Order Natural Frequency Research Articles

Longitudinal micro-waviness (LMW) formation mechanism on large optical surface during ultra-precision fly cutting

During fly cutting of large aperture flat optical components, mid-spatial frequency micro-waviness is formed on the machined surface, which greatly affects the optical performance of the components. This study aims to explore the mechanism of formation of micro-waviness perpendicular to the feed direction, which is called longitudinal micro-waviness (LMW). A finite element model (FEM) of the ultra-precision fly cutting spindle system is developed to analyze the axial vibrations of the tool nose. The analysis shows that the formation of LMW is the result of coupling of the response of the spindle system and its higher order natural frequency response under the excitation of the tangential cutting force. The vibration frequency of the tool nose is closely related to the structure of the spindle system. By changing the stiffness of the cutting head, the frequency is significantly changed, and the LMW formed on the machined surfaces has a spatial period of 39.2 mm, which is out of the range of mid-spatial frequency waviness. This result has great significance in the design of fly cutting machines, and can be used to improve the quality of the optical surface and thereby improve the performance of large aperture flat optical devices.

Finite Element Analysis of Static and Dynamic Characteristics of Elevator Desk Structure Based on ANSYS Workbench

Through the SolidWorks software for elevator computer desk 3 d entity modeling, and using the ANSYS Workbench software to model the stress analysis of meshing and the applied load for elevating computer desk overall deformation and stress distribution, thus carries on the strength, stiffness and modal analysis, the model for the first six order natural frequency and modal vibration mode, the analysis of dynamic performance of the model. The analysis results show that the strength and stiffness of the computer table meet the design requirements, and verify that no resonance occurs during the working process.

Modal Analysis of L Type Compressor Crankshaft

Reciprocating compressor is an important equipment in industrial production. The crankshaft turns the thrust of the compressor piston rod into torque, which is an important component of the compressor. When reciprocating compressor works, there will be various forms of vibration such as torsion and bending. Therefore, the study of the crankshaft vibration becomes particularly important. Analyze the modal analysis of L type compressor crankshaft by using the finite element simulation. The first six order natural frequency and the corresponding mode of vibration of the crankshaft are obtained. And analyze the influence of the hollow and solid on the natural frequency and mode of vibration of the crankshaft. The results show: With the increase of vibration order, the natural frequency of the crankshaft increase. The crankshaft deformation is mainly bending at low frequency. The deformation of crankshaft is mainly composed of bending and torsional vibration at higher frequency. Moreover, the ends of solid crankshafts are less restrained. Extend the service life and performance of the crankshaft and other parts of the compressor by increasing the strength and stiffness of the crankshaft's local materials. And increasing the fillet radius at the transition point are adopted to reduce the deformation and torsion of the crankshaft.

Impact localization on composite laminates using fiber Bragg grating sensors and a novel technique based on strain amplitude

Carbon fiber reinforced composite materials have been widely used in aerospace and other high-tech fields because of their excellent performance. However barely visible impact damage can be introduced by low velocity impact, which might bring out tremendous risk. In this paper, a new method is proposed to predict the position of low velocity impact. The dynamic strain signal that is caused by low velocity impact is obtained by the fiber Bragg grating (FBG) sensor. The amplitude of the first K order natural frequency is extracted by Fast Fourier Transform (FFT). The amplitude data is normalized, and then establish k order vector matrix model is established. It is proposed that K order sum of squares of deviations can be used as the basis to predict positioning. Two different validation tests were performed. The experimental model was made of different layers. FBG were used to embed and paste type method, experiments were conducted with impact of different energy levels. The results show that proposed method is feasible.

Study on dynamic characteristics of hydraulic pumping unit on offshore platform

A new technology of offshore oil rod pumping production is developed for offshore heavy oil recovery. A new type of miniature hydraulic pumping unit with long-stroke, low pumping speed and compact structure is designed based on the spatial characteristics of offshore platforms. By combining the strengths of sinusoidal velocity curve and trapezoidal velocity curve, a kinematical model of the acceleration, the velocity and displacement of the pumping unit’s hanging point is established. The results show that the pumping unit has good kinematic characteristics of smooth motion and small dynamic load. The multi-degree-of-freedom dynamic model of the single-well pumping unit is established. The first and second order natural frequencies of the sucker rod string subsystem and the pumping unit subsystem are studied. The results show that the first and the second order natural frequencies among the pumping rod string, pumping unit-platform subsystem and the dynamic excitation have differences over 5 times from each other, indicating that resonance phenomenon will not appear during the operation and the dynamic requirements for field use are met in the system.

The Harmonic Response Analysis of Unbalanced Force Acting on Induced Draft Fan Shaft

This paper studies the harmonic response analysis in steam turbine parts, gear box, induced draft fan part of induced draft fan shaft system based on the theory of simple harmonic excitation by using ANSYS software platform. It mainly studies the response characteristics near the low order natural vibration frequency. It investigates the response of each key position in the condition of the coupling system, and adopts harmonic response analysis (ANSYS software) to gain steady-state response of each point on the shaft system.

Study on variable pressure/position preload spindle-bearing system by using piezoelectric actuators under close-loop control

Abstract Angular contact ball bearings have been widely utilized in machine tool spindles and bearing preload has a great influence on the performance of the spindle. The variable preload control technology, including variable pressure preload and variable position preload, is the key technology for intelligent spindle. In order to implement variable pressure/position preload control, the control method and control performance of the variable pressure/position preload spindle-bearing system by using piezoelectric actuators under close-loop control are systematically studied in this paper. A test rig of variable pressure/position spindle-bearing system is developed, and the piezoelectric actuators are adopted to realized preload or axial clearance close-loop control automatically. Both variable pressure preload and variable position preload can be realized on the test rig. The mechanical model of the variable pressure/position preload spindle-bearing system by using piezoelectric actuators is established. Then stiffness model considering the external axial load in static state, and axial displacement as well as operational preload model in rotational state of the spindle-bearing system with piezoelectric actuators in variable pressure preload and variable position preload are proposed and simulated. The design method of the preload mechanism by using piezoelectric actuators is presented. PI controller is employed to regulate the preload or axial clearance of the spindle-bearing system in real-time. A series of experiments are implemented to verify the validity of the variable preload control method and the superiority of the variable pressure/position preload control performance by using piezoelectric actuators. The results show that the variable pressure/position preload spindle-bearing system by using piezoelectric actuators shows excellent performance in controlling preload or axial clearance. The static and dynamic characteristics as well as the operational behaviors of the spindle-bearing system under variable position preload and variable pressure preload are verified by experiments. It is illustrated that the stiffness and the first order natural frequency will be changed with the change of preload methods and preload values. The operational behaviors vary greatly with the preload method, initial preload (negative axial clearance) and rotational speed. The variable preload control method plays a great important role on the performance of spindle-bearing system. Furthermore, this paper provides a foundation for the future research of preloading intelligent control technology as well as investigating the thermal-mechanical-dynamic characteristic of high speed spindle-bearing system.

Free vibration analysis for a non-contact piezoelectric motor modulated by electromagnetic field

For a non-contact piezoelectric motor modulated by electromagnetic field, the equation of the free vibration for the driving system of the motor is given. Using the boundary conditions and continuity conditions, the natural frequencies and mode functions of the driving system are obtained. The vari ation law of the natural frequency is investigated, when the system parameters of the driving system are changed in a certain range. The results show that the change of the system parameters of piezoelectric stacks and driving beams has obvious effects on odd order natural frequencies of the driving system; the change of the system parameters of the center shaft have obvious effects on even order natural frequencies; In the odd order modes, the maximum vibration amplitude of the driving system occurs at the junction of the driving beam and the center shaft. It is conducive to output of the motor rotation angle. All the results are useful for design and control of operating performance of the motor.

Nonlinear Mechanical Behaviors for System of Bearing on the Top of First Story Column

According to the system of bearing on the top of first story column, the mathematical model of isolation system based on geometric nonlinear is investigated by using Hamilton's principle. The natural frequency of the system is investigated, and the effects of axial pressure and difference column size to the isolation system in seismic response are discussed. The isolation system dynamics model based on geometric nonlinear is established considering the cross section rotated and the influence of the shear deformation and axial pressure. The differential quadrature element method is employed for discrete processing on governing equations and boundary conditions. The natural frequency and seismic response of isolation system are solved numerically. Results show that: the axial force will reduce the lower order natural frequencies significantly. With increase of slenderness ratio of cantilever column, stiffness degradation of isolation system decreases, lateral displacement of the top of cantilever column increases, which seriously influences the stability of the isolation system and decrease the security of isolated structure, finally.

Dynamic characteristics for system of bearing on the top of first story column based on geometry nonlinearity

According to the serial system of bearing with column, the natural frequency of serial system is investigated, and the effects of axial load and different rubber bearings are discussed. Taking into account the effects of the cross-section rotation, shear distortion and compression axial force, the mathematical model for free vibration of the system is established. The differential quadrature element method is employed for the discrete processing in governing equations and boundary conditions. The natural frequency of serial system with clampedfree boundary conditions is solved numerically, and the figures of natural frequency with compression axial force are presented. It is shown that the axial force will reduce the lower order natural frequencies significantly, and in certain case of total height, the equivalent bending stiffness of rubber bearings reduces the natural frequencies to different extent.

Shaking table testing and numerical modeling of continuous welded ballast track on bridges under longitudinal seismic loading

In order to confirm the validity of the ideal elasto-plastic resistance model applied to the ballast track under seismic loading, this paper studies the seismic response of continuous welded ballast track on bridges through the shaking table test and presents a process of updating the model based on the test results. The results indicate that the track constraint can improve the low order natural frequency of bridges significantly, and reduce the displacement response of the bridge. When ballast beds are effectively in a dynamic reciprocating state while under seismic loading, a structural change between the granules will occur, wherein some will flow and redistribute. The dynamic hysteretic change of the ballast longitudinal resistance is complex and quite different from that of the ideal elasto-plastic hysteretic route, and the ballast longitudinal resistance performance degenerates. If ballast longitudinal resistance is assumed to be ideal elastic-plastic resistance, the actual beam displacement response will be underestimated and the calculated rail seismic force will be greater than the test result. Moreover, the equivalent stiffness coefficient Ke and damping coefficient Ce of the ballast dynamic resistance characteristics could be obtained by model updating, and the simulation results coincide well with the test results.

Numerical Simulation and Experimental Validation of Failure Caused by Vibration of a Fan

This paper presents the root cause analysis of an unexpected fracture occurred on the blades of a motor fan used in a natural gas reciprocating compressor unit. A finite element model was established to investigate the natural frequencies and modal shapes of the fan, and a modal test was performed to verify the numerical results. It was indicated that the numerical results agreed well with experimental data. The third order natural frequency was close to the six times excitation frequency, and the corresponding modal shape was the combination of bending and torsional vibration, which consequently contributed to low-order resonance and fracture failure of the fan. The torsional moment obtained by a torsional vibration analysis of the compressor shaft system was exerted on the numerical model of the fan to evaluate the dynamic stress response of the fan. The results showed that the stress concentration regions on the numerical model were consistent with the location of fractures on the fan. Based on the numerical simulation and experimental validation, some recommendations were given to improve the reliability of the motor fan.

Vibration Modal Analysis of Thin-walled Component with Variable Curvature Based on Finite Element

Thin-walled titanium alloy components with variable curvature are widely used in aerospace. During machining process, chatter is induced frequently because stiffness of the components is low. This paper present a finite element method to analyze modal parameters of thin-walled components with variable curvature. Solidworks and Ansys are used to build solid model, set finite element model and carry out modal analysis. Then, the first 20 order natural frequencies and mode shapes are obtained and analyzed. With simulation results, machining parameters can be optimized to avoid machining chatter, and machining precision will be improved. In addition, the main advantage of the approach is that the modal parameters can be obtained quickly without modal tests.

Dynamic and Static Characteristics Analysis and Research for Key Components of the NC Lathe CK61125

Based on the principle of static and modal analysis, carry on the static and dynamic characteristics analysis to the spindle of CK61125 machine tool using the finite element method (FEM). Then, got the static stress and deformation cloud, solve the first six order natural frequency and mode shape of the structure, provides a reference of engineering design and application for the machine tool spindle.

Vibration response analysis of wind towers considering coupling effects of wind and tide level

Wind power towers located in the intertidal zone are not only influenced by wind load but also affected by the rising and falling of the tides. Little research examining the dynamic characteristics of wind power towers under multi-factor coupling loads has been conducted. Based on the finite element method and field testing, dynamic characteristics of the wind towers under complex loads were studied. Change laws of natural frequencies of wind power towers under different water levels were analyzed, and change laws of acceleration, displacement, strain and failure characteristics of a wind power tower under the coupling load of wind and tide levels were analyzed. The wind tower blade in expansion and deformation characteristics of two types of feathering were analyzed. The results showed that the influence of water levels on the low order natural frequency of a wind power tower structure was slight, but the influence on the high order frequency was higher. The maximum displacement of a wind power tower structure under a fluctuating wind load increased with increasing height. In extreme cases, a wind power tower will appear to have buckling instability destruction when the blades are in a state of suitable slurry. The top displacement of a wind power tower was less than a state displacement. Field monitoring results validate the correctness of the numerical simulation analysis.

Analysis and Optimization of a Hybrid Electric Bus's Starting Condition

The engine starting process of hybrid electric buses equipped with clutches usually generates overlarge torques on the main axle, which is undesirable. This paper targets at eliminating the torque strike on the main axle during this process. The powertrain mechanics is modeled. A novel multi-objective downhill simplex optimization method is proposed to optimize the rigidity, damping and other axle parameters. Simulation results show that with optimized parameters, the maximum torque upon the axle is reduced by 64.7%, and the first order natural frequency is increased by up to 1.02%. A pareto front is also presented to provide an overview at the fundamental performance.

Frequency Sweep Test and Modal Analysis of Watermelon during Transportation

Abstract Determining the natural frequency of watermelon is important to reduce loss by vibration during transportation. The purpose of frequency sweep test is to determine the tolerance of watermelon to vibration within a certain frequency range and to search the resonant frequency of watermelon in a certain frequency range. Frequency sweep test of Xinong No.8 watermelon cultivar was conducted, and the acceleration transmissibility curve was obtained. Furthermore, the 1st and 2nd order natural frequencies of watermelon were determined as 35.125 Hz and 71.034 Hz respectively from the acceleration transmissibility curve. Based on Geometric and mechanical parameters of Xinong No.8 watermelon cultivar, a finite element analysis model was developed and modal analysis of watermelon was carried out to obtain its natural frequencies and mode shapes. Since the value of 1st and 2nd order resonance frequency were the same or similar to the value of 3rd, 4th, and 5th order resonance frequency, this study only focused on 1st and 2nd order modes. The 1st order and 2nd order natural frequency test data fit to the corresponding simulation data well which validated the FEA model. This study demonstrated the feasibility of detecting the resonant frequency of watermelon vibration during transportation using FEA methods and provided a theoretical basis for watermelon transportation device design to reduce damage by avoiding resonant frequency.

Passive Methods for the Fast Seismic Characterization of Structures: The Case of Silea Bridge

This paper provides useful information about a passive method, usually applied on soils, for defining the frequencies of most infrastructures. Today, the eigen-frequency determination is one of the most significant and binding requirement aspects, especially in relation to the recent earthquakes in Italy (Accumoli, Norcia 2016; Finale Emilia 2012; L’Aquila 2009). The development of inexpensive, fast and reliable procedures to define the eigen-frequency of construction in general and of infrastructures in particular, is the aim of modern civil engineering. Currently, experimental tests are widely applied to evaluate the dynamic behavior of bridges. While the natural frequencies of a structure can be determined using different methods, passive methods are attractive because of their low costs and easy and fast procedures. In this paper, two passive methods, called standard spectral ratio (SSR) and horizontal to vertical spectral ratio (HVSR), are introduced and analyzed. The two methods are applied to estimate the frequencies in the transversal direction of a composite steel-concrete viaduct recently built in Italy. The comparison of the results obtained from SSR and HVSR and a finite element model confirms the possibility of applying the two methods for the dynamic characterization of bridges. In particular, the SSR method provides a correct estimation of the lower order natural frequencies and their degree of amplification. HVSR, which is typically used only on soil studies, provides a reliable early estimation of the frequency of a structure, if the latter is flexible, compared to the soil characteristics. The HVSR method is directly applied to the viaduct, so that an analogy is created between the soil layer and the structural elements. This paper is intended to show how the HVSR method typically applied to soil can reach good results in the dynamic characterization of Silea steel-concrete viaduct.

Modal identification of single layer graphene nano sheets from ambient responses using frequency domain decomposition

Abstract In this paper, a new method has been proposed for determining mechanical properties of single-layer graphene sheets, without applying any external force and simply by measuring natural deformations of these sheets due to their ambient environmental conditions. Furthermore, the merits and potential applications of this method have been investigated by using Non-Equilibrium Molecular Dynamics (NEMD) virtual laboratory. Contrary to the ordinary methods of identifying mechanical systems, which rely on dynamic response of one structure to a predefined excitation, here the output-only frequency domain decomposition method has been employed. After presenting the theory behind the employed approaches, a virtual laboratory called the Laboratory of Nanometric Operational Modal Analysis (LNOMA) was set up and by using this laboratory, mechanical properties of single-layer graphene sheets were determined and compared with those obtained in previous works. Equivalent elastic modulus, Poisson's ratio and thickness of the examined graphene sheet were found to be 1.05 Tpa, 0.17 and 2.885 A, respectively. For the higher order natural frequencies, the equivalent thickness varies as 1.941, 2.00133, 1.4575, 1.307 and 1.3335 A for the 2nd to 6th mode shapes,respectively. An important point is that with the increase of the mode number, the equivalent thickness decreases, and after the 4th mode, the thickness ratio (equivalent thickness/frequency) does not change significantly and could be considered as 0.2 for the higher order modes. All the results obtained by applying random excitations; and this shows the importance of the present work for future experiments.

An upper bound theory to approximate the natural frequencies and parameters identification of composite beams

For the free vibration of composite beams and non-uniform beams we propose a new upper bound theory to approximate the first few natural frequencies. The Rayleigh quotient is expressed in terms of boundary functions, instead of that in terms of eigenfunctions. The boundary function satisfies all boundary conditions of the given beam, and is at least the fourth-order polynomial with leading coefficient to be one. We prove that the maximality of the Rayleigh quotient in the space of the kth order boundary functions is equivalent to the orthogonality of the kth order boundary function to lower order optimal boundary functions. Hence, we can easily find the kth order natural frequency through an orthogonalization technique provided. When the first three natural frequencies are compared with the exact or numerically found ones, good results are obtained, which confirm the applicability of the present upper bound theory. We address the inverse problems of composite beam equations, where we use the orthogonal system of boundary functions as bases to expand the unknown functions and derive linear algebraic equations to determine the expansion coefficients. As a consequence, we can fast and accurately estimate the unknown rigidity function and planar inertial function with the help of the first three natural frequencies, and the supplemented measured data of recovered function on two boundaries. The robustness of the present inversion methods is demonstrated by numerical examples.