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The handheld micro tiller is a typical small agricultural machine. It vibrates severely during the rotary tillage process, which harms the users’ health. It is necessary to study its vibration characteristics and propose vibration isolation measurements. Firstly, the external forces applied on various components of the micro-tiller were analyzed. The main components of the handheld micro tiller were simplified. And then the micro-tiller vibration model was built. The time-frequency domain characteristics of the micro-tiller were analyzed. The main components’ RMS values were calculated. It shows that the excitation force of the engine is the main source of vibration of the micro-tiller. The simulated RMS values of the frame and the gearbox were compared to the tested values. The errors indicate the established model is to some extent reasonable. In order to reduce the vibration transmitted to the handrail, firstly, the ordinary bolts connecting the engine and the frame were replaced with rubber bolts. And then the RMS value was analyzed and calculated. The results showed that this method could not effectively reduce the vibration of other main components. Furthermore, it is considered to install a vibration isolator between the engine and the frame of the tiller. Time-frequency domain simulation results show that after adding the vibration isolator, the vibration RMS value of each component was much smaller than before. It shows that it isolates the engine vibration effectively. The research in this paper laid the foundation for designing a reasonable vibration isolator and reducing the vibration of the main components of the tiller.

The unsteady lubrication is one of the major causes for self-excited vibration in rolling. But it is difficult to build a rolling chatter model which considers the unsteady lubrication state in roll bite. Using the regression exponential function model of rolling friction coefficient, a dynamic rolling process model was built. Coupling the dynamic rolling process model with a mill stand structure model, a chatter model which considers the unsteady lubrication state at roll bite was established. Based on the proposed chatter model, the friction coefficient, rolling force and critical velocity of a rolling mill stand under different working conditions were calculated. The computed results were compared to the test results. And it proves the validity of the proposed model. With the proposed chatter model, the effects of rolling process parameters and emulsion lubricant characteristic parameters on friction coefficient and critical velocity were both analyzed and discussed. The chatter model successfully introduces the unsteady friction model into the rolling mill chatter model. It better explains the negative damping effect of the rolling chatter and reflects the rolling mill dynamic vibration characteristic.

Considering the unstable oscillation in the rolling process caused by the lubrication conditions change, a dynamic rolling process model considering the nonlinear friction is built using the Bland-Ford-Hill rolling force model. In addition, based on the structure model which can characterize the coupling vibration of rolling mill, and taking the dynamic variations of rolling force and rolling torque as the feedback excitation, the rolling mill vertical-torsional-horizontal coupled dynamic model under nonlinear friction is established. On this basis, the system Hopf bifurcation points at different rolling speeds are calculated by Hurwitz algebraic criterion. And the system stability domain is determined by analyzing the eigenvalue of the system. Finally, using the parameters of a 2030 cold rolling mill, the correctness of the bifurcation point calculation and the stability domain analysis are verified by numerical simulation. The results show that the system stability domain is enclosed by the instability critical lines of vertical vibration modal, torsional vibration modal and horizontal vibration modal. And under different conditions, the system Hopf bifurcation induced by the variation of the friction coefficient can cause system instability with different vibration modals. The study can help to optimize the rolling process, and achieve a reasonable dynamic modification strategy of the rolling mill structure as well.