English abstract
Tube expansion is attained by pushing or pulling a mandrel to permanently enlarge its inner diameter. 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 the friction force. This sticking and slipping of mandrel during expansion is termed as stick-slip and results in unexpected changes in tubular length and thickness after expansion. In addition, the expansion force fluctuates considerably to overcome undesirable sticking. A mathematical model was developed to study the dynamics of a stick-slip phenomenon in tube expansion. Three different sets of equation; one each for slip, stick and the transition phases were derived using equilibrium equations, incompressibility condition and Karnopp's friction model. A zero velocity interval was used to define slip, stick and transition phases. A MATLAB program was written to obtain analytical solution using developed governing equations. Further to this, finite element simulation was done using ABAQUS software. Two separate user-defined subroutines were written in FORTRAN to incorporate newly developed stick-slip model. Comparison between experimental, analytical and simulation results showed good agreement for various parameters such as expansion force, thickness reduction and length shortening. The proposed model was able to mimic the stick-slip behavior observed during experimental study. The fluctuation in the displacement-time plot clearly showed sticking of mandrel. Subsequent slipping resulted in large thickness reduction which will reduce the structural integrity of the tube during its service life. Sensitivity analysis showed that the mandrel velocity, friction coefficient, mandrel geometry, and expansion ratio affect the thickness reduction and expansion force required for tube expansion. A careful selection of these parameters is important for enhanced performance of expandable tubular during its service life
