| In grinding process,vibration ball mill plays a key role as one of important tools with broad applications in mineral,chemical and ceramic industries.Conventional ball mills,such as planetary ball mills and cone ball mills,require multi-stage transmission devices,which inevitably leads to complicated structure,low grinding quality and efficiency.However,the vibration synchronization technology can make the system structure more compact and improve grinding quality with less production time and cost.On the basis of former studies,combining with the practical needs of engineering,three new vibration ball milling systems are proposed in this paper.They are double grinding drums driven by two exciters,double grinding drums driven by four exciters and three grinding drums driven by three exciters respectively.The synchronization principle and the coupling dynamic characteristics of the ball mill system from two to four machines and from two to three grinding drums are investigated,and the ideal working areas and matching parameters of the three systems are analyzed as well.These provide a reference for optimization design of vibration ball mills.The main research contents include:(1)Based on the model of the double vibration ball mill system driven by two exciters,the dynamic characteristics and parameter matching rules are investigated.By building the system motion differential equations,the synchronization and stability conditions are derived according to the averaging method and Hamilton principle.Based on the numerical analysis method of the theoretical results,the amplitude-frequency response,synchronization and stability of the system under different excitation frequencies and the three kinds of phase relations at the steady state are analyzed qualitatively.The synchronous stable region where the system geometric parameters are matched with the frequency parameters is divided,and the parameter matching relations corresponding to the ideal working area of the system are determined.Ultimately,the effectiveness of the theoretical results is verified by numerical simulations.The parameter design and function optimization of the machine system are also achieved.(2)On the basis of the last chapter,the driving force of the system is enhanced by increasing the quantity of motors.Under the horizontally symmetrical arrangement of double grinding drums and the four motors,the dynamic model of the vibration ball mill with double grinding drums driven by four exciters is given.Its dynamic characteristics and parameter optimization problem are discussed.The synchronization and stability criteria of the system are also given.In numerical analysis,the natural frequency is used as the dividing point.The amplitude frequency characteristics are analyzed in different areas.The synchronization,stability and phase relationships of the exciter(unbalanced rotor driven by an AC motor)with different mass ratios are given.Meanwhile,the machine function in each area is pointed out.Besides,the simulations are made to verify the reliability of the above theoretical analysis.According to the results,the optimal working range could be determined through avoiding the multiple equilibrium point area.(3)The dynamic characteristics and parameter matching of the vibration ball mill with three grinding drums driven by three exciters are discussed.The system motion differential equation is derived by using the Lagrange equation.The coupling synchronization criterion of three exciters is obtained according to the average method.The stability criterion in the synchronous state is acquired by using the Hamilton principle.In numerical simulations,the three types of phase relations,the steady states and the final motion type in different resonance regions.The simulation results show that the best working point of the system should be set in zone I when the three main working mass can go around in a circle with high vibration strength,and the vibration forces among them can cancel each other out,which makes the load of the foundation from the external body close to 0.Under the premise of improving the machine efficiency,the vibration isolation problem is solved without adding the vibration isolation mechanism from the angle of the system synchronization,which makes the structure more compact.(4)Based on the theoretical analysis results of the above three vibration ball mill mechanical systems,it is concluded that each system has the following characteristics in its ideal working area:the motion form of the mass center of the internal mass(the working mass)is circular motion or approximate circular motion;the operating frequency,amplitude and trajectory of multiple working bodies are completely consistent.Therefore,this chapter considers the particle flow effect of materials,and the kinematic parameters of the above theory are only given to a single grinding drum for EDEM simulation analysis.According to the control variable method,the matching parameters corresponding to a good ball milling effect are obtained.Finally,a summary is presented for further research. |
