转子-轴承系统中滚动球轴承的非线性动力学相似特性研究
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国家重点基础研究发展计划项目(2012CB026005)、国家自然科学基金资助项目(51105064,11572082)、教育部基本科研业务费专项资金资助项目(N150304004, N140301001)及大连理工大学精密与特种加工教育部重点实验室研究基金资助项目(JMTZ201602)


Similarity researchon the nonlinear dynamic characteristics of rolling bearing in rotor-bearing system
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    摘要:

    针对转子-轴承系统中滚动球轴承的动力学相似问题,提出一种考虑非线性振动特性的轴承系统相似模型建立方法.首先,建立滚动球轴承整体的非线性振动微分方程,运用积分模拟法推导了轴承整体的非线性振动特性相似关系,并结合滚动球轴承的动力学相似关系得到滚动球轴承系统的相似设计准则;其次,应用所得的相似准则,以深沟球轴承C204JUT为原型、6208为模型进行数值仿真实例计算,通过采用Newmark-β算法计算得到的分叉图分析了转速ω、径向载荷Fr、阻尼C及径向游隙γ大小对原型和模型轴承系统振动位移或速度响应的影响;最后,通过对比原型和模型的各参数(ω、Fr、C、γ)分叉图中分叉区间、趋于稳定运动参数值大小以及进入稳定周期运动时的稳态响应值大小验证相似准则的准确性和有效性.通过分析得到以下结论:①滚动球轴承非线性振动特性参数(如振动响应、结构阻尼等)相似关系可由轴承结构参数相似关系确定;②原型与模型非线性运动的分叉图形状一致,且模型能够很好的预测原型稳态振动响应,因此可将模型轴承用来预测原型轴承的非线性振动行为.

    Abstract:

    A similarity model considering the nonlinear dynamic characteristics of rolling ball bearing in rotorbearing system was put forward to examine the problem of dynamic similarity. The nonlinear vibration differential equation of rolling ball bearing was firstly established. The similarity relationship on the nonlinear dynamic characteristics was deduced by the integral simulation method, and the similarity design criteria of the rolling ball bearing was then achieved. Afterwards, the groove ball bearing of C204JUT and 6208 were set as a prototype and a model for numerical simulation, respectively. The effect of rotational speed, radial load Fr, damping C and radial clearance on the vibration displacement and velocity of rolling ball bearing system were investigated by bifurcation. Finally, through comparing the bifurcation range, the stable parameter value, the response value for the stable motion in the bifurcation diagram, the similarity criteria was verified. The conclusions were obtained as follow: i)The similarity relationship of the nonlinear vibration characteristics for the rolling ball bearing can be established by its structural similarity. ii)The bifurcation shape of the prototype and the model was consistent, and the steady response of the model matched that of the prototype very well.

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罗忠,郭健,唐瑞,韩清凯,王德友.转子-轴承系统中滚动球轴承的非线性动力学相似特性研究[J].动力学与控制学报,2016,14(3):223~228; Luo Zhong, Guo Jian, Tang Rui, Han Qingkai, Wang Deiyou. Similarity researchon the nonlinear dynamic characteristics of rolling bearing in rotor-bearing system[J]. Journal of Dynamics and Control,2016,14(3):223-228.

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  • 收稿日期:2015-05-14
  • 最后修改日期:2015-06-29
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  • 在线发布日期: 2016-05-26
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