新型振动机中两偏心转子自同步理论的研究

发布时间：2018-08-26 20:17

【摘要】：不平衡转子的自同步现象为振动技术的应用提供了新途径,并导致了振动利用工程的确立。目前,各类自同步振动机已经广泛应用于工业生产中,如：自同步给料机、自同步输送机、自同步概率筛等。这些振动机都是工作在远共振状态或近共振状态。对于远共振式振动机,其工作频率为2-10倍的系统固有频率,隔振性能良好,但同时所需的激振力较大。另外,随着处理物料量的增加,工作振幅略有下降。而近共振式振动机的工作频率在0.95到1.05倍的系统固有频率范围内,所需激振力较小,但同时传递给基础的动载荷很大。另外,当处理物料的量偏离设计值时,工作振幅大大降低。本文提出了一种新型的双机驱动振动机结构,振动机是由物料箱刚体和支撑刚体组成的组合结构,而两个偏心转子设置两种安装形式。一种安装形式为沿水平面对称安装,两个偏心转子的旋转中心位于y轴上,旋转平面关于垂直面xoz对称。这种安装形式下,物料箱有水平x、y方向、垂直z方向以及绕z轴旋转ψ方向四个自由度,支撑刚体仅有垂直z方向自由度。另一种安装形式为沿垂直轴对称安装,两个偏心转子的旋转中心位于z轴上,旋转平面关于水平面xoy对称。这种安装形式下,物料箱有水平x、y方向、垂直z方向三个自由度,支撑刚体仅有垂直z方向自由度。为了减小振动机z方向振动对基础的影响,对振动机结构进行了隔振处理。当工作频率小于系统z方向的固有频率时,此类振动机的固有频率随所处理物料量的增加而减小,激振频率与z方向固有频率比向1接近,该方向振幅则随处理物料量的增加而增加,从而适应生产线上变给料量的要求。结合数值计算分析和计算机仿真,本文研究了此类振动系统的自同步问题,主要完成了以下几个方面的工作： (1)利用拉格朗日方程建立了偏心转子两种安装形式下振动系统及隔振振动系统的运动微分方程。对于隔振振动系统的运动微分方程,利用传递函数法求出了耦合方程的解析解。 (2)提出了此类振动系统的自同步理论。首先,通过引入两偏心转子的角速度波动系数并将其作为小参数,对振动系统进行无量纲处理,得到了两偏心转子的无量纲耦合方程；然后,由无量纲耦合方程的零解存在得到了振动系统实现同步条件；最后,根据Routh-Hurwitz判据得到振动系统同步运行的稳定性条件。 (3)定义了此类振动系统的同步能力系数。通过数值计算方法,分析了系统同步能力系数与系统结构参数的关系,并验证了系统同步运行状态下的稳定性。 (4)对此类振动系统进行了计算机仿真,得到了振动系统从启动到稳态运行时,两电机转速、两偏心转子相位差以及振动系统各方向位移等计算结果,验证了上述理论的正确性。
[Abstract]:The self-synchronization of unbalanced rotor provides a new way for the application of vibration technology and leads to the establishment of vibration utilization engineering. At present, various kinds of self-synchronous vibration machines have been widely used in industrial production, such as: self-synchronous feeder, self-synchronous conveyor, self-synchronous probability screen and so on. These vibration machines all work in the far resonance state or near resonance state. For the far resonance vibration machine, the natural frequency of the system is 2-10 times, and the isolation performance is good, but the excitation force required is larger at the same time. In addition, with the increase of the amount of material treated, the working amplitude decreased slightly. But the operating frequency of the near-resonance vibration machine is in the range of 0.95 to 1.05 times of the system natural frequency, the excitation force is small, but the dynamic load transmitted to the foundation is very large at the same time. In addition, when the amount of material processed deviates from the design value, the working amplitude is greatly reduced. In this paper, a new type of two-machine driven vibration machine structure is proposed, which is composed of rigid body of material box and supporting rigid body, and two eccentric rotors are installed in two kinds of installation forms. One type of installation is symmetrical installation along the horizontal plane. The rotation center of the two eccentric rotors is located on the y axis and the rotating plane is xoz symmetry on the vertical plane. In this installation mode, the material box has four degrees of freedom: horizontal x y direction, vertical z direction and rotating 蠄 direction around z axis, and the supporting rigid body has only vertical z direction freedom. The other is the vertical axisymmetric installation in which the center of rotation of the two eccentric rotors is located on the z axis and the rotating plane is symmetrical to the horizontal plane xoy. In this installation mode, the material box has three degrees of freedom in the horizontal xy direction, the vertical z direction, and the supporting rigid body has only the vertical z direction degree of freedom. In order to reduce the effect of vibration in z direction on the foundation, vibration isolation is carried out on the vibration machine structure. When the operating frequency is less than the natural frequency in the z direction of the system, the natural frequency of this kind of vibration machine decreases with the increase of the material quantity, and the exciting frequency is close to the natural frequency in the z direction. The amplitude of this direction increases with the increase of the material quantity, which can meet the requirement of variable feed quantity on the production line. Combined with numerical analysis and computer simulation, the self-synchronization problem of this kind of vibration system is studied in this paper. The main works are as follows: (1) the differential equations of motion of vibration system and vibration isolation system under two kinds of installation forms of eccentric rotor are established by using Lagrange equation. For the motion differential equation of vibration isolation system, the analytical solution of the coupling equation is obtained by using the transfer function method. (2) the self-synchronization theory of this kind of vibration system is proposed. Firstly, by introducing the angular velocity fluctuation coefficient of two eccentric rotors and taking it as a small parameter, the dimensionless coupling equation of two eccentric rotors is obtained by dimensionless processing. From the existence of zero solution of the dimensionless coupling equation, the synchronization condition of the vibration system is obtained. Finally, according to the Routh-Hurwitz criterion, the stability conditions for the synchronous operation of the vibration system are obtained. (3) the synchronization ability coefficient of the vibration system is defined. The relationship between system synchronization capability coefficient and system structure parameters is analyzed by numerical method, and the stability of the system under synchronous operation is verified. (4) computer simulation of this kind of vibration system is carried out. The calculation results of the speed of two motors, the phase difference of two eccentric rotors and the displacement of the vibration system from start-up to steady state operation are obtained, and the correctness of the above theory is verified.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113.1

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