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倍频激励双转子振动同步机理与实验研究

邹敏 方潘 侯勇俊 彭欢 王德金

邹敏, 方潘, 侯勇俊, 彭欢, 王德金. 倍频激励双转子振动同步机理与实验研究. 力学学报, 2021, 53(10): 2823-2840 doi: 10.6052/0459-1879-21-359
引用本文: 邹敏, 方潘, 侯勇俊, 彭欢, 王德金. 倍频激励双转子振动同步机理与实验研究. 力学学报, 2021, 53(10): 2823-2840 doi: 10.6052/0459-1879-21-359
Zou Min, Fang Pan, Hou Yongjun, Peng Huan, Wang Dejin. Study on synchronization mechanism and experiment of vibrating system actuated with double-frequency and dual-rotor. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2823-2840 doi: 10.6052/0459-1879-21-359
Citation: Zou Min, Fang Pan, Hou Yongjun, Peng Huan, Wang Dejin. Study on synchronization mechanism and experiment of vibrating system actuated with double-frequency and dual-rotor. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2823-2840 doi: 10.6052/0459-1879-21-359

倍频激励双转子振动同步机理与实验研究

doi: 10.6052/0459-1879-21-359
基金项目: 国家自然科学基金项目(51705437)和四川省重点研发项目(2020YFG0181)资助
详细信息
    作者简介:

    方潘, 副教授, 主要研究方向: 机械振动利用与控制. E-mail: 201699010075@swpu.edu.cn

    侯勇俊, 教授, 主要研究方向: 非线性动力学、机电一体化. E-mail: 199531010017@swpu.edu.cn

  • 中图分类号: TH113.1

STUDY ON SYNCHRONIZATION MECHANISM AND EXPERIMENT OF VIBRATING SYSTEM ACTUATED WITH DOUBLE-FREQUENCY AND DUAL-ROTOR

  • 摘要: 振动筛作为第一级钻井液净化设备, 其筛分性能直接决定后续固控系统的生产效率. 针对在筛分工程中由相同驱动频率激励的振动系统所表现出的单一振动特性难以与筛面上的物料粒度相匹配, 从而引发筛孔堵塞的问题, 本文提出了倍频激励双转子自同步振动系统. 首先根据数学模型运用广义Lagrange公式建立多自由度振动系统的运动微分方程, 并引入复变函数求解箱体的稳态幅值响应; 其次探明了振动系统实现倍频同步的前提条件和稳定性评估标准; 然后通过数值计算定量地讨论转子间的倍频动力学特征与系统结构参数之间的关系, 并结合Runge−Kutta算法建立振动系统的多自由度机电耦合动力学仿真模型, 详细讨论转子与箱体间的倍频同步机理; 最后设计实验样机, 针对系统在不同工况下的动态特性和同步运动状态展开实验测试, 进一步验证理论研究和计算机模拟的正确性. 研究表明, 系统的倍频同步能力指数随安装距离的不断增加而接近于零值附近, 此时高频转子与低频转子获得稳定同步振动的可能性越来越高; 电机同步状态几乎不受弹簧刚度的影响, 但稳态相位差值在单周期内会随激振器安装倾角和距离的变化而逐渐减小并趋于在一个恒定值. 研究成果不仅对石油工业新型振动筛系统的研制具有重要的参考价值, 也将促进其他同步振动机械的发展.

     

  • 图  1  倍频激励双转子振动系统数学模型

    Figure  1.  Mathematical model of the vibration system actuated with double-frequency and dual-rotor

    图  2  坐标转换原则

    Figure  2.  Principle of coordinate transformation

    图  3  倍频激励双转子振动同步范围

    Figure  3.  Synchronization region of two rotors driven by double-frequency

    图  4  β1 = 120°, β2 = 60°时的倍频同步能力

    Figure  4.  Double-frequency synchronization capacity with β1 = 120°, β2 = 60°

    图  5  β2 = 60°, ro = 0.16时的倍频同步能力

    Figure  5.  Double-frequency synchronization capacity with β2 = 60°, ro = 0.16

    图  6  β1 = 120°, β2 = 60°时的倍频同步转矩

    Figure  6.  Double-frequency synchronization torque with β2 = 60°, ro = 0.16

    图  7  倍频激励双转子相位差近似稳态值

    Figure  7.  Double-frequency phase difference between the two rotors in steady state

    图  8  倍频激励双转子振动系统机电耦合动力学仿真模型

    Figure  8.  Electromechanical coupling dynamics simulation model of dual-rotor vibration system excited by double-frequency

    9  β1 = 150°, β2 = 30°, rl = 1.2时的仿真结果

    9.  Simulation result when β1 = 150°, β2 = 30° and rl = 1.2

    图  9  β1 = 150°, β2 = 30°, rl = 1.2时的仿真结果(续)

    Figure  9.  Simulation result when β1 = 150°, β2 = 30° and rl = 1.2 (continued)

    图  10  β1 = 142°, β2 = 38°, rl = 1时的仿真结果

    Figure  10.  Simulation result when β1 = 150°, β2 = 30° and rl = 1

    图  11  试验样机: 1 二极振动电机; 2 四极振动电机; 3 偏心块; 4 电机座; 5 钢架; 6 锁紧螺栓; 7 箱体; 8 支撑弹簧; 9 基座

    Figure  11.  Experimental prototype: 1 two-pole motor; 2 four-pole motor; 3 eccentric block; 4 motor base; 5 steel frame.; 6 locking bolt; 7 oscillating body; 8 supporting spring; 9 foundation support

    图  12  倍频同步振动系统的实验测试方案

    Figure  12.  Experimental testing scheme of double-frequency synchronization vibration system

    图  13  β1 = 150°, β2 = 30°, rl = 1.2的位移响应

    Figure  13.  Displacement responses with β1 = 150°, β2 = 30°, rl = 1.2

    图  14  β1 = 150°, β2 = 30°, rl = 1.2的同步运动状态: (a) ~ (f) 分别为转子瞬时相位差

    Figure  14.  Synchronous motion state with β1 = 150°, β2 = 30°, rl = 1.2: (a) ~ (f) the instantaneous phase differences between rotors

    图  15  β1 = 142°, β2 = 38°, rl = 1的位移响应

    Figure  15.  Displacement responses with β1 = 142°, β2 = 38°, rl = 1

    图  16  β1 = 142°, β2 = 38°, rl = 1的同步运动状态: (a) ~ (f) 分别为转子瞬时相位差

    Figure  16.  Synchronous motion state with β1 = 150°, β2 = 30°, rl = 1: (a) ~ (f) the instantaneous phase differences between rotors

    表  1  激振电机的技术参数

    Table  1.   Technical parameters of the exciting motors

    ParametersMotor 1Motor 2
    model numberYZS-1.5-2YZS-1.5-4
    rated voltage/V380380
    rated power/kW0.120.12
    exciting force/kN1.51.5
    velocity/(r·min−1)28601430
    pole pairs12
    rated frequency/Hz5050
    rated current/A0.360.4
    下载: 导出CSV

    表  2  动力学响应的理论、仿真和实验对比结果

    Table  2.   Comparison results among the theories, simulations and experiments of the dynamic responses

    α /radx /mmy /mm
    theoretical value−0.67————
    simulation value−0.631.20.72
    experimental value−0.611.10.65
    error/%98.39.7
    下载: 导出CSV

    表  3  动力学响应的理论、仿真和实验对比结果

    Table  3.   Comparison results among the theories, simulations and experiments of the dynamic responses

    α /radx /mmy /mm
    theoretical value−1.335————
    simulation value−1.3210.45
    experimental value−1.381.10.4
    error/%3.31011.1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-27
  • 录用日期:  2021-09-13
  • 网络出版日期:  2021-09-14
  • 刊出日期:  2021-10-26

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