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

Volume 1D: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-4162 ◽

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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Vibrational Interaction of Two Rotors with Friction Coupling

Advances in Acoustics and Vibration ◽

10.1155/2016/9275147 ◽

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.

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Vibration and Analysis of Multi-Disk Friction Systems

Volume 1A: 25th Biennial Mechanisms Conference ◽

10.1115/detc98/mech-5811 ◽

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.

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Lumped Parameter Model of Planetary Gear Systems

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1978_192_026_02 ◽

1978 ◽

Vol 192 (1) ◽

pp. 251-258 ◽

Cited By ~ 5

Author(s):

J. W. Polder

Keyword(s):

Degrees Of Freedom ◽

Planetary Gear ◽

Lumped Parameter Model ◽

Damping Coefficients ◽

Planetary Gear Trains ◽

Lumped Parameter ◽

Vibration Model ◽

Close Relationship ◽

Angular Velocities ◽

Gear Trains

A model system is described by parameters for shafts, planetary gear trains and nodes. Moments of inertia, spring stiffnesses and damping coefficients are assigned to the shafts; gear ratios and efficiencies are assigned to planetary gear trains. The equivalence of angular velocities and torques is demonstrated for shafts (vibration model), as well as for planetary gear trains and nodes (configuration of the system). This brings about a new view on the concept of degrees of freedom. The close relationship between gear ratios and torque ratios yields identical functions for these ratios when applied to the input and output shafts of a system. The full use of this relationship requires strict conventions of signs and an extension of the interpretation of values. The introduction of a new concept, named responsivity, expresses the relationships between torques and between powers of arbitrary shafts. With suitable equations, it becomes possible to investigate torque and power distributions exhaustively.

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

Volume 2: Diagnostics and Detection; Drilling; Dynamics and Control of Wind Energy Systems; Energy Harvesting; Estimation and Identification; Flexible and Smart Structure Control; Fuels Cells/Energy Storage; Human Robot Interaction; HVAC Building Energy Management; Industrial Applications; Intelligent Transportation Systems; Manufacturing; Mechatronics; Modelling and Validation; Motion and Vibration Control Applications ◽

10.1115/dscc2015-9714 ◽

2015 ◽

Cited By ~ 1

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.

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A Lumped Parameter Vibration Model Developed Based on a Realistic Kinematic Description of the Hand-Arm System

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2010-40466 ◽

2010 ◽

Author(s):

Shrikant Pattnaik ◽

Jay Kim

Keyword(s):

Prolonged Exposure ◽

Lumped Parameter Model ◽

Accurate Analysis ◽

Response Characteristics ◽

Lumped Parameter ◽

Vibration Model ◽

Lumped Parameter Models ◽

Musculoskeletal Abnormalities ◽

Matching Response ◽

Gripping Force

Prolonged exposure of hand to vibration causes vascular, neurological and musculoskeletal abnormalities, which are collectively known as hand-arm vibration syndrome (HAVS). A significant number of construction workers, miners and even dentists are affected by HAVS. The precise mechanism or pathogenesis of the syndrome is still not clearly understood. Accurate analysis of hand-arm vibration response is very difficult due to the complexity of the hand-arm structure such as redundancy of the musculo-tendon unit, active participation from central nervous system, inherent non-linearity and heavy damping effect. Various types of lumped parameter models have been developed, typically by matching response characteristics of the model with the measurement. Not being based on the actual physics of the hand-arm, such a model has limited applications such as qualitative, relative analysis of the hand-arm response. A new lumped parameter model is developed in this work retaining as much actual kinematic characteristics of the hand and arm system as possible. The model includes descriptions of relevant musculo-tendon systems and the effect of the gripping force to enable calculation of the forces transmitted through the musculo-tendon system and joints.

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