尺寸效应对微转子临界转速的影响分析

Influence of Size Effect on Critical Speed of Rotating Machine Rotor

在微米尺度下,传统的力学理论无法描述转子尺寸效应现象。基于修正偶应力理论,建立了微转子计算模型,应用微分法得到了计算模型的控制方程和边界条件,推导了转子临界转速解析解表达式,分析了尺寸效应和结构参数对转子临界转速的影响。结果发现,微尺度下,转子的临界转速显著提高,当材料内禀尺寸与转子半径相等时,与经典理论计算结果相比,本模型计算结果提高了1.5倍。随着半径的增加,当半径超过材料内禀尺寸的15倍,尺寸效应的影响可忽略。此外,转子临界转速与转子长径比和圆盘质量成反比。

At the micrometer scale,The rotor is the core component of a rotary machinery.With the improving of the machining accuracy,the size of the rotor has decreased from macro scale to micro scale gradually.Due to the size effect,the mechanical properties of the rotor will be changed significantly at the micro scale.However,the classical mechanical theory can’t describe the size effect phenomenon of rotor.Based on the modified couple stress theory,a micro rotor theoretical model considering the size effect of the rotor is established.The governing equations and boundary conditions are derived by using the differential method.The analytical solution of the rotor critical speed is obtained.The influences of the size effect and structural parameters on the rotor critical speed are analyzed.From the results,it is shown that at the micro scale,the critical speed of the rotor increased significantly.When the material length scale parameter is equal to the radius,the rotor critical speed which obtained by the present model is 1.5 times larger than the classical result.With the increasing of the radius,when the radius exceeds 15 times the material length scale parameter,the influence of size effect can be ignored.In addition,the rotor critical speed is inversely proportional to the length-diameter ratio of the rotor and the mass of the disc.