“Snapping” Torsional Response of an Anisotropic Radially Loaded Rotor

1997 ◽  
Vol 119 (2) ◽  
pp. 397-403 ◽  
Author(s):  
D. E. Bently ◽  
P. Goldman ◽  
A. Muszynska
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamic Stiffness ◽  
Radial Force ◽  
Lateral Stiffness ◽  
Frequency Range ◽  
Torsional Response ◽  
Specific Shape ◽  
Lateral Resonance ◽  
Laterally Loaded

A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a snapping (accelerated) torsional response of the rotor at twice synchronous frequency (2×), and it is especially pronounced at 1× and 2× torsional resonances. The snapping response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1× lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.

scholarly journals “Snapping” Torsional Response of an Anisotropic Radially Loaded Rotor

1995 ◽  
Author(s):  
Donald E. Bently ◽  
Paul Goldman ◽  
Agnes Muszynska
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamic Stiffness ◽  
Radial Force ◽  
Lateral Stiffness ◽  
Frequency Range ◽  
Torsional Response ◽  
Specific Shape ◽  
Lateral Resonance ◽  
Laterally Loaded

A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a “snapping” (accelerated) torsional response of the rotor at twice synchronous frequency (2 ×), and it is especially pronounced at 1 × and 2 × torsional resonances. The “snapping” response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1 × lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.

Research on the dynamic characteristic of semi-active hydraulic damping strut

2019 ◽  
Vol 234 (6) ◽  
pp. 1779-1791 ◽  
Author(s):  
Daoyong Wang ◽  
Wencan Zhang ◽  
Mu Chai ◽  
Xiaguang Zeng
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Maxwell Model ◽  
Friction Model ◽  
Damping Capacity ◽  
Frequency Range ◽  
Stiffness Model ◽  
Rubber Bushing

To reduce the vibration and shock of powertrain in the process of engine key on/off and vehicle in situ shift, a novel semi-active hydraulic damping strut is developed. The purpose of this paper is to study and discuss the dynamic stiffness model of the semi-active hydraulic damping strut. In this study, the dynamic characteristics of semi-active hydraulic damping strut were analyzed based on MTS 831 test rig first. Then, the dynamic stiffness model of semi-active hydraulic damping strut was established based on 2 degrees of freedom vibration system. In this research, a linear, fractional derivative and friction model was used to represent the nonlinear rubber bushing characteristic; the Maxwell model was used to describe the semi-active hydraulic damping strut body model; and the parameters of rubber bushing and semi-active hydraulic damping strut body were identified. The dynamic stiffness values were calculated with solenoid valve energized and not energized at amplitudes of 1 mm and 4 mm, which were consistent with experimental results in low-frequency range. Furthermore, the simplified dynamic stiffness model of the semi-active hydraulic damping strut was discussed, which showed that bushing can be ignored in low-frequency range. Then, the influence of equivalent spring stiffness, damping constant, and rubber bushing stiffness on the stiffness and damping capacity of the semi-active hydraulic damping strut were analyzed. Finally, the prototype of the semi-active hydraulic damping strut was developed and designed based on the vehicle in situ shift and engine key on/off situations, and experiments of the vehicle with and without semi-active hydraulic damping strut were carried out to verify its function.

scholarly journals Study on Multi-Degree of Freedom Dynamic Vibration Absorber of the Carbody of High-Speed Trains

2021 ◽  
Author(s):  
Yu SUN ◽  
Jinsong Zhou ◽  
Dao Gong ◽  
Yuanjin Ji
Keyword(s):  
Vibration Control ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
High Speed Train ◽  
Dynamic Vibration Absorber ◽  
Multiple Degrees Of Freedom ◽  
Dynamic Vibration

Abstract To absorb the vibration of the carbody of the high-speed train in multiple degrees of freedom, a multi-degree of freedom dynamic vibration absorber (MDOF DVA) is proposed. Installed under the carbody, the natural vibration frequency of the MDOF DVA from each DOF can be designed as a DVA for each single degree of freedom of the carbody. Hence, a 12-DOF model including the main vibration system and a MDOF DVA is established, and the principle of Multi-DOF dynamic vibration absorption is analyzed by combining the design method of single DVA and genetic algorithm. Based on a high-speed train dynamics model including an under-carbody MDOF DVA, the vibration control effect on each DOF of the MDOF DVA is analyzed by the virtual excitation method. Moreover, a high static and low dynamic stiffness (HSLDS) mount is proposed based on a cam–roller–spring mechanism for the installation of the MDOF DVA due to the requirement of the low vertical dynamic stiffness. From the dynamic simulation of a non-linear model in time-domain, the vibration control performance of the MDOF DVA installed with nonlinear HSLDS mount on the carbody is analyzed. The results show that the MDOF DVA can absorb the vibration of the carbody in multiple degrees of freedom effectively, and improve the running ride quality of the vehicle.

scholarly journals Performance research and safety verification of compound structure air spring

2020 ◽  
Vol 12 (12) ◽  
pp. 168781402097479
Author(s):  
Lihang Yin ◽  
Wei Xu ◽  
Zechao Hu ◽  
Yuanchao Zhang ◽  
Chuang Li
Keyword(s):  
Natural Frequency ◽  
Dynamic Stiffness ◽  
Lateral Stiffness ◽  
Test Results ◽  
Air Spring ◽  
Compound Structure ◽  
Static And Dynamic Characteristics ◽  
Vertical Stiffness ◽  
Safety And Reliability ◽  
Performance Research

To further reduce the vertical stiffness of the air spring, appropriately reduce its lateral stiffness to attenuate the transmission of vibration along the lateral and longitudinal directions, a compound structure air spring (CSAS) was designed. It is a laminated structure with a hard elastic layer at the lower end of the original air spring. Prototypes of the air spring and the CSAS were produced, then related static and dynamic characteristics tests were conducted. Compared with the test results of the air spring, it can be found that under the same air pressure, the bearing capacity of the CSAS is decreased slightly; under rated load, the vertical static/dynamic stiffness and natural frequency is decreased slightly, and the lateral static/dynamic stiffness is decrease significantly. Furthermore, the CSAS was subjected to the safety and reliability tests, and its performance was stable without damage. This article expands the stiffness range of the air spring, and provides a new idea for the design of the air spring with low lateral to vertical stiffness ratio and low natural frequency.

Broadening of the Sound Absorption Bandwidth of the Perforated Panel Using a Membrane-Type Resonator

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Xuezhi Zhu ◽  
Zhaobo Chen ◽  
Yinghou Jiao ◽  
Yanpeng Wang
Keyword(s):  
Absorption Coefficient ◽  
Sound Absorption ◽  
Degrees Of Freedom ◽  
Low Frequency ◽  
Absorption Capacity ◽  
Sound Absorption Coefficient ◽  
Sound Waves ◽  
Frequency Range ◽  
Absorption Bandwidth ◽  
Membrane Type

In order to broaden the sound absorption bandwidth of a perforated panel in the low frequency range, a lightweight membrane-type resonator is installed in the back cavity of the perforated panel to combine into a compound sound absorber (CSA). Because of the great flexibility, the membrane-type resonator can be vibrated easily by the incident sound waves passing through the holes of the perforated panel. In the low frequency range, the membrane-type resonator and the perforated panel constitute a two degrees-of-freedom (DOF)-resonant type sound absorption system, which generates two sound absorption peaks. By tuning the parameters of the membrane type resonator, a wide frequency band having a large sound absorption coefficient can be obtained. In this paper, the sound absorption coefficient of CSA is derived analytically by combining the vibration equation of the membrane-type resonator with the acoustic impedance equation of the perforated panel. The influences of the parameters of the membrane-type resonator on the sound absorption performance of the CSA are numerically analyzed. Finally, the wide band sound absorption capacity of the CSA is validated by the experimental test.

Approaches to Predicting the Vertical Transmissibility of a Suspension Seat With a Seated Subject

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Jun Wu ◽  
Meihuan Wang ◽  
Yi Qiu
Keyword(s):  
High Frequency ◽  
Dynamic Stiffness ◽  
The Other ◽  
Human Model ◽  
Apparent Mass ◽  
Frequency Range ◽  
Air Suspension ◽  
In Series ◽  
Inert Mass ◽  
Good Agreement

Abstract In this paper, four methods were put forward to predict the transmissibility of an air suspension seat with a seated subject. For characterizing the dynamics of the suspension seat, two of the methods were based on developing a model of the air suspension seat and calibrating the parameters using the transmissibilities of the suspension and complete seat respectively with an inert mass from the experiment. The other two methods substituted the detailed modeling of the seat by two dynamic stiffness connecting in series calculated from two same transmissibilities measured in the experiment. For characterizing the biodynamics of the human body, two of the methods took advantage of the normalized apparent mass from published papers to take the place of the human model, while the other two methods made use of one measured seat transmissibility with a subject to deduce the apparent masses of all the subjects. Good agreement was illustrated between the experiment and model prediction for all the four methods. In addition, it also exhibited that a large discrepancy can be resulted in, especially in the high-frequency range, if the seat model was substituted by one integrated dynamic stiffness.

Advancements in Machinery Management Using the Measurement of Rotor Torsional Response

1997 ◽  
Author(s):  
Alan S. Thomson
Keyword(s):  
Dynamic Stiffness ◽  
Management Tool ◽  
Large Deflections ◽  
Dynamic Motion ◽  
Torsional Response ◽  
Machine Failure ◽  
Shaft System ◽  
Lateral Forces ◽  
Torsional Excitation ◽  
Many Sources

Rotor torsional (angular, steady and dynamic) motion, in response to the interaction of torque and torsional/lateral cross coupled forces with torsional dynamic stiffness, exist in rotating and reciprocating machinery for many reasons. The dynamic torsional response however, is commonly not measured on a continual basis. In the torsional dynamic stiffness, damping parameters are generally several magnitudes weaker than their lateral counterpart. This yields the opportunity for torsional responses, especially when exciting a resonance, to produce relatively large deflections and corresponding stresses, sometimes large enough to cause machine failure. Due to their rigid coupling, long shaft system lengths (a series of shafts coupled together), and large polar moments of inertia, the turbomachinery used in the power generation industry are particularly sensitive to forced torsional excitation. The forcing can come from many sources, including lateral forces which cross couple into torsional forces. Recent research introduces new sources of cross coupled excitation and a method to indirectly measure their and other effects on the mechanical integrity of the mechanical system. A modified and a prototype technique for continuously measuring directly and indirectly the rotor torsional response, and using it to evaluate rotor torsional dynamic stiffness as a machinery management tool is discussed in this paper.

An Overview on a Nonideal System With Three and a Half Degrees of Freedom

2005 ◽  
Author(s):  
Karen de Lolo Guilherme ◽  
Jose´ Manoel Balthazar ◽  
Paulo Roberto Gardel Kurka ◽  
Masayoshi Tsuchida
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamical Behavior ◽  
Mathematical Formulation ◽  
Rotation Frequency ◽  
Steady State Solution ◽  
Dc Motor ◽  
Physical Parameters ◽  
Phase Coordinates ◽  
Limited Power

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor.

Reduction of Hybrid FE-SEA Model for the Mid-Frequency Vibration of Vibro-Acoustic Systems Using Dynamic Condensation Approach

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Ruxin Gao ◽  
Yahui Zhang ◽  
David Kennedy
Keyword(s):  
Present Method ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Fe Model ◽  
Dynamic Matrix ◽  
Acoustic Cavity ◽  
Hybrid Finite Element ◽  
Flexibility Matrix ◽  
Point Of Interest ◽  
Dynamic Condensation

In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.

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