Stick-Slip Modeling

A model to study the dynamics of a stick-slip phenomenon in expansion of tubes was developed. During the permanent deformation process, the system experiences large friction forces at mandrel/tubular interface. This result in an increase of drawing force required for expansion as well as variation in tube thickness along its length. Three different sets of equation; one each for slip phase, stick phase and the transition from stick to slip were derived using equilibrium equations, incompressibility conditions and Karnopp's model. A zero velocity interval was used to define slip, stick and transition phases. The model captured the effect of stick-slip phenomenon on varying thickness reduction along the tube length. The fluctuation in the displacement-time plot clearly indicates the time when the mandrel stuck to the tube. Subsequent slip phase resulted in higher thickness reduction in tube compared to the preceding section. This uneven thickness lowers the structural integrity of the tube during its service life. The results showed that the velocities of mandrel and friction coefficient are critical parameters in minimizing thickness variation after expansion as well as lowering the force required to expand the tube.

The `no-slip' is a fundamental assumption and generally-accepted boundary condition in rheology, tribology and fluid mechanics with strong experimental support. The violations of this condition, however, are widely recognized in many situations, especially in the flow of non-Newtonian fluids. Wall slip could lead to large errors and flow instabilities, such as sharkskin formation and spurt flow, and hence complicates the analysis of fluid systems and introduces serious practical difficulties. In this article, we discuss slip at fluid-solid interface in an attempt to highlight the main issues related to this diverse complex phenomenon and its implications.

A model to study the dynamics of a stick-slip phenomenon in expansion of tubes was developed. During the permanent deformation process, the system experiences large friction forces at mandrel/tubular interface. This result in an increase of drawing force required for expansion as well as variation in tube thickness along its length. Three different sets of equation; one each for slip phase, stick phase and the transition from stick to slip were derived using equilibrium equations, incompressibility conditions and Karnopp's model. A zero velocity interval was used to define slip, stick and transition phases. The model captured the effect of stick-slip phenomenon on varying thickness reduction along the tube length. The fluctuation in the displacement-time plot clearly indicates the time when the mandrel stuck to the tube. Subsequent slip phase resulted in higher thickness reduction in tube compared to the preceding section. This uneven thickness lowers the structural integrity o...

Tube expansion is a metal forming process attained by propagating a rigid mandrel inside the tubular to permanently enlarge its diameters. During this permanent deformation process, the system experiences large friction forces at mandrel/tubular interface. The mandrel ceases to move because of large friction and again moves at higher velocity once the applied force exceeds a threshold friction value. Such friction-induced phenomenon in mandrel movement is termed as stick-slip and results in fluctuations in the force required for expansion as well as variations in the tubular post-expansion dimensions. Analytical, numerical, and experimental analyses of the dynamics of stick-slip phenomenon in tubular expansion were carried out. Three different sets of equation; one each for stick, slip and the transition phases were derived using equilibrium equations, incompressibility condition and Karnopp's friction model. A zero velocity interval was used to define stick, slip and transition phases. A Matlab program was written to obtain analytical solution using the developed governing equations. Numerically, the solution was attained by modifying the process in the commercial finite element software ABAQUS. Two user-defined subroutines were written in Fortran to incorporate the newly developed model. Comparison between experimental, analytical and simulation results showed that a good agreement has been attained for various parameters such as expansion force, thickness reduction and length shortening.

This paper investigates the dynamics a simple dry-friction oscillator which is composed of a block, modeled as a particle, connected to a fixed support by a spring. The block moves over a continuous belt that is driven by rollers. The frictional force between the block and the belt is modeled as a Coulomb friction. Due to this friction model, the resulting motion of the block can be characterized into two qualitatively different modes, the stick- and slip-modes, with a non-smooth transition between them. The focus of the paper is to quantify the percent of time in which the block stays in the stick-mode for a non-constant belt velocity and for different values of the friction coefficient from a deterministic and from a stochastic view point.
keywords. Friction-induced vibration, stick-slip, non-smooth system, nonlinear-dynamics, stick duration, stochastic quantification.

A model to study the dynamics of a stick-slip phenomenon in expansion of tubes was developed. During the permanent deformation process, the system experiences large friction forces at mandrel/tubular interface. This result in an increase of drawing force required for expansion as well as variation in tube thickness along its length. Three different sets of equation; one each for slip phase, stick phase and the transition from stick to slip were derived using equilibrium equations, incompressibility conditions and Karnopp's model. A zero velocity interval was used to define slip, stick and transition phases. The model captured the effect of stick-slip phenomenon on varying thickness reduction along the tube length. The fluctuation in the displacement-time plot clearly indicates the time when the mandrel stuck to the tube. Subsequent slip phase resulted in higher thickness reduction in tube compared to the preceding section. This uneven thickness lowers the structural integrity of...

Tube expansion is a metal forming process attained by propagating a rigid mandrel inside the tubular to permanently enlarge its diameters. During this permanent deformation process, the system experiences large friction forces at mandrel/tubular interface. The mandrel ceases to move because of large friction and again moves at higher velocity once the applied force exceeds a threshold friction value. Such friction-induced phenomenon in mandrel movement is termed as stick-slip and results in fluctuations in the force required for expansion as well as variations in the tubular post-expansion dimensions. Analytical, numerical, and experimental analyses of the dynamics of stick-slip phenomenon in tubular expansion were carried out. Three different sets of equation; one each for stick, slip and the transition phases were derived using equilibrium equations, incompressibility condition and Karnopp's friction model. A zero velocity interval was used to define stick, slip and transition...