Low-order Frequency Research Articles

Acoustic Emission Monitoring of Burn Damage Occurring Under Different Grinding Conditions Using the Low-Order Frequency Moments of a Spectrogram

Acoustic Emission Monitoring of Burn Damage Occurring Under Different Grinding Conditions Using the Low-Order Frequency Moments of a Spectrogram

Aerodynamic interference and unsteady loads for a hovering intermeshing rotor

Synchropters are increasingly applied for precision work in placing suspended loads due to their unique flying characteristics. However, the special intermeshing rotor structural helicopter easily introduces rotor-and-rotor interference, leading to unsteady aerodynamic loads on the rotor blades in mission flight. Hence, we use the unsteady vortex lattice method to validate and analyze the aerodynamic characteristics of the intermeshing rotor in hover. In this method, a circulation suppression technique on the blade root is introduced to enhance the stability of the rotor wake in the steady-state hover. Results show that the meniscus truncated regions on the intermeshing rotor disks formed by the blade–vortex impact are nearly unchanged to collective pitches. The low-order frequency harmonic components and phase lag phenomenon universally found in dual rotor loads and additional oscillating roll moment become inherent characteristics of the intermeshing rotor in hover, especially for kΩ caused by interference of rotor downwash flow and 2 kΩ produced by the blade–vortex interaction at 10° and 190° azimuth. Finally, the left/right rotor loads exist harmonic components of 1, 2, and 3 kΩ. In contrast, the total thrust of the intermeshing rotor system eliminates the odd-order harmonic components but aggravates the even-order harmonic components.

Encoding Frequency Constraints in Preventive Unit Commitment Using Deep Learning With Region-of-Interest Active Sampling

With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interests active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which significantly enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is verified on the the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments.

Design and test of adaptive torsional vibration suppression method for helicopter power system with variable rotor speed

In order to solve the problem of torsional vibration instability of the control system for turboshaft engine caused by low-order torsional vibration modal drift under variable rotor speed effectively, an adaptive torsional vibration suppression method based on the least mean square algorithm is proposed and designed. First, based on Lagrange equation and state space method, the structural dynamic model of torque transmission chain system is established, which takes into account fixed and variable gear ratio. It is beneficial to express the dynamic characteristics of torsional vibration in real time, so that the variation laws of low-order torsional vibration modal under variable rotor speed and gear ratio are revealed. Then, an adaptive torsional vibration filter based on least mean square algorithm is proposed and designed combined with the active control objective of helicopter power system. Finally, the effectiveness of adaptive torsional vibration suppression method is validated based on numerical simulation and hardware-in-loop simulation separately. The results show that compared with the conventional constant-coefficient notch filter, the adaptive torsional vibration filter can decrease the peaks of all low-order torsional vibration frequency by more than 50%. It proves better robustness, more remarkable effectiveness and superior adaptive ability of the adaptive torsional vibration suppression method.

Scalogram-Based Instantaneous Features of Acoustic Emission in Grinding Burn Detection

Time-frequency methods are effective tools in identifying the frequency content of a signal and revealing its timevariant features. This paper presents the use of instantaneous features (i.e., instantaneous energy and signal phase) of acoustic emission (AE) in the detection of thermal damage to the workpiece in grinding. The low-order frequency moments of a scalogram are used to obtain both the instantaneous energy and the mean frequency at which the signal phase is recovered. The grinding process is monitored using AE for a variety of operating conditions, including regular grinding, grinding at higher cutting speed and larger feed, and small dressing depth of cut. The instantaneous features extracted by the scalogram are compared with the results obtained by the empirical mode decomposition. It has been found that both the instantaneous energy and phase deviation indicate the presence of burn damage and serve as robust and reliable indicators, providing a basis for detecting the grinding burn.

Multiobjective Topology Optimization of Spatial-Structure Joints

To realize the static and dynamic multiobjective topology optimization of joints in spatial structures, structural topology optimization is carried out to maximize the stiffness under static multiload conditions and maximize the first third-order dynamic natural frequencies. According to the single-objective optimization results, the objective function of the multiobjective topology optimization of joints is established by using the compromise programming method, and the weight coefficient of each static load condition is determined by using the analytic hierarchy process. Subsequently, under the constraint of the volume fraction, the multiobjective topology optimization of joints is realized by minimizing the multiobjective function. Finally, the optimized structure is smoothed to obtain a smoother joint, and its mechanical properties are compared with those of the hollow ball joint. The results indicate that the multiobjective topology optimization that considers the static stiffness and dynamic frequency can effectively improve the mechanical properties of the structure. Through the research on multiobjective topology optimization, a new type of spatial joint with reasonable stress, a novel form, and aesthetic shape can be obtained, which mitigates the shortcomings of single-objective topology optimization. In comparison to hollow spherical joints with the same weight, topology-optimized joints have a superior ability to resist deformation and improve low-order frequency, which verifies the feasibility of applying multiobjective topology optimization to the lightweight design of joints.

Simulation research on active control of low frequency modal vibration of double-joint flexible manipulator

In order to solve the problems of low precision and high noise in the traditional vibration control method of manipulator, an active control method of low frequency modal vibration is proposed. The dynamic model is constructed by using the finite element equation and modal technology. The low-frequency and high-frequency modes are distinguished. The low-frequency mode is transformed into the state space equation based on the state variable. The volume and velocity are controlled to 0 by the method of 0 volume velocity mode construction. Finally, the coupling modal space control method is used to control the low frequency order frequency, damping ratio and modal shape. The active control is realised by displacement amplitude vector and velocity amplitude vector. The simulation results show that the position error of the elastic displacement of the arm and the moving platform centre in X and Y directions, is less than 0.02 mm.

An analytical solution to the vibration characteristics for continuous girder bridge-track coupling system and its application

To study the vibration characteristics of a high-speed railway continuous girder bridge-track coupling system (HSRCBT), a coupling vibration analysis model of an m-span continuous girder bridge-subgrade-track system with n-span approach bridge was established. The model was based on the energy and its variational method, where both the interlaminar slip and shear deformation effects were considered. In addition, the free vibration equations and natural boundary conditions of the HSRCBT were derived. Further, according to the coordination principle of deformation and mechanics, an analytical method for calculating the natural vibration frequencies of the HSRCBT was obtained. Three typical bridge-subgrade-track coupling systems of high-speed railway were taken and the results of finite element analysis were compared to those of the analytical method. The errors between the simulation results and calculated values of the analytical method were less than 3%, thus verifying the analytical method proposed in this paper. Finally, the analytical method was used to investigate the influence of the number of the approach bridge spans and the interlaminar stiffness on the natural vibration characteristics of the HSRCBT based on the degree of sensitivity. The results suggest the approach bridges have a critical number of spans and in general, the precision requirements of the analysis could be met by using 6-span approach bridges. The interlaminar vertical compressive stiffness has very little influence on the low-order natural vibration frequency of HSRCBT, but does have a significant influence on higher-order natural vibration frequency. As the interlaminar vertical compressive stiffness increases, the degree of sensitivity to interlaminar stiffness of each of the HSRCBT natural vibration characteristics decrease and gradually approach zero.

Scalogram-Based Instantaneous Features of Acoustic Emission in Grinding Burn Detection

Time-frequency methods are effective tools in identifying the frequency content of a signal and revealing its time-variant features. This paper presents the use of instantaneous features (i.e. instantaneous energy and signal phase) of acoustic emission (AE) in the detection of thermal damage to the workpiece in grinding. Both the instantaneous energy and mean frequency are obtained using the low-order frequency moments of a scalogram. While the zero-order frequency moment yields the instantaneous energy, the first-order frequency moment gives the instantaneous frequency by which the signal phase is recovered. The grinding process is monitored using acoustic emission for various operating conditions, including the regular grinding, grinding at a higher cutting speed and larger infeed, and small dressing depth of cut. It has been found that both the instantaneous energy and phase deviation indicate the presence of burn damage and serve as robust and reliable indicators, providing a basis for detecting the grinding burn.

Coupled dynamic analysis of low and medium speed maglev vehicle-bridge interaction using SIMPACK

The low- and medium-speed maglev vehicle generally operates on elevated bridges with a levitation gap of only 8--10 mm, which makes it very sensitive to the vehicle--bridge coupled vibration. To conduct the corresponding modeling and simulation with common dynamics tools, an equivalent processing of the levitation system is required. Using the dynamics software SIMPACK, this paper first introduces the methods of building the multi-body vehicle system, levitation control system and the elastic bridge, respectively, in the SIMPACK railway module, levitation control module and SIMBEAM elastomer module, thus providing a modeling idea for the simulation of the active levitation and operation of low- and medium-speed maglev vehicles through multi-span bridges. It then goes on to simulate and analyze the coupled vibration of a 160 km/h low- and medium-speed maglev vehicle passing through 25 m + 25 m double-span continuous bridges. The research results show that the modeling method introduced in this paper can simulate the low- and medium-speed maglev vehicle--bridge coupled vibration phenomenon, which can be affected significantly by the low-order frequency of the elastic bridge, and can also be intensified under the bridge end impact when the vehicle enters and leaves the bridge. As the running speed of the vehicle increases and the dynamic force increases, the vertical vibration amplitudes of the elastic bridge mid-span, the car body as well as the levitation frame approximate a linear fitting with the vehicle speed. The variation amplitudes of the levitation gap and of the electromagnet current approximate a quadratic fitting with the vehicle speed.

Buckling and free vibration of a side-cracked Mindlin plate under axial in-plane load

In this paper, the buckling and free vibration of a Mindlin plate with a side crack are presented considering a uniaxial in-plane compressive or tensile load. The side crack is through the thickness of the plate. In the Ritz method, a series of corner functions are incorporated into the admissible functions which consist of the modified characteristic functions. With this treatment, one can describe the singularity in stress near the tip of the crack as well as the discontinuities in both displacement and bending rotations across the crack. The buckling loads and natural frequencies are solved through eigenvalue problems considering the existence of the crack. The effects of location, length and orientation of the crack on the buckling and free vibration of the loaded plate are demonstrated. The coupling effect of the crack and the in-plane load on the vibrational characteristics of the plate is analyzed with varying parameters. It is shown that the influences of the tensile and compressive preloads are enhanced by the crack, and the tensile preload can cause the low-order frequency to increase with the growing crack.

Quasi-Resonant Control for Harmonic Current Suppression of a Magnetically Suspended Rotor

In the magnetically suspended rotor (MSR) system of the flywheel, harmonic current produced mainly by mass imbalance and sensor runout would cause undesirable harmonic vibration. Resonant control (RSC) is one of the remarkable performance alternatives for rejecting a set of selected frequency components of the periodic disturbance in a control system. Based on the intrinsic relationship between RSC and repetitive control, which is deduced and clarified, this paper proposes a novel quasi-resonant control (QRSC) scheme for a baseline prestable MSR system to suppress the harmonic current. By introducing a damping factor, QRSC achieves a good balance between stability and dynamic performance. With hybrid phase compensation, it provides system absolute stability and expands the stability margin of the MSR system. Further, as the domination of harmonic current, low-order frequency components are suppressed by parallel QRSCs (PQRSC). A stability criterion with rigorous proof for the plug-in PQRSC-controlled MSR system is addressed as well. Experimental results obtained with a magnetically suspended flywheel prototype corroborate the theoretical approach.

Finite Element Model Updating of Satellite Sailboard Based on Sensitivity Analysis

The modal analysis of a satellite sailboard finite element model is carried out to accurately investigate the response of a satellite sailboard in a complex loaded space environment through simulation. The basic excitation vibration test of the satellite sailboard is used to perform model matching and a correlation test. Appropriate design variables are selected through sensitivity analysis. Modal analysis data and vibration table excitation test response data are used to modify the finite element model. After optimization, the orthogonality of the simulated vibration mode and experimental vibration mode is good. The low‐order frequency errors in the simulation model are less than 5%, the high‐order errors are less than 10%, and the modal confidence MAC values are above 0.8. The modal frequency and mode shape are closer to the experimental modal frequency and mode shape, respectively. The simulation and test acceleration response of the modified finite element model of a honeycomb panel are compared under the two conditions of sine sweep and random vibration. The acceleration response curves of reference points are consistent, and amplitude and frequency errors are within acceptable limits. The model updating effect is evident, which provides good reference for research on satellites and other aerospace products.

Integrated optimal design of a high-speed planar parallel manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

Ultrashort polarization-tailored bichromatic fields from a CEP-stable white light supercontinuum.

We apply ultrafast polarization shaping to an ultrabroadband carrier envelope phase (CEP) stable white light supercontinuum to generate polarization-tailored bichromatic laser fields of low-order frequency ratio. The generation of orthogonal linearly and counter-rotating circularly polarized bichromatic fields is achieved by introducing a composite polarizer in the Fourier plane of a 4 f polarization shaper. The resulting Lissajous- and propeller-type polarization profiles are characterized experimentally by cross-correlation trajectories. The scheme provides full control over all bichromatic parameters and allows for individual spectral phase modulation of both colors. Shaper-based CEP control and the generation of tailored bichromatic fields is demonstrated. These bichromatic CEP-stable polarization-shaped ultrashort laser pulses provide a versatile class of waveforms for coherent control experiments.

Performance Enhancement of Battery Charger for Electric Vehicles Using Resonant Controllers

This paper proposes a current proportional-resonant control strategy to reduce second-order harmonic of electric vehicle battery charger. Using the PR controller, the charger reference tracking performance can be enhanced. The steady-state errors in single-phase charging system can be reduced effectively. The PR controller stability influence factors including proportion coefficient, resonant coefficient and cutoff frequency are discussed in the paper. Finally, simulation results achieved on a 3.3kW charging model prove the proposed strategy effectively minimizes the low-order frequency ripple in grid-interfaced converter.

Strand Tension Control in Anchor Span for Suspension Bridge Using Dynamic Balance Theory

Strand tension control is essential in suspension bridge safety. However, few quantitative studies have examined the bending rigidity and boundary condition behavior of strands in the anchor span of suspension bridges because of their special structure and complex configuration. In this paper, a new calculation method for strand tension is explored by using dynamic balance theory to determine the effect of bending rigidity and boundary conditions. The accuracy and effectiveness of the proposed method are tested and confirmed with verification examples and application on Nanxi Yangtze Suspension Bridge in China. The results indicated that only low-order frequency calculation could be used to calculate the strand tension without considering the effect of bending rigidity to ensure control accuracy. The influence of bending rigidity on the control precision is related to the tension and the length of the strands, which is significantly determined by the specific value between the stress rigidity and the bending rigidity. The uncertain boundary conditions of the anchor span cable, which are fixed between consolidated and hinged, also have a major effect on the control accuracy. To improve the accuracy of strand tension control, the least squares method is proposed during the tension construction control of the anchor span. This approach can significantly improve the accuracy of the tension control of the main cable strand. Some recommendations for future bridge analysis are provided based on the results of this study.

Coupling Vibration Research of a Turbine Blade-Disc System with Symmetric-Acyclic Structure

The blade-disc in a turbine is characterized by symmetric-acyclic opening structure on the disc body. Four different numerical models with 3-D finite element method were established in the present investigation. The wave propagation technique was employed and the modal analysis of the blade disc was performed. The modal and vibration characteristics of different models in the same rotational speeds were compared in consideration of non-linear coupling/ interactions between blade and disc. The results indicate that in the modal analysis of symmetric-acyclic blade-disc system, the openings structure has low impact on the low-order mode frequency. Thus, cyclic symmetric model without the opening structure can help to get general frequency forecast to improve the analysis efficiency.

Wind-Induced Vibration Analysis of Overhead Working Truck

As to the complicated characteristics of overhead working truck under effects of random dynamic wind, the traditional method is difficult to reflect its dynamic response in real time, in the study; it proposes the random wind induced vibration response analysis method based on the finite element method and pseudo-excitation method. An it regards the vibration of the fluctuating wind load as coherent random vibration under stationary random excitation, and it uses Davenport wind velocity spectrum which does not change with height, the correlation of the wind excitation are considered. It takes the folding type arm overhead working truck as example, the random wind vibration analysis are performed, and it gets the acceleration response spectrum and root mean square the of aerial work platform. The analysis results show that the low-order frequency will cause great vibration of the work platform, and the vertical one third of the root-mean-square of acceleration is below international standards, it has no uncomforted effect on operation workers.

Calculation and Analysis of Dynamic Characteristic for Four-Cylinder Engine’s Crankshaft

In order to profoundly study on the dynamic characteristic of crankshaft, this thesis applies planar bearing element Combi214 to simulating the bearing supports on both sides of the crankshaft. This study carried out the modal analysis of the crankshaft in multi-step load, and has calculated the low-order vibration mode and frequency of the crankshaft, besides, the top four critical speed and resonant frequency of the crankshaft is obtained via the Campbell chart. The safe range of first critical rotate speed has also been worked out, which is an important reference for the study of structural design and dynamics optimization of crankshaft, and the analysis results and reference in this thesis would provide some valuable basis to improve the four-cylinder engine’s dynamics characteristics.