【作者】 王志辉；

【导师】 张学良；

【作者基本信息】 东北大学 ， 机械设计及理论， 2020， 硕士

【摘要】 随着科学技术的不断发展,对机械性能的要求也越来越高。为了提高效率,常常需要安装两个或多个电机同时协同工作,因此研究振动同步理论意义重大。自两机驱动自同步振动机械出现以来,许多科研工作者研究了激振器实现同步的耦合机理,也发表了部分相关论文。但这些研究成果大多是建立在相同驱动频率基础上的,而关于激振器的倍频同步理论研究甚少。因此,本课题将双机及多机驱动的基频同步拓展到倍频同步(二倍频及三倍频),以此实现系统双频激励之目的。提出四类典型机械系统动力学模型,研究两个或多个激振器在不同分布方式、不同旋转方向等条件下的倍频同步机理,可为工程中新型双频驱动振动设备的设计提供参考。具体研究内容如下:(1)揭示了超远共振条件下两激振器同向回转时的二倍频及三倍频同步机理。基于Lagrange方程求出系统运动微分方程,利用渐近法得到两激振器间相位关系式,推导出转速比分别为1:2和1:3时两激振器实现同步的条件,得到稳定性条件,其结果符合Routh-Hurwith稳定性准则。数值上分析了系统的动力学特性,定义了稳定性指数并分析其与无量纲参数之间的关系。应用Runge-Kutta程序进行仿真,得到了电机转速、相位差、质体位移及稳态时平面运动轨迹等曲线图,最后通过试验验证了理论及仿真结果的有效性。(2)研究了超远共振状态下同向回转三激振器的二倍频同步。理论上得到直线分布三机驱动单质体机械系统动力学模型的运动微分方程,结合渐近法和平均法得到激振器在二倍频条件下的同步性判据及稳定性判据,并定义了稳定性指数。数值上给出稳定性指数等特性曲线,讨论了系统的稳定性能力。通过仿真及试验结果的对比分析,验证了理论结果的有效性及所用理论分析方法的可行性,为工程中复频振动筛分设备的功能化设计提供理论指导。(3)分析了反向回转四机驱动单质体机械系统的二倍频和三倍频同步理论。基于Lagrange方程推导出系统的运动微分方程,应用渐近法得到四个激振器在二倍频和三倍频条件下的相位关系表达式,并推导出激振器间实现同步的同步性和稳定性条件解析表达式。数值上分析了系统的动力学特性,揭示结构参数对系统稳定性的影响,并给出仿真及试验结果,以此验证和修正理论模型。该研究可以为新型振动摇筛及振动成型设备的设计提供参考。(4)揭示了隔振条件下四机驱动双质体机械系统在二倍频和三倍频条件下的振动同步机理。运用渐近法推导出四个激振器实现倍频同步的同步性判据,得到其同步状态下的稳定性判据,其结果符合Routh-Hurwith准则。同时定义了稳定性能力指数,数值上讨论了系统的稳定性能力,得到了激振器间的稳定相位差。应用Runge-Kutta程序对系统实现仿真,验证了理论结果的有效性,为工程中新型振动密实装备的设计提供理论基础。更多还原

【Abstract】 With the continuous development of science and technology,the requirement of machine performance is becoming higher and higher.In order to improve efficiency,it is necessary to install two or more motors to work together at the same time,it is,therefore,of great significance to study the theory of vibratory synchronization.Since the emergence of self-synchronous vibrating machines driven by two motors,many researchers have studied the coupling mechanism of exciters to achieve synchronization,and published some relevant papers.However,most of these research achievements are based on the same driving frequency,and few theoretical studies on the multi-frequency synchronization of exciters.So,this paper will extend the fundamental frequency synchronization to multi-frequency synchronization(double-frequency and triple-frequency synchronization),which achieves the purpose of dual frequency excitation for the system.Four typical dynamical models of mechanical system are proposed,the multi-frequency synchronization mechanisms of two or multiple exciters with different distribution modes,different rotational directions and other conditions are studied,which can provide a reference for the design of new dual-frequency driving vibration equipment in engineering.Specific research contents are as follows:(1)The mechanisms of double-frequency and triple-frequency synchronization for two exciters in the same direction under the far super-resonance condition are revealed.The differential equations of the system are obtained based on Lagrange equation.Using the asymptotic method yields the expression of phase relationship between two exciters,the synchronization condition of two exciters is deduced when the speed ratio is 1:2 or 1:3,respectively.And the stability condition is obtained,which is in accordance with Routh-Hurwith criterion.The dynamic characteristics of the system are numerically analyzed,the stability index is defined and its relationship with the dimensionless parameters is analyzed.The simulations are performed by applying Runge-Kutta routine,and the curves of motor speed,phase difference,displacement and plane motion trajectory at the steady-state of the rigid frame are obtained.Finally,the validity of the theoretical results is verified by experiments.(2)The double-frequency synchronization of three exciters in the same direction in the far super-resonant state is studied.Theoretically,the motion differential equation of a rigid frame dynamical model of the mechanical system driven by three exciters with linear distribution is obtained.Combining the asymptotic method and the averaging method yields the synchronization criterion and stability criterion of exciters under the double-frequency condition,the stability index is also defined.Numerically,the stability index and other characteristic curves are given,and the stability ability of the system is discussed.The comparisons and analyses of simulation and experimental results verify the validity of the theoretical results and the feasibility of the theoretical analysis methods used,which provide a theoretical guidance for the functional design of complex frequency vibration screening equipment in engineering.(3)The theory of the double-frequency and triple-frequency synchronization for the mechanical system with a rigid frame driven by four exciters rotating in reversed directions is analyzed.By Lagrange equation,the motion differential equations of the system are derived.Applying the asymptotic method yields the expressions of phase relationships among four exciters under the conditions of double-frequency and triple-frequency,and the analytical expressions of the synchronization and stability conditions for achieving synchronization among exciters are given.The dynamic characteristics of the system are numerically analyzed,which reveals the influences of structural parameters on stability of the system,and the simulation and experimental results are given to verify and modify the theoretical model.The research can provide a reference for the design of new shaker and vibration forming equipment.(4)The vibratory synchronization mechanisms under the double-frequency and triple-frequency condition of the four-motor-driven mechanical system with two rigid frames under vibration isolation are revealed.Using the asymptotic method deduces the synchronization criterion of four exciters to realize multi-frequency synchronization.The stability criterion in the synchronous state is proposed,and the results are in accordance with Routh-Hurwith criterion.Simultaneously,the stability index is defined,the stability ability of the system is discussed,and the stable phase differences among exciters are obtained.The Runge-Kutta routine is applied to simulate the system,and the correctness of the theoretical results is verified,which can provide a theoretical basis for the design of new vibration compaction equipment in engineering.更多还原