Basic Theory of Dynamically Similar Design for Basic Structural Components of Large High-Speed Rotating Machinery*

Luo Zhong,Han Qingkai,Wang Deyou,Liu Yongquan

Basic Theory of Dynamically Similar Design for Basic Structural Components of Large High-Speed Rotating Machinery*

Luo Zhong,Han Qingkai,Wang Deyou,Liu Yongquan

Luo Zhong Doctor of Engineering,Associate Professor,School of Mechanical Engineering and Automation,Northeastern University,Shenyang,Liaoning 110819,zhluo@mail.neu.edu.cn

Han Qingkai Doctor of Engineering,Professor,School of Mechanical Engineering,Dalin University of Technology,Dalian 116023,China;Hunan Provincial Key Laboratory of Mechanical Equipment Health Maintenance,Hunan University of Science and Technology,Xiangtan 411201,China,hanqingkai@dlut. edu.cn

Wang Deyou Doctor of Engineering,Researcher,Shenyang Institute of Motor Design,Shenyang, Liaoning 110015,wangdy606@163.com

Liu Yongquan Doctor of Engineering,Researcher,Shenyang Institute of Motor Design

*National Basic Research Program of China(973 Program)Project“Basic research for high-efficiency reliability and intelligentization of high-end compressors”(No.2012CB026000),National Nature Science Fund Project“Research for dynamic similarity theory of rotating structural component model tests and its application”(No. 51105064),and Ministry of Education’s Central University Basic Research Fund-Supported New Century Talent Project“Research for design method of dynamically similar model for hybrid complex rotor subsystem”(No.N1305030011)

This is a report of the results from our study on the theory of dynamically similar design regarding basic structural components of large high-speed rotation machinery based on theory of similarity, funded jointly by the National Basic Research Program of China(973 Program)Project"Basic research for high-efficiency reliability and intelligentization of high-end compressors",National Nature Science Fund Project"Research for dynamic similarity theory of rotating structural component model tests and its application",and Ministry of Education's Central University Basic Research Fund-Supported New Century Talent Project"Research for design method of dynamically similar model for hybrid complex rotor subsystem".

Basic structural components of large high-speed rotation machinery are affected by many factors such as rotation speed,centrifugal force,centrifugal moment,load of restoring moment,gyroscopic moment, and size effect.Its dynamic design is a problem that cannot be solved using only theoretical analysis and numerical simulation,and must be verified through physical tests.We used thin elastic plates as the typical structural component,and formulated a design method of models in dynamically similar tests for basic structural components of large high-speed rotating machinery.

By analyzing the relevant theories and methods of similar model design for basic structural components in structural vibration tests,we reached a definition for dynamic similarity:the similarity between model and original under working conditions where their intrinsic dynamic characteristics,modal and mode of vibration,dynamic response behavior,and typical fault characteristics,are similar or proportional within certain ranges.

We formulated the basic theoretical system of dynamically similar design for basic structural components,which consists of the principles for designing completely similar test models,methods for creating similarity relations,methods for designing distortion models,and methods for correcting the similarity relations of distortion models.Using an approach that combines theoretical analysis,numerical simulation and verification by testing,we formulated the correlations of similarity proportions in structural parameters,material parameters,load conditions and edge conditions between models and originals.Four principles of dynamic similarity were obtained:a original and its similar model have the same primary mode of vibration;for a original and its reduced-scale models that are completely geometrically similar, the intrinsic frequencies are inversely proportional to the geometric shrink ratios;when a reduced-scale model is composed of a different material from the original,its intrinsic frequency is proportional to the square root of the elastic modulus-density scale ratio;the intrinsic frequency of a structure can be modified by attaching masses,which may also cause significant change to the modal sequence.

Similar model tests allows for effective physical simulation of dynamic characteristics and response processes,recreation of the original's typical fault characteristics,and determining the original's dynamic parameters and features from results of model tests.When the relations between model parameters and conditions and the original are not completely and correspondingly proportional,distortion of basic structural component test models will occur.Distortions in materials and geometric sizes are the causes of model distortion.Based on the mechanism of distortion,we formulated a method for correcting model distortions,and a method for determining the applicable range of model geometry.Certain correctable ranges exist for distorted models.The applicable ranges of geometry for dynamically similar models depend on both their error control ranges and control ranges for modes of vibration.Designing similar test models for high-order dynamically similar parameter would have stricter requirements for the models.

Using the elastic thin plate structural component as subject,we set out to simplify the similarity relations.We used the method of dimensional analysis and proposed a method for formulating the similarity relations between the original and completely geometrically similar models as well asincompletely geometrically similar models(i.e.distorted models)for elastic thin plates.First,we conducted parameter sensitivity analysis on the intrinsic characteristics of elastic thin plates with analytical and numerical methods,and reached the following conclusions:for elastic thin plates,the intrinsic frequencies corresponding to different modes of vibration have different sensitivities to variations in geometric size;the sensitivity to geometric parameters of the amplitude at any point in the plate's mode of vibration depends on its relative displacement;the effects of Poisson ratio are very small as to be negligible,and also self-similar;materials are not a factor in vibration similarity,while geometric size is a condition that affects dynamic similarity.Second,we derived the distortion coefficient of elastic thin plate's distorted model through censtructing distorted test models;we proposed a method for determining the applicable ranges of the plate model geometry;we proposed a method for correcting basic structural components:the correction coefficients of dynamically similar parameters are obtaired by creating numerical correction equations for intermediate models,and then the coefficients are used to correct the model test results.Our study indicated that results from similar models made from the same type of material as the original are better than different types of materials,and results from a model reduced by a larger shrink ratio are better than a smaller shrink ratio.

We summarized the common applicable steps for dynamically similar design,created a theoretical framework for dynamically similar design for basic structural components of large high-speed rotating machinery,and obtained 11 conclusions that can be applied in dynamically similar design.

theory of similarity,dynamic similarity,principle of similarity,geometric similarity,large high-speed rotating machinery,basic structural component,elastic thin plate,test model distortion, correction of model distortion,numerical fitting,applicable range of model geometry,model design, dimensional analysis,intrinsic characteristics,response characteristics,lumped mass,modal adjustment

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