Study On Nonlinear Law Of Sliding Friction Force Of Granular

Through two experiments to explore the problem of friction in the granular system.(1) Study on the Vibration rule of the sandglass pendulum in different flow rate(2) The friction law of the penetration process of the probe rod in the granular reactor.The amplitude and period of sandglass pendulum were studied at different flow rate. The results showed that the amplitude decayed exponentially with time and the period increased exponentially with time. The rate of the change of the swing and period with time increased with the flow rate, and for the same time of vibration, the amplitude and period changed nonlinearly with flow rate.The dynamic equation of sandglass pendulum was established and solved numerically using Matlab. The theoretical results were in better agreement with the experimental results. In the numerical solution can be obtained under six different flow resistance coefficient, can be roughly seen resistance coefficient and flow into a linear relationship. Because sandglass pendulum by the resistance and flow, mass and angular velocity is proportional to, and sandglass pendulum flow, mass and angular velocity are function of time, visible sandglass pendulum by resistance is nonlinear.In granular bed, due to gravity-induced, the detecting rod penetrates down. The experiment shows: Increasing thickness of granular bed, the trajectory of displacement z vs time t changes from concave to convex and its distorting extent changes too. Through the comparison of the experimental results, for the same particle height, when the silo radius is smaller, the friction force in the granular medium is larger, with the increase of the radius of the silo, the friction force is gradually reduced.The experimental data of the resistant factor ? vs time t was obtained indirectly through the dynamical equation and z-t experimental data. The result shows that Increasing thickness of granular bed, ?-t relationship changes from oscillating decrease to oscillating increase and its oscillating extent changes too. The experimental data of ?-t is fitted using a cyclical function. After the ?-t relationship in dynamical equation is substituted by the fitting function, the dynamical function is solved through Matlab software. It is found that the theoretical results are in good agreement with the experimental results.It is the nonlinear characteristics of resistance of the moving object in granular medium that resistant factor decrease oscillatory, increase oscillatory, and their transform with thickness of granular bed.