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 In order to get the modal characteristics of turbine blades in working state more accurately and extensively,the influence of spin softening produced by centrifugal force was further studied based on the reference [3]. The theory basis of spin softening was introduced and the finite element implementation of the three dimensional vibration equation with considering the influence of spin softening was presented. The one dimensional modal problem of spin softening and stress stiffening... In order to get the modal characteristics of turbine blades in working state more accurately and extensively,the influence of spin softening produced by centrifugal force was further studied based on the reference [3]. The theory basis of spin softening was introduced and the finite element implementation of the three dimensional vibration equation with considering the influence of spin softening was presented. The one dimensional modal problem of spin softening and stress stiffening was discussed. The modal analysis of the turbine blade in reference ER[3] considering spin softening only and considering both spin softening and stress stiffening was done. The results show that the natural frequencies of the turbine blade in rotating state was lower than the ones in static state when considering spin softening only;but the influence upon the turbine blade produced by spin softening was less than the influence produced by stress stiffening. So,the natural frequencies of the turbine blade in rotating state was still higher than the ones in static state when considering both spin softening and stress stiffening.  在文献［３］的基础上，进一步探讨了高速旋转时，离心惯性力产生的旋转软化效应对增压器涡轮叶 片模态特性的影响。介绍了旋转软化效应的理论基础，给出了考虑旋转软化效应的三维振动方程有限元 列式。在一维情形下，进行了旋转软化及应力刚化模态问题的讨论。对文献［３］中的涡轮进行了仅考虑旋 转软化效应及同时考虑旋转软化和应力刚化的模态分析。计算结果表明，仅考虑旋转软化时，旋转状态 涡轮叶片的固有频率较零速时低；但与应力刚化相比，旋转软化对涡轮叶片模态特性的影响较小，因此 综合考虑旋转软化和应力刚化时涡轮叶片的固有频率仍较零速时高。  Based upon the general FEA platform ANSYS,the numerical results of the modal analysis of a radial inflow turbine impeller are presented.The dynamical equation of impeller in the form of FEM is derived.The initial stress matrix and centripetal stiffness matrix are linearized.The eigenproblem of the dynamical equation is solved by means of BlockLanzos method,so the 25 modes of the impeller are obtained.In addition,the simplified dynamical equation is founded upon the dynamical equation of spinning beam,in order... Based upon the general FEA platform ANSYS,the numerical results of the modal analysis of a radial inflow turbine impeller are presented.The dynamical equation of impeller in the form of FEM is derived.The initial stress matrix and centripetal stiffness matrix are linearized.The eigenproblem of the dynamical equation is solved by means of BlockLanzos method,so the 25 modes of the impeller are obtained.In addition,the simplified dynamical equation is founded upon the dynamical equation of spinning beam,in order to explain the major dynamic characteristics of the impeller,which are validated by numerical analysis.The results of the analysis indicate:because of spin softening,when approaching to critical rotation speed,the frequency of each mode is decreased,especially for the first bending mode it is more evident.Then after,when running over the critical rotation speed,the frequency of the first bending mode rises greatly.The major shapes of the impeller are coupled bending and torsion.  应用ANSYS有限元软件对一个小型燃气轮机向心涡轮的叶轮固有频率进行了数值分析 .基于有限元方法建立了叶轮的振动方程 ,对方程中非线性的初应力刚度矩阵与离心刚度矩阵采用了线性简化 ,应用Block Lanzos法求解振动方程的特征值 .结果表明 ,当叶轮转速上升时 ,旋转柔化效应使叶轮的低阶振动频率 ,尤其是第 1阶弯振频率不断下降 ,到某个转速时出现“零频”现象 ,原高阶静频依次成为低阶频率 ;第 1阶振型发生变化 ,但是基频大小基本没有变化 ;整体式叶轮主要振动形式是叶轮的弯扭振动 .  Based on the general FEA platform ANSYS, this paper presents the numerical results of the modal analysis of a radial inflow turbine impeller. The dynamical equation of impeller in the form of FEM is derived with linearized initial stress and centripetal stiffness matrices are linearized. Eigen problem of the dynamical equation is solved by means of BlockLanczos method with the first 25 modes of the impeller obtained. In addition, the simplified dynamical equation is founded upon the dynamical equation of... Based on the general FEA platform ANSYS, this paper presents the numerical results of the modal analysis of a radial inflow turbine impeller. The dynamical equation of impeller in the form of FEM is derived with linearized initial stress and centripetal stiffness matrices are linearized. Eigen problem of the dynamical equation is solved by means of BlockLanczos method with the first 25 modes of the impeller obtained. In addition, the simplified dynamical equation is founded upon the dynamical equation of spinning beam, in order to explain the major dynamics characteristics of the impeller, which are validated in numerical analysis. Results indicate that because of the spin softening, as a critical rotation speed is approached, the frequencies of each modes tend to fall, the first bending mode is especially more evident. Then, the frequency of the first bending mode jumps abruptly. The shapes of major modes are bending and torsion.  应用ANSYS有限元软件对一个小型燃气轮机向心涡轮的叶轮模态进行了数值分析。建立了有限元形式叶轮的动力学方程,对方程中非线性的初应力刚度矩阵与离心刚度矩阵采用了线性化简化,应用 Block Lanzos法求解动力学方程的特征值问题,得到了该叶轮的前25阶模态。此外还基于旋转梁的动力学方程,建立叶轮的简化的动力学方程以说明叶轮基本的振动特性。这些特性在数值分析结果中得到了验证。结果表明:由于旋转柔化效应,当叶轮转速上升时,在某一个转速前,各阶频率有不同程度下降,尤其是一阶弯振频率,过了这个转速一阶弯振频率有个突然的阶越。整体式叶轮振动形式主要是叶轮的弯扭振动。  
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