Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems

2005 ◽  
Vol 127 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Parameter Optimization ◽  
Substantial Improvement ◽  
Design Parameters ◽  
Feedback Gain ◽  
Primary System ◽  
Tuned Mass Dampers ◽  
H2 Control ◽  
Damping Coefficients ◽  
The Individual ◽  
Stiffness And Damping

The characteristics of multiple tuned-mass-dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers. Several papers have included some parameter optimization, all based on restrictive assumptions. In this paper, we propose an efficient numerical algorithm to directly optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system. We formulate the parameter optimization as a decentralized H2 control problem where the block-diagonal feedback gain matrix is composed of the stiffness and damping coefficients of the TMDs. The gradient of the root-mean-square response with respect to the design parameters is evaluated explicitly, and the optimization can be carried out efficiently. The effects of the mass distribution, number of dampers, total mass ratio, and uncertainties in system parameters are studied. Numerical results indicate that the optimal designs have neither uniformly spaced tuning frequencies nor identical damping coefficients, and that optimization of the individual parameters in the MTMD system yields a substantial improvement in performance. We also find that the distribution of mass among the TMDs has little impact on the performance of the system provided that the stiffness and damping can be individually optimized.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

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.

Free Parameter Optimization of DTMDs Based on Improved Hybrid Genetic-Simulated Annealing Algorithm

2020 ◽  
Vol 20 (03) ◽  
pp. 2050031
Author(s):  
Qiang Han ◽  
Xuan Zhang ◽  
Kun Xu ◽  
Xiuli Du
Keyword(s):  
Simulated Annealing ◽  
Parameter Optimization ◽  
Free Parameter ◽  
Simulated Annealing Algorithm ◽  
Optimization Method ◽  
Design Parameters ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
Genetic Simulated Annealing Algorithm ◽  
Annealing Algorithm

The optimum design of distributed tuned mass dampers (DTMDs) is normally based on predefined restrictions, such as the location and/or mass ratio of the tuned mass dampers (TMDs). To further improve the control performance, a free parameter optimization method (FPOM) is proposed. This method only restricts the total mass of the DTMDs system and takes the installation position, mass ratio, stiffness and damping of each TMD as parameters to be optimized. An improved hybrid genetic-simulated annealing algorithm (IHGSA) is adopted to find the optimum values of the design parameters. This algorithm can solve the non-convexity and multimodality problems of the objective function and is quite effective in dealing with the large amount of computations in the free parameter optimization. A numerical benchmark model is adopted to compare the control efficiency of FPOM with conventional control scenarios, such as single TMD, multiple TMDs and DTMDs optimized through conventional methods. The results show that the DTMDs system optimized by using FPOM is superior to the other control scenarios for the same value of mass ratio.

On the Dynamics of Elastohydrodynamic Mixed Lubricated Ball Bearings. Part II: Non-Linear Structural Vibration

2005 ◽  
Vol 219 (6) ◽  
pp. 423-433 ◽  
Author(s):  
M Sarangi ◽  
B. C. Majumdar ◽  
A. S. Sekhar
Keyword(s):  
Contact Stiffness ◽  
Equations Of Motion ◽  
Structural Vibration ◽  
Outer Race ◽  
Damping Coefficients ◽  
Lagrange’S Equation ◽  
Non Linear ◽  
Lubricated Contact ◽  
The Individual ◽  
Stiffness And Damping

Equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange's equation considering the vibrational characteristics of the individual constituents such as inner race, outer race, cage, and balls, in order to investigate the structural vibration of the bearing. This article is the second part of the present study dealing with structural vibration, whereas in the first part, elastohydrodynamic mixed lubricated contact stiffness and damping coefficients are determined. Utilizing these stiffness and damping coefficients, a non-linear load-deflection contact model is developed. This is then used in the equations of motion. The equations of motion are solved using Runge-Kutta integration technique. This work differs from the previous studies in the sense that the model simulates the vibration, considering that both the lubricated contact stiffness and damping correspond to the conservative and dissipative energies, respectively. It is observed that under undamped conditions, all the elements of the bearing actively participate in energy sharing and oscillate periodically, containing more than one frequency. The system vibration, however, died down rapidly in the presence of damping.

Stability of Multirecess Hybrid-Operating Oil Journal Bearings

1985 ◽  
Vol 107 (1) ◽  
pp. 116-121 ◽  
Author(s):  
Y. S. Chen ◽  
H. Y. Wu ◽  
P. L. Xie
Keyword(s):  
Finite Difference Method ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Design Parameters ◽  
Stability Threshold ◽  
Damping Coefficients ◽  
Hybrid Bearing ◽  
The Stability ◽  
Stiffness And Damping ◽  
Bearing System

An analysis and a numerical solution using finite difference method to predict the dynamic performance of multirecess hybrid-operating oil journal bearings are presented. The linearized stiffness and damping coefficients of a typical capillary-compensated bearing with four recesses are computed for various design parameters. The corresponding stiffness and the stability threshold of the bearing are then obtained, and the opposite influences of the hydrodynamic action on them are demonstrated. The effect of rotor flexibility on the onset of self-excited whirl is discussed, and a method is given to determine the stability threshold of a rotor-hybrid bearing system.

Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Lei Zuo
Keyword(s):  
Total Mass ◽  
Primary System ◽  
Vibration Absorbers ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
In Series ◽  
New Type ◽  
Parameter Variance ◽  
Stiffness And Damping ◽  
Optimal Series

Various types of tuned-mass dampers (TMDs), or dynamic vibration absorbers, have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multidegree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Decentralized H2 and H∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio of 5% can appear to have 31–66% more mass than the classical TMD, and it can perform better than the optimal parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter variance of the primary system than other TMD(s). Unlike in the parallel multiple TMDs where at the optimum the absorber mass is almost equally distributed, in the optimal series TMDs the mass of the first absorber is generally much larger than the second one. Similar to the 2DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections, and further increased effectiveness can be obtained if a negative dashpot is allowed. The optimal performance and parameters of series two TMDs are obtained and presented in a form of ready-to-use design charts.

scholarly journals Multi-Objective Optimisation of an Aerostatic Pad: Design of Position, Number and Diameter of the Supply Holes

2020 ◽  
Vol 36 (3) ◽  
pp. 347-360
Author(s):  
F. Colombo ◽  
F. Della Santa ◽  
S. Pieraccini
Keyword(s):  
Genetic Algorithm ◽  
Load Capacity ◽  
Design Parameters ◽  
Objective Functions ◽  
Aerostatic Bearing ◽  
Multiobjective Optimisation ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Design Variables ◽  
Stiffness And Damping

ABSTRACTIn this paper, a rectangular aerostatic bearing with multiple supply holes is optimised with a multiobjective optimisation approach. The design variables taken into account are the supply holes position, their number and diameter, the supply pressure, while the objective functions are the load capacity, the air consumption and the stiffness and damping coefficients. A genetic algorithm is applied in order to find the Pareto set of solutions. The novelty with respect to other optimisations which can be found in literature is that number and location of the supply holes is completely free and not associated to a pre-defined scheme. A vector x associated with the supply holes location is introduced in the design parameters and given in input to the optimizer.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

2018 ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Time Domain ◽  
High Speed ◽  
Substantial Improvement ◽  
Reliable Operation ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Radial Injection ◽  
Parametric Studies ◽  
Stiffness And Damping

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid Air Foil Bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB’s film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrate substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Characteristics and Optimization of Series Multiple Tuned-Mass Dampers

2007 ◽  
Author(s):  
Lei Zuo
Keyword(s):  
Total Mass ◽  
Vibration Suppression ◽  
Primary System ◽  
Mass Ratio ◽  
Dynamic Vibration Absorber ◽  
Tuned Mass Dampers ◽  
In Series ◽  
New Type ◽  
Stiffness And Damping ◽  
Better Than

Tuned-mass damper (TMD), or dynamic vibration absorber (DVA), is a very practical and effective device for vibration suppression. Various types of tuned-mass dampers have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multi-degree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Structured H2 and H∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio 5% can appear to have 31%–66% more mass than the classical TMD, and it can perform better than parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter changes of the primary system than other TMD(s). Unlike the parallel multiple TMDs, the optimal mass distribution among absorbers in series TMDs is far from the case of equal masses, but instead the first absorber mass is much larger than the second one. Similar to the two-DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections and further increased effectiveness can be obtained if negative dashpot is allowed.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearing: Part 4 — Fitted Type of Bearings

Tribology ◽  
2006 ◽  
Author(s):  
A. W. Yacout ◽  
A. S. Ismaeel ◽  
S. Z. Kassab
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Major Effect ◽  
Design Parameters ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Spherical Bearing ◽  
Stiffness And Damping ◽  
Fluid Compressibility

Analytical solutions are not available for spherical bearing problems except for very specialized cases. However, this study offers a theoretical analysis, using the first order perturbations, to evaluate the frequency dependent stiffness and damping characteristics of compensated hydrostatic thrust spherical bearing including the surface roughness, the shaft rotation and the recess volume fluid compressibility effects. The dynamic stiffness and damping coefficients are presented for capillary tube and/or office compensated bearing. Results are obtained for various vibration frequencies or squeeze parameters (frequency parameters) and recess volume fluid compressibility parameters in addition to the other usual bearing design parameters. The study shows that both of the surface roughness and the centripetal inertia have slight effect on the stiffness and the damping coefficients while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics.

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