Displacement Excitation Research Articles

A mathematically-based study of the random wheel-rail contact irregularity by wheel out-of-roundness

The wheel-rail rolling contact finite element model has been generally considered to be a better choice for solving the high-frequency wheel-rail responses and local stress/strain states, compared to the traditional multi-body dynamics model. However, some thorny issues in the wheel-rail finite element analysis need to be solved or avoided, such as difficulties in geometry modelling especially for describing those multiple irregular wheel tread defects, possible computation termination by mesh distortion, and the balance between the computational efficiency and accuracy. Thus, an innovative computational method was proposed in this study, to transform the geometric irregularities induced by wheel out-of-roundness (wheel flat, tread spalling and wheel polygonization) to the randomly irregular displacement excitation of the wheel-rail contact, where the randomisation of the size, shape and distribution of wheel tread defects were considered. Based on geometrical relationships of the wheel-rail contact, the formulas of the wheel-rail contact displacement irregularity caused by various wheel tread defects, which was equivalent to the corresponding wheel-rail geometrical irregularity, were derived. And then the randomly irregular wheel-rail displacement satisfied to several various random distribution functions were generated by pseudo-random number sequence. Finally, the proposed method is demonstrated to facilitate applications of the explicit wheel-rail contact finite element model.

Vibration of structures subjected to vortex excitation and forced displacement excitation

Vibration of structures subjected to vortex excitation and forced displacement excitation

Dual-chamber pneumatically interconnected suspension: Modeling and theoretical analysis

Increasing concerns on the compromise between the vehicle ride comfort and roll stability call for the continuous developments of the vehicle suspension systems. This paper devotes a theoretical study in developing a dual-chamber pneumatically interconnected suspension (DCPIS) system to enhance the vehicle ride comfort while maintaining good anti-roll performance. A quarter car with the dual-chamber air suspension is modeled to study the vibration characteristics in terms of the vertical stiffness and the natural frequency of the suspension. Further, a novel DCPIS system of a vehicle is proposed. By assuming the displacement excitations are small from the equilibrium position, the vibration equations of the mechanical-pneumatic coupled system for a roll-plane 4-degree-of-freedom (4-DOF) half-car model with DCPIS are derived in frequency domain, which include the dynamic equations of the mechanical system, the linear differential equations of the dual-chamber air springs, and the pipes. Based on the system dynamic equations, both the vehicle free vibration modes and frequency response functions (FRFs) are compared between the half-car with the DCPIS and that with the standalone dual-chamber air suspension. The results show that the DCPIS can alleviate the vertical and roll vibration because it decreases the suspension stiffness and meanwhile increases the system damping ratio. The effects of the DCPIS system parameters on the vehicle bounce and roll vibration transmissibility properties are further investigated. In addition, the bounce and roll stiffness characteristics of the DCPIS are studied. It shows that its nonlinear bounce and roll stiffness behaviors have the advantages not only to alleviate shocks under extreme impact from the road obstacle and but also prevent rollovers in sharp steering maneuvers.

Fuzzy-neural network control for a Magnetorheological elastomer vibration isolation system

This paper proposes the design method of a fuzzy-neural network controller (FNNC) for a MRE vibration control system with sinusoidal excitations to improve the vibration attenuation. A semi-active fuzzy controller (FC) is employed to obtain the controlled force based on the feedback signals of the relative displacement and absolute displacement of the isolation structure. Then the dynamic performance experiment of MRE isolator is carried to obtain the output forces generated by the isolator with variable amplitude and frequency displacement excitation and controlled current. Based on the test results, BPNN (back propagation neural network) with good learning capability is employed to emulate the nonlinear relationship between output force of FC, excitation displacement, velocity and controlled current applied to the coil in MRE isolator. The acceleration responses of the system with FNNC are evaluated by physical experiments, and the results show that the proposed FNNC could achieve satisfactory control effect for the sinusoidal excitation, which also outperforms conventional FC. The reason is that the neural network controller can approximate the nonlinear function relationship among the controlled force, excitation displacement, velocity and controlled current. However, the function relationship with conventional FC is only considered as the linear function.

Performance Analysis of a Novel Magnetorheological Damper with Displacement Self-Sensing and Energy Harvesting Capability

External sensors are vulnerable to the external magnetic field, temperature, noise, and other factors in the semi-active control system based on magnetorheological (MR) damper, which not only reduces the reliability and stability but also increases the complexity, installation space, and system cost. Meanwhile, mechanical energy is generally dissipated as heat due to the friction between the cylinder and damper piston of the MR damper. To further broaden the applications of MR damper, it is essential to maintain excellent functions when the power supply is cut off in various emergencies. Based on this, a novel MR damper with displacement self-sensing and energy harvesting capability is proposed to solve the problems such as large structural size, high system cost, and vibration energy dissipation. Firstly, the structures of the MR damping, displacement self-sensing, and vibration energy harvesting are designed and integrated into the proposed MR damper. Then, the distribution of the magnetic flux density, displacement self-sensing voltage, and energy harvesting efficiency with a single induction coil and double induction coil is obtained using the finite element method. The experimental test system is set up and the performance of MR damping, displacement self-sensing voltage, and energy harvesting efficiency is experimentally tested. The experimental results show that the damping force reaches 513 N at the applied current of 0.25 A. At the same time, the amplitude of self-sensing voltage increases linearly with the increase of the amplitude of sinusoidal displacement excitation, and the displacement sensitivity comes up to 54.37 mV/mm. Moreover, the self-sensing voltage of the vibration energy harvesting component with a double induction coil is 2.512 V, and the energy harvesting efficiency is about twice than that with a single induction coil. It is found that the proposed MR damper, with a relatively compact structure and lower cost compared with traditional MR damper, not only promisingly achieves excellent dynamic damping performance but also simultaneously possesses displacement self-sensing ability and energy harvesting capability.

Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness

Roundness and surface waviness are main manufacturing errors on the components of single row angular contact ball bearings (ACBBs). An analytical study for vibrations of the ACBBs with coupling errors including the roundness and waviness can be useful for the vibration control of the rotating machinery. However, most previous works only focused on the single error modelling method. In this paper, an improved time dependent displacement excitation (TDDE) model is proposed to consider the coupling errors including the roundness and waviness on the inner and outer races of an ACBB. The TDDE model for the roundness and waviness is established by using a combination of several sinusoidal functions. A dynamic model in the previous study is improved to consider the influences of coupling errors including the roundness and waviness. The Hertzian contact theory and Dowson’s method are adopted to calculate the bearing contact stiffness. The time- and frequency-domain vibrations for the experimental and simulation results are compared to show some model validation. The influences of roundness orders and waviness amplitudes on the vibrations of the ACBB are analysed. The obtained results show that the coupling errors including the roundness and waviness have some influence on the time-domain impulse waveform and frequency-domain spectrum characteristics of the bearing accelerations. The differences of the vibrations between the coupling errors and sing error are from 4% to 42%. This paper can provide a useful guidance for the accurate diagnosis of surface imperfections in the ACBBs.

Vibration analysis of the axle bearings considering the combined errors for a high-speed train

Axle bearings are critical elements of high-speed trains. Although the quality and precision of axle bearings have been significantly improved, the manufacturing errors, such as the roundness and waviness errors, cannot be eliminated during their manufacturing processes. The axle bearings with the roundness and waviness errors have great influences on vibration performances of the high-speed trains. To obtain an in-depth understanding of the vibrations caused by the axle bearing with the combined errors considering both the roundness and waviness errors. This work conducts an improved analytical model for a high-speed train considering the axle bearings with the combined errors, which cannot be formulated by the previous train model considering single roundness or waviness errors. The combined errors are defined to include both the roundness and waviness errors. A new multiple cosine function is presented to model the combined errors. The time-depended force excitations produced by the combined errors are also considered in the dynamic model. A track irregularities model is utilized to formulate the road spectrum displacement excitations from the rail and roadbed. The influences of the error amplitude and order on the vibrations of high-speed train are analyzed. The results for the single roundness error model, single waviness error model, and combined errors model are compared to represent the superiority of proposed model. It depicts that this work can provide a more reasonable analytical method for understanding the vibrations of high-speed train considering the axle bearings with the combined manufacturing errors compared to the reported single error models.

Method for solving dynamic equilibrium equations based on displacement excitation

Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis. However, the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation. A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced. The dynamic equilibrium equation is decomposed into two parts, namely displacement excitation and velocity excitation, and precise integration and mode superposition methods are combined to solve the equation. Ritz vectors are then used to calculate the static response of the truncated modes of the structure, and a method for determining the number of participating modes is obtained. Using multi-degree-of-freedom systems as two computational examples, the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed. It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation.

Analytical modeling of axial oscillation-supported drillstrings in high-angle wells

Downhole vibrations generated from axial oscillation tools (AOTs) in axial oscillation-supported drillstrings (AOSDs) has become one of the efficient means of reducing friction and improving weight transfer during sliding operations in horizontal and extended-reach wells. Dynamic modeling of AOT-excited drillstrings is needed for validating the functionality of axial oscillation tools during surface tests and predicting their response under downhole conditions.An analytical model is presented in this study to predict the behavior of axial oscillation-supported drillstrings working under downhole and surface conditions. The model is useful to perform parametric studies, downhole data correlation and placement study of AOTs along the drillstring in horizontal and extended-reach wells. Unlike existing models, the nonlinear equation of motion is derived from a model damped in a viscous medium with Coulomb friction and subjected to displacement excitation. The model also accounts for the spring rate of the axial oscillation tool. The displacement excitation is obtained from the spring rate, which is a critical input to the model. The nonlinear damping is approximated with an equivalent viscous damping coefficient to obtain an analytical solution. The developed model in this study is validated with published experimental measurements obtained from field-scale drillstrings.Correlations between predicted and measured axial displacement and accelerations at different excitation frequencies, pressure drops and spring rates show an approximate average deviation of 14.5%. Also, results from this study strongly accentuates that flow rate is the most critical operating parameter for axial oscillation tools because it affects the amplitude of pressure drop, excitation force, and operating frequency of AOTs.

A two-degree-of-freedom string-driven rotor for efficient energy harvesting from ultra-low frequency excitations

The aim of this study is to report a two-degree-of-freedom (2-DOF) string-driven rotor to convert ultra-low frequency vibrations to high-speed rotation motion of a rotor, which enables the efficient exploitation of ultra-low frequency mechanical energy. The proposed rotor structure consists of a disk-shaped rotor, a spring and two pieces of string, featuring extremely simple configuration. Based on the proposed rotor, we designed an electromagnetic energy harvester (EMEH) to show the feasibility of utilizing the rotor to achieve improved energy harvesting performance. Experimental results showed that the fabricated harvester with various structural parameters could provide two peak power outputs and generate up to 9.4 mW power when actuated at 3 Hz by a displacement excitation with an amplitude of 8 mm. With the electric power converted from the treadmill vibration by the EMEH, a hygrothermograph could be continuously driven to work with full functionality. Under the manual operation, the harvester could also sustainably charge some portable electronic gadgets. The results of this study exhibit the promising potential of the proposed rotor in efficiently harvesting the ambient ultra-low frequency energy.

Highly sensitive transient reflection measurement in extreme ultraviolet region for tracking carrier and coherent phonon dynamics.

A highly sensitive method for detecting transient reflection in the extreme ultraviolet (XUV) region was developed on the basis of high-order harmonics for tracking carrier and coherent phonon dynamics. The use of lock-in detection and boxcar integration enables us to observe optical modulation (ΔR/R) as high as 1 × 10-4, and the data acquisition takes only four minutes. XUV transient reflections of bismuth exhibited exponential decay originating from excited carriers and periodic oscillation originating from A1g optical phonons. The linear power dependence of the electronic and phonon amplitudes indicated that one-photon excitation occurred under the experimental conditions. The cosine of the initial phase of the phonon oscillation revealed that a displacive excitation mechanism contributed to phonon generation. The phonon parameters obtained by the XUV and NIR probes were consistent even though their penetration depths were different. The result indicated that the XUV and NIR pulses probe the same excited region, which should be near the surface due to the short penetration depth of the NIR pump pulses. The present highly sensitive means of detecting XUV transient reflections in solid-state materials could be utilized for detecting attosecond dynamics in the future.

Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary

Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary

Entrainment phenomenon by forced displacement excitation in vortex induced vibration

Entrainment phenomenon by forced displacement excitation in vortex induced vibration

A dynamic modelling method of a rotor-roller bearing-housing system with a localized fault including the additional excitation zone

Rotor-roller bearing-housing systems (RBHSs) are widely utilized in many industrial machinery, such as aero-engines, high speed trains, wind turbine, etc. A clearly investigation of vibrations for the RBHSs is very valuable for condition monitoring and fault detection applications for the above industrial machines. A new analytical dynamic model for a RBHS is conducted, which can consider the time dependent additional contact zone excitation caused by the fault on the raceways, deformable interface between the outer raceway and housing, lubricating oil film, and deformable rotor and housing. The time dependent addition contact zone is determined by Hertzian contact theory and the relative relationship between the roller and fault. Influences of the rotor speed, roller load and fault length on the additional excitation zone are studied. The ratio of the additional excitation zone to the fault length is also discussed. To consider the complex profiles of the outer raceway, an analytical method combined with a slice method and an integral method is used to obtain the total interface stiffness at the interface. Influences of the housing materials and height on the total interface stiffness are analyzed. A time dependent displacement excitation model with a half-sine function profile is applied to formulate the time dependent displacement excitation due to the fault. The dynamics of the RBHS from the presented model with the additional excitation zone are compared with those from the previous model without the additional excitation zone. An experimental study is presented to validate the proposed model. Influences of the housing materials, housing height, additional excitation zone of the fault, and fault length on the dynamics of the RBHS are studied. The simulation results provide that the presented model can give an accurate simulation method for investigating the dynamics of the RBHS with a localized fault.

Energy harvesting from a novel contact-type dielectric elastomer generator

A novel contact-type (CT) dielectric elastomer generator (DEG), which can harvest energy from two dielectric elastomer membranes (DEMs) under a regular contact-type displacement excitation, is proposed and studied in this paper. The operating principle of the proposed CT DEG is introduced with its electrical outputs under a contact being derived. This is further verified by capacitance and output voltage measurement experiments, thus making the theoretical analysis credible. Furthermore, the energy harvesting (EH) performance of the CT DEG in simulated contact environments is fully investigated through the conducted numerical simulations, and the influences of the excitation parameters, the system structure parameters, the pre-stretched ratio of DEM and input voltage are studied. It was found that the system demonstrates a better EH performance under a larger amplitude and a smaller period of the excitation, and the system EH performance can be enhanced by increasing the plate’s radius, the pre-stretched ratio, the input voltage or decreasing the DEM’s radius. By adjusting these parameters appropriately, the system output voltage can be 10 times higher than the input voltage, and the system output power can be achieved as high as 22.94 mW under a given displacement excitation. The research results can provide some effective solutions for the design and improvement of the proposed CT DEG in contact-type energy harvesting.

Angular displacement modeling and excitation signal optimization for a stepping giant magnetostrictive rotary actuator.

Giant magnetostrictive rotary actuators (GMRAs) can realize rotary motion in large scale and with high precision. A series of rectangular voltage signals organized in strict order exerted on GMRA helps its clamping mechanism and driving mechanism complete specific actions such as clamping, loosening, and actuating, thus leading to the stepping output of the rotor. In order to describe the overall performance of GMRA, an angular displacement model is established, which can be divided into four parts, namely, the current model, magnetic field model, output force model, and vibration model. The experimental results indicate that the established model agrees well with the actual performance of GMRA in operating conditions. After that, utilizing the established model, simulations are conducted to analyze the angular response of GMRA. According to the simulation results, the order of driving signals is optimized, making the maximum driving frequency rise from 160 Hz to 210 Hz, while the peak angular speed of GMRA reaches 70.77 mrad/s. The modeling and optimization methods proposed in this paper can be helpful for the structural optimization and controller design of GMRA as well.

A Two-Dimensional Axisymmetric Finite Element Analysis of Coupled Inertial-Viscous-Frictional-Elastic Transients in Magnetorheological Dampers Using the Compressible Herschel-Bulkley Fluid Model

It has been challenging to accurately predict the unique characteristics of magnetorheological (MR) dampers, due to their inherent nonlinear nature. Multidimensional flow simulation has received increasing attentions because it serves as a general methodology for modelling arbitrary MR devices. However, the compressibility of MR fluid which greatly affects the hysteretic behavior of an MR damper is neglected in previous multidimensional flow studies. This paper presents a two-dimensional (2D) axisymmetric flow of the compressible Herschel-Bulkley fluid in MR dampers. We simulated the fully coupled inertial-viscous-frictional-elastic transients in MR dampers under low-, medium- and high frequency excitations. An arbitrary Lagrangian-Eulerian kinematical description is adopted, with the piston movements represented by the moving boundaries. The viscoplasticity and compressibility of MR fluid are respectively modeled by the modified Herschel-Bulkley model and the Tait equation. The streamline-upwind Petrov–Galerkin finite element method is used to solve the model equations including the conservation laws and mesh motion equation. We tested the performances of an MR damper under different electric currents and different frequency displacement excitations, and the model predictions agree well with the experimental data. Results showed that the coupled transients of an MR damper are frequency dependent. The weak compressibility of MR fluid, which mainly happens in the chamber rather than in the working gap, is crucial for accurate predictions. A damper’s transition from the pre-yield to the post-yield is essentially a step-response of a second order mass-spring-viscous system, and we give such step-response a detailed explanation in terms of mass flow rate.

Study on Vibration Characteristics of Cables Excited by Lateral Displacement of Ends

Considering the axial vibration, the partial differential nonlinear vibration equations of the cable excited by the lateral displacement of the end is established. The Galerkin method is used to perform the modal truncation and transform the equations into the ordinary differential nonlinear equations. The typical examples are selected and the vibration characteristics are studied by numerical simulation. The conclusions of the study are as follows: when the frequency ratio is close to 2, the resonance phenomenon occurs. When the frequency ratio is greater than 3, the nonlinear characteristic is obvious. The amplitude of the in-plane vibration of the cable increases with the increase of the excitation amplitude, and small displacement excitation at the end causes large amplitude vibrations in the cable surface. The initial disturbance outside the plane is introduced. When the excitation frequency is close to 2.1 times the natural frequency of the in-plane vibration, the resonance phenomenon occurs and the amplitude is large.

A fault dynamic model of high-speed angular contact ball bearings

Angular contact ball bearings (ACBBs) are widely used in rotary machines especially in high-speed rotating machines because of their excellent properties. However, the traditional dynamic model of a rolling bearing is mainly applied to simulate the dynamic response at low speed, and uses the simple displacement excitation function to characterize the fault, thus its accuracy will decrease under high speed condition. Aiming at the shortcomings of the traditional model, a new high-speed fault dynamic model of ACBB is proposed by considering the influences of centrifugal force, gyroscopic moment and time-varying contact angles on the rolling element under high-speed running and using a B-spline fitting displacement excitation method to represent the fault excitation. With this model, high-speed dynamic responses under different fault sizes and rotation speeds are calculated by the Runge–Kutta method and Newton– Raphson method. Then the corresponding time and frequency domain characteristics are analyzed. From the simulation results, it can be seen that all the simulated acceleration signals of ACBBs are more in line with the actual situation than the traditional model, especially for the shape of an impulse. Finally, the effectiveness and correctness of the proposed model are verified by the experiment on aero-engine spindle bearings.

Damping Term Related to Ground Velocity Affects Structural Response Calculated by Displacement Excitation

The structural seismic responses obtained by a displacement excitation approach and an acceleration excitation approach respectively are sometimes significantly different. Regarding the causes of this difference, researchers have not provided a plausible explanation. For the aim of determining the effects of damping terms related to ground velocity on the structural seismic response calculated by the displacement excitation approach, the mode superposition method and Duhamel’s integral are applied to solving the dynamic equilibrium equations. The analysis indicates that the difference of structural seismic response caused by the method of displacement excitation, obtained by integral acceleration is small. When calculating the structural seismic response, a time step for displacement excitation and acceleration excitation can be assumed as the same value.