The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear bo...The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So,the effect of the axis force on the pile is considered.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
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...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
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
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
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
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
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
Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force lea...Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force leads to time-varying currents and air gap with a specific frequency,which makes the stiffness of appear decrease and even worsens control performance for the whole system.In this paper,an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness.The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method.The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing.Moreover,compared with the stiffness model without considering the variation of flux density across the air gap,the improved dynamic stiffness results are closer to the actual results.Through the dynamic stiffness measurement method of AMB,experiments of AMB in magnetically suspended molecular pump(MSMP)are carried out and the experimental results are consistent with theoretical analysis results.This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap,which improves the accuracy of the AMB stiffness analysis.展开更多
Under the same aerodynamic load,the load transmitted by the kick-reaction link actuator to the aircraft structure is only 1/5 to 1/3 of that of the point-to-point actuator,which can significantly reduce the weight of ...Under the same aerodynamic load,the load transmitted by the kick-reaction link actuator to the aircraft structure is only 1/5 to 1/3 of that of the point-to-point actuator,which can significantly reduce the weight of the structure,and is widely used in the main flight control surface of large and medium-sized civil airliners.In order to restrain the flutter of aircraft rudder surface,it is necessary to design the servo stiffness of the kick-reaction link actuator in the development stage,so that it can meet the dynamic stiffness requirement within the frequency range.Taking the actuator of a civil airliner as the research object,the dynamic stiffness modeling of elevator actuator is carried out on MATLAB platform,and the dynamic stiffness test is carried out to verify the correctness of dynamic stiffness modeling.The simulation and test results show that the actuator can meet the dynamic stiffness design requirements.展开更多
The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape...The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.展开更多
The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then...The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.展开更多
For dynamic stiffness enhancement, this paper presents a new method for synthesizing repetitive controllers capable of rejecting periodic vibration disturbance. Dynamic stiffness of the control system is analyzed. Dir...For dynamic stiffness enhancement, this paper presents a new method for synthesizing repetitive controllers capable of rejecting periodic vibration disturbance. Dynamic stiffness of the control system is analyzed. Direct and quadrature dynamic stiffness are defined for the repetitive controllers’ design. A trade-off method between the determinations of the controller’s parameters is necessary such that both the rejecting performance and stability can be achieved simultaneously. An illustrated example of a twin linear drive system is given to verify the performance of the proposed control design. The control performance of the present method is evaluated in the experimental disturbance rejecting control system, where the real-time control algorithms are implemented using a floating-point digital signal processor. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.展开更多
The author proposes to obtain the dynamic stiffness for the multiply-supported structures condensed to the supports in the frequency domain using the modal approach. Thus, previously proposed approach, requiring the d...The author proposes to obtain the dynamic stiffness for the multiply-supported structures condensed to the supports in the frequency domain using the modal approach. Thus, previously proposed approach, requiring the dynamic inertia matrix for the single-base system, is extended for the multiply-supported systems. Modal analysis is performed twice： once for the structural model with one base fixed, then for the same model with all bases fixed. The applicability of the proposed approach is checked for a sample two-base system enabling analytical solutions both in precise and modal approaches. The format of the condensed dynamic stiffness in the frequency domain enables to combine finite-element-method （FEM） codes like ABAQUS and Soil-Structure Interaction （SSI） codes like SASSI or CLASSI in a complex to perform effective soil-structure interaction analysis.展开更多
Taking the rubber torsion bushing of a certain type of all-terrain tracked vehicle as the research object,a theoretical model of torsional stiffness was proposed according to the non-linear characteristics of rubber c...Taking the rubber torsion bushing of a certain type of all-terrain tracked vehicle as the research object,a theoretical model of torsional stiffness was proposed according to the non-linear characteristics of rubber components and structural feature of the suspension. Simulations were carried out under different working conditions to obtain root mean square of vertical weighted acceleration as the evaluation index for ride performance of the all-terrain tracked vehicle,with a dynamics model of the whole vehicle based on the theoretical model of the torsional stiffness and standard road roughness as excitation input. Response surface method was used to establish the parametric optimization model of the torsional stiffness. The evaluation index showed that ride performance of the vehicle with optimized torsional stiffness model of suspension was improved compared with previous model fromexperiment. The torsional stiffness model of rubber bushing provided a theoretical basis for the design of the rubber torsion bushing in light tracked vehicles.展开更多
This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic p...This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.展开更多
To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis o...To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.展开更多
In this paper,the metal hydraulic engine mount (HEM) with the orifice is presented,the construction of HEM is consist of hydraulic cylinder and the spring on the bottom,its mechanical model is given and dynamics equat...In this paper,the metal hydraulic engine mount (HEM) with the orifice is presented,the construction of HEM is consist of hydraulic cylinder and the spring on the bottom,its mechanical model is given and dynamics equations are set up with considering kinematics conditions and continuous of fluid,the dynamics behavior of HEM including dynamic stiffness of fluid and transferability of HEM are studied here.The example of hydraulic engine mount is calculated,it is shown that the vibration reduction performance of the hydraulic engine mount of this paper is better.The analysis method of vibration reduction behavior for HEM in this paper can be used in designing of the reduction vibration devices and the HEM in this paper can be used in the practical engineering for reduction vibration.展开更多
基金Project supported by the National Natural Science Foundation of China ( No. 50278051) the Shanghai Key Subject Program
文摘The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So,the effect of the axis force on the pile is considered.
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.
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 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.
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.
基金Excellent Youth Science Foundation of China(Grant No.51722501)National Natural Science Foundation of China(Grant No.51575025)+1 种基金National Natural Science Foundation of China-Youth Science Foundation(Grant No.61603052)Opening Foundation of State Key Laboratory of Advanced Welding and Joining(Grant No.AWJ-20-R02).
文摘Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force leads to time-varying currents and air gap with a specific frequency,which makes the stiffness of appear decrease and even worsens control performance for the whole system.In this paper,an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness.The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method.The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing.Moreover,compared with the stiffness model without considering the variation of flux density across the air gap,the improved dynamic stiffness results are closer to the actual results.Through the dynamic stiffness measurement method of AMB,experiments of AMB in magnetically suspended molecular pump(MSMP)are carried out and the experimental results are consistent with theoretical analysis results.This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap,which improves the accuracy of the AMB stiffness analysis.
文摘Under the same aerodynamic load,the load transmitted by the kick-reaction link actuator to the aircraft structure is only 1/5 to 1/3 of that of the point-to-point actuator,which can significantly reduce the weight of the structure,and is widely used in the main flight control surface of large and medium-sized civil airliners.In order to restrain the flutter of aircraft rudder surface,it is necessary to design the servo stiffness of the kick-reaction link actuator in the development stage,so that it can meet the dynamic stiffness requirement within the frequency range.Taking the actuator of a civil airliner as the research object,the dynamic stiffness modeling of elevator actuator is carried out on MATLAB platform,and the dynamic stiffness test is carried out to verify the correctness of dynamic stiffness modeling.The simulation and test results show that the actuator can meet the dynamic stiffness design requirements.
基金Project (No. 9040831) supported by the Hong Kong Research GrantCouncil, China
文摘The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.
文摘The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.
文摘For dynamic stiffness enhancement, this paper presents a new method for synthesizing repetitive controllers capable of rejecting periodic vibration disturbance. Dynamic stiffness of the control system is analyzed. Direct and quadrature dynamic stiffness are defined for the repetitive controllers’ design. A trade-off method between the determinations of the controller’s parameters is necessary such that both the rejecting performance and stability can be achieved simultaneously. An illustrated example of a twin linear drive system is given to verify the performance of the proposed control design. The control performance of the present method is evaluated in the experimental disturbance rejecting control system, where the real-time control algorithms are implemented using a floating-point digital signal processor. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.
文摘The author proposes to obtain the dynamic stiffness for the multiply-supported structures condensed to the supports in the frequency domain using the modal approach. Thus, previously proposed approach, requiring the dynamic inertia matrix for the single-base system, is extended for the multiply-supported systems. Modal analysis is performed twice： once for the structural model with one base fixed, then for the same model with all bases fixed. The applicability of the proposed approach is checked for a sample two-base system enabling analytical solutions both in precise and modal approaches. The format of the condensed dynamic stiffness in the frequency domain enables to combine finite-element-method （FEM） codes like ABAQUS and Soil-Structure Interaction （SSI） codes like SASSI or CLASSI in a complex to perform effective soil-structure interaction analysis.
文摘Taking the rubber torsion bushing of a certain type of all-terrain tracked vehicle as the research object,a theoretical model of torsional stiffness was proposed according to the non-linear characteristics of rubber components and structural feature of the suspension. Simulations were carried out under different working conditions to obtain root mean square of vertical weighted acceleration as the evaluation index for ride performance of the all-terrain tracked vehicle,with a dynamics model of the whole vehicle based on the theoretical model of the torsional stiffness and standard road roughness as excitation input. Response surface method was used to establish the parametric optimization model of the torsional stiffness. The evaluation index showed that ride performance of the vehicle with optimized torsional stiffness model of suspension was improved compared with previous model fromexperiment. The torsional stiffness model of rubber bushing provided a theoretical basis for the design of the rubber torsion bushing in light tracked vehicles.
文摘This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.
基金Transformation Program of Science and Technology Achievements of Jiangsu Province(No.BA2008030)
文摘To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.
基金Supported by National Fund Committee for Study Abroad
文摘In this paper,the metal hydraulic engine mount (HEM) with the orifice is presented,the construction of HEM is consist of hydraulic cylinder and the spring on the bottom,its mechanical model is given and dynamics equations are set up with considering kinematics conditions and continuous of fluid,the dynamics behavior of HEM including dynamic stiffness of fluid and transferability of HEM are studied here.The example of hydraulic engine mount is calculated,it is shown that the vibration reduction performance of the hydraulic engine mount of this paper is better.The analysis method of vibration reduction behavior for HEM in this paper can be used in designing of the reduction vibration devices and the HEM in this paper can be used in the practical engineering for reduction vibration.
