Model generation and parametric study of stick-slip induced vibration for mechanics under friction

As friction is inherently nonlinear, simulating its dynamics in a system is never an easy process. The study suggests a novel friction model that mimics the stiction friction model using sigmoid and exponential functions. The friction force value at 0.01 m/s, or just 1% of the whole velocity range, is precisely provided by the suggested model. The model is found to be more appropriate for linearizing the friction force and is less complex than the comparable friction model that is currently available in literature. The accuracy of computer simulation in proposed friction modeling is contingent upon the value of the sigmoid index. The sigmoid index value of n = 5000 validates the accuracy of the modeling. The simulation results produced by the current LuGre friction model are used to validate the suggested model responses. To comprehend the qualitative and quantitative impact of system factors on its stick-slip behavior under friction, additional interventions are made to the suggested model. It is discovered that the damping ratio (ζ) has the least effect on sticking time, and the static friction to kinetic friction ratio ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) has the largest impact. The novelty of the work is the faster dynamic responses in computer simulation and the correlation between the sticking time and other influencing parameters.