解松霖,艾延廷,赵丹,田晶,刘玉,关鹏,刘俊男.基于随机过程的三维粗糙表面接触刚度研究[J].表面技术,2022,51(9):326-334.
XIE Song-lin,AI Yan-ting,ZHAO Dan,TIAN Jing,LIU Yu,GUAN Peng,LIU Jun-nan.Contact Stiffness of Three-dimensional Rough Surface Based on Stochastic Process[J].Surface Technology,2022,51(9):326-334
基于随机过程的三维粗糙表面接触刚度研究
Contact Stiffness of Three-dimensional Rough Surface Based on Stochastic Process
  
DOI:10.16490/j.cnki.issn.1001-3660.2022.09.034
中文关键词:  Gauss随机分布理论  三维粗糙表面  有限元建模  响应面法  法向接触刚度  临界自相关系数
英文关键词:Gauss stochastic distribution theory  three-dimensional rough surface  finite element modeling  response surface method  normal contact stiffness  critical autocorrelation coefficient
基金项目:国家自然科学基金(11702177);辽宁省自然科学基金(2020–BS–174);辽宁省教育厅项目(JYT2020019)
作者单位
解松霖 沈阳航空航天大学,沈阳 100136 
艾延廷 沈阳航空航天大学,沈阳 100136 
赵丹 中国航发四川燃气涡轮研究院,成都 610500 
田晶 沈阳航空航天大学,沈阳 100136 
刘玉 沈阳航空航天大学,沈阳 100136 
关鹏 沈阳航空航天大学,沈阳 100136 
刘俊男 沈阳航空航天大学,沈阳 100136 
AuthorInstitution
XIE Song-lin Shenyang Aerospace University, Shenyang 110136, China 
AI Yan-ting Shenyang Aerospace University, Shenyang 110136, China 
ZHAO Dan AECC Sichuan Gas Turbine Establishment, Chengdu 610500, China 
TIAN Jing Shenyang Aerospace University, Shenyang 110136, China 
LIU Yu Shenyang Aerospace University, Shenyang 110136, China 
GUAN Peng Shenyang Aerospace University, Shenyang 110136, China 
LIU Jun-nan Shenyang Aerospace University, Shenyang 110136, China 
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中文摘要:
      目的 建立三维粗糙表面法向接触刚度的有限元模型,研究法向接触刚度对粗糙度、自相关系数、弹性模量、屈服极限等参数的敏感性。方法 首先基于随机过程理论,采用二维数字滤波技术,生成满足Gauss分布和指数自相关函数的粗糙表面,建立三维粗糙表面接触有限元模型。然后根据结合面静位移与结合面受力关系推导出静刚度表达式,得到两粗糙表面的法向接触刚度。根据中心复合试验设计方法选取的样本点和有限元计算结果,建立二阶响应面模型。最终定义了临界自相关系数,并研究了临界自相关系数与其他参数的关系。结果 有限元计算得到的法向接触刚度结果合理,与试验结果相比最大误差不超过12.34%。弹性变形、塑性变形及真实接触面积随载荷的增加逐渐增大。法向接触刚度与粗糙度呈现负相关趋势,粗糙度不变时法向接触刚度随自相关系数的增大先增大后减小;法向接触刚度与弹性模量呈负相关趋势,法向接触刚度与屈服强度呈正相关趋势,且粗糙度的改变对法向接触刚度影响最大。当压力为200 MPa时,粗糙度、自相关系数、弹性模量、屈服极限分别为0.8 μm、18.91、240 GPa、355 MPa,法向接触刚度达到最大值121.53 MPa/mm,优化后接触面的法向接触刚度提高247%,并给出了临界自相关系数选取公式。结论 所建立模型正确、准确,为粗糙表面法向接触刚度计算提供一种有效方法,可为航空发动机安装边结构设计提供理论指导。
英文摘要:
      Aircraft engines are the jewel in the crown of modern industry The aero-engine is a complex mechanical assembly containing many mechanical joint surfaces, and the casing flange is a typical mechanical joint surface. The mechanical joint surfaces is not smooth but consists of many micro-convex bodies in contact with each other, and the sum of the stiffness of the micro-convex bodies is called contact stiffness. Accurate calculation of contact stiffness is essential to the stability and dynamic characteristics analysis of the whole aircraft engine The work aims to establish a three-dimensional finite element model of normal contact stiffness for rough surfaces, and to study the sensitivity of normal contact stiffness to roughness, autocorrelation coefficient, elastic modulus, yield limit and other parameters. Firstly, based on stochastic process theory, two-dimensional digital filtering technology was used to generate rough surfaces satisfying Gauss distribution and exponential autocorrelation function, and a three-dimensional finite element model of rough surface contact was established. Then the static stiffness expression was derived according to the relationship between the static displacement of the joint surface and the force on the joint surface, and the normal contact stiffness of the two rough surfaces was obtained. The second-order response surface model was established according to the sample points selected by the central composite design method and the results of finite element calculation. Finally, the critical autocorrelation coefficient is defined and the relationship between the critical autocorrelation coefficient and other parameters is studied. The results of normal contact stiffness calculated by finite element method are reasonable, and the maximum error is less than 12.34% compared with the experimental results. The elastic deformation, plastic deformation and real contact area increase with the increase of load. Normal contact stiffness has a negative correlation with roughness. When the roughness is constant, normal contact stiffness increases first and then decreases with the autocorrelation coefficient. Normal contact stiffness has a negative correlation with the elastic modulus, and normal contact stiffness has a positive correlation with the yield strength. The change of roughness has the greatest influence on normal contact stiffness. When the pressure is 200 MPa, the roughness, autocorrelation coefficient, elastic modulus and yield limit are 0.8 μm, 18.91, 240 GPa and 355 MPa respectively, and the maximum normal contact stiffness reaches 121.53 MPa/mm. After optimization, the normal contact stiffness of the contact surface is increased by 247%. The change in the autocorrelation coefficient only affects the normal contact stiffness. The critical autocorrelation coefficient with roughness, modulus of elasticity and yield limit for optimal normal contact stiffness is obtained by response surface design. The formula for selecting the critical autocorrelation coefficient is given. The conclusion of this paper is that the established model is correct and accurate. A simple method is provided for the finite element modeling and calculation of rough surface normal contact stiffness. This paper can provide a guiding reference for the optimal design of the mounting edge contact stiffness of aero-engine, and provides theoretical guidance for the design of mounting edge parameters. At the same time, it also enriches and develops the aero-engine mounting side connection design system.
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