机械结构固定结合部虚拟材料的动力学建模
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摘要
随着数控机床向高精化、高速化、智能化的方向发展,人们对数控机床的性能指标尤其是动态特性性能指标的要求越来越高。对高端数控机床而言,动态特性是整机性能的关键,因此机床动力学性能已成为当今新的研究热点。然而,有资料表明整机结构中60~80%的总动刚度、90%的总阻尼都来自结合部。显然,机床结合部的动力学特性显著影响整机结构的动力学行为。长期以来人们从理论和实验上对此进行了大量的研究。结合部动力学建模是研究结合部动力学特性的重要手段。由于数控机床的结合部类型以及描述结合部模型参数的多样性,目前结合部的模型不能满足高端要求以及尚没有参数化模型,因此急需一种高精度的参数化建模方法。本文工作如下
第一,提出一种基于虚拟材料的机床固定结合部动力学参数化建模法,即将固定结合部看成一种等截面的虚拟材料,从而将固定结合部等效为虚拟材料与两结合表面零件的固定连接,以工程数据(结合面积、结合力、结合面粗糙度、结合零件的弹性模量和泊松比等)为参数建立固定结合部动力学解析模型,解决了动力学模型工程实用性问题。
第二,建立了虚拟材料弹性模量、切变模量、泊松比、密度的解析解模型,应用赫兹接触理论和分形理论,分析了固定结合部法向和切向特性的相互影响,在此基础上利用商用有限元软件,开发了基于虚拟材料的参数化固定结合部动力学模式嵌入方法,从而为机床机械结构整机的高精度动力学建模工程化应用提供了一种新方法。
第三,研究了基于表面粗糙度(Ra)估计分形维数和分形粗糙度参数的方法。推导表面轮廓的结构函数,给出确定分形维数和分形粗糙度参数的实验方法。给出分形维数、分形粗糙度参数与表面粗糙度之间的近似换算式。实验结果表明:分形维数和分形粗糙度参数与取样长度无关,分形维数随表面粗糙度减小而增加,分形粗糙度参数随表面粗糙度减小而减小。
最后,对虚拟材料的理论解进行有效性验证。以4类零件结合部为研究对象,以测试试件的实验结果为基准,对一系列试验试件的理论模态与实验模态(考虑模态保证准则)进行比较,即相似振型定性比较、相应的固有频率定量比较。理论模型的振型与实验的振型基本一致,理论与实验固有频率的相对误差大多小于10%。在分析前4类零件结合部结果的基础上,以CKX5680七轴五联动车铣数控装备整机结合部为研究对象,对解析法进行有效性验证,理论振型与实验振型基本一致,理论与实验固有频率的相对误差小于9%。
With the development of high precision, high speed and intelligentization of NC machine tools, the need for characteristic indexes (especially dynamic ones) in NC machine tools is much higher. To high-grade NC machine tools, the dynamic property is a key of whole machine tools, therefore, the dynamic performance in machine tools becomes a novel research hot point. However, 60~80% of the total dynamic stiffness and 90% of the total damping in a whole machine tool structure come from joint interfaces. Apparently, the dynamic characteristics of joint interfaces in machine tools affect the dynamic behaviors of a whole machine tool structure considerably. The dynamic characteristics of joint interfaces had been widely studied from theory and experiment for so many years. Dynamic modeling on joint interface plays an important part in studying the dynamic characteristics of joint interface. Now, it is difficult for current models of joint interfaces to satisfy the high-grade need of a set of joint interface in NC machine tools and there lacks a parameterized model because of the diversity of joint interface’s type in NC machine tools and some parameters of describing joint interface model. Thus there urgently needs a parameterized establishing way with high precision. Some works in the manuscript are as follows.
In the first, a dynamic parameterized modeling approach on fixed joint interface in machine tools was conducted using virtual material, i.e., (1) the fixed joint interface may be considered as a virtual material with the same cross area, (2) the fixed joint interface could be equaled that the virtual material is rigidly connected with two joint surface components and (3) the analytic model on fixed joint interface can be constructed if engineering data (joint area, joint force, joint surface roughness, joint components’elastic moduli and Poisson ratios, et al) are treated as parameters, thereby the model can solve the engineering practical problem about dynamic model.
In the other, an analytic model of virtual material’s elastic modulus, shear modulus, Poisson ratio and density was proposed. Using Hertz contact theory and fractal theory, the interaction between normal and tangential characteristics of fixed interface was taken into account. In view of commercial finite element software, the dynamic-mode inserting method for parameterized fixed joint interface could be exploited adopting virtual material, therefore, a new approach is provided about the high-accuracy dynamic modeling engineering application for a whole machine tool with mechanical structure.
Thirdly, a method to estimate the fractal dimension and fractal roughness parameter is studied employing surface roughness. Structure function of surface profile was derived. An experimental technique was given to determine fractal dimension and fractal roughness parameter. Two approximate expressions were proposed about fractal dimension-surface roughness, and fractal roughness parameter-surface roughness. The experimental results reveal that fractal dimension and fractal roughness parameter have nothing to do with the sampling length. Decreasing the surface roughness increases the fractal dimension and reduces the fractal roughness parameter.
Finally, the analytic solutions for virtual material were effectively verified. Four component joint interfaces selected as some research examples, on the basis of experimental results about test specimen, the theoretical mode shapes were compared with the experimental ones (considering modal assurance criterion), i.e., qualitative comparison of similar mode shape and quantitative comparison of the corresponding natural frequency. The theoretical mode shapes basicly agree well with the experimental results. The relative errors betweenn the theoretical natural frequencies and experimental ones are mostly less than 10 %. Analyzing the results of aforementioned four component joint interfaces, the verification of the analytic method was assured when the whole machine tool’s joint interface from CKX5680 seven-five axis lathe-milling equipment was selected as a study example. The theoretical mode shapes basically agree with the experimental ones. The relative errors betweenn the theoretical natural frequencies and experimental results are mostly less than 9 %.
第一,提出一种基于虚拟材料的机床固定结合部动力学参数化建模法,即将固定结合部看成一种等截面的虚拟材料,从而将固定结合部等效为虚拟材料与两结合表面零件的固定连接,以工程数据(结合面积、结合力、结合面粗糙度、结合零件的弹性模量和泊松比等)为参数建立固定结合部动力学解析模型,解决了动力学模型工程实用性问题。
第二,建立了虚拟材料弹性模量、切变模量、泊松比、密度的解析解模型,应用赫兹接触理论和分形理论,分析了固定结合部法向和切向特性的相互影响,在此基础上利用商用有限元软件,开发了基于虚拟材料的参数化固定结合部动力学模式嵌入方法,从而为机床机械结构整机的高精度动力学建模工程化应用提供了一种新方法。
第三,研究了基于表面粗糙度(Ra)估计分形维数和分形粗糙度参数的方法。推导表面轮廓的结构函数,给出确定分形维数和分形粗糙度参数的实验方法。给出分形维数、分形粗糙度参数与表面粗糙度之间的近似换算式。实验结果表明:分形维数和分形粗糙度参数与取样长度无关,分形维数随表面粗糙度减小而增加,分形粗糙度参数随表面粗糙度减小而减小。
最后,对虚拟材料的理论解进行有效性验证。以4类零件结合部为研究对象,以测试试件的实验结果为基准,对一系列试验试件的理论模态与实验模态(考虑模态保证准则)进行比较,即相似振型定性比较、相应的固有频率定量比较。理论模型的振型与实验的振型基本一致,理论与实验固有频率的相对误差大多小于10%。在分析前4类零件结合部结果的基础上,以CKX5680七轴五联动车铣数控装备整机结合部为研究对象,对解析法进行有效性验证,理论振型与实验振型基本一致,理论与实验固有频率的相对误差小于9%。
With the development of high precision, high speed and intelligentization of NC machine tools, the need for characteristic indexes (especially dynamic ones) in NC machine tools is much higher. To high-grade NC machine tools, the dynamic property is a key of whole machine tools, therefore, the dynamic performance in machine tools becomes a novel research hot point. However, 60~80% of the total dynamic stiffness and 90% of the total damping in a whole machine tool structure come from joint interfaces. Apparently, the dynamic characteristics of joint interfaces in machine tools affect the dynamic behaviors of a whole machine tool structure considerably. The dynamic characteristics of joint interfaces had been widely studied from theory and experiment for so many years. Dynamic modeling on joint interface plays an important part in studying the dynamic characteristics of joint interface. Now, it is difficult for current models of joint interfaces to satisfy the high-grade need of a set of joint interface in NC machine tools and there lacks a parameterized model because of the diversity of joint interface’s type in NC machine tools and some parameters of describing joint interface model. Thus there urgently needs a parameterized establishing way with high precision. Some works in the manuscript are as follows.
In the first, a dynamic parameterized modeling approach on fixed joint interface in machine tools was conducted using virtual material, i.e., (1) the fixed joint interface may be considered as a virtual material with the same cross area, (2) the fixed joint interface could be equaled that the virtual material is rigidly connected with two joint surface components and (3) the analytic model on fixed joint interface can be constructed if engineering data (joint area, joint force, joint surface roughness, joint components’elastic moduli and Poisson ratios, et al) are treated as parameters, thereby the model can solve the engineering practical problem about dynamic model.
In the other, an analytic model of virtual material’s elastic modulus, shear modulus, Poisson ratio and density was proposed. Using Hertz contact theory and fractal theory, the interaction between normal and tangential characteristics of fixed interface was taken into account. In view of commercial finite element software, the dynamic-mode inserting method for parameterized fixed joint interface could be exploited adopting virtual material, therefore, a new approach is provided about the high-accuracy dynamic modeling engineering application for a whole machine tool with mechanical structure.
Thirdly, a method to estimate the fractal dimension and fractal roughness parameter is studied employing surface roughness. Structure function of surface profile was derived. An experimental technique was given to determine fractal dimension and fractal roughness parameter. Two approximate expressions were proposed about fractal dimension-surface roughness, and fractal roughness parameter-surface roughness. The experimental results reveal that fractal dimension and fractal roughness parameter have nothing to do with the sampling length. Decreasing the surface roughness increases the fractal dimension and reduces the fractal roughness parameter.
Finally, the analytic solutions for virtual material were effectively verified. Four component joint interfaces selected as some research examples, on the basis of experimental results about test specimen, the theoretical mode shapes were compared with the experimental ones (considering modal assurance criterion), i.e., qualitative comparison of similar mode shape and quantitative comparison of the corresponding natural frequency. The theoretical mode shapes basicly agree well with the experimental results. The relative errors betweenn the theoretical natural frequencies and experimental ones are mostly less than 10 %. Analyzing the results of aforementioned four component joint interfaces, the verification of the analytic method was assured when the whole machine tool’s joint interface from CKX5680 seven-five axis lathe-milling equipment was selected as a study example. The theoretical mode shapes basically agree with the experimental ones. The relative errors betweenn the theoretical natural frequencies and experimental results are mostly less than 9 %.
引文
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