工程科学学报，第40卷，第12期：1540-1548,2018年12月 Chinese Journal of Engineering,Vol.40,No.12:1540-1548,December 2018 DOI:10.13374/j.issn2095-9389.2018.12.013;http://journals.ustb.edu.cn 口环密封对多级离心泵湿转子横-轴双向耦合动特性 的影响 周文杰)☒，王孝军，邱宁)，王乐勤)，高波14) 1)江苏大学能源与动力工程学院，镇江2120132)江苏大学流体机械工程技术研究中心，镇江212013 3)浙江大学能源工程学院，杭州3100274)北卡罗莱纳州立大学机械与宇航工程系，罗利27606 区通信作者，E-mail:zhouwenjiezwj(@js.cd.cn 摘要为探究口环密封对多级离心泵转子横-轴双向耦合振动的影响，基于空间欧拉角变换及有限元法，建立了多级离心 泵转子系统叶轮和轴系的微分运动方程，在此基础上，充分考虑口环流体激振力和多种轴向力的耦合作用，利用矩阵运算方 法建立了多级离心泵湿转子的横-轴双向耦合振动模型，并采用Newmark法对双向耦合系统的瞬态动力学特性进行求解，重 点研究了口环密封长度、压差和间隙对系统耦合振动特性的变化规律，计算了不同密封参数下的流体激振力.计算结果表明， 口环密封对转子系统横向振动的洛马金效应随着密封长度和压差的增大以及间隙的减小愈发明显，转子系统的横向稳态振 动收敛速度快于轴向稳态振动的收敛速度，两向瞬态振动的振动频率呈现出完全不同的特性。此外，密封的流体激振力与密 封长度呈现非线性变化关系，而与密封压差和间隙呈现线性变化关系. 关键词多级离心泵：湿转子系统；双向耦合振动：瞬态特性：轴向力 分类号TQ051.1 Effect of annular seal on the lateral-axial bi-direction coupled dynamic characteristics of a multi-stage pump wet rotor ZHOU Wen-jie,WANG Xiao-jun),QIU Ning?,WANG Le-qin,GAO Bo'4) 1)School of Energy and Power Engineering,Jiangsu University,Zhenjiang 212013,China 2)Research Center of Fluid Machinery Engineering and Technology,Jiangsu University,Zhenjiang 212013,China 3)Institute of Process Equipment,Zhejiang University,Hangzhou 310027,China 4)Department of Mechanical and Aerospace Engineering,North Carolina State University,Raleigh 27606.USA Corresponding author,E-mail:zhouwenjiezwj@ujs.edu.en ABSTRACT Because of the increasingly rigid and complex operating conditions for multi-stage pumps,the annular seal is playing an important role in determining the dynamic characteristics of a rotor system.The annular seal can prevent fluid leakage to ensure that the pump system can satisfy the design requirements,such as the head and efficiency.However,the fluid-induced force that is caused in- side the annular seal by the pressure reduction and nonconcentric motion directly acted on the rotor system,which presents transient characteristics with a variation in the operating conditions.Based on the Euler angle transformation and the finite element method,the differential equations of motions for impeller and shaft were determined in this study,and the coupled effects,including the fluid-in- duced force of the annular seal and multiple axial forces,were considered.These equations of motions and coupled effects were conduc- ted to investigate the effect of the annular seal on the lateral-axial bi-direction coupled vibration for a multi-stage pump rotor system. Finally,the lateral-axial bi-direction coupled vibration model for a multi-stage pump wet rotor was integrated with the matrix operation, 收稿日期：2017-12-27 基金项目：国家自然科学基金资助项目(51706087)工程科学学报,第 40 卷,第 12 期:1540鄄鄄1548,2018 年 12 月 Chinese Journal of Engineering, Vol. 40, No. 12: 1540鄄鄄1548, December 2018 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2018. 12. 013; http: / / journals. ustb. edu. cn 口环密封对多级离心泵湿转子横鄄鄄 轴双向耦合动特性 的影响 周文杰1)苣 , 王孝军1) , 邱 宁2) , 王乐勤3) , 高 波1,4) 1) 江苏大学能源与动力工程学院, 镇江 212013 2) 江苏大学流体机械工程技术研究中心, 镇江 212013 3) 浙江大学能源工程学院, 杭州 310027 4) 北卡罗莱纳州立大学机械与宇航工程系, 罗利 27606 苣通信作者, E鄄mail: zhouwenjiezwj@ ujs. edu. cn 摘 要 为探究口环密封对多级离心泵转子横鄄鄄轴双向耦合振动的影响,基于空间欧拉角变换及有限元法,建立了多级离心 泵转子系统叶轮和轴系的微分运动方程,在此基础上,充分考虑口环流体激振力和多种轴向力的耦合作用,利用矩阵运算方 法建立了多级离心泵湿转子的横鄄鄄轴双向耦合振动模型,并采用 Newmark 法对双向耦合系统的瞬态动力学特性进行求解,重 点研究了口环密封长度、压差和间隙对系统耦合振动特性的变化规律,计算了不同密封参数下的流体激振力. 计算结果表明, 口环密封对转子系统横向振动的洛马金效应随着密封长度和压差的增大以及间隙的减小愈发明显,转子系统的横向稳态振 动收敛速度快于轴向稳态振动的收敛速度,两向瞬态振动的振动频率呈现出完全不同的特性. 此外,密封的流体激振力与密 封长度呈现非线性变化关系,而与密封压差和间隙呈现线性变化关系. 关键词 多级离心泵; 湿转子系统; 双向耦合振动; 瞬态特性; 轴向力 分类号 TQ051郾 1 收稿日期: 2017鄄鄄12鄄鄄27 基金项目: 国家自然科学基金资助项目(51706087) Effect of annular seal on the lateral鄄鄄 axial bi鄄direction coupled dynamic characteristics of a multi鄄stage pump wet rotor ZHOU Wen鄄jie 1) 苣 , WANG Xiao鄄jun 1) , QIU Ning 2) , WANG Le鄄qin 3) , GAO Bo 1,4) 1) School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China 2) Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang 212013, China 3) Institute of Process Equipment, Zhejiang University, Hangzhou 310027, China 4) Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh 27606, USA 苣Corresponding author, E鄄mail: zhouwenjiezwj@ ujs. edu. cn ABSTRACT Because of the increasingly rigid and complex operating conditions for multi鄄stage pumps, the annular seal is playing an important role in determining the dynamic characteristics of a rotor system. The annular seal can prevent fluid leakage to ensure that the pump system can satisfy the design requirements, such as the head and efficiency. However, the fluid鄄induced force that is caused in鄄 side the annular seal by the pressure reduction and nonconcentric motion directly acted on the rotor system, which presents transient characteristics with a variation in the operating conditions. Based on the Euler angle transformation and the finite element method, the differential equations of motions for impeller and shaft were determined in this study, and the coupled effects, including the fluid鄄in鄄 duced force of the annular seal and multiple axial forces, were considered. These equations of motions and coupled effects were conduc鄄 ted to investigate the effect of the annular seal on the lateral鄄鄄 axial bi鄄direction coupled vibration for a multi鄄stage pump rotor system. Finally, the lateral鄄鄄axial bi鄄direction coupled vibration model for a multi鄄stage pump wet rotor was integrated with the matrix operation