Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade compone...Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.展开更多
A general procedure to capture the 'dynanmic Stiffness' is presented in this paper. The governing equations of motion are formulated for an arbitrary flexible body in large overall motion based on Kane's ...A general procedure to capture the 'dynanmic Stiffness' is presented in this paper. The governing equations of motion are formulated for an arbitrary flexible body in large overall motion based on Kane's equations . The linearization is performed peroperly by means of geometrically nonlinear straindisplacement relations and the nonlinear expression of angular velocity so that the 'dynamical stiffness' terms can be captured naturally in a general tcase. The concept and formulations of partial velocity and angular velocity arrays of Huston's method are extended to the flexible body and form the basis of the analysis. The validity and generality of the procedure presented in the paper are verified by numerical results of its application in both the beam and plate models.展开更多
Tensile stiffness of ocean dynamic power umbilical is an important design parameter for functional implementation and structural safety. A column with radial stiffness which is wound by helical steel wires is construc...Tensile stiffness of ocean dynamic power umbilical is an important design parameter for functional implementation and structural safety. A column with radial stiffness which is wound by helical steel wires is constructed to predict the tensile stiffness value of umbilicals in the paper. The relationship between the tension and axial deformation is expressed analytically so the radial contraction of the column is achieved in the relationship by use of a simple finite element method. With an agreement between the theoretical prediction and the tension test results, the method is proved to be simple and efficient for the estimation of tensile stiffness of the ocean dynamic power umbilical.展开更多
The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinea...The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator. The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero. A comparison between the results of frequency domain and those of time domain is studied. Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed. The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics. Limit cycle oscillations （LCOs） are observed within linear flutter boundary. The response of the actuator-fin system is related to the initial disturbance. In the nonlinear condition, the amplitude of the control command has an influence on the flutter characteristics.展开更多
Most current researches working on improving stiffness focus on the application of control theories.But controller in closed-loop hydraulic control system takes effect only after the controlled position is deviated,so...Most current researches working on improving stiffness focus on the application of control theories.But controller in closed-loop hydraulic control system takes effect only after the controlled position is deviated,so the control action is lagged.Thus dynamic performance against force disturbance and dynamic load stiffness can’t be improved evidently by advanced control algorithms.In this paper,the elementary principle of maintaining piston position unchanged under sudden external force load change by charging additional oil is analyzed.On this basis,the conception of raising dynamic stiffness of electro hydraulic position servo system by flow feedforward compensation is put forward.And a scheme using double servo valves to realize flow feedforward compensation is presented,in which another fast response servo valve is added to the regular electro hydraulic servo system and specially utilized to compensate the compressed oil volume caused by load impact in time.The two valves are arranged in parallel to control the cylinder jointly.Furthermore,the model of flow compensation is derived,by which the product of the amplitude and width of the valve’s pulse command signal can be calculated.And determination rules of the amplitude and width of pulse signal are concluded by analysis and simulations.Using the proposed scheme,simulations and experiments at different positions with different force changes are conducted.The simulation and experimental results show that the system dynamic performance against load force impact is largely improved with decreased maximal dynamic position deviation and shortened settling time.That is,system dynamic load stiffness is evidently raised.This paper proposes a new method which can effectively improve the dynamic stiffness of electro-hydraulic servo systems.展开更多
Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key c...Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.展开更多
Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitation...Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.展开更多
Engineering-oriented modeling and synthesized modeling of the fin-actuator system of a missile fin are introduced, including mathematical modeling of the fin, motor and multi-stage gear reducer. The fin-actuator model...Engineering-oriented modeling and synthesized modeling of the fin-actuator system of a missile fin are introduced, including mathematical modeling of the fin, motor and multi-stage gear reducer. The fin-actuator model is verified using dynamic stiffness testing. Good agreement is achieved between the test and theoretical results. The parameter-variable analysis indicates that the inertia of the motor rotor, reduction ratio of the reducer, connection stiffness and damping between the actuator and fin shaft have significant impacts on the dynamic stiffness characteristics. In flutter analysis, test data are directly used in the frequency domain method and indirectly used in the time domain method through the updated fin-actuator model. The two methods play different roles in engineering applications but are of equal importance. The results indicate that dynamic stiffness and constant stiffness treatments may lead to completely different flutter characteristics. Attention should be paid to the design of the fin-actuator system of a missile.展开更多
A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, appli...A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.展开更多
The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic ...The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system.Therefore,this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system.Then,the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.展开更多
The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are propose...The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.展开更多
This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling in...This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration(non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity,that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second-or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.展开更多
Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discusse...Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.展开更多
Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of ...Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β_0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform( TW) and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs( degree of freedom) are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness( SW),the results show that dynamical factors and perturbation under the excitation of TW( β < β_0) are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet( R- P) is stronger than sun-planet( S-P) which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.展开更多
The dynamic response of the rotor depends on not only itself but also the dynamical characteristics of the structures that support it. In this paper, the coupling vibration characteristics of the rotor and supporting ...The dynamic response of the rotor depends on not only itself but also the dynamical characteristics of the structures that support it. In this paper, the coupling vibration characteristics of the rotor and supporting structure are studied using one simple rotor-supports model firstly, and then the dynamic stiffness of the typical supporting structure of an aero-engine is investigated in use of both numerical and experimental methods. While, one simulation strategy is developed to include dynamic stiffness of realistic supports in the dynamical analysis of the rotor system. The simulated and tested results show that the dynamic stiffness of the supporting structure not only depends on the structural parameters but also is related to the frequency of the excitation force. The dynamic stiffness is affected by the damping and inertia effect when the excitation frequency is high and closed to the resonance frequency of the support, which may decrease the dynamic stiffness sharply.More resonance frequencies may be induced and the critical speed could be reduced or increased.While higher vibration response peak and overload of the bearing may also be caused by the varied dynamic stiffness, which needs to be avoided in the design of the rotor-supports system.展开更多
Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed...Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.展开更多
The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fl...The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.展开更多
In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular cont...In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.展开更多
Dynamic stiffness matrix method is applied to compute vibration of hull girder in this paper. This method can not only simplify the computational model, but also get much higher frequencies and responses accurately. T...Dynamic stiffness matrix method is applied to compute vibration of hull girder in this paper. This method can not only simplify the computational model, but also get much higher frequencies and responses accurately. The analytical expressions of dynamic stiffness matrix of a Timoshenko beam for transverse vibration are presented in this paper. All effects of rotatory inertia and shear deformation are taken into account in the formulation. The resulting dynamic stiffness matrix combined with the Wittrick-Williams algorithm is used to compute natural frequencies and mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solved by the mode superposition method. The computational results are compared with those obtained from other approximate methods and experiment, and it indicates that the method is accurate and efficient.展开更多
The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid ...The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12372071 and 12372070)the Aeronautical Science Fund of China(No.2022Z055052001)the Foundation of China Scholarship Council(No.202306830079)。
文摘Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.
文摘A general procedure to capture the 'dynanmic Stiffness' is presented in this paper. The governing equations of motion are formulated for an arbitrary flexible body in large overall motion based on Kane's equations . The linearization is performed peroperly by means of geometrically nonlinear straindisplacement relations and the nonlinear expression of angular velocity so that the 'dynamical stiffness' terms can be captured naturally in a general tcase. The concept and formulations of partial velocity and angular velocity arrays of Huston's method are extended to the flexible body and form the basis of the analysis. The validity and generality of the procedure presented in the paper are verified by numerical results of its application in both the beam and plate models.
基金financially supported by the National High Technology Research and Development Program of China(863 ProgramGrant No.2012AA09A212)+1 种基金the National Natural Science Foundation of China(Grant No.11372060)the China Postdoctoral Science Foundation(Grant No.20110491521)
文摘Tensile stiffness of ocean dynamic power umbilical is an important design parameter for functional implementation and structural safety. A column with radial stiffness which is wound by helical steel wires is constructed to predict the tensile stiffness value of umbilicals in the paper. The relationship between the tension and axial deformation is expressed analytically so the radial contraction of the column is achieved in the relationship by use of a simple finite element method. With an agreement between the theoretical prediction and the tension test results, the method is proved to be simple and efficient for the estimation of tensile stiffness of the ocean dynamic power umbilical.
基金National Natural Science Foundation of China(90716006, 10902006)Research Fund for the Doctoral Program of Higher Education of China (20091102110015)
文摘The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator. The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero. A comparison between the results of frequency domain and those of time domain is studied. Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed. The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics. Limit cycle oscillations （LCOs） are observed within linear flutter boundary. The response of the actuator-fin system is related to the initial disturbance. In the nonlinear condition, the amplitude of the control command has an influence on the flutter characteristics.
基金supported by National Natural Science Foundation of China(Grant No.51075291)Shanxi Scholarship Council of China(Grant No.2012-076)
文摘Most current researches working on improving stiffness focus on the application of control theories.But controller in closed-loop hydraulic control system takes effect only after the controlled position is deviated,so the control action is lagged.Thus dynamic performance against force disturbance and dynamic load stiffness can’t be improved evidently by advanced control algorithms.In this paper,the elementary principle of maintaining piston position unchanged under sudden external force load change by charging additional oil is analyzed.On this basis,the conception of raising dynamic stiffness of electro hydraulic position servo system by flow feedforward compensation is put forward.And a scheme using double servo valves to realize flow feedforward compensation is presented,in which another fast response servo valve is added to the regular electro hydraulic servo system and specially utilized to compensate the compressed oil volume caused by load impact in time.The two valves are arranged in parallel to control the cylinder jointly.Furthermore,the model of flow compensation is derived,by which the product of the amplitude and width of the valve’s pulse command signal can be calculated.And determination rules of the amplitude and width of pulse signal are concluded by analysis and simulations.Using the proposed scheme,simulations and experiments at different positions with different force changes are conducted.The simulation and experimental results show that the system dynamic performance against load force impact is largely improved with decreased maximal dynamic position deviation and shortened settling time.That is,system dynamic load stiffness is evidently raised.This paper proposes a new method which can effectively improve the dynamic stiffness of electro-hydraulic servo systems.
基金Supported by National Key R&D Program of China(Grant No.2018YFB1702503)National Program on Key Basic Research Project of China(973 Program,Grant No.2013CB035403)Startup Fund for Youngman Research at SJTU(SFYR at SJTU)
文摘Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.
基金financially supported by the project‘Research on Key Technologies of Condition Monitoring and Intelligent Early Detection of Wind Turbine Based on Big Data’from State Grid Corporation of China(No.NYB17201600300)
文摘Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.
基金supported by the National Natural Science Foundation of China (Nos. 11372023 and 11402013)
文摘Engineering-oriented modeling and synthesized modeling of the fin-actuator system of a missile fin are introduced, including mathematical modeling of the fin, motor and multi-stage gear reducer. The fin-actuator model is verified using dynamic stiffness testing. Good agreement is achieved between the test and theoretical results. The parameter-variable analysis indicates that the inertia of the motor rotor, reduction ratio of the reducer, connection stiffness and damping between the actuator and fin shaft have significant impacts on the dynamic stiffness characteristics. In flutter analysis, test data are directly used in the frequency domain method and indirectly used in the time domain method through the updated fin-actuator model. The two methods play different roles in engineering applications but are of equal importance. The results indicate that dynamic stiffness and constant stiffness treatments may lead to completely different flutter characteristics. Attention should be paid to the design of the fin-actuator system of a missile.
基金Project(51175505)supported by the National Natural Science Foundation of China
文摘A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.
基金the National Natural Science Foundation of China(Nos.11872148 and U1908217)the Fundamental Research Funds for the Central Universities of China(Nos.N2224001-4 and N2003013)the Basic and Applied Basic Research Foundation of Guangdong Province of China(No.2020B1515120015)。
文摘The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system.Therefore,this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system.Then,the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.
文摘The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.
基金supported by the National Natural Science Foundation of China (Grants 11602090, 11622216, and 11672115)
文摘This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration(non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity,that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second-or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.
基金Project supported by the National Natural Science Foundation of China(Nos.11772181 and11422214)the “Dawn” Program of Shanghai Education Commission(Nos.17SG38 and 2019-01-07-00-09-E00018)the Key Research Project of Shanghai Science and Technology Commission(No.18010500100)
文摘Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.
基金Sponsored by the National High-tech R&D Program of China(Grant No.2009AA04Z404)
文摘Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β_0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform( TW) and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs( degree of freedom) are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness( SW),the results show that dynamical factors and perturbation under the excitation of TW( β < β_0) are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet( R- P) is stronger than sun-planet( S-P) which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.
基金the financial support from the National Natural Science Foundation of China(No.52075018)the National Science and Technology Major Project of the Ministry of Science and Technology of China(Nos.2017-Ⅳ-0011-0048 and 2017-I-0008-0009)。
文摘The dynamic response of the rotor depends on not only itself but also the dynamical characteristics of the structures that support it. In this paper, the coupling vibration characteristics of the rotor and supporting structure are studied using one simple rotor-supports model firstly, and then the dynamic stiffness of the typical supporting structure of an aero-engine is investigated in use of both numerical and experimental methods. While, one simulation strategy is developed to include dynamic stiffness of realistic supports in the dynamical analysis of the rotor system. The simulated and tested results show that the dynamic stiffness of the supporting structure not only depends on the structural parameters but also is related to the frequency of the excitation force. The dynamic stiffness is affected by the damping and inertia effect when the excitation frequency is high and closed to the resonance frequency of the support, which may decrease the dynamic stiffness sharply.More resonance frequencies may be induced and the critical speed could be reduced or increased.While higher vibration response peak and overload of the bearing may also be caused by the varied dynamic stiffness, which needs to be avoided in the design of the rotor-supports system.
基金Supported by the Major State Basic Research Development Program of China(2011CB706501)the National Natural Science Foundation of China(51276157)
文摘Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.
文摘The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.
基金Sponsored by the National Basic Research Program of China (Grant No. 2013CB632305)the National Natural Science Foundation of China (GrantNo. 51275125)
文摘In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.
文摘Dynamic stiffness matrix method is applied to compute vibration of hull girder in this paper. This method can not only simplify the computational model, but also get much higher frequencies and responses accurately. The analytical expressions of dynamic stiffness matrix of a Timoshenko beam for transverse vibration are presented in this paper. All effects of rotatory inertia and shear deformation are taken into account in the formulation. The resulting dynamic stiffness matrix combined with the Wittrick-Williams algorithm is used to compute natural frequencies and mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solved by the mode superposition method. The computational results are compared with those obtained from other approximate methods and experiment, and it indicates that the method is accurate and efficient.
基金supported by National Natural Science Foundation of China(Grant No.51175208)National Key Basic Research Program of China(973 ProgramGrant No.2011CB706803)
文摘The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.
