The Stability Analysis of Planar Model for Horizontal Axis Washing Machine with a Ball Balancer
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摘要: 应用平衡环技术抑制滚筒洗衣机脱水振动已成为发展趋势。但由于轴线水平,重力的作用使得球体相对脱水桶周期振荡,且模型本身难以转为合适的自治形式。为分析带有球体平衡环的滚筒洗衣机振动稳定性,建立了滚筒洗衣机平面振动模型,开发了适合周期解稳定性分析的伪弧长单参数延拓算法与分岔点的双参数追踪算法。应用该算法求解发现了系统周期解的倍周期、半周期、环面与叉形分岔现象,并指出了低速区的3个失稳区域。通过数值仿真验证了分岔结论的正确性。Abstract: Vibration suppression of the spin drying process in a horizontal axis washing machine through a ball bal-ancer is being more and more popular. However,due to the effect of gravity,the balls in the balancer vibrate peri-odically even at a high rotation speed,then the system has a periodic solution and transformation of the system into a proper autonomous form is not easy. For stability analysis of the system,at first,a planar model for the horizontal axis washing machine with a ball balancer is built based on the model described in reference [1 ],and a special one parameter pseudo-arc algorithm for continuation of the periodic solution and an additional algorithm for tracing the bifurcation point with two parameters are developed,then employing the algorithms,the bifurcations of period dou-bling,period halving, torus and pitchfork are detected and three unstable regions when the rotation speed is low are observed. At last,the bifurcation results are validated by using the numerical simulations.
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Key words:
- mathematical models /
- algorithms /
- computer simulation /
- washing machine
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[1] 陈海卫, 张秋菊. 波轮式全自动洗衣机平面模型分岔特性的分 析[J]. 机械科学与技术, 2009, 28(12):1670 ~1676 [2] Chen H W,Zhang Q J. Study on steady-state response of a vertical axis automatic washing machine with a hydraulic balancer using a new approach and a method for getting a smaller deflection angle[J]. Journal of Sound and Vibration, 2011, 330(9):2017 ~2030 [3] Chen H W,Ji W X, Zhang Q J,et al. A method for vibration iso-lation of a vertical axis automatic washing machine with a hydraulic balancer[J]. Journal of Mechanical Science and Technology, 2012, 26(2):335 ~343 [4] 李德葆, 张元润, 闫东鹏. 大型滚筒式洗涤脱水机械的动特性 设计[J]. 清华大学学报(自然科学版), 1997, 37(8):5 ~8 [5] Turkay O S, Sumer I T, Tugcu A K. Modeling and dynamic analysis of the suspension system of a front loaded washing machine[A ]. Pro-ceedings of the ASME on Advances in Design Automation[C], New York:ASME, 1992:383 ~390 [6] Cristiano S,Fabio P, et al. Control of magnetorheological dampers for vibration reduction in a washing machine[J]. Mechatronics, 2009, 19(3):410 ~421 [7] Nygads T. Washing Machine Design Optimization Based on Dynamics Modeling[D ]. Doctor thesis, Chalmers University, 2011 [8] 魏玉东. 滚筒洗衣机动态性能研究[D]. 天津大学, 2008
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