基于分形理论的电主轴系统热态分布特性研究  

Research on Thermal Distribution Characteristics of Motorized Spindle System Based on Fractal Theory

作　　者：孟庆宇 刘杨[1] 鄢欣欣 马亚新 李炎臻 MENG Qingyu;LIU Yang;YAN Xinxin;MA Yaxin;LI Yanzhen(School of Mechanical Engineering and Automation,Northeastern University,Shenyang 110819;School of Mechatronics Engineering,Harbin Institute of Technology,Harbin 150001;The Institute of High Energy Physics,Chinese Academy of Sciences,Beijing 100049;AECC Shenyang Liming Aero Engine Co.,Ltd.,Shenyang 110043)

机构地区：[1]东北大学机械工程与自动化学院,沈阳110819 [2]哈尔滨工业大学机电工程学院,哈尔滨150001 [3]中国科学院高能物理研究所,北京100049 [4]中国航发沈阳黎明航空发动机有限责任公司,公司沈阳110043

出　　处：《机械工程学报》2021年第13期63-69,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51875093);教育部基本科研业务费种子(N2103020)资助项目。

摘　　要：分形理论中的Weierstrass-Mandelbrot(W-M)函数描述了微观接触表面的连续性、自相似性、自亲和性等数学特性,能够很好地考虑三种变形状态(弹性,弹塑性和塑性状态)下圆弧接触面之间的接触热阻。以分形理论为基础建立了电主轴系统的热阻网络模型,对电主轴系统的热态分布特性进行了相关研究。分别列出了电主轴系统的关键节点热平衡方程,分析节点的稳态和瞬态温度。分形参数识别试验和热传导试验验证了圆弧形接触面间接触热阻的准确性,电主轴系统的温升试验验证了热阻网络模型的准确性。结果表明:电主轴系统各部件的温度在一定时间内迅速上升后趋于稳定;同时,分形维数D的升高将导致节点温度的降低;分形幅度系数G的升高会导致电主轴系统温度的升高。The mathematical properties of continuity,self-similarity and self-affinity of microscopic contact surfaces are described in the Weierstrass-Mandelbrot(W-M)function of fractal theory,and thermal contact resistance(TCR)between circular-arc contact surfaces under three deformation states(elastic,elastic-plastic and plastic state)are considered.Based on the fractal theory,the thermal resistance network model of the high speed motorized spindle system is established and the thermal distribution characteristics of the motorized spindle system is studied.The heat balance equations are listed for the key nodes of the motorized spindle system,and the steady and transient temperature of the nodes are analyzed.The accuracy of TCR between the circular-arc contact surfaces is verified by the fractal parameter identification experiment and heat conduction experiment.The accuracy of the thermal resistance network model is verified by the temperature rise experiment of the motorized spindle system.The results show that the temperature of each component of the motorized spindle system rises rapidly in a certain period of time and then tends to be stable.At the same time,the increase of the fractal dimension D will lead to the decrease of the node temperature;the increase of the fractal–amplitude coefficient G will cause an increase in the temperature of the motorized spindle system.

关 键 词：高速电主轴 分形理论 热态分布特性 热阻网络 接触热阻 

分 类 号：TH117[机械工程—机械设计及理论] TH161