scholarly journals Impedance Synthesis Based Vibration Analysis of Geared Transmission System

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Yafeng Ren ◽  
Shan Chang ◽  
Geng Liu ◽  
Liyan Wu ◽  
Teik C. Lim

The severity of gear noise response depends on the sensitivity of geared rotor system dynamics to the transmission error. As gearbox design trending towards lighter weight and lower noise, the influence of housing compliance on system dynamic characteristics cannot be ignored. In this study, a gear-shaft-bearing-housing coupled impedance model is proposed to account for the effect of housing compliance on the vibration of geared transmission system. This proposed dynamic model offers convenient modeling, efficient computing, and ability to combine computed parameters with experimental ones. The numerical simulations on system dynamic characteristics are performed for both a rigid housing configuration and a flexible one. Natural frequencies, dynamic mesh forces, and dynamic bearing reaction loads are computed, and the housing compliance contribution on system dynamic characteristics is analyzed. Results show that increasing housing compliance will decrease the system natural frequencies and will affect the dynamic bearing reaction loads significantly but have very little influence on the dynamic mesh force. Also, the analysis shows that bearing stiffness has significant influence on the degree of housing contribution on system dynamic characteristics.

2012 ◽  
Vol 510 ◽  
pp. 529-535 ◽  
Author(s):  
Li Jun Shan ◽  
Yu Ting Liu ◽  
Wei Dong He

RV (Rotate Vector) transmission is a new precision transmission system. In order to improve its accuracy, we study the RV transmission system. It is researched in comprehensive factors including displacement errors, elastic deformation (static transmission error, design transmission error), gear meshing errors, backlash of gear, time-varying mesh stiffness, mesh damping, bearing stiffness, torsional stiffness of input shaft, etc. The mathematical and mechanical model of dynamic transmission accuracy is established by the concentrated mass method and the dynamic substructure method. Then, the meshing force of each part is analyzed in RV reducer. The motion differential equation of RV drive system is obtained, which lays the foundation for the calculation and analysis of the transmission error.


1993 ◽  
Vol 115 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. Kahraman

In this paper, a linear dynamic model of a helical gear pair has been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational (rocking) motions due to the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of the helix angle in the analysis.


Author(s):  
Jinyuan Tang ◽  
Zehua Hu ◽  
Siyu Chen ◽  
Duncai Lei

The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near [Formula: see text] . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.


2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Huan Bai ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Jianjun Tan ◽  
Xinzi Li

Abstract Using finite element and lumped parameter methods, a gear–shaft–bearing coupled vibration model was developed for a single-stage gear transmission system considering bearing waviness, bearing clearance, time-varying transmission error excitation, and shaft flexibility. Runge–Kutta algorithm was applied for solving the dynamic response of the coupled model. The influences of rotational speed, the number, and amplitude of bearing waviness on the dynamics were studied. Results show that any change in the number of bearing waviness has an obvious impact on the dominant frequency component of the dynamic transmission error. When the number of bearing waviness is equal to the number or multiples of the rolling element, the dynamic mesh force occurs peak response and the system vibrates violently. At low and medium speeds range, the gear transmission system with bearing waviness has larger vibrational energy than the gear transmission system without bearing waviness, leading to unstable dynamic response, which would potentially cause a significant chaotic response. The dominant frequencies of the dynamic transmission error for the gear transmission system with bearing waviness are the ball passage frequency (BPF) and its harmonic frequency. At high speeds range, the main excitation is the transmission error both for the gear transmission systems with and without bearing waviness. In addition, the increasing amplitude of bearing waviness would enlarge the dynamic mesh force and decrease the number of loaded rolling elements.


Author(s):  
Ahmet Kahraman

Abstract In this paper, a linear dynamic model of a helical gear pair has. been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational motions because of the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of helix angle in the analysis.


Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.


2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.


2021 ◽  
Author(s):  
Zhiyong Yang ◽  
Junchen Song ◽  
Wei Cai ◽  
Danqiu Qiao ◽  
Gaoxiang Lu

Abstract Focusing on the problem that the polarization aberration caused by the non-normal incidence of the polarized beam affects the accuracy of the azimuth transmission during the fiber coupling process of the non-line-of-sight azimuth transmission system, this paper starts from the principle of non-line-of-sightazimuth transmission. The polarization aberration relation of the lens-fiber combined interface is established based on the Fresnel formulafor the attenuation difference between the horizontal and vertical electric vectors. Further, the azimuth solution model affected by polarization aberration is established. Numerical simulation results show that in non-normal incidence, no polarization aberration will occur when the polarization angle between the incident ray and incident surface is 0° or 90°. Otherwise, the polarization aberration changes toward the incident surface, and the azimuth transmission error will increase with the increase of the polarization aberration. Last, the optimization measures are proposed. This is of great significancefor further improvement of the azimuth transmission system based on polarization-maintaining fibers, the selection of the instrument,and the improvement of the system measurement accuracy.


2017 ◽  
Vol 24 (19) ◽  
pp. 4465-4483 ◽  
Author(s):  
Mohsen Amjadian ◽  
Anil K Agrawal

Horizontally curved bridges have complicated dynamic characteristics because of their irregular geometry and nonuniform mass and stiffness distributions. This paper aims to develop a simplified and practical method for the calculation of the natural frequencies and mode shapes of horizontally curved bridges that would be of interest to bridge engineers for the estimation of the seismic response of these types of bridges. For this purpose, a simple three-degree-of-freedom (3DOF) dynamic model for free vibration equation of this type of bridge has been developed. It is shown that the translational motion of the deck of horizontally curved bridges in the direction that is perpendicular to their axis of symmetry is always coupled with the rotational motion of the deck, regardless of the location of the stiffness center. The model is further exploited to develop closed-form formulas for the estimation of the maximum displacements of the corners of the deck of one-way asymmetric horizontally curved bridges. The accuracy of the model is verified by finite-element model of a horizontally curved bridge prototype in OpenSEES. Finally, the model is utilized to study the influence of the location of the stiffness center with respect to the deck curvature center on the natural frequency and the maximum displacements of the corners of the deck for different curvatures of the deck. The results of free vibration analysis show that the natural frequencies of one-way asymmetric horizontally curved bridges, in general, increase with the increase of the subtended angle of the deck. The results of earthquake response spectrum analysis show that the increase in the subtended angle of one-way asymmetric horizontally curved bridges decreases the radial displacements of the corners of the deck but increases the azimuthal displacement. These two responses both increase with the increase in the distance between the stiffness center and the curvature center.


2016 ◽  
Vol 836-837 ◽  
pp. 348-358
Author(s):  
Zhe Li ◽  
Song Zhang ◽  
Yan Chen ◽  
Peng Wang ◽  
Ai Rong Zhang

Dynamic characteristics of numerical control (NC) machine tools, such as natural frequency and vibration property, directly affect machining efficiency and finished surface quality. In general, low-order natural frequencies of critical components have significant influences on machine tool’s performances. The headstock is the most important component of the machine tool. The reliability, cutting stability, and machining accuracy of a machining center largely depend on the structure and dynamic characteristics of the headstock. First, in order to obtain the natural frequencies and vibration characteristics of the headstock of a vertical machining center, modal test and vibration test in free running and cutting conditions were carried out by means of the dynamic signal collection and analysis system. According to the modal test, the first six natural frequencies of the headstock were obtained, which can not only guide the working speed, but also act as the reference of structural optimization aiming at frequency-shift. Secondly, by means of the vibration test, the vibration characteristics of the headstock were obtained and the main vibration sources were found out. Finally the corresponding vibration reduction plans were proposed in this paper. That provides the reference for improving the performance of the overall unit.


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