附加气室空气弹簧隔振的振动筛动力学建模与分析

Dynamic modeling and analysis of vibrating screen for vibration isolation of air spring with auxiliary chamber

  • 摘要: 附加气室空气弹簧在两个气室之间设有节流元件,可吸收振动的能量,具有良好的阻尼特性。 作为一种新型隔振元件,附加气室空气弹簧能缩短振动筛过共振区时间,减小共振振幅及附加倾摆运动,提高振动筛运行的平稳性。分析振动筛二自由度动力学模型,并求解运动学微分方程,发现振动筛实际振动方向角不等于激振力作用方向角,振幅和抛掷指数也可用单自由度模型表征;利用热力学和流体力学理论建立附加气室空气弹簧的线性模型,得到其刚度阻尼的表达式,基于此,推导出附加气室空气弹簧的振动筛动力学模型,并建立运动学微分方程;搭建附加气室空气弹簧隔振系统和振动实验台,测试实验台的运动学参数;在MATLAB/Simulink环境下对所建动力学模型进行仿真研究,并与实验台测试结果进行了比较分析。 结果表明:模型仿真振幅为5.321 mm,实验测试的稳态振幅为5.372 mm,二者误差仅为1%,具有较高的准确性。模型仿真结果显示:电机转速对振幅影响较小,对抛掷指数影响较大,随着电机转速由840 r/min增加到990 r/min时,振幅由4.549 mm降为4.427 mm,抛掷指数由3.6上升到4.9;改变隔振系统的初始气压可以调节振幅,当初始气压由0.1 MPa增加到0.6 MPa时,振幅由4.446 mm增加到6.159 mm;节流孔直径对振幅的影响不明显,当节流孔直径由2 mm增加到20 mm时,振幅由4.443 mm变为4.467 mm;通过改变电机转速和隔振系统初始气压组合,可以使试验台振幅在4.45~6.16 mm、抛掷指数在3.46~6.16内变化,实现对振动筛的调节。

     

    Abstract: The air spring with auxiliary chamber has throttle element between two chambers,which can absorb vibra- tion energy and has good damping characteristics. As a new type of vibration isolation element,the air spring with aux- iliary chamber can shorten the time of vibrating screen passing through the resonance area,reduce the resonance am- plitude and additional tilting motion,and improve the smoothness of vibration screen operation. By analyzing the two- degree-of-freedom (DOF) dynamic model of the vibrating screen and solving the kinematic differential equation,it is found that the vibration direction angle of the vibrating screen is not equal to the direction angle of the exciting force. The amplitude and throwing index can be represented by the single DOF model. Based on the theory of thermodynam- ics and fluid mechanics,a linear model of the air spring with auxiliary chamber was established,and the expressions of stiffness and damping were obtained. Then,the dynamic model of vibration screen based on the air spring with auxilia- ry chamber was deduced,and the kinematic differential equation was established. The vibration isolation system of air spring with auxiliary chamber and vibration test prototype was built to test the kinematics parameters of the prototype. The dynamic model was implemented in MATLAB / Simulink,and compared with the test results of the experimental prototype. The results show the accuracy of the model,i. e. ,the simulation amplitude of the model is 5. 321 mm,and the steady-state amplitude of the experimental prototype is 5. 372 mm,and the error is only 1% . The simulation results show that the motor speed has a small impact on the amplitude and a large impact on the throwing index. When the motor speed increases from 840 r / min to 990 r / min,the amplitude decreases from 4. 549 mm to 4. 427 mm,and the throwing index rises from 3. 6 to 4. 9. The amplitude can be adjusted by changing the initial pressure of the vibration i- solation system. When the initial pressure increases from 0. 1 MPa to 0. 6 MPa, the amplitude increases from 4. 446 mm to 6. 159 mm. The effect of orifice diameter on amplitude is not obvious. When the diameter of orifice in- creases from 2 mm to 20 mm,the amplitude changes from 4. 443 mm to 4. 467 mm. By changing the motor speed and the initial air pressure combination of the vibration isolation system,the amplitude of the test bed can be changed with- in 4. 45-6. 16 mm and the throwing index within 3. 46-6. 16,so as to adjust the vibrating screen.

     

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