In this paper we study a single-degree-of-freedom model with the parallel presence of a linear spring and a Coulomb's contact friction device, the mass slider of which is mounted on the belt which running forward at a constant speed. We prove that no matter what the parameters are, the mass upon starting to slide never comes to stick on the belt. The oscillating amplitude of the slider is proportional to the belt running speed υ, and is inverse proportional to the natural frequency ω. In order to depress the vibration amplitude we may either decrease the belt running speed, increase the stiffness, or decrease the mass; however, the last two strategies may lead to high frequency oscillation of the tool. Increasing the friction bound ry gives no effect on the vibration amplitude, but increases the mean of vibration of the slider; conversely, increasing the stiffness makes the decreasing of the mean of vibration. We also investigate the friction behavior under the dependence of the friction force bound on relative speed, whose curve has negative slope when the relative speed is less than a critical value υ*. According to the qulitative analysis in the phase plane we give simple criteria of the parameters for the stable equilibrium point as well as for the stable limit cycle. When υ varies from υ > υ* to υ < υ*, there undergoes a subcritical Hopf bifurcation of the long term behavior.
"Coulomb Friction Applied to Analyze the Cutting Vibration of Tool on Workpiece,"
Journal of Marine Science and Technology: Vol. 9:
2, Article 7.
Available at: https://jmstt.ntou.edu.tw/journal/vol9/iss2/7