Vibration and Analysis of Multi-Disk Friction Systems

1998 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Frictional Contact ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Lumped Parameter ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Slip Region ◽  
Stiffness And Damping

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.

scholarly journals Vibrational Interaction of Two Rotors with Friction Coupling

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
H. Larsson ◽  
K. Farhang
Keyword(s):  
Lumped Parameter Model ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Lumped Parameter ◽  
Disk Friction ◽  
Axial Behavior ◽  
Stiffness And Damping Coefficient ◽  
Stiffness And Damping ◽  
Two Parameter ◽  
Very High

A lumped parameter model is presented for studying the dynamic interaction between two disks in relative rotational motion and in friction contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping coefficient in the axial as well as torsional direction. The formulation accounts for the coupling between the axial and angular motions by viewing the contact normal force a result of axial behavior of the system. The model is used to investigate stick-slip behavior of a two-disk friction system. In this effort the friction coefficient is represented as an exponentially decaying function of relative angular velocity, varying from its static value at zero relative velocity to its kinetic value at very high velocities. This investigation results in the establishment of critical curve defining two-parameter regions: one in which stick-slip occurs and that in which stick-slip does not occur. Moreover, the onset and termination of stick-slip, when it occurs, are related to the highest component frequency in the system. It is found that stick-slip starts at a period nearly equal to that of the highest component frequency and terminates at a period almost three times that of the highest component frequency.

Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots

2004 ◽  
Vol 126 (3) ◽  
pp. 498-508 ◽  
Author(s):  
Brandon J. Jellison ◽  
Harold R. Kess ◽  
Douglas E. Adams ◽  
David C. Nelson
Keyword(s):  
Raw Materials ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Mass Distributions ◽  
Lumped Parameter ◽  
Fabrication Procedure ◽  
Modes Of Vibration ◽  
Systemic Problems ◽  
Vibration Tests ◽  
Degenerate Modes

The modes of vibration of manufactured parts can be good indicators of the overall quality of the manufacturing process. That is, deviations in the modal frequencies or modal vectors of mechanical parts can help to identify outlier or systemic problems in the raw materials or fabrication procedure. A novel method for characterizing nonuniformities in homogeneous symmetric parts using pseudorepeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudorepeated roots in dominantly symmetric manufactured parts is a direct indicator of nonuniformities (i.e., inclusions, voids) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less nonuniformity, and hence, higher quality parts. A simple fourth-order lumped parameter model is used to elaborate on this technique analytically, a representative finite element model is used to further this development, root locus techniques are used to study the sensitivity to nonuniformities, and acceleration response data from impact vibration tests on deep drawn hemispherical shells are used to verify the approach experimentally.

Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 1—Stick-Slip Contact Kinematics

1998 ◽  
Vol 120 (2) ◽  
pp. 410-417 ◽  
Author(s):  
B. D. Yang ◽  
C. H. Menq
Keyword(s):  
Friction Force ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Operating Conditions ◽  
Force Model ◽  
Blade Vibration ◽  
Stick Slip ◽  
Friction Forces ◽  
Contact Kinematics ◽  
Stiffness And Damping

Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering, blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.

scholarly journals Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Hailong Xu ◽  
Zhongsheng Chen ◽  
Yongmin Yang ◽  
Limin Tao ◽  
Xuefeng Chen
Keyword(s):  
Natural Frequency ◽  
Vibration Amplitude ◽  
Crack Detection ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Crack Model ◽  
Breathing Crack ◽  
Vibration Localization ◽  
Lumped Parameter ◽  
Amplitude Increase

Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs). Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.

Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model

1996 ◽  
Vol 118 (4) ◽  
pp. 819-823 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Simple Model ◽  
Steady State Solution ◽  
Partial Loss ◽  
Positive Real ◽  
Stick Slip ◽  
Complex Modes ◽  
Constant Friction ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Loss Of Contact

The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. These self-excited oscillations can lead either to partial loss-of-contact or to stick-slip. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.

scholarly journals Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part I — Stick-Slip Contact Kinematics

1997 ◽  
Author(s):  
B. D. Yang ◽  
C. H. Menq
Keyword(s):  
Friction Force ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Operating Conditions ◽  
Force Model ◽  
Blade Vibration ◽  
Stick Slip ◽  
Friction Forces ◽  
Contact Kinematics ◽  
Stiffness And Damping

Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.

scholarly journals Study on the vibration characteristics of coke pushing ram in the coke pushing process

2018 ◽  
Vol 10 (6) ◽  
pp. 168781401878340
Author(s):  
Jin Xiang ◽  
Huanwu Sun ◽  
Qi Shao ◽  
Naixin Sun ◽  
Min Li ◽  
...  
Keyword(s):  
Coke Oven ◽  
Vibration Characteristics ◽  
Low Velocity ◽  
Heavy Load ◽  
Stick Slip ◽  
Factors Affecting ◽  
Regular Production ◽  
Simulation And Experiment ◽  
The Difference ◽  
Stiffness And Damping

Serious vibrations can occur in the coke pushing ram in the coke pushing process and may directly affect the regular production of coke oven, in order to avoid vibration, it is necessary to study the vibration characteristics of coke pushing ram. In this article, the coke pushing resistance is derived via the coke pushing current and a mathematical model of coke pushing ram in the coke pushing process is established to study the vibration mechanism of coke pushing ram. The results indicate that in the low-velocity and heavy-load coke pushing process after the slipper enters the carbonization chamber, the coke pushing velocity is less than the critical velocity, which indicates that the stick-slip vibration occurs in the coke pushing ram, and the factors affecting the coke pushing ram stability mainly include the difference between the static and dynamic friction coefficients, stiffness, and damping. The results are validated by numerical simulation and experiment test.

Modeling and Control of Coupled Torsional and Lateral Vibrations in Drill Strings

2015 ◽  
Author(s):  
Liu Hong ◽  
Jaspreet Singh Dhupia
Keyword(s):  
Sliding Mode ◽  
Good Control ◽  
Friction Torque ◽  
Lumped Parameter Model ◽  
Oil Well ◽  
Lateral Instability ◽  
Stick Slip ◽  
Rock Interaction ◽  
Lateral Vibrations ◽  
Lumped Parameter

Excessive vibrations of the drill strings, e.g., the stick-slip vibration, are the primary cause of premature failures and drilling inefficiencies in oil well drilling. To investigate and suppress such vibrations, this paper studies the dynamics of drill strings using a lumped parameter model, in which both the torsional stick-slip and lateral vibrations are taken into consideration. The friction torque due to the downhole bit-rock interaction, which plays a key role in stick-slip vibration, is modeled as a hysteretic dry friction function. Simulated results of this developed model are shown to have a close qualitative agreement with the field observations in terms of stick-slip vibrations. Afterwards, a sliding mode controller is applied to mitigate the undesired vibrations of drill strings. A good control performance in suppressing the stick-slip phenomenon is demonstrated for the proposed controller. However, numerical simulations also demonstrate that the control action can excite lateral instability in the system, which can result in impacts between the drill collars and the borehole wall due to the large amplitude in lateral vibrations. Thus, a proper choice of the control parameters is essential to suppress the vibrations in the drill strings. The developed lumped parameter model describing the coupled torsional and lateral response in the controlled drill strings presented in this paper can be used to aid in offline tuning of those control variables.

Numerical Analysis of Intermittent Stick-Slip Behaviour of Tube-Support Interaction in Heat-Exchangers

2012 ◽  
Author(s):  
Reza Azizian ◽  
Njuki Mureithi
Keyword(s):  
Heat Exchangers ◽  
Friction Model ◽  
Fretting Wear ◽  
System Response ◽  
Coefficient Function ◽  
Lugre Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Stribeck Effect ◽  
Slip Region

Flow induced excitation forces in heat exchangers cause tube-support interactions. The long-term interaction is an important phenomenon which may cause fretting-wear of the tubes. Experimental tests of the interaction show the occurrence of stick-slip intermittent behavior in the tube response. Many factors are involved to precisely predict the interaction behavior including flow excitation forces, impact and friction forces. One of the explanations behind the intermittent stick-slip behavior may be interpreted by refinements in the conceptual choice of friction model and coefficient of friction. Therefore, among the factors above, the incorporated friction model plays an important role in the determination of the level of fretting-wear in the system. The friction model should satisfy two important criteria: the first important aspect is the strategy of the friction model to detect the cessation of sticking, the beginning of partial slipping and establishment of the sliding region. The second important aspect is defining a friction coefficient function for the entire system response to precisely represent the transient stick-slip regions. In the present work, the velocity limited friction model was compared with the LuGre model which is a rate dependent friction model. The effect of varying the break-away force and Stribeck effect on the stick-slip region was also investigated. Furthermore, the criteria to demarcate the stick-slip region in the LuGre model are discussed and a different method to incorporate the Stribeck effect and presliding damping in the Dahl friction model are proposed. Finally, a new hybrid spring-damper friction model inspired by the Cattaneo-Mindlin stress distribution in the contact region is proposed.

Investigation of Stick-Slip Phenomenon Using a Two-Disk Friction System Vibration Model

1997 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Normal Force ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Disk Friction ◽  
System Vibration ◽  
Axial Behavior ◽  
Two Parameter ◽  
Very High

Abstract A lumped parameter model is presented for studying the dynamic interaction between two disks in relative rotational motion and in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffnesses and damping coefficients in the axial as well as torsional directions. The formulation accounts for the coupling between the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The model is used to investigate stick-slip behavior of a two-disk friction system. In this effort the friction coefficient is represented as an exponentially decaying function of relative angular velocity, varying from its static value at zero relative velocity to its kinetic value at very high velocities. This investigation result in establishment of critical curve defining two parameter regions: one in which stick-slip occurs and that in which stick-slip does not occur. Moreover, the onset and termination of stick-slip, when it occurs, is related to the highest component frequency in the system. It is found that stick-slip starts at a period nearly equal to that of the highest component frequency and terminates at a period almost three times that of the highest component frequency.

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