Coupled Vibration Characteristics Research Articles

Analysis of longitudinal-vertical coupling vibration of four hub motors driven electric vehicle under unsteady condition

The influence of hub motor unbalanced magnetic force (UMF) on the vibration of electric vehicle under steady state conditions has been known, but under unsteady conditions, the hub motor UMF will change with the vehicle operation condition, and there would exist complex coupling vibration for the hub motors driven electric vehicle. Here, the longitudinal-vertical coupling dynamics of the four hub motors driven electric vehicle under unsteady condition is studied. Integrating the motor electromagnetic excitation and electric vehicle dynamics, a longitudinal-vertical coupling dynamics model of the four hub motors driven electric vehicle is established. Based on the variable switching frequency field-oriented control model, analytical model of the UMFs acting on the motor stator and rotor parts under unsteady condition are developed. For model validation, a four hub motors driven electric vehicle has been tested, the accuracy of the longitudinal-vertical coupling dynamics model established in this paper was verified. Then, longitudinal-vertical coupling vibration characteristics of the four hub motors driven electric vehicle under road excitation and coupling excitation are analyzed. The results show that the longitudinal and vertical movement of the four hub motors driven electric vehicle is coupled by hub motor. In addition, under unsteady condition, the motor UMFs will cause vertical vibration of the electric vehicle body and hub motor stator, the vibration shows order characteristics including low order harmonic hfc and inverter switching frequency sideband harmonic k1 fs±k2 fc ( fc = pn/60, fs is inverter switching frequency, k1 and k2 are positive integers, p is the number of pole pairs and n is motor speed.). The motor electromagnetic torque will cause longitudinal vibration of the electric vehicle body, the vibration shows order characteristics including harmonics fs±3 fc and 2 fs. The main harmonic of vehicle body pitch angle acceleration is 2 fs.

Brake-Induced Landing Gear Walk Vibration Analysis and Suppression Method Research

During aircraft braking, brake-induced frequent wheel slippage may cause coupling vibration between the antiskid brake system and landing gear. Brake-induced longitudinal coupled vibration is also known as “gear walk” vibration. Gear walk vibration not only reduces the structural life of the landing gear but also impairs the efficiency of the aircraft braking system. This paper focuses on the landing gear walk vibration mechanism and suppresses the method by modifying the antiskid brake control law. Firstly, a comprehensive multiwheel landing gear walk vibration model is developed. This model describes not only the longitudinal and vertically coupled vibration characteristics of the landing gear but also the dynamics of the aircraft braking system and the fuselage. Secondly, by simplifying the landing gear walk to the transverse vibration of a cantilever beam with a tip mass, the landing gear walk vibration mechanism is revealed in the frequency domain. Finally, a method to suppress landing gear walk vibration by modifying the pressure-bias-modulated (PBM) antiskid braking control law is proposed, which can solve the serious landing gear walk vibration problem caused by the conventional PBM control law. Simulation and experimental results show that the proposed method can suppress the landing gear walk vibration while improving braking efficiency.

Analysis of Vehicle-Bridge Coupling Vibration Characteristics of Curved Girder Bridges

When vehicles move on a bridge, the coupling effect between vehicles and bridges can affect driving safety and comfort, especially for curved bridges, therefore, choosing reasonable design parameters for curved bridges is crucial. In this article, a three-span curved continuous box-girder bridge was taken as the research object; the entire process of vehicle-bridge coupling vibration of highway curved girder bridges was conducted via numerical simulation and the vehicle-bridge coupling vibration analysis program Cmck 1.0 was developed. Then, the influence factors such as curvature radius, constraint mode, and vehicle characteristics on the vehicle-bridge coupling vibration of curved girder bridges were explored. The results showed that as the curvature radius increased, the dynamic response of the bridge offered a gradually decreasing trend and compared to the vertical dynamic response, the torsional response was more sensitive to the influence of the curvature radius. Different constraint methods significantly impacted the dynamic response of bridges, and the vertical and torsional dynamic responses of bridges under general constraint arrangement of straight bridges were increased compared to those under boundary conditions for curved beam bridges. As the axle load of the car decreases, the bridge mid-span vertical and torsional dynamic responses showed a decreasing trend. In contrast, the lateral dynamic response gradually increased.

Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing

This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark-β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity.

Analysis of Coupled Vibration Characteristics of Linear-Angular and Parameter Identification

Abstract A steady-state sinusoidal and distortion-free excitation source is very important for the accuracy and consistency of the calibration parameters of micro-electro-mechanical systems (MEMS) inertial sensors. To solve the problem that the current MEMS inertial measurement unit (IMU) calibration device is unable to reproduce the spatial motion of linear and angular vibration coupling, research topics on the coupling vibration characteristics and parameter identification for an electromagnetic linear-angular vibration exciter are proposed. This research paper used Ampere’s law and Lorentz force to establish the analytical expressions for the electromagnetic force and electromagnetic torque of the electromagnetic linear-angular vibration exciter. Then, the main purpose of this paper is to establish uniaxial and coupled vibration electromechanical analogy models containing mechanical parameters based on the admittance-type electromechanical analogy principle, and the parameter identification model is also obtained by combining the impedance formula with the additional mass method. Finally, the validity of the coupling vibration characteristics and the parameter identification model are verified by the frequency response simulation and the additional mass method, and the relative error of each parameter identification is within 5% in this paper.

Analysis of electromechanical coupling vibration characteristics of motor-gear system based on bond graph theory

In recent years, there has been a growing demand in the field of engineering systems for research on the vibration response of motor-gear systems under non-steady state conditions. However, conventional modeling and simulation techniques are primarily restricted to systems within a single energy domain. When dealing with intricate electromechanical coupling systems, the modeling process becomes increasingly intricate. Consequently, this study adopts bond graph theory as the foundation for analyzing the vibration characteristics of motor-gear coupling systems. In addressing the vibration issue of the motor-gear transmission system, a nonlinear bond graph model is established that takes into account the time-varying mesh stiffness, static errors, and tooth surface friction, among other nonlinear factors. Then, according to the coupling relationship between motor mechanical systems and electrical systems, the electromechanical coupling dynamic model of the motor-gear system is established using the method of bond graph. In addition, the state equation of the system is derived based on the bond graph model. Finally, the system is simulated using 20-sim software, and the electromechanical coupled vibration characteristics of the simulation results are analyzed. This article lays the foundation for the design and analysis of motor-gear coupling systems and multi-energy domain complex systems.

Bending-torsional coupling vibration characteristics of asynchronous motorized spindle considering electromechanical coupling and multi-excitation effect

For the asynchronous motorized spindle directly driven by the induction motor, the load-dependent slip ratio determines that its transient characteristics are sensitive to load. For the accurate evaluation of transient characteristics, it is necessary to deeply analyze the bending-torsional coupling vibration characteristics of the asynchronous motorized spindle with the non-ideal energy source. In this work, starting from energy conservation and clarifying the multi-physical field coupling mechanism, the bending-torsional coupling dynamic model is developed. Considering the speed fluctuation, the mass eccentricity excitation is deconstructed to explore its contribution to the coupling vibration. From the load-displacement relationship, the unbalanced excitation experienced by the journal from the bearing is modeled, considering the friction. According to the T-type equivalent circuit and mechanical characteristics of the induction motor, the electromagnetic torque considering power conservation is obtained. Furthermore, combined with Maxwell's stress formula, the electromagnetic excitation from electromagnetic torque and magnetic pull is obtained, considering the tangential and normal magnetic stress. Based on the projection and synthesis of forces, the semi-empirical mechanical cutting force model is employed to calculate the milling load. And a numerical algorithm for the fast acquisition of state-dependent delay is proposed. In particular, to reasonably characterize the energy characteristics in the system, the influence of structural vibration as an energy sink on the multi-physical field composed of mechanical, electromagnetic, and thermal fields is explored from the energy conservation. The proposed model was validated experimentally. The effects of electrical and mechanical parameters on the response are numerically discussed.

Coupled vibration characteristics of marine shafting with complex change of inclination under ice loads

With the intensifying exploitation of the resources and the waterway of the Arctic region in worldwide, the variable inclination propulsion system are gradually used in the ice-sailing ship, its design and strength study are of great engineering significance and application value. A variable inclination propulsion shafting with universal joint is introduced and its mechanical model is established in this paper. By combine torsional stress and inclination angle calculation, a decoupling algorithm based on Newmark is designed, and then the analysis of ice loads response in both frequency domain and time domain are completed. The results show that due to the complex triangle function relation among the various components of the shafting, there is an interaction between the propeller and the transmission shafting. In particular, when considering the dynamic change of inclination, nonlinear bending-torsional coupling vibration may occur and further lead to the enhancement effect of torsional vibration. Among the three working conditions defined by DNV, the bending-torsional coupling effect vary with rotation speed and inclination angle, and is mainly concentrated in high frequency bands. In the ice loads condition 2, with the largest time domain excitation amplitude and the smallest high order component, it’s vibration response is the strongest, and the change law of dangerous phase angle is similar to the bending moment. With the increase of initial inclination angle, the amplitude of low frequency vibration decreases, yet the amplitude of high frequency vibration increase. This trend is more obvious with the increase of rotation speed, and more high frequency resonance points appear in the condition 1 and condition 3.

Investigation of Rear Blisk Drum Dynamics Under Consideration of Multi-Stage Coupling

Abstract The analysis of the structural dynamics of multistage cyclic structures as linked components is required to model the interstage coupling. In turbomachinery, this can result in a collaboration between different compressor or turbine stages. This paper investigates the coupling between two rear drum blade integrated disk stages of an axial compressor to support the mechanical design process. Considering the vibration modeshapes of a multistage system, different components may coparticipate in the dynamics. For this reason, criteria to identify the modes affected by the coupling and to quantify this coupling are defined. This allows to distinguish between modes with interstage coupling, requiring the multistage system for their description, and uncoupled modes, involving a single stage. In addition, it is of interest to research methods to reduce the impact of the coupling on the vibrating system without drastically altering the geometry of the components. The vibration analyses of a two-stage compressor generalized geometry, representative of a compressor rear drum blisk, are presented as a study case. The use of a reducing method allows to describe the behavior of the nominal multistage system with a computationally efficient technique, enabling a parametric analysis of the stages' coupling. The investigation considers the effect of a set of geometrical and mechanical parameters on the dynamics, identifying the driving parameters of the coupled vibration characteristics.

Study on small modulus modified gear damage fault and electromechanical coupling vibration characteristics under multiple working conditions

The fault of transmission system seriously affects the life of robot joints, so it is urgent to study the crack of the displacement wheel set. Firstly, the tooth profile equation of the modified gear is established, and the time-varying mesh stiffness (TVMS) is obtained. Secondly, the multi-degree-of-freedom electromechanical coupling dynamic equation is established. Finally, the vibration displacement under steady state, start-up and shock conditions is analyzed. The results show that: (a)The positive displacement can increase TVMS, while negative displacement is the opposite. (b) The appearance of cracks accelerates the damage to two adjacent teeth. (c) The decrease of TVMS increases with the increase of crack depth. (d) The crack causes the gear pair to generate vibration shock, and the vibration displacement increases significantly in the case of broken teeth. (e) Statistical analysis of the vibration displacement reveals that the root means square value can detect early cracks, and the kurtosis index can predict life. (f) Cracks have a large effect on the transient process at start-up and shock, but the effect of cracks is weakened during no-load steady-state operation.

Analysis of Train-Track-Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle.

This paper introduces an innovative model for heavy-haul train-track-bridge interaction, utilizing a coupling matrix representation based on the virtual work principle. This model establishes the relationship between the wheel-rail contact surface and the bridge-rail interface concerning internal forces and geometric constraints. In this coupled system's motion equation, the degrees of freedom (DOFs) of the wheelsets in a heavy-haul train lacking primary suspension are interdependent. Additionally, the vertical and nodding DOFs of the bogie frame are linked with the rail element. A practical application, a Yellow River Bridge with a heavy-haul railway line, is used to examine the accuracy of the proposed model with regard to discrepancy between the simulated and measured displacement ranging from 1% to 11%. A comprehensive parametric analysis is conducted, exploring the impacts of track irregularities of varying wavelengths, axle load lifting, and the degradation of bridge stiffness and damping on the dynamic responses of the coupled system. The results reveal that the bridge's dynamic responses are particularly sensitive to track irregularities within the wavelength range of 1 to 20 m, especially those within 1 to 10 m. The vertical displacement of the bridge demonstrates a nearly linear increase with heavier axle loads of the heavy-haul trains and the reduction in bridge stiffness. However, there is no significant rise in vertical acceleration under these conditions.

Magneto-thermo-elastic coupling vibration and bifurcation characteristics of functionally graded rotating cylindrical shell

The magneto-thermo-elastic coupling vibration of rotating ferromagnetic functionally graded cylindrical shell is investigated in this paper. Based on the physical neutral surface theory and Donnell's theory, the expressions of kinetic energy and strain energy are obtained by introducing geometric nonlinearity. The magneto-thermo-elastic vibration equations of the rotating ferromagnetic functionally graded cylindrical shell in multi-physical field are derived via the Hamilton's principle. Considering the magnetization effect of ferromagnetic shell in magnetic field, the expression of magnetization force is obtained according to the nonlinear magnetic constitutive relation. For simply supported boundary conditions, Galerkin's method is used to obtain the discretized ordinary differential equations, and the static deflection of the shell under static load is solved. The steady-state response of the system during primary resonance and the stability of solutions are given by the multi-scale method and the Lyapunov stability theory. Through numerical examples, the characteristic curves and surfaces of amplitude are plotted, and the parameter ranges corresponding to regions of multi-valued solutions and stable solutions are determined. The system dynamics laws describing the coupling effect between multiple parameters such as force, magnetism, heat, and rotational speed are evaluated. The Global bifurcation diagrams and the maximum Lyapunov exponent spectrums under different control parameters are plotted to analyze the effect of parameter changes on the dynamic response of system. The results show that the vibration characteristics of the system are significantly influenced by the external physical fields, in addition to the shell size and material volume fraction. Slight changes in parameters can lead to violent changes in the dynamic response of the system, exhibiting intermittent, jumping, and chaotic characteristics.

Vibration characteristics of industrial robot joint servo transmission system based on electromechanical coupling

The complex electromechanical coupling effect of an industrial robot’s electromechanical system significantly influences the dynamic characteristics and stability of the joint servo transmission system. This study proposes a kind of electromechanical coupling dynamic model for the industrial robot’s joint servo transmission system, incorporating multiple parameters, and investigates the vibration response characteristics of the system. Firstly, an electromechanical coupling analysis of the industrial robot’s joint servo transmission system is conducted, simplifying it as a ‘motor-reducer-load’ system and establishing the corresponding electromechanical coupling vibration mathematical model. Secondly, a dynamic model of the robot’s joint servo transmission system is developed to analyze its speed characteristics. Finally, the model is used to analyze the electromechanical coupling vibration process of the joint servo transmission system with the introduction of mechanical and electrical parameters and other factors to obtain the vibration characteristics of the industrial robot joint servo transmission system under electromechanical coupling. The experimental results show that this model can better analyze the electromechanical coupling vibration characteristics of the joint servo transmission system, which is significant for improving the performance and fault traceability of the industrial robot joint transmission.

Investigation on the vibration mechanisms of a rotating FG-GPLRC shaft-disk-shell combined system

In this paper, a dynamics model of a rotating shaft-disk-shell (SDK) combined system is proposed to solve the vibration characteristics of a flexible rotor system. Unlike many previous researches that only studied shaft-disk systems, this paper simplifies the rotor into a combined structure of shaft, disk and cylindrical shell. The functionally graded graphene platelet (GPL) reinforced composites are innovatively applied in the disk to achieve the system lightweight. Timoshenko beam theory and first-order shear deformation theory are used to model the substructures. And the energy expressions of each substructure are derived based on the multi-body dynamics theory. Finally, the differential quadrature finite element method is used to discretize and reassemble the energy matrix to obtain the overall system’s motion differential equation. The model is proved to have excellent convergence and accuracy. Then the influence mechanism of GPL parameters, system geometry, etc. on the system’s coupled vibration characteristics is further explored, and important conclusions are drawn, like when the shell parameters h/R < 0.08 and l/R < 0.03, the system’s 3rd coupled natural frequency is insensitive to these parameters.

A 3-D finite element modeling method for time-varying rotor-support system based on rotating-fixed coordinates

The asymmetry of rotor systems is sometimes evident, such as keyed shafts, crack rotors, two-pole generator rotors and especially shaft-disk-blade systems. Meanwhile, the coupling vibration problem between rotor and support structure is becoming more and more prominent due to the light weight of aero-engines. The design and analysis method for the dynamic characteristics of time-varying rotor-support system with detailed structure is needed. Therefore, a modeling method is proposed by using 3-D finite element for time-varying rotor-support system based on rotating-fixed coordinates. The rotor is modeled in rotating coordinate system and the support structure is modeled in fixed coordinate system respectively. The force, energy and displacement between rotor and support structure are transmitted by bearing mechanical parameters. Thus, the time-varying characteristics of the system are expressed explicitly by bearing mechanical parameters, and the dynamic equation of time-varying rotor-support system can be obtained. Then, Floquet theory and Hill infinite determinant method are used to analyze quasi-mode frequency characteristics and stability of time-varying rotor-support system. The results of a typical asymmetric rotor-support system got by the proposed method were compared with existed methods, and more coupling vibration characteristics such as the coupling vibration of rotor axial motion and support plate bending, the coupling vibration of shaft bending and support plate torsion were obtained.

Analytical, numerical, and experimental methods to study thermo-elastic coupling inherent and vibration characteristics of a flexible rotor system

The thermal deformation of a flexible rotor system in a high-temperature environment causes changes in the inherent and vibration characteristics. A theoretical model of the flexible rotor was established based on the theory of thermal deformation, the assumed mode method, and the Lagrangian principle. The mode natural frequencies and shapes were explored in detail when the temperature of different nickel-based alloy rotor blades increased gradually (from 0 to 1200°C). The changes in the unstable speed points as the temperature gradually increased were studied based on the rotation speed–frequency diagram. In addition, experimental methods were performed. Mode and steady-state speed tests in a supported state were conducted. Mode experiments were completed on a five-blade rotor test rig with a thermal insulation device, and the acceleration frequency-domain signal showed that the natural frequency decreased with increasing temperature. Through steady-state speed experiments, it was found that the position of the unstable speed points moved forward, and the displacement amplitude increased after local heating.

Solid-liquid coupling of in-phase and out-of-phase vibrations for two piezoelectric disks

Theoretical analysis is used to solve the solid–liquid coupled vibration characteristics for two piezoelectric disks in a limited space and verified with experimental measurements. Based on the Navier–Stoke equation and equilibrium of motion, the Rayleigh-Ritz and energy methods were developed to analyze the solid–liquid coupled system. Following an entire systematic procedure, two piezoelectric disks immersed in hydrostatic compressible fluids were analyzed using the piezoelectric constitutive equation to perform the in-phase and out-of-phase vibration. The full-field, non-contact, optical technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), was applied to experimentally measure the vibration properties in a solid–liquid coupling system, including the mode shapes and resonant frequencies. The experimental results are presented in good agreement with the theoretical solutions and finite element calculations. Under the solid–liquid coupled system, the distributions of pressure fields and velocity vectors of fluids were also determined in the correspondent vibrating modes. Finally, it is interesting to show the tendency to close the same resonant frequency both on the in-phase and out-of-phase vibrations when the fluid depth increases. The research outcomes can provide a guide in the design of hydrostatic components.

Research on the Coupled Phase-Tuning Vibration Characteristics of a Two-Stage Planetary Transmission System

Mesh phasing has a dramatic impact on the static and dynamic behaviours of planetary gear systems. This research investigates the coupled phase-tuning mechanism of two-stage planetary gear systems and the corresponding relationship with the coupled vibration of the system. Due to the inherent meshing symmetry of the system, the phase-coupled tuning mechanism of the two-stage planetary system is derived based on meshing force relationships and coupling characteristics between different stages. The excitation and suppression relationships associated with the teeth number, harmonic order, and coupling vibration of the coupled system are clearly described. To study the effect of coupled phase tuning on the vibration response of a two-stage planetary gear system, a nonlinear dynamic model was established. The vibration responses under different tuning modes were calculated, and a coupled phase-tuning law for two-stage planetary systems was verified. Model 3 was used as a research tool to build a two-stage planetary transmission experimental platform, and the transverse vibration and torsional vibration of the first stage sun gear were analysed to further verify the correctness of the phase-coupling tuning law.

Dynamic characteristics analysis of a coaxial rotor system with shared bearing bore structure

The nonlinear dynamic model of a shared bearing bore-coaxial rotor system was established with nonlinear forces of the rolling bearings and squeeze film dampers considered, Cross coupling frequency was found in cross coupling vibration simulation. Numerical studies were conducted to reveal the mechanism of the coupling vibration for the shared bearing bore-coaxial rotor system. The coupling vibration characteristics and influencing factors of the shared bearing bore-coaxial rotor system were studied. The results show that the coupling vibration is featured by cross-excitation phenomenon and orbit which shows a “circle in circle” pattern. Besides, the angular stiffness of the shared bearing bore has great influences on the coupling vibration. However, the radial stiffness has almost no effect on the coupling vibration.

Analysis of Fluid-Structure Coupling Vibration Characteristics of Pipeline Transporting Bubbly Fluid Medium: With Application to Luxury Passenger Ship Life Area Pipeline

When pipelines are transporting bubbly fluid medium, due to the coalescence and breakage behaviours of the bubbles, the pressure distribution at the wall is not uniform and the structure response is more complex. The bubbly beverage pipeline in the life area of the luxury passenger ship is a typical scene of the pipeline transporting bubbly fluid medium. In this paper, the two-way fluid-structure coupling analysis is carried out on such a scene with the aid of ANSYS software and the PBM model is introduced to characterize the dynamic properties of bubbles. At the same time, the accuracy of this calculation method is verified by the scaling experiment. On this basis, the response of the pipeline under the excitation of bubbly fluid is calculated for different inlet velocities and gas volume fractions, and the effectiveness of common vibration damping measures is evaluated. The result shows that the addition of bubbles to the fluid medium has a significant effect on the distribution of the flow field in the pipeline during transport, and the vibration acceleration values of the pipe wall also increase significantly. This method enables accurate simulation of the vibration characteristics of bubbly fluid medium pipelines.