STUDY ON SYNCHRONIZATION MECHANISM AND EXPERIMENT OF VIBRATING SYSTEM ACTUATED WITH DOUBLE-FREQUENCY AND DUAL-ROTOR
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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.Abstract: As the first-stage equipment of purifying drilling fluid, the screening performance of drilling shaker will directly determine the production efficiency of subsequent solid-control system. Meanwhile, in material screening engineering, the dynamics characteristics of vibrating system with single frequency actuation is difficult to match with the particle size of material, which usually leads to blocking of the screen mesh. Thus, to solve the problem mentioned above, a self-synchronous vibratory system actuated with multiple-frequency and dual-rotor is proposed in the present work. Firstly, motion differential equation of the multi-degree-of-freedom vibration system is obtained according to mathematical model and generalized Lagrange’s equations, and amplitude responses of the oscillating body in stable state are solved by applying complex number method. Then, considering revised small parameters method and Poincare−Lyapunov theory, the precondition and the stability evaluation criterion of implementing multiple-frequency synchronization are systematically revealed. Subsequently, relationship among the synchronous characteristics of rotors and the structural parameters of system is discussed quantitatively by numerical calculation. Moreover, combining with Runge−Kutta algorithm, an electromechanical coupling dynamics simulation model related to the proposed vibration system is established, and the double-frequency synchronization mechanism among the rotors and the oscillating body are analyzed in detail. Finally, an experimental platform is established to test the synchronous motion state and the dynamic characteristics of the system under different working conditions, which further demonstrates correctness of the theoretical investigation and the computation simulation. Research shows that synchronous ability index of the system is infinitely closed to zero with the increase of mounting distance. In this case, the possibility that the high-speed rotor and the low-speed rotor achieve steady synchronous vibration is gradually increased. Furthermore, the synchronous state of the motors is hardly affected with the stiffness coefficients of springs, but the phase difference value will be decreased and locked around a constant value with the change of dip angle and mounting distance of the exciters in a single period. This study not only has important reference value for the invention of vibrating screen in petroleum industry, but also will promote the development of other vibration machines.
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Key words:
- vibration system /
- synchronization /
- double-frequency /
- rotor dynamics /
- exciters
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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 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 当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 当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 当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
Parameters Motor 1 Motor 2 model number YZS-1.5-2 YZS-1.5-4 rated voltage/V 380 380 rated power/kW 0.12 0.12 exciting force/kN 1.5 1.5 velocity/(r·min−1) 2860 1430 pole pairs 1 2 rated frequency/Hz 50 50 rated current/A 0.36 0.4 
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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 /rad x /mm y /mm theoretical value −0.67 —— —— simulation value −0.63 1.2 0.72 experimental value −0.61 1.1 0.65 error/% 9 8.3 9.7
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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 /rad x /mm y /mm theoretical value −1.335 —— —— simulation value −1.32 1 0.45 experimental value −1.38 1.1 0.4 error/% 3.3 10 11.1
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