Vibration Displacement Amplitude Research Articles

A novel OPR-free method for blade tip timing based on adaptive variable reference blades

Monitoring rotor blade vibrations is imperative in aero-engine testing and service. Blade tip timing (BTT), a promising technique for such monitoring, assesses the operational status of rotor blades through non-intrusive measurement of blade tip displacement. Traditional BTT technology relies on the Once-Per-Revolution (OPR) probe, which poses installation challenges and introduces measurement uncertainties in practical applications. This paper introduces a novel OPR-free approach, employing Adaptive Variable Reference Blades (AVRB) for non-intrusive measurement of rotor blade vibrations. The method assumes a stochastic mistuning of blades within the same stage, resulting in non-simultaneous resonance of blades at a given speed. In each revolution, the vibration level of individual blades is determined by assessing the deviation between the average speed of a blade, as measured by two adjacent BTT probes, and the average speed across the entire circumference. Consequently, a non-vibrating blade is adaptively identified and selected as the reference blade. The relative vibration levels among blades vary dynamically during different revolutions, influenced by mistuning features, leading to variability in the reference blades. These adaptive variable reference blades can then replace the OPR probe, aiding in the computation of vibration displacement and further parameter identification of blades. To validate the effectiveness of the proposed method, a five-degree-of-freedom numerical model is utilized for simulation. Additionally, experiments involving both a five-bladed disk and an eight-bladed disk are conducted to validate the proposed approach. Numerical simulations and two sets of test results demonstrate a fundamental agreement between the blade vibration displacement calculated using the proposed method and the outcomes obtained through the traditional BTT method with OPR. The relative error in the identified blade vibration frequency derived from the blade vibration displacement, as determined by both methods, does not exceed 1 %. Additionally, the relative error in the amplitude of the blade vibration displacement is within the range of 10 %.

Investigation on the Damping Effect of FST System under Moving Load Using the Track–Tunnel-Layered Saturated Ground Model

In this paper, a single-tier beam-spring-damping system and a two-tier beam-spring-damping system are adopted to simulate the FT (fixed track) and FST (floating slab track) system, respectively. The tunnel is modeled as an infinitely long Euler—Bernoulli beam embedded in the layered saturated soil. By solving the governing equations of the saturated soil and employing the TRM (transmission and reflection matrices) method, the frequency response function of the tunnel-layered saturated soil model is obtained. Making use of the interaction between the tunnel and track systems, the track system is coupled with the tunnel-layered saturated ground model. The solutions for the dynamic response of the track system–tunnel-layered saturated ground model under moving loads in the time–space domain are obtained using the inverse Fourier integral transform. To evaluate the damping effect of the FST system on the vibration of tunnel and soil, four damping coefficients are defined and the vibration results of the FT system–tunnel-layered saturated soil model are compared with those of the FST system–tunnel-layered saturated soil under different moving loads and soil conditions. The numerical results show that both the vibration displacement and acceleration amplitude are attenuated after using the FST system, and the damping coefficient of acceleration is about 30% greater than that of the displacement. In addition, the damping effect of the FST system on the ground surface vibration is associated with the embedded depth of the tunnel and the soil stiffness.

Evaluation on the possibility of sound conduction independent of tympanic air cavity for severe tympanic adhesion patients by finite element analysis.

Background: For patients with severe tympanic adhesion, reconstructing the tympanic air cavity is often challenging, resulting in poor hearing reconstruction outcomes. Therefore, establishing a sound conduction pathway independent of the tympanic air cavity may be a viable method for reconstructing hearing in these patients. Purpose: The objective of this study was to evaluate the feasibility of sound conduction independent of the tympanic air cavity (i.e., replacing the original cavity with a tympanic vibrating material) using finite element analysis. Methods: We established a sound-structure coupling finite element model of the tympanum vibration conduction system, which included the tympanic membrane (TM), ossicular prosthesis, and tympanic vibrating material. This model was used to simulate middle ear vibrations under sound pressure, and we extracted the frequency response curve of the ossicular prosthesis' vibration displacement amplitude to evaluate the sound conduction effect of the middle ear. Next, we adjusted the structural and mechanical parameters of the tympanic vibrating material to analyze its impact on the sound conduction effect of the middle ear. Finally, we compared the frequency response curve of the stapes footplate in normal subjects to evaluate the feasibility of sound conduction independent of the tympanic air cavity. Results: The Shell tympanic vibrating material had a better vibration conduction effect compared to solid or porous tympanic vibrating material. The vibration amplitude decreases with the increasing elastic modulus of the tympanic vibrating material. Implantation of 40kPa-shell tympanic vibrating material had the lowest hearing loss less than 5dB, and the hearing loss with 1MPa-porous tympanic vibrating material was largest and less than 25dB. Conclusion: Our study suggests that replacing the tympanic air cavity with a tympanic vibrating material is feasible. The establishment of a sound conduction pathway independent of the tympanic air cavity could potentially provide a method for hearing reconstruction in patients with severe tympanic adhesion.

Analytical Simulation of the Microbubble Collapsing in a Welding Fusion Pool.

This paper explains the use of remote ultrasound vibration at the optimum position and frequencies to vibrate plates under welding, with the aim of initiating cavitation in the molten pool area. It has been shown in the literature that ultrasound cavitation changes microstructure morphology and refines the grain of the weld. In practice, the plates are excited through narrow-band high-power ultrasound transducers (HPUTs). Therefore, a theoretical investigation is carried out to identify the plate-mode shapes due to the ultrasound vibration aligned with the frequency bandwidth of HPUTs available in the marketplace. The effect of exciting the plate at different locations and frequencies is studied to find the optimum position and frequencies to achieve the maximum pressure at the area of the fusion zone. It was shown that applying the excitation from the side of the plate produces an order of 103 higher vibration displacement amplitude, compared with excitation from the corner. The forced vibration of cavitation and bursting time are studied to identify vibration amplitude and the time required to generate and implode cavities, hence specifying the vibration-assisted welding time. Thus, the proposed computational platform enables efficient multiparametric analysis of cavitation, initiated by remote ultrasound excitation, in the molten pool under welding.

Effect of Machined Tooth Surface Mixed Lubrication Sliding Wear on Gear Dynamic Characteristics

Tooth surface wear causes variation in meshing stiffness and transmission error of the gear system and further causes the fluctuation of dynamic characteristics. In this study, a dynamic behavior prediction model of the gear transmission system was established, which considered the machined tooth surface wear based on the mixed lubrication sliding wear model and the gear tribology-dynamic model. The gear pair wear characteristics along the meshing line were analyzed through simulations, and the impacts of wear conditions, operating torque, and speed on the dynamic characteristics of the gear transmission system with tooth surface wear were discussed. The results demonstrated that the transmission error and the vibration displacement amplitude of the gear system had increased gradually with the increase of the wear degree and that the fluctuation intensified. The fluctuation of gear dynamic characteristics increased with the increase in torque, and the fluctuation of gear dynamic characteristics initially increases and then decreases with the increase in rotating speed.

Design of Longitudinal-Torsional Transducer and Directivity Analysis during Ultrasonic Vibration-Assisted Milling of Honeycomb Aramid Material.

This paper presents a longitudinal-torsional transducer for use during the ultrasonic vibration-assisted milling (UVAM) of honeycomb aramid material. The mechanism of longitudinal-torsional conversion was analyzed to guide the design of a vibration transducer. The transducer features five spiral grooves around the front cover plate, which function under the excitation of a group of longitudinal piezoelectric ceramics. A portion of the longitudinal vibration was successfully converted into torsional vibration. The resonant frequency, longitudinal vibration displacement and torsional amplitude at the top of the disk milling cutter were 24,609 Hz, 19 μm and 9 μm, respectively. In addition, the directivity of the longitudinal-torsional transducer was theoretically analyzed. Compared with conventional milling, UVAM with the longitudinal-torsional could significantly reduce the cutting force (40-50%) and improve the machining stability.

Case study: Analysis of acoustic-structure coupling noise characteristics of the exhaust muffler of an internal combustion engine

Exhaust noise produced by internal combustion engines is one of the main problems of vehicle noise, and exhaust mufflers can significantly improve this problem. In fact, the sound waves inside the exhaust muffler will cause the muffler shell to vibrate, causing the muffler to produce shell radiation noise. Therefore, it is necessary to carry out the acoustic-structure coupling analysis of the muffler. This paper improved the design of a prototype straight-through perforated pipe-resistant muffler (design A) and designed a straight-through perforated pipe-resistant muffler with a corrugated lining (design B). Structural modal analysis, acoustic modal analysis, and transmission loss analysis of the two mufflers were carried out. The coupling of the acoustic cavity and structure was considered, and the radiation noise of two kinds of resistant mufflers was comparatively analyzed by the direct-boundary-element method. The acoustic radiation of two kinds of resistant mufflers was studied. The pressure loss of the two kinds of mufflers was studied by aerodynamic analysis. The results suggested that the design B muffler effectively improved the noise reduction performance of the prototype muffler, reduced the vibration displacement amplitude of the shell, and reduced the sound power level of the design A muffler.

Research on Dynamic Response and Construction Safety Countermeasures of an Adjacent Existing Line Foundation under the Influence of a New Railway Line

The excavation of a new high-speed railway causes the side slope adjacent to the existing line foundation to become airborne, and the excessive dynamic deformation or cumulative deformation caused by the dynamic load of trains will affect the normal service of the subgrade, even leading to its instability. To date, there are no relevant experimental data regarding this, and there is also a lack of corresponding specifications. The only available numerical simulation research results need to be verified in practice. Therefore, this study relies on the Shanghai–Nanjing intercity high-speed railway construction project adjacent to the existing Beijing–Shanghai line to carry out a subgrade dynamic response test to ensure the safe operation of the existing line. The test obtained the vibration displacement, frequency, acceleration, and other parameters of the existing subgrade construction in three stages: subgrade excavation, pile formation, and subgrade filling. From the test results: During the test period, the vertical surface vibration displacement and vibration acceleration have a certain attenuation along the depth direction. In the stage of subgrade excavation, the vibration displacement and vibration acceleration generated are the largest. The vertical vibration displacement amplitude reaches 1.9 mm, and the horizontal vibration displacement amplitude reaches 0.15 mm. The vibration frequency of the roadbed under the action of the train load is concentrated in the range of 0–50 Hz, and the vibration energy at the peak value is relatively large, which reflects the load action frequency of the train, and the peak value is mainly concentrated in the range of 20–40 Hz. These results show that the maximum vibration response peak appears in the subgrade excavation stage, that is, the most dangerous stage of the existing subgrade. The vibration acceleration and vibration displacement of each dynamic response parameter are important in that they reflect the dynamic performance of the subgrade and establish the index control standard, which can be used as a control index for roadbed dynamic stability monitoring. The dynamic test of the subgrade state provides data support for the reasonable opening of the construction skylight and the protection of the excavation slope. Taking into account the impact of piling vibration, technical measures such as static pressure, jumping construction, and setting up stress relief holes are adopted. The test results and engineering measures ensure the safe operation of the existing subgrade, and have important theoretical significance for guiding the construction of the new subgrade adjacent to the existing line.

Analysis of Nonlinear Vibration Characteristics of the Concentric Face-Gear Split-Torque Transmission System

The concentric face-gear split-torque transmission system (CFGSTTS) is a new type of transmission that has significant applications in helicopter main gearboxes. To study the influence of various parameters on the dynamic characteristics of the CFGSTTS, a 23-degree-of-freedom translation-torsion nonlinear dynamic model was established based on the lumped parameter theory. The model includes tooth backlash, error excitation, time-varying meshing stiffness with meshing phase difference, meshing damping, and elastic support deformation. The excitation conditions for the time-varying meshing stiffness of face-gear pairs were calculated based on the strain energy theory. The bifurcation characteristics of the system with different parameters were obtained by the nonlinear dynamics numerical analysis method. The research shows that the system exhibits rich vibration response characteristics at different rotating speeds. The amplitude of the vibration displacement in the system bifurcation diagram increases significantly with the increase of the tooth backlash and input torque, whereas the amplitude decreases constantly with the increase of the meshing damping. The critical rotational speed at which chaotic motion occurs increases significantly with increasing input torque and damping ratio but decreases with increasing tooth backlash. The bearing clearance has a weak influence on the vibration displacement amplitude of the system and the speed range of chaotic motion.

Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

A Magnetoelectric Hybrid Hydraulic Damper for the Mining Robot Suspension System

In order to improve the damping and controllability of the mining robot suspension system, a new magnetoelectric hybrid suspension hydraulic damper, which is a semiactive suspension damper, is proposed based on the traditional hydraulic damper by introducing the magnetic-electric hybrid suspension structure. The structure and working principle of the damper are introduced, respectively, and the mathematical models of the equivalent stiffness and equivalent damping of the system are calculated by the magnetic circuit method and the oil circuit method, while AMESim/Simulink cosimulation is carried out. In order to test the damping performance, a prototype of the magnetoelectric hybrid suspension hydraulic damper was fabricated. The results show that the vibration displacement amplitude can be reduced by 20% and the vibration acceleration amplitude can be reduced by 10% by adjusting the stiffness and damping of the system due to the magnetoelectric hybrid suspension structure. Moreover, the experimental results are consistent with the simulation results, which verify the effectiveness and superiority of this type of damper.

Characterization of hydrodynamic properties from free vibration tests of a large-scale bridge model

To accurately predict the dynamic response of a structure subjected to fluid induced loading, a thorough understanding of the dynamic properties (mass, stiffness, and damping) and associated interactions is required. Limited data are available to characterize dynamic fluid–structure interactions. Data are particularly limited for large-scale and flexible structural models. This article reports the results of the first free vibration tests of a dynamic large-scale laboratory highway bridge superstructure model. The dynamic response characteristics of the model were extracted and analyzed from free vibration tests under varying levels of water submersion and for different horizontal substructure flexibilities. The nature of the damping response was identified based on the empirically measured logarithmic decrements of the model’s free vibration displacement amplitudes, and a suitable equation of motion (EOM) was subsequently developed. Using the classical fourth-order Runge–Kutta method, the EOM was solved for the different test trials and the dynamic properties of the model were obtained through an optimization approach. The concept of added mass was introduced to explain the observed decrease in natural frequency with increasing levels of water submersion. Finally, added mass factor was computed for the case where the water level was even with the top of the bridge superstructure model. This study provides a suitable EOM needed for numerical simulations of this and similar models that study fluid–structure interaction and also provides a methodology for establishing the structural dynamic properties of generalized hydrodynamic analytical models.

Design of a Long-stroke Low-frequency Sound Device

In order to improve the radiation performance of low-frequency sound device, a design method for a long-stroke low-frequency sound device is proposed, which mainly involves the design of the drive structure and radiation structure and the drive structure is designed with an electric long stoke. The flat plate and conical structures of piston plate of radiation structure are compared, and a long-stroke radiation structure with a low-damping guide support motion pair uniformly distributed in the circumferential direction is proposed. The numerical simulation results show that, with six straight-line bearings circumferentially and uniformly distributed, the displacement and stress distribution of piston plate are better than those of piston plate with three straight-line bearings installed in the same manner. The sound device is further tested in the experiment, and it is found that the vibration displacement amplitude at the center of piston plate is 3.9 mm (20 Hz), and the maximum sound pressure level of 40 Hz is found at the location 10 m from the center of sound device along the axial direction, reaching 105.3 dB.

Study on the bending vibration of bimorph rectangular transducer based on type 2-2 piezoelectric composites

In order to improve the acoustic radiation capability of piezoelectric ultrasonic transducer in gas, a bimorph rectangular transducer based on type 2-2 piezoelectric composites is proposed in this paper, which is composed of two piezoelectric composite rectangular slices with thickness polarization. First, the bending vibration of the rectangular transducer is divided into two bending vibrations of the thin rods in the x and y directions using the equivalent elastic method. When the mechanical coupling coefficient is introduced and combined with the anisotropic piezoelectric equations, the resonance frequency equations of the thickness-polarized transducer are derived with simply supported boundary conditions. Then the bending vibration of the transducer is numerically simulated. The results show that the resonance frequency obtained by the analytical method is in good agreement with the numerical simulation results. Finally, the influence of geometrical size and two-phase volume ratio on the bending vibration performance of the transducer is analyzed. Compared with the piezoelectric bimorph transducer, the piezoelectric composite bimorph transducer has a larger bending vibration displacement amplitude, a larger transmitting voltage response, a lower resonant frequency and better acoustic radiation capability.

Pipe-soil vibration characteristics of natural gas pipelines during the pigging process

During the pigging process in long-distance natural gas transportation pipelines, the pig is easy to block and cannot be located accurately, resulting in serious economic losses. The analysis of pipe and soil vibration rule can be used as the basis for pig positioning. How to locate accurately the pig has become an urgent problem. In this study the coupled pipe-soil vibration model under the pigging action is proposed, and a three-dimensional symmetric pipe-soil vibration finite element model is established through ABAQUS. The influence of the pig running velocity and the friction coefficient of the inner surface on the vibration of the pipeline, as well as the influence of the propagation direction and the soil elastic modulus on the vibration propagation of the soil are studied. The research results show that the displacement amplitude of pipeline vibration increases with the increase of the running velocity of the pig, and at 0.8 m/s, the displacement reaches a peak of 27 μm. At the same time, the amplitude of pipe displacement increases as the friction coefficient between the pig and the pipeline increases. In the soil different directions, it is concluded that at 200 mm, the maximum displacement amplitude in the 45° direction can reach 15 μm. For the soil elastic modulus, when the propagation distance is 200 mm in soil with an elastic modulus of 10 MPa, the vibration velocity is significantly higher than that in other soils, and the maximum can reach 70 μm/s. Under the same conditions, the elastic modulus in the soil with an elastic modulus of 50 MPa, the maximum vibration velocity is 27 μm/s, indicating that the elastic modulus of the soil has a greater influence on the vibration velocity.

Transmission of bee-like vibrations in buzz-pollinated plants with different stamen architectures

In buzz-pollinated plants, bees apply thoracic vibrations to the flower, causing pollen release from anthers, often through apical pores. Bees grasp one or more anthers with their mandibles, and vibrations are transmitted to this focal anther(s), adjacent anthers, and the whole flower. Pollen release depends on anther vibration, and thus it should be affected by vibration transmission through flowers with distinct morphologies, as found among buzz-pollinated taxa. We compare vibration transmission between focal and non-focal anthers in four species with contrasting stamen architectures: Cyclamen persicum, Exacum affine, Solanum dulcamara and S. houstonii. We used a mechanical transducer to apply bee-like vibrations to focal anthers, measuring the vibration frequency and displacement amplitude at focal and non-focal anther tips simultaneously using high-speed video analysis (6000 frames per second). In flowers in which anthers are tightly arranged (C. persicum and S. dulcamara), vibrations in focal and non-focal anthers are indistinguishable in both frequency and displacement amplitude. In contrast, flowers with loosely arranged anthers (E. affine) including those with differentiated stamens (heterantherous S. houstonii), show the same frequency but higher displacement amplitude in non-focal anthers compared to focal anthers. We suggest that stamen architecture modulates vibration transmission, potentially affecting pollen release and bee behaviour.

Dynamic Characteristics of a Misaligned Rigid Rotor System with Flexible Supports

A misaligned rigid rotor system with flexible supports differing from the traditional flexible rotor system, which refers to its practical rotating center line determined by supports offset from the theoretical one, often suffers support structure damage risk. In the present work, the dynamic characteristics of a misaligned rigid rotor system with flexible squirrel cage supports are focused, and the vibrations and the stress of its support structures under different misaligned offsets are investigated with experimental and simulated analysis. The finite element model for a rigid rotor system with flexible supports in a scaled test rig is established, and its strain energy distribution is analyzed to find that the first two modes of the system are referred to rigid-body modes and the strain energy is mainly distributed on the squirrel cage supports. Based on the analysis results, a rigid-flexible coupling dynamic model is proposed through a data exchange between ADAMS and ANSYS and validated by measurements. The misaligned conditions are focused on, and the influences of misalignment on the vibrations of the rigid rotor system and the reaction force and stress of its support structures are investigated analytically and experimentally. The results from simulation agree very well with the measurements and reveal that the static stress of squirrel cage increases just about proportionally with misalignment levels, but the vibration displacement amplitudes and stress amplitudes show very little change. The more serious the misaligned condition, the higher the static stress of the squirrel cage. Because misalignment will bring out the additional reaction forces in the misaligned direction, it will further result in higher stress and even more serious damage risk for the flexible supports than other parts in the rigid rotor system.

Diagnostics of Bridge Bed Sections and Approaches in Zones of Expansion Joints on Road Bridges

The object of the study is durability of expansion joints in bridge structures; the subject of the research is the vibration response of a structure obtained under conditions of natural operation. Diagnostics of the road bridge expansion joints has been carried out in order to identify characteristic dependences between the value of structure vibration response and types of expansion joint designs during the period of their operation while taking into account the features of the bridge structure. For this purpose, we have tested the methodology for collecting and processing data on the vibration response of the structure under natural conditions of its operation. The paper presents results of data collection on the coverage topology which have been obtained while using three-dimensional scanning method. Data collection on the vibration response of the structure has been carried out by measuring the vibration velocity and deformation of the structure. The data obtained are analyzed. As a result of testing and analysis of the obtained data, the main characteristics have been revealed: the value of base unevenness, the amplitude of vibration velocity and vibration displacement of the structure elements. Two main parameters of the dynamic impact have been assigned, adjusted for the mass of a moving vehicle, which can be used as main parameter for assessing the magnitude of the dynamic impact. A comprehensive method for assessing the dynamic impact on bridge structures has been developed and proposed in the paper, and its use will make it possible to differentiate various designs of expansion joints according to the magnitude of the dynamic impact of vehicles. This, in its turn, will contribute to formulate new recommendations on the use of specific types of expansion joints for various categories of highway, which will increase operational durability of expansion joints and the structure as a whole.

Vibration Feedforward Compensation for Magnetically Suspended Control and Sensitive Gyroscope with Spherical Rotor

Magnetically suspended control and sensitive gyroscope (MSCSG) with two capabilities including attitude control and attitude measurement is promising in meeting the requirements of novel spacecraft. When the momentum vector of a high-speed rotor suspended in five directions is tilted by Lorentz force-type magnetic bearing, the instantaneous large control moment is obtained. The spacecraft attitude can be sensed by a high-speed rotor without deflection interference torque. In this paper, a novel MSCSG with sphere rotor is presented, and its spherical structure and working principle are introduced. The magnetic bearing-rotor dynamic model is established based on Newton’s second law and the gyrokinetic equations. The generating mechanism of three interferences, including bearing dynamic reaction force, deflection torque, and centrifugal force, is analyzed. The feedforward compensation control against three interferences for MSCSG is adopted, and the loading sequence of three interferences is simulated. The optimal sequence of bearing dynamic reaction force, deflection torque, and centrifugal force is used. The radial and axial vibration displacement amplitudes are reduced from 20.8 μm and 31.7 μm to 9.4 μm and 14.9 μm, respectively. The experimental results are in good agreement with the simulation, which indicates the MSCSG rotor unbalance vibration is suppressed effectively by the feedforward compensation method.

The technology of printed circuit board microdrilling

The paper describes the device and operating principle of a high-precision positioning drive based on a magnetorheological (MR) elastomer for micro-drilling blind holes in multilayer printed circuit boards. The results of experimental studies of a drive with a closed control system for step-by-step movement are presented. The operation of the drive in the mode of active vibration isolation is shown and the coefficient of transmission of the vibration displacement amplitude is determined.