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.

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.

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.

Prediction of Resonant Response of Shrouded Blades With 3D Shroud Constraint

1998 ◽  
Author(s):  
B. D. Yang ◽  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Normal Load ◽  
Three Dimensional ◽  
Force Model ◽  
Resonant Response ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Contact Plane ◽  
Blade System ◽  
Stiffness And Damping

In this paper, the 3D shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely 2D constraint and 3D constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

scholarly journals Active Control Method Based on Equivalent Stiffness and Damping Coefficient for an Electromagnetic Isolation System

2020 ◽  
Vol 10 (22) ◽  
pp. 7953
Author(s):  
Lei Zhang ◽  
Xiangtao Zhuan
Keyword(s):  
Control Method ◽  
Dynamic Performance ◽  
Damping Coefficient ◽  
Stiffness Coefficient ◽  
Equivalent Stiffness ◽  
Isolation System ◽  
Performance Indexes ◽  
Stiffness And Damping Coefficient ◽  
Stiffness And Damping ◽  
Active Control Method

For improving the performance of an electromagnetic isolation system with reasonable parameters and avoid the parameter tuning problem of a PID controller, an active control method is put forward based on equivalent stiffness and damping coefficient. In this paper, the range of equivalent stiffness coefficient and damping coefficient of the electromagnetic force are calculated based on the required range of dynamic performance indexes. According to the nonlinear expression between electromagnetic force and coil current and gap, the relationships between the coil current and equivalent stiffness coefficient and damping coefficient are established. Then, the equivalent stiffness coefficient and damping coefficient can be satisfied by the controlled current in different gaps for meeting the required dynamic performance indexes. For reducing the maximum overshoot and the number of oscillations of the system, the active control method with the piecewise equivalent stiffness and damping coefficient is proposed based on the piecewise control strategy to realize the variable control parameters of the isolation system. Simulation and experimental results verify that the control method based on the equivalent stiffness and damping coefficient can obtain the desired dynamic performance indexes and the proposed control method with the piecewise strategy can not only reduce the setting time of the system, but also ensure the stability of the system.

Prediction of Resonant Response of Shrouded Blades With Three-Dimensional Shroud Constraint

1999 ◽  
Vol 121 (3) ◽  
pp. 523-529 ◽  
Author(s):  
B. D. Yang ◽  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Normal Load ◽  
Three Dimensional ◽  
Force Model ◽  
Resonant Response ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Contact Plane ◽  
Blade System ◽  
Stiffness And Damping

In this paper, the three-dimensional shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely two-dimensional constraint and three-dimensional constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

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.

A Theoretical Model for Calculating Vibration Characteristics of A Kind of Driver Seat with Air Spring and MR Damper

2011 ◽  
Vol 141 ◽  
pp. 8-14 ◽  
Author(s):  
Xing Xing Zhu ◽  
Si Hong Zhu
Keyword(s):  
Mr Damper ◽  
Damping Coefficient ◽  
Orifice Diameter ◽  
Equivalent Stiffness ◽  
Air Spring ◽  
Seat Suspension ◽  
Study Results ◽  
Stiffness And Damping Coefficient ◽  
Mr Damping ◽  
Stiffness And Damping

In order to further reduce the vibration transmitted from vehicle to driver, a new model of driver scissors linkage seat suspension was put forward, in which an air spring with auxiliary chamber and a MR damper are between the face and floor of the seat. The motion differential equation of this seat suspension system was established and the theoretical computing formulation of it’s equivalent vertical stiffness, equivalent damping coefficient, natural frequency and damping rate were deduced. Besides, taking HY-Z04 scissors linkage seat, SK37-6 air spring of ContiTech and RD-1005-3 MR damper of LORD as an example, the equivalent stiffness and damping coefficient in different conditions of the air spring pressure, the sprung mass, the orifice diameter and MR damping were computed and analyzed. The study results show that the air spring pressure, the sprung mass, the orifice diameter and MR damping all have obvious influence on the equivalent stiffness and damping coefficient, so the seat comfort can be improved by changing the air spring pressure, the orifice diameter and MR damping according to driver’s weight and road condition.

Dynamic Response of Two-Disk Systems With Friction and Misalignment

1998 ◽  
Author(s):  
Ahmed Anabtawi ◽  
Kambiz Farhang
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Contact Stiffness ◽  
Stick Slip ◽  
Torsional Response ◽  
Damping Characteristics ◽  
Disk Friction ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Friction Induced Vibration

Abstract Friction induced vibration and noise pose one of the most challenging problems. The complexity of the friction system arises due to the nonlinear nature of friction phenomena and that of contact stiffness and damping. This paper presents a mathematical model for studying the dynamic response of two-disk friction system in the presence of misalignment. The contact stiffness and damping characteristics of the system are represented in the axial as well as the torsional directions. In addition, the axial and torsional responses of the system are coupled by assuming dependency between the torsional response and the normal force between the two disks. Using the mathematical model, various scenarios are examined to study the effect of misalignment. These include cases of symmetric and asymmetric actuation forces as well as forces applied at unequal actuation times. The results suggest that asymmetry in actuation forces has negligible effect on stick-slip behavior of the system.

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