A Method for the Optimal Design of Split Ring Dampers for Aviation Gears

2017 ◽  
Author(s):  
Hang Ye ◽  
Yanrong Wang ◽  
Xianghua Jiang
Keyword(s):  
Damping Ratio ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Forced Response ◽  
Design Parameters ◽  
Dissipated Energy ◽  
Vibration Energy ◽  
Equivalent Damping ◽  
Important Approach ◽  
Energy Dissipated

In order to reduce the resonance of aviation bevel gears, designing frictional interfaces for gear systems is an important approach through dissipate vibration energy. One emerging technology uses ring dampers, which are ring-like substructures constrained to move inside a groove at the rim of the gear. Ring dampers are in contact with the rim of the gear due to centrifugal force, and they create nonlinear dissipation by relative motion between the ring and the gear. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. In this paper an efficient methodology to predict the effect of the ring damper based on energy method, predicting the dissipated energy by friction force, converting into equivalent damping and to identify the main design parameters affecting the damper performance is proposed. The approach is based on expressing the vibration energy dissipated by nonlinear forces per vibration cycle as equivalent nonlinear damping ratio. This method avoids computing the forced response of the gear with ring damper in the frequency domain, that can increase the efficiency of the ring damper design. The methodology is applied to an aviation bevel gear. The effect of the principal design parameters of the ring damper is identified.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1992 ◽  
Vol 114 (2) ◽  
pp. 280-283
Author(s):  
H. Ashrafiuon
Keyword(s):  
Optimal Design ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Flexible Models

This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. Optimal design parameters are computed and compared for the rigid, and flexible models of the base as well as different levels of base flexibility.

Beneficial performance of a quasi-zero stiffness vibration isolator with generalized geometric nonlinear damping

2020 ◽  
pp. 095745652097238
Author(s):  
Chun Cheng ◽  
Ran Ma ◽  
Yan Hu
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Equivalent Damping ◽  
Frequency Responses ◽  
Geometric Nonlinear ◽  
Resonant Region ◽  
Force Transmissibility ◽  
Isolation Performance ◽  
Force And Displacement Transmissibility

Generalized geometric nonlinear damping based on the viscous damper with a non-negative velocity exponent is proposed to improve the isolation performance of a quasi-zero stiffness (QZS) vibration isolator in this paper. Firstly, the generalized geometric nonlinear damping characteristic is derived. Then, the amplitude-frequency responses of the QZS vibration isolator under force and base excitations are obtained, respectively, using the averaging method. Parametric analysis of the force and displacement transmissibility is conducted subsequently. At last, two phenomena are explained from the viewpoint of the equivalent damping ratio. The results show that decreasing the velocity exponent of the horizontal damper is beneficial to reduce the force transmissibility in the resonant region. For the case of base excitation, it is beneficial to select a smaller velocity exponent only when the nonlinear damping ratio is relatively large.

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

2020 ◽  
pp. 107754632094378
Author(s):  
Haiping Liu ◽  
Kaili Xiao ◽  
PengPeng Zhao ◽  
Dongmei Zhu
Keyword(s):  
Resonant Frequency ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Experimental Studies ◽  
Harmonic Balance Method ◽  
Design Parameters ◽  
Base Excitation ◽  
Oscillation System ◽  
Equivalent Damping ◽  
Vibration Transmissibility

Stiffness and damping of a structure usually show the opposite change so that the resonant frequency and the static load bearing capacity of a mechanical system often exhibit contradiction. To solve this dilemma, a novel high-damping oscillator which is constructed by a nested diamond structure with the purpose of enhancing the damping property is proposed in this study without reducing the overall systematic stiffness. The mathematical model and geometrical relationships are established at first. And then, the steady-state solutions under base excitation are derived by using the harmonic balance method and further verified by numerical simulation. In addition, the effects of some design parameters on the equivalent damping ratio for the high-damping oscillator are studied to reveal the nonlinear characteristic. Besides, the natural frequency of the nonlinear oscillator is also presented and investigated. By using the displacement transmissibility and comparing with the traditional linear isolator with the same overall stiffness, the vibration suppression performance of the high-damping oscillator is addressed. The obtained calculating results demonstrate that the vibration control performance of the high-damping oscillator outperforms the linear counterpart around resonant frequency. Moreover, the influences of systematic parameters of the high-damping oscillator for the base excitation case on the vibration transmissibility are also discussed, respectively. Finally, an experimental campaign is conducted on an in-house-built test rig to corroborate the accuracy of the analytical solutions of the high-damping oscillation system. The results discussed in this study provide a useful guideline, which can help to design this class of high-damping oscillation system.

Plain and Full Floating Bearing Simulations With Rigid Shaft Dynamics

2007 ◽  
Author(s):  
Ian McLuckie ◽  
Scott Barrett
Keyword(s):  
System Development ◽  
Equations Of Motion ◽  
Time Integration ◽  
Forced Response ◽  
Design Parameters ◽  
Integration Scheme ◽  
Damping Coefficients ◽  
Time Integration Scheme ◽  
Combined Solution ◽  
Stiffness And Damping

This paper shows a promising predictive bearing model that can be used to reduce turbocharger bearing system development times. Turbocharger development is normally done by varying design parameters such as bearing geometry in a very time consuming experimentation process. Full Floating Bearings (FFB) are used in most automotive turbochargers and, due to emissions regulations, there has been a push towards downsizing engines and applying turbo charging to generate optimized engine solutions for both gasoline and diesel applications. In this paper the turbocharger rotor is regarded as being rigid, and the equations of motion are solved using the Bulirsch Stoer time integration scheme. These equations are solved simultaneously with the bearing model which is used also to determine nonlinear stiffness and damping coefficients. The bearings are solved using a Rigid Hydro Dynamic (RHD) Finite Difference Successive Over Relaxation (SOR) scheme of Reynolds equation that includes both rotational and squeeze velocity terms. However the solver can also consider bearing and rotor elasticity in a Multi-Body Dynamic (MBD) and Elasto-Hydro Dynamic (EHD) combined solution. Two bearing types have been studied, a plain grooved (PGB) and a full floating bearing (FFB) for comparative purposes. The mathematical models used are generic and suitable for whole engine bearing studies. The results in this paper show they are suitable for determining the onset of turbocharger bearing instability, and also the means by which bearing instability may be suppressed. The current study has investigated forced response with the combined effects of gravity and unbalance. It is worth noting that the effects of both housing excitation and aerodynamic excitation from the compressor and turbine can be easily accommodated, and will be the subject of a future paper. Other topics introduced here that will be explored further in the future include the effect of bearing and rotor flexibility in the MBD and EHD solution and the use of automatically generated stiffness and damping coefficients for any bearing geometry.

Optimal Vibration Control and Energy Scavenging Using Collocated Nonlinear Energy Sinks and Piezoelectric Elements

2018 ◽  
Author(s):  
Zahra Nili Ahmadabadi ◽  
Siamak Esmaeilzadeh Khadem
Keyword(s):  
Piezoelectric Element ◽  
Dissipated Energy ◽  
Vibration Energy ◽  
Energy Scavenging ◽  
Optimization Approach ◽  
Energy Harvesters ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Energy Dissipated ◽  
Nonlinear Energy

This paper presents an optimal design for a system comprising multiple nonlinear energy sinks (NESs) and piezoelectric-based vibration energy harvesters attached to a free–free beam under shock excitation. The energy harvesters are used for scavenging vibration energy dissipated by the NESs. Grounded and ungrounded configurations are examined, and the systems parameters are optimized globally to maximize the dissipated energy by the NESs. The performance of the system was optimized using a dynamic optimization approach. Compared to the system with only one NES, using multiple NESs resulted in a more effective realization of nonlinear energy pumping particularly in the ungrounded configuration. Having multiple piezoelectic elements also increased the harvested energy in the grounded configuration relative to the system with only one piezoelectric element.

scholarly journals A Truncated Low Approach of Intrinsic Linear and Nonlinear Damping in Thin Structures

2006 ◽  
Vol 129 (1) ◽  
pp. 32-38
Author(s):  
Yves Gourinat ◽  
Victorien Belloeil
Keyword(s):  
Experimental Data ◽  
Damping Ratio ◽  
Vibrational Analysis ◽  
Nonlinear Damping ◽  
Thin Structures ◽  
Adaptive Approach ◽  
Equivalent Damping ◽  
Linear And Nonlinear ◽  
Algebraic Representations

An adaptive approach of vibrating thin structures is proposed here. The method consists in applying an equivalent adimensional damping ratio to each potential resonance. This ratio is deduced from experimental data obtained in vacuum facility, in relation with frequencies, for several structural technologies. Consequently, it is possible to calculate the structure in a linear nondissipative context, valid out of resonance bands, and truncated in those bands. Thus, the equivalent damping ratio is directly used to define adimensional resonance truncation bandwith and level. The contribution consists in tested and applied modal methodology and algebraic representations of damping including several dissipations—viscous and internal microfrictions—inducing a nonmonotonous model. The here aim is to provide realistic recommendations for simple vibrational analysis of aerospace thin structures—panels and stiffeners.

scholarly journals A Prediction Method for the Damping Effect of Ring Dampers Applied to Thin-Walled Gears Based on Energy Method

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 677 ◽  
Author(s):  
Yanrong Wang ◽  
Hang Ye ◽  
Xianghua Jiang ◽  
Aimei Tian
Keyword(s):  
Numerical Method ◽  
Prediction Method ◽  
Normal Pressure ◽  
Nonlinear Damping ◽  
Forced Response ◽  
Design Parameters ◽  
Response Analysis ◽  
Friction Damping ◽  
Resonance Amplitude ◽  
Thin Walled

In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce resonance amplitude. Ring dampers are installed in the groove. They are held in contact with the groove by normal pressure generated by interference or centrifugal force. Vibration energy is attenuated (converted to heat) by frictional force on the contact interface when the relative motion between ring dampers and gears takes place. In this article, a numerical method for the prediction of friction damping in thin-walled gears with ring dampers is proposed. The nonlinear damping due to the friction is expressed as equivalent mechanical damping in the form of vibration stress dependence. This method avoids the forced response analysis of nonlinear structures, thereby significantly reducing the time required for calculation. The validity of this numerical method is examined by a comparison with literature data. The method is applied to a thin-walled gear with a ring damper and the effect of design parameters on friction damping is studied. It is shown that the rotating speed, geometric size of ring dampers and friction coefficient significantly influence the damping performance.

Analysis of the Dynamic Behavior of the Antiseismic Elastomeric Isolators Based on the Evaluation of the Internal Dissipated Energy

2013 ◽  
Vol 430 ◽  
pp. 317-322 ◽  
Author(s):  
Carmen Alexandru
Keyword(s):  
Dynamic Stiffness ◽  
Damping Ratio ◽  
Viscoelastic Behavior ◽  
Order System ◽  
Dissipated Energy ◽  
Equivalent Damping ◽  
Hysteretic Damping ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
Definition Of

The method of testing the elastomeric isolators at shearing, in a system formed of two elements in parallel, is presented. The exterior actions can be represented by harmonic functions defined as:kinematic excitation through the instantaneous displacement of the form (t)=Asinωt;dynamic excitation through the instantaneous force of the form F(t)=F0sintωt or P(t)=m0rω2sintωt.The linear viscoelastic behavior of the elastomer enables the obtainment of hysteresis curves of elliptical shape for each harmonic loading.In the end, the dynamic stiffness as well as the equivalent damping can be evaluated, with the mention that the stand testing individualizes the dynamic system only through viscous, elastic and inertial forces. Due to this reason, the 1storder differential equation eliminates the definition of the critical damping ratio as for a second order system, which leads to the introduction of the concept of equivalent damping, originating in the hysteretic damping or the loss factor.

scholarly journals Estimation of Additional Equivalent Damping Ratio of the Damped Structure Based on Energy Dissipation

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Xiuyan Hu ◽  
Qingjun Chen ◽  
Dagen Weng ◽  
Ruifu Zhang ◽  
Xiaosong Ren
Keyword(s):  
Energy Dissipation ◽  
Damping Ratio ◽  
Theoretical Concept ◽  
Estimation Methods ◽  
External Excitation ◽  
Single Degree Of Freedom ◽  
Equivalent Damping ◽  
Seismic Motion ◽  
Practical Engineering ◽  
Energy Dissipation Capacity

In the design of damped structures, the additional equivalent damping ratio (EDR) is an important factor in the evaluation of the energy dissipation effect. However, previous additional EDR estimation methods are complicated and not easy to be applied in practical engineering. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the additional EDR. First, an energy governing equation is established to calculate the structural energy dissipation. By means of dynamic analysis, the ratio of the energy consumed by dampers to that consumed by structural inherent damping is obtained under external excitation. Because the energy dissipation capacity of the installed dampers is reflected by the additional EDR, the abovementioned ratio can be used to estimate the additional EDR of the damped structure. Energy dissipation varies with time, which indicates that the ratio is related to the duration of ground motion. Hence, the energy dissipation during the most intensive period in the entire seismic motion duration is used to calculate the additional EDR. Accordingly, the procedure of the proposed method is presented. The feasibility of this method is verified by using a single-degree-of-freedom system. Then, a benchmark structure with dampers is adopted to illustrate the usefulness of this method in practical engineering applications. In conclusion, the proposed method is not only explicit in the theoretical concept and convenient in application but also reflects the time-varying characteristic of additional EDR, which possesses the value in practical engineering.

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