, two hysteresis point sets and one double limit point set are obtained. The bifurcation diagrams are also plotted. It is indicated that the resonance regions of the two variables will shift to the right when the aircraft is maneuvering. Furthermore, the movement along the horizontal direction is faster than that along the vertical direction. Thus, the different overlapping modes of the two resonance regions will bring about different bifurcation modes due to the nonlinear coupling effects. This result lays a theoretical foundation for controlling the stability of the aero-engine＇s rotor system under a maneuver load.展开更多
An electromagnetic nonlinear energy harvester(NEH)based on a rotating system is proposed,of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction.This kind of device exh...An electromagnetic nonlinear energy harvester(NEH)based on a rotating system is proposed,of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction.This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH.The governing equation of motion for the NEH is derived,and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions.The effects of system parameters including the nondimensional external frequency,the rotating speed,and the nonlinear stiffness on the responses of free vibration for the system are studied.The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node(SN)bifurcation.The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation.Moreover,the effects of system parameters on the average output power are investigated.The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands.The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance.Moreover,the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power.The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device.Suitable parameter conditions could help optimize the power harvesting in design.展开更多
A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the...A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.展开更多
The transient proper orthogonal decomposition(TPOD) method is used to study dynamic behaviors of the reduced rotor-bearing models,and the fault-free model is compared with the models with looseness fault.A 22 degree o...The transient proper orthogonal decomposition(TPOD) method is used to study dynamic behaviors of the reduced rotor-bearing models,and the fault-free model is compared with the models with looseness fault.A 22 degree of freedoms(DOFs) rotor model supported by bearings is established.Both one end and two ends pedestal looseness of the liquid-film bearings are studied by analyzing the time history and the frequency-spectrum curves.The effects of the initial displacement and velocity values to frequency components of the original systems and the dimension reduction efficiency are discussed.Moreover,the effects of variation of initial conditions on the efficiency of the TPOD method are studied.Reduced models can provide guidance significance from the perspectives of the theory and numerical simplification to discuss the characteristics of pedestal looseness fault.展开更多
Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper.First,the transient proper orthogonal decomposition(T-POD)method is introduced based on the high-dimensiona...Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper.First,the transient proper orthogonal decomposition(T-POD)method is introduced based on the high-dimensional nonlinear dynamic system.The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends.The efficiency of the T-POD method is verified via comparing with the results of the original system.Second,the polynomial dimensional decomposition(PDD)method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response.The numerical results obtained by the PDD method agree well with the Monte Carlo simulation(MCS)method.The results of the PDD method can approximate to MCS better with the increasing of the polynomial order.Meanwhile,the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.展开更多
A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet m...A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and the universal unfolding （UU） of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of non- linear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.展开更多
This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable and robust vibration analyses.To this end,the regression-based polynomial chaos ex...This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable and robust vibration analyses.To this end,the regression-based polynomial chaos expansion(PCE)is used to track aleatory uncertainties,and the polynomial surrogate approach(PSA)is developed to treat the epistemic uncertainties.This non-intrusive dual-layer framework shares the same collocation pool,which is extracted from the Legendre series.Moreover,the regression technique has been implemented in both layers to enhance calculation efficiency.Numerical validation is carried out to show the effectiveness of the proposed method.New vibration behaviors of the geared transmission system are observed,and the mechanism behind is discussed in detail.The findings of this paper will contribute to the insightful understanding of such wind turbine geared systems under hybrid uncertainties and are beneficial for the condition monitoring.展开更多
In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. ...In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. Bearing clearance,Hertz contact between the ball and race and the varying compliance effect are included in the model of ball bearing. The system response is obtained through numerical integration method,and the vibration due to the periodic change of bearing stiffness is investigated. The motions of periodic,quasiperiodic and even chaotic are found when bearing clearance is used as control parameter to simulate the response of rotor system. The results reveal two typical routes to chaos: quasi-periodic bifurcation and intermittent bifurcation. Large cubic stiffness of elastic support may cause jump and hysteresis phenomena in resonance curve when rotors run at the critical-speed region. The modeling results acquired by numerical simulation will contribute to understanding and controlling of the nonlinear behaviors of the dual-rotor system.展开更多
The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus vol...The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1：3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus （TMIB） power system.展开更多
In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor syst...In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.展开更多
In recent years, the crack fault is one of the most common faults in the rotor system and it is still a challenge for crack position diagnosis in the hollow shaft rotor system. In this paper, a method based on the Con...In recent years, the crack fault is one of the most common faults in the rotor system and it is still a challenge for crack position diagnosis in the hollow shaft rotor system. In this paper, a method based on the Convolutional Neural Network and deep metric learning(CNN-C) is proposed to effectively identify the crack position for a hollow shaft rotor system. Center-loss function is used to enhance the performance of neural network. Main contributions include: Firstly, the dynamic response of the dual-disks hollow shaft rotor system is obtained. The analysis results show that the crack will cause super-harmonic resonance, and the peak value of it is closely related to the position and depth of the crack. In addition, the amplitude near the non-resonant region also has relationship with the crack parameters. Secondly, we proposed an effective crack position diagnosis method which has the highest 99.04% recognition accuracy compared with other algorithms. Then,the influence of penalty factor on CNN-C performance is analyzed, which shows that too high penalty factor will lead to the decline of the neural network performance. Finally, the feature vectors are visualized via t-distributed Stochastic Neighbor Embedding(t-SNE). Naive Bayes classifier(NB) and K-Nearest Neighbor algorithm(KNN) are used to verify the validity of the feature vectors extracted by CNN-C. The results show that NB and KNN have more regular decision boundaries and higher recognition accuracy on the feature vectors data set extracted by CNN-C,indicating that the feature vectors extracted by CNN-C have great intra-class compactness and inter-class separability.展开更多
基金Supported by National Natural Science Foundation of China (Grant No.11972129)National Science and Technology Major Project of China (Grant No.2017-IV-0008-0045)+1 种基金Heilongjiang Provincial Natural Science Foundation (Grant No.YQ2022A008)the Fundamental Research Funds for the Central Universities。
文摘The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics caused by the crack rather than estimating the crack depth and position based on the obtained vibration signals.In this paper,a novel crack fault diagnosis and location method for a dual-disk hollow shaft rotor system based on the Radial basis function(RBF)network and Pattern recognition neural network(PRNN)is presented.Firstly,a rotor system model with a breathing crack suitable for a short-thick hollow shaft rotor is established based on the finite element method,where the crack's periodic opening and closing pattern and different degrees of crack depth are considered.Then,the dynamic response is obtained by the harmonic balance method.By adjusting the crack parameters,the dynamic characteristics related to the crack depth and position are analyzed through the amplitude-frequency responses and waterfall plots.The analysis results show that the first critical speed,first subcritical speed,first critical speed amplitude,and super-harmonic resonance peak at the first subcritical speed can be utilized for the crack fault diagnosis.Based on this,the RBF network and PRNN are adopted to determine the depth and approximate location of the crack respectively by taking the above dynamic characteristics as input.Test results show that the proposed method has high fault diagnosis accuracy.This research proposes a crack detection method adequate for the hollow shaft rotor system,where the crack depth and position are both unknown.
基金supports from the National Natural Science Foundation of China (Grant No.11972129)the Natural Science Foundation of Heilongjiang Province (Outstanding Youth Foundation,Grant No.YQ2022A008)the Fundamental Research Funds for the Central Universities.
文摘In this paper,the aero-engine test with inter-shaft bearing fault is carried out,and a dataset is proposed for the first time based on the vibration signal of rotors and casings.First,a test rig based on a real aero-engine is established,driven by motors and equipped with a lubricating system.Then,the aero-engine is disassembled and assembled following the specification process,and the inter-shaft bearing with artificial fault is replaced.Next,the aero-engine test is conducted at 28 groups of high-and low-pressure speeds.Six measuring points are arranged,including two displacement sensors to test the displacement vibration signals of the low-pressure rotor and four acceleration sensors to test the acceleration vibration signals of the casing.The test results are integrated into an inter-shaft bearing fault dataset.Finally,based on the dataset in this paper,frequency spectrum,envelope spectrum,CNN,LSTM,and TST are used for fault diagnosis,and the results are compared with those of CWRU and XJTU datasets.The results show that the characteristic fault frequency cannot be found directly in the spectrum and envelope spectrum corresponding to this paper’s dataset but in CWRU and XJTU datasets.Using CNN,LSTM,and TST for fault diagnosis of the dataset in this paper,the accuracy is 83.13%,85.41%,and 71.07%,respectively,much lower than the diagnosis results of CWRU and XJTU datasets.It can be seen that the dataset in this paper is closer to the actual fault diagnosis situation and is a more challenging dataset.This dataset provides a new benchmark for the validation of fault diagnosis methods.Mendeley data:https://github.com/HouLeiHIT/HIT-dataset.
基金Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)+3 种基金the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006)the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980)the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
文摘The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2015CB057405)the National Natural Science Foundation of China(No.11372082)the State Scholarship Fund of China Scholarship Council(CSC)(2014)
文摘A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.
基金Project supported by National Basic Research Program(973 Program)of China(No.2015CB057400)
文摘When an aircraft is hovering or doing a dive-hike flight at a fixed speed, a constant additional inertial force will be induced to the rotor system of the aero-engine, which can be called a constant maneuver load. Take hovering as an example. A Jeffcott rotor system with a biased rotor and several nonlinear elastic supports is modeled, and the vibration characteristics of the rotor system under a constant maneuver load are analytically studied. By using the multiple-scale method, the differential equations of the system are solved, and the bifurcation equations are obtained. Then, the bifurcations of the system are analyzed by using the singularity theory for the two variables. In the EG-plane, where E refers to the eccentricity of the rotor and G represents the constant maneuver load, two hysteresis point sets and one double limit point set are obtained. The bifurcation diagrams are also plotted. It is indicated that the resonance regions of the two variables will shift to the right when the aircraft is maneuvering. Furthermore, the movement along the horizontal direction is faster than that along the vertical direction. Thus, the different overlapping modes of the two resonance regions will bring about different bifurcation modes due to the nonlinear coupling effects. This result lays a theoretical foundation for controlling the stability of the aero-engine＇s rotor system under a maneuver load.
基金the National Natural Science Foundation of China(Nos.11702111,11572205,and 11732014)the Natural Science Foundation of Shandong Province of China(Nos.ZR2017QA005 and ZR2017BA031)。
文摘An electromagnetic nonlinear energy harvester(NEH)based on a rotating system is proposed,of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction.This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH.The governing equation of motion for the NEH is derived,and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions.The effects of system parameters including the nondimensional external frequency,the rotating speed,and the nonlinear stiffness on the responses of free vibration for the system are studied.The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node(SN)bifurcation.The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation.Moreover,the effects of system parameters on the average output power are investigated.The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands.The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance.Moreover,the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power.The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device.Suitable parameter conditions could help optimize the power harvesting in design.
基金Project supported by the National Basic Research Program(973 Program)of China(No.2015CB057400)the National Natural Science Foundation of China(No.11602070)+1 种基金the China Postdoctoral Science Foundation(No.2016M590277)the Heilongjiang Postdoctoral Financial Assistance(No.LBH-Z16067)
文摘A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.
基金Sponsored by the National Basic Research Program of China(Grant No.2015CB057400)
文摘The transient proper orthogonal decomposition(TPOD) method is used to study dynamic behaviors of the reduced rotor-bearing models,and the fault-free model is compared with the models with looseness fault.A 22 degree of freedoms(DOFs) rotor model supported by bearings is established.Both one end and two ends pedestal looseness of the liquid-film bearings are studied by analyzing the time history and the frequency-spectrum curves.The effects of the initial displacement and velocity values to frequency components of the original systems and the dimension reduction efficiency are discussed.Moreover,the effects of variation of initial conditions on the efficiency of the TPOD method are studied.Reduced models can provide guidance significance from the perspectives of the theory and numerical simplification to discuss the characteristics of pedestal looseness fault.
基金funding for this study from the National Natural Science Foundation of China(Grant No.11802235)the National Basic Research Program(973 Program)of China(Grant No.2015CB057400)the Basic Scientific Research Operating Expenses of Central Universities(Grant No.G2018KY0305).
文摘Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper.First,the transient proper orthogonal decomposition(T-POD)method is introduced based on the high-dimensional nonlinear dynamic system.The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends.The efficiency of the T-POD method is verified via comparing with the results of the original system.Second,the polynomial dimensional decomposition(PDD)method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response.The numerical results obtained by the PDD method agree well with the Monte Carlo simulation(MCS)method.The results of the PDD method can approximate to MCS better with the increasing of the polynomial order.Meanwhile,the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.
基金supported by the National Basic Research Program of China(973 Program)(No.2015CB057400)the National Natural Science Foundation of China(No.11602070)the China Postdoctoral Science Foundation(No.2016M590277)
文摘A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and the universal unfolding （UU） of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of non- linear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.
基金Project supported by the National Natural Science Foundation of China(Nos.12072263 and 11972295)the Fundamental Research Funds for the Central Universities(No.G2021KY0601)。
文摘This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable and robust vibration analyses.To this end,the regression-based polynomial chaos expansion(PCE)is used to track aleatory uncertainties,and the polynomial surrogate approach(PSA)is developed to treat the epistemic uncertainties.This non-intrusive dual-layer framework shares the same collocation pool,which is extracted from the Legendre series.Moreover,the regression technique has been implemented in both layers to enhance calculation efficiency.Numerical validation is carried out to show the effectiveness of the proposed method.New vibration behaviors of the geared transmission system are observed,and the mechanism behind is discussed in detail.The findings of this paper will contribute to the insightful understanding of such wind turbine geared systems under hybrid uncertainties and are beneficial for the condition monitoring.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11302058)
文摘In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. Bearing clearance,Hertz contact between the ball and race and the varying compliance effect are included in the model of ball bearing. The system response is obtained through numerical integration method,and the vibration due to the periodic change of bearing stiffness is investigated. The motions of periodic,quasiperiodic and even chaotic are found when bearing clearance is used as control parameter to simulate the response of rotor system. The results reveal two typical routes to chaos: quasi-periodic bifurcation and intermittent bifurcation. Large cubic stiffness of elastic support may cause jump and hysteresis phenomena in resonance curve when rotors run at the critical-speed region. The modeling results acquired by numerical simulation will contribute to understanding and controlling of the nonlinear behaviors of the dual-rotor system.
基金Project supported by the National Natural Science Foundation of China(No.10632040)
文摘The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1：3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus （TMIB） power system.
基金supported by the National Natural Science Foundation of China(No.11972129)the National Science and Technology Major Project,China(No.2017-Ⅳ-00080045)。
文摘In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.
基金the financial supports from the National Natural Science Foundation of China(No.11972129)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)。
文摘In recent years, the crack fault is one of the most common faults in the rotor system and it is still a challenge for crack position diagnosis in the hollow shaft rotor system. In this paper, a method based on the Convolutional Neural Network and deep metric learning(CNN-C) is proposed to effectively identify the crack position for a hollow shaft rotor system. Center-loss function is used to enhance the performance of neural network. Main contributions include: Firstly, the dynamic response of the dual-disks hollow shaft rotor system is obtained. The analysis results show that the crack will cause super-harmonic resonance, and the peak value of it is closely related to the position and depth of the crack. In addition, the amplitude near the non-resonant region also has relationship with the crack parameters. Secondly, we proposed an effective crack position diagnosis method which has the highest 99.04% recognition accuracy compared with other algorithms. Then,the influence of penalty factor on CNN-C performance is analyzed, which shows that too high penalty factor will lead to the decline of the neural network performance. Finally, the feature vectors are visualized via t-distributed Stochastic Neighbor Embedding(t-SNE). Naive Bayes classifier(NB) and K-Nearest Neighbor algorithm(KNN) are used to verify the validity of the feature vectors extracted by CNN-C. The results show that NB and KNN have more regular decision boundaries and higher recognition accuracy on the feature vectors data set extracted by CNN-C,indicating that the feature vectors extracted by CNN-C have great intra-class compactness and inter-class separability.
