A New Structural Dynamic Model for Pump Mechanical Seals Vibration Analysis Incorporating Squeeze Motion of O-Ring Seals and General Dynamic Motion of the Pump Housing and the Pump Shaft

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Dara Childs
Keyword(s):  
Reaction Force ◽  
Excitation Frequency ◽  
Nonlinear Function ◽  
Force Model ◽  
Mechanical Seals ◽  
Structural Dynamic ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Force Components ◽  
Stiffness And Damping

New models are developed for flexibly mounted stator (FMS) and flexibly mounted rotor (FMR) mechanical seals that incorporate the radial reaction force components produced by supporting O-rings due to relative squeezing motion across the O-rings. Supporting data come from tests done in relation to O-ring supports for ball bearing races. The reaction-force model is linear but a nonlinear function of excitation frequency. The model accounts for the axial displacement doz of the O-ring from the mass center of the seal stator (FMS configuration) or seal rotor (FMR configuration), which couples the radial and pitch–yaw motion of the model's stiffness and damping matrices. Greens' coned-face-seal model is used to define the reaction moment arising across the seal faces via stiffness and damping matrices. The damping matrix does not coincide with Green's. His is constant; the matrix developed here contains terms that are harmonic at twice theprecession frequency. When averaged over one precession cycle, the new average damping matrix coincides with Green's result. When the averaged damping matrix is used, the resultant model is linear. However, because of the viscoelastic reaction-force and reaction-moment models used for the O-ring coefficients, most of the stiffness and damping matrices are strong functions of the assumed precession frequency. The new FMR model contains a skew-symmetric stiffness matrix due to the O-ring damping terms. In rotordynamics, skew symmetric stiffness matrices due to internal damping in the rotor can lead to rotordynamic instabilities.

scholarly journals Dynamic Forces of Swaying Human and Responses of Temporary Demountable Grandstand Based on Experiment and Simulation

2018 ◽  
Vol 2018 ◽  
pp. 1-22
Author(s):  
Lin He ◽  
Jian Yuan ◽  
Feng Fan ◽  
Cong Liu
Keyword(s):  
Force Plate ◽  
Dynamic Responses ◽  
Experimental Program ◽  
Force Model ◽  
Lateral Vibration ◽  
Structural Dynamic ◽  
Important Research Topic ◽  
Dynamic Forces ◽  
Semiempirical Formula ◽  
Stiffness And Damping

Modern temporary demountable structures must be designed to withstand the dynamic forces which generated by crowd occupants. The human forces and that cause the dynamic responses of structure have become an important research topic. In this paper, the human swaying forces and responses of temporary demountable grandstand are studied through an experimental program. The dynamic forces that were induced by participants who have swayed 0.5–1.8 Hz are recorded by a triaxial human biomechanics force plate, and the structural dynamic responses of a temporary grandstand occupied twenty swaying human are investigated. The constraint parameters of swaying force model which derives from a semiempirical formula are developed and can be represented for crowd. Crowd can able to induce excessive lateral vibration of structure due to the lower frequency of temporary grandstand and make them in panic. The dynamic responses of a large temporary grandstand are predicted by finite element method, and the results show that a person was considered as a load with stiffness and damping, and the structural lateral dynamic responses are higher than the model of person just only considered as load.

Estimation of Mass, Stiffness and Damping Matrices from Frequency Response Functions

1996 ◽  
Vol 118 (1) ◽  
pp. 78-82 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Least Squares Method ◽  
Transformation Matrix ◽  
Frequency Domain Method ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Normal Frequency ◽  
Stiffness And Damping

A frequency-domain method for estimating the mass, stiffness and damping matrices of the model of a structure is presented. The developed method is based on our previous work on the extraction of normal modes from the complex modes of a structure. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the damping matrix of the system. The mass and the stiffness matrices are identified from the normal frequency response functions by using the least squares method. Two simulated systems are employed to illustrate the applicability of the proposed method. The results indicate that the damping matrix can be identified accurately by the proposed method. The reason for the good results is that the damping matrix is identified independently from the mass and the stiffness matrices. In addition, the robustness of the new approach to uniformly distributed measurement noise is also addressed.

scholarly journals Journal Bearing Impedance Descriptions for Rotordynamic Applications

1977 ◽  
Vol 99 (2) ◽  
pp. 198-210 ◽  
Author(s):  
D. Childs ◽  
H. Moes ◽  
H. van Leeuwen
Keyword(s):  
Finite Length ◽  
Reaction Force ◽  
Squeeze Film ◽  
Damping Coefficients ◽  
Analytic Expressions ◽  
Complete Set ◽  
Impedance Vector ◽  
Force Components ◽  
Stiffness And Damping ◽  
Vector Magnitude

Bearing impedance vectors are introduced for plain journal bearings which define the bearing reaction force components as a function of the bearing motion. Impedance descriptions are developed directly for the approximate Ocvirk (short) and Sommerfeld (long) bearing solutions. The impedance vector magnitude and the mobility vector magnitude of Booker are shown to be reciprocals. The transformation relationships between mobilities and impedance are derived and used to define impedance vectors for a number of existing mobility vectors including the finite-length mobility vectors developed by Moes. The attractiveness and utility of the impedance-vector formulation for transient simulation work is demonstrated by numerical examples for the Ocvirk “π”, and “2π” bearing impedances and the cavitating finite-length-bearing impedance. The examples presented demonstrate both bearing and squeeze-film damper application. A direct analytic method for deriving a complete set of (analytic) stiffness and damping coefficients from impedance descriptions is developed and demonstrated for the cavitating finite-length-bearing impedances. Analytic expressions are provided for all direct and cross-coupled stiffness and damping coefficients, and compared to previously developed numerical results. These coefficients are used for stability analysis of a rotor, supported in finite-length cavitating bearings. Onset-speed-of-instability results are presented as a function of the L/D ratio for a range of bearing numbers. Damping coefficients are also presented for finite-length squeeze-film dampers.

A Review of Damping Matrix Identification Methods in Structural Dynamics

2012 ◽  
Author(s):  
Sharad Pradhan ◽  
S. V. Modak
Keyword(s):  
Model Updating ◽  
Element Model ◽  
Finite Element Model Updating ◽  
Structural Dynamic ◽  
Identification Methods ◽  
Damping Matrix ◽  
Matrix Modeling ◽  
Stiffness Matrices ◽  
And Control ◽  
Damping Model

Damping matrix modeling and identification has important applications in many engineering fields such as vibration analysis and control, modal analysis, condition monitoring and structural dynamic modifications. A damping model should represent both the mechanism and spatial distribution of the energy loss in the system. In contrast to the mass and stiffness matrices, formulation of the damping matrix still stands as a big challenge in modeling a linear dynamic system. Several methods have been proposed in the literature to identify the damping and the parameters of a damping matrix from measurements on a vibrating system. It is felt that a review of the various approaches developed would help to compare their main features and their relative advantages or limitations to allow for choosing the most suitable method for a particular application. In view of this, this paper presents a review of the methods of damping identification in general, but with more emphasis on the methods developed in the framework of finite element model updating.

Design and structural performance measurements of a novel multi-cantilever foil bearing

2014 ◽  
Vol 229 (10) ◽  
pp. 1830-1838 ◽  
Author(s):  
Kai Feng ◽  
Xueyuan Zhao ◽  
Zhiyang Guo
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Foil Bearing ◽  
Load Tests ◽  
Stiffness And Damping ◽  
Motion Amplitude

With increasing need for high-speed, high-temperature, and oil-free turbomachinery, gas foil bearings (GFBs) have been considered to be the best substitutes for traditional oil-lubricated bearings. A multi-cantilever foil bearing (MCFB), a novel GFB with multi-cantilever foil strips serving as the compliant underlying structure, was designed, fabricated, and tested. A series of static and dynamic load tests were conducted to measure the structural stiffness and equivalent viscous damping of the prototype MCFB. Experiments of static load versus deflection showed that the proposed bearing has a large mechanical energy dissipation capability and a pronounced nonlinear static stiffness that can prevents overly large motion amplitude of journal. Dynamic load tests evaluated the influence of motion amplitude, loading orientation and misalignment on the dynamic stiffness and equivalent viscous damping with respect to excitation frequency. The test results demonstrated that the dynamic stiffness and damping are strongly dependent on the excitation frequency. Three motion amplitudes were applied to the bearing housing to investigate the effects of motion amplitude on the dynamic characteristics. It is noted that the bearing dynamic stiffness and damping decreases with incrementally increasing motion amplitudes. A high level of misalignment can lead to larger static and dynamic bearing stiffness as well as to larger equivalent viscous damping. With dynamic loads applied to two orientations in the bearing midplane separately, the dynamic stiffness increases rapidly and the equivalent viscous damping declines slightly. These results indicate that the loading orientation is a non-negligible factor on the dynamic characteristics of MCFBs.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

Identification of Viscously Damped Distributed Structural Dynamic Systems

1991 ◽  
Author(s):  
R. Chander ◽  
M. Meyyappa ◽  
S. Hanagud
Keyword(s):  
Dynamic Systems ◽  
Beam Theory ◽  
Continuous Functions ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Structural Dynamic ◽  
Domain Identification ◽  
Forcing Function ◽  
Cardinal Splines ◽  
Stiffness And Damping

Abstract A frequency domain identification technique applicable to damped distributed structural dynamic systems is presented. The technique is developed for beams whose behavior can be modeled using the Euler-Bernoulli beam theory. External damping of the system is included by means of a linear viscous damping model. Parameters to be identified, mass, stiffness and damping distributions are assumed to be continuous functions over the beam. The response at a discrete number of points along the length of the beam for a given forcing function is used as the data for identification. The identification scheme involves approximating the infinite dimensional response and parameter spaces by using quintic B-splines and cubic cardinal splines, respectively. A Galerkin type weighted residual procedure, in conjunction with the least squares technique, is employed to determine the unknown parameters. Numerically simulated response data for an applied impulse load are utilized to validate the developed technique. Estimated values for the mass, stiffness and damping distributions are discussed.

scholarly journals Road Vehicle-Bridge Interaction considering Varied Vehicle Speed Based on Convenient Combination of Simulink and ANSYS

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Helu Yu ◽  
Bin Wang ◽  
Yongle Li ◽  
Yankun Zhang ◽  
Wei Zhang
Keyword(s):  
Reaction Force ◽  
Sudden Change ◽  
Vertical Direction ◽  
Dynamic Responses ◽  
Force Model ◽  
Vertical Acceleration ◽  
Vehicle Speed ◽  
Road Vehicle ◽  
The Road ◽  
Bridge Model

In order to cover the complexity of coding and extend the generality on the road vehicle-bridge iteration, a process to solve vehicle-bridge interaction considering varied vehicle speed based on a convenient combination of Matlab Simulink and ANSYS is presented. In this way, the road vehicle is modeled in state space and the corresponding motion equations are solved using Simulink. The finite element model for the bridge is established and solved using ANSYS. The so-called inter-history iteration method is adopted to realize the interaction between the vehicle model and the bridge model. Different from typical method of road vehicle-bridge interaction in the vertical direction, a detailed longitudinal force model is set up to take into account the effects of varied vehicle speed. In the force model, acceleration and braking of the road vehicle are treated differently according to their mechanical nature. In the case studies based on a simply supported beam, the dynamic performance of the road vehicle and the bridge under varied vehicle speeds is calculated and discussed. The vertical acceleration characteristics of the midpoint of beam under varied vehicle speed can be grouped into two periods. The first one is affected by the load transform between the wheels, and the other one depends on the speed amplitude. Sudden change of the vertical acceleration of the beam and the longitudinal reaction force are observed as the wheels move on or off the bridge, and the bridge performs different dynamic responses during acceleration and braking.

Research on Stiffness and Damping Characteristics of Fixed Oily Porous Materials Joint Interface

2011 ◽  
Vol 422 ◽  
pp. 575-579
Author(s):  
Chong Nian Qu ◽  
Liang Sheng Wu ◽  
Jian Feng Ma ◽  
Yi Chuan Xiao
Keyword(s):  
Porous Material ◽  
Porous Materials ◽  
Parallel Plate ◽  
Joint Interface ◽  
Force Model ◽  
Equivalent Stiffness ◽  
Contact State ◽  
Damping Characteristics ◽  
Stiffness And Damping ◽  
Damping Model

In this document, using the anti-squeezed force model in the narrow parallel plate when fluid is squeezed, the equivalent stiffness and damping model is derived. It is further verified that it can increase the stiffness and damping while there are oil between the joint interfaces theoretically. Because the contact state of oily porous material can divide into liquid and solid parts, the document supposes that it is correct and effective to think the stiffness and damping of the two parts as shunt connection.

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