基于接触力学的滚珠直线导轨副建模与动态特性分析研究
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摘要
在机械系统整机性能分析中，确定各零部件之间的连接参数至关重要，已成为当前机械系统设计与分析中的热点，是动态系统研究领域中的前沿课题。滚珠直线导轨副作为制造装备中最重要的连接部件之一，其特殊的结构和独特的运动形式使得很难准确建立其静、动力学模型。在制造装备设计过程中，滚珠直线导轨副的模型往往过于简化甚至被忽略，这也是导致无法准确预测制造装备整机特性的原因之一。因此，提出准确表征滚珠直线导轨副静、动力学特性的方法，揭示导轨副动力学行为的演变规律，对于研制出“高速、高精、重载，低噪音”制造装备具有重要科学价值，是研制高端制造装备所需的基础技术，具有重大的理论意义和广阔的应用前景。
针对传统方法在求解滑动摩擦条件下弹性非相似接触问题时存在多项式积分过多的困难，本文提出了一种基于修正的高斯-雅可比积分公式的求解方法，能够更有效、更直接地求解滑动摩擦条件下弹性非相似接触问题。计算了抛物线型压头和圆柱型压头与弹性半平面在滑动摩擦条件下的接触应力分布，分析了摩擦系数对接触表面应力分布的影响规律，探讨了接触表面产生裂纹的原因。
基于滚珠直线导轨副的弹性变形协调条件，提出了一种计及滑块裙部变形的滚珠直线导轨副垂直刚度模型。通过计算滚珠直线导轨副在受预紧力和垂直载荷同时作用时的垂直变形量及滑块裙部变形量，求得了滚珠直线导轨副的垂直刚度值，为设计出高刚度、高精度的滚珠直线导轨副提供理论指导。
基于建立的滚珠直线导轨副垂直刚度模型，推导了导轨副的接触刚度表达式，提出了一种计及滑块裙部变形的滚珠直线导轨副模态分析方法。利用杆单元模拟滚珠与滚道之间的接触特征，建立了某型号滚珠直线导轨副的三维有限元模型并利用有限元分析软件PATRAN/NASTRAN求解了导轨副的模态参数。由于导轨副接触刚度的非线性特征，研究了锤击法中激励力幅值对特征频率测量误差的影响。
针对使用滚珠直线导轨副作为连接件的制造装备表现出的非线性响应问题，设计了一种滚珠直线导轨副动态测试装置，基于实验测试数据，利用Volterra和Wiener理论提出了一种在随机激励条件下辨识导轨副非线性参数的方法。该计算模型可用于对含有滚珠直线导轨副的制造装备进行整机动力学特性预测分析。
利用贝叶斯推断方法以及马尔可夫链蒙特卡罗模拟方法，结合模态参数的测试数据，修正了滚珠直线导轨副名义计算模型中的不确定性参数。基于预测误差的方法，研究了修正后的模型的不确定性程度。本文的方法可有效修正滚珠直线导轨副名义计算模型中的不确定性参数，使得模型修正后的计算结果与实验测试结果之间的误差更小。
The determination of connection parameters between different parts and components inmanufacturing equipments are of great importance for the design of a machine tool capableof high-precision and high-speed machining. It is a hot topic in mechanical system designand analysis and becomes a frontier research field for the dynamical system. Linear rollingbearing is one of the most important connecting components in manufacturing equipments. Itis difficult to effectively and precisely characterize the physical properties of the linearrolling bearing because of its complex configuration. Linear rolling bearing is characterizedby the contact problem between the raceway and rolling elements. Because of thecomplexity of this type of problem, the modeling for linear rolling bearing is generally eitherover-simplified or ignored. It is one of the resons for the difficulty in precisely predicting thedynamic performance for the manufacturing equipments in the design stage. Therefore, it isnecessary to study the static and dynamic properties associated with the linear rollingbearing. It is significant for revealing the nature of the dynamical behavior of the linearrolling bearing and has great potential for developing the high-speed, high-precision and lownoise manufacturing equipment.
An efficient and straightforward technique based on the improved Gauss-Jacobiquadrature rule for solving elastically dissimilar contact problems under sliding condition isproposed in the thesis. The efficiency has been well validated by a rough stamp with sharpcorners frictionally sliding on an elastically dissimilar half-plane. This work investigates anddemonstrates the effects of frictional coefficient on the contact pressure distributionsbetween the generallied punch and the elastically dissimilar half-plane. The possible reasonsfor crack initiation associated with fatigue and fracture of the contacting components are alsoelaborated.
Based on the Hertzian contact theory and elastic beam theory, a theoretical model of thevertical stiffness of preloaded linear rolling bearing considering the flexibility of the carriageis established. The calculated outward carriage deformations match the finite element analysis results well. Clearly, the theoretical model could deal with the vertical stiffness ofpreloaded linear motion guide more accurately compared with the traditional rigid model.
Based on the rigidity model of a linear rolling bearing incorporating the flexibility of thecarriage, a modal analysis method of a linear rolling bearing using finite element analysismethod is proposed. A three dimensional finite element model of a linear rolling bearing hasbeen established. The finite element modal analysis is conducted and the modal frequenciesand vibration modes are presented. The modal testing experiment was conducted on the typeof linear rolling bearing. For the occurrence of the modes, the finite element analysis resultsbased on the presented method match the experimental results well. It should be pointed outthat, because of the nonlinear property of the contact stiffness, the variance of the amplitudeof the exciting force would result in the fluctuation of the eigenfrequency and lead to themeasurement error.
Prediction of machine dynamics at the design stage is a challenge due to lack of adequatemethods for identifying and handling the nonlinearities in the linear rolling bearing, whichappear as the nonlinear restoring force function of relative displacement and velocity acrossthe joint. This thesis discusses identification of such a nonlinear restoring force function fora linear rolling bearing. An innovative test rig is designed and the nonlinear parameters ofthe linear rolling bearing are extracted from the measurements of the applied random forceand the resultant response based on the Volterra and Wiener theories. The identified model isvalidated by comparing the frequency response function calculated from the identified modeland that from the mearsurment. Good agreement is achieved. The identified model can befurther used to predict the dynamic performance of the manufacturing equipment.
The problem of updating a finite element model representing a family of linear rollingbearings and its associated uncertainties by utilizing measured modal parameters isaddressed using a Bayesian statistical framework that can handle the inherentill-conditioning and possible nonuniqueness in model updating applications. The objective isnot only to give more accurate response predictions for the finite element model representinga family of linear rolling bearings but also to provide a quantitative assessment of thisaccuracy. The quantification of model uncertainties is carried out by means of the predictionerror. The results point out that an improvement of the prior model can be achieved and the prediction error variance provides a means for bridging the remaining gap between themeasured data and the computed output. The updated, i.e. improved, finite element modelcan be used for more reliable predictions of the structural performance in the targetmechanical environment.
针对传统方法在求解滑动摩擦条件下弹性非相似接触问题时存在多项式积分过多的困难，本文提出了一种基于修正的高斯-雅可比积分公式的求解方法，能够更有效、更直接地求解滑动摩擦条件下弹性非相似接触问题。计算了抛物线型压头和圆柱型压头与弹性半平面在滑动摩擦条件下的接触应力分布，分析了摩擦系数对接触表面应力分布的影响规律，探讨了接触表面产生裂纹的原因。
基于滚珠直线导轨副的弹性变形协调条件，提出了一种计及滑块裙部变形的滚珠直线导轨副垂直刚度模型。通过计算滚珠直线导轨副在受预紧力和垂直载荷同时作用时的垂直变形量及滑块裙部变形量，求得了滚珠直线导轨副的垂直刚度值，为设计出高刚度、高精度的滚珠直线导轨副提供理论指导。
基于建立的滚珠直线导轨副垂直刚度模型，推导了导轨副的接触刚度表达式，提出了一种计及滑块裙部变形的滚珠直线导轨副模态分析方法。利用杆单元模拟滚珠与滚道之间的接触特征，建立了某型号滚珠直线导轨副的三维有限元模型并利用有限元分析软件PATRAN/NASTRAN求解了导轨副的模态参数。由于导轨副接触刚度的非线性特征，研究了锤击法中激励力幅值对特征频率测量误差的影响。
针对使用滚珠直线导轨副作为连接件的制造装备表现出的非线性响应问题，设计了一种滚珠直线导轨副动态测试装置，基于实验测试数据，利用Volterra和Wiener理论提出了一种在随机激励条件下辨识导轨副非线性参数的方法。该计算模型可用于对含有滚珠直线导轨副的制造装备进行整机动力学特性预测分析。
利用贝叶斯推断方法以及马尔可夫链蒙特卡罗模拟方法，结合模态参数的测试数据，修正了滚珠直线导轨副名义计算模型中的不确定性参数。基于预测误差的方法，研究了修正后的模型的不确定性程度。本文的方法可有效修正滚珠直线导轨副名义计算模型中的不确定性参数，使得模型修正后的计算结果与实验测试结果之间的误差更小。
The determination of connection parameters between different parts and components inmanufacturing equipments are of great importance for the design of a machine tool capableof high-precision and high-speed machining. It is a hot topic in mechanical system designand analysis and becomes a frontier research field for the dynamical system. Linear rollingbearing is one of the most important connecting components in manufacturing equipments. Itis difficult to effectively and precisely characterize the physical properties of the linearrolling bearing because of its complex configuration. Linear rolling bearing is characterizedby the contact problem between the raceway and rolling elements. Because of thecomplexity of this type of problem, the modeling for linear rolling bearing is generally eitherover-simplified or ignored. It is one of the resons for the difficulty in precisely predicting thedynamic performance for the manufacturing equipments in the design stage. Therefore, it isnecessary to study the static and dynamic properties associated with the linear rollingbearing. It is significant for revealing the nature of the dynamical behavior of the linearrolling bearing and has great potential for developing the high-speed, high-precision and lownoise manufacturing equipment.
An efficient and straightforward technique based on the improved Gauss-Jacobiquadrature rule for solving elastically dissimilar contact problems under sliding condition isproposed in the thesis. The efficiency has been well validated by a rough stamp with sharpcorners frictionally sliding on an elastically dissimilar half-plane. This work investigates anddemonstrates the effects of frictional coefficient on the contact pressure distributionsbetween the generallied punch and the elastically dissimilar half-plane. The possible reasonsfor crack initiation associated with fatigue and fracture of the contacting components are alsoelaborated.
Based on the Hertzian contact theory and elastic beam theory, a theoretical model of thevertical stiffness of preloaded linear rolling bearing considering the flexibility of the carriageis established. The calculated outward carriage deformations match the finite element analysis results well. Clearly, the theoretical model could deal with the vertical stiffness ofpreloaded linear motion guide more accurately compared with the traditional rigid model.
Based on the rigidity model of a linear rolling bearing incorporating the flexibility of thecarriage, a modal analysis method of a linear rolling bearing using finite element analysismethod is proposed. A three dimensional finite element model of a linear rolling bearing hasbeen established. The finite element modal analysis is conducted and the modal frequenciesand vibration modes are presented. The modal testing experiment was conducted on the typeof linear rolling bearing. For the occurrence of the modes, the finite element analysis resultsbased on the presented method match the experimental results well. It should be pointed outthat, because of the nonlinear property of the contact stiffness, the variance of the amplitudeof the exciting force would result in the fluctuation of the eigenfrequency and lead to themeasurement error.
Prediction of machine dynamics at the design stage is a challenge due to lack of adequatemethods for identifying and handling the nonlinearities in the linear rolling bearing, whichappear as the nonlinear restoring force function of relative displacement and velocity acrossthe joint. This thesis discusses identification of such a nonlinear restoring force function fora linear rolling bearing. An innovative test rig is designed and the nonlinear parameters ofthe linear rolling bearing are extracted from the measurements of the applied random forceand the resultant response based on the Volterra and Wiener theories. The identified model isvalidated by comparing the frequency response function calculated from the identified modeland that from the mearsurment. Good agreement is achieved. The identified model can befurther used to predict the dynamic performance of the manufacturing equipment.
The problem of updating a finite element model representing a family of linear rollingbearings and its associated uncertainties by utilizing measured modal parameters isaddressed using a Bayesian statistical framework that can handle the inherentill-conditioning and possible nonuniqueness in model updating applications. The objective isnot only to give more accurate response predictions for the finite element model representinga family of linear rolling bearings but also to provide a quantitative assessment of thisaccuracy. The quantification of model uncertainties is carried out by means of the predictionerror. The results point out that an improvement of the prior model can be achieved and the prediction error variance provides a means for bridging the remaining gap between themeasured data and the computed output. The updated, i.e. improved, finite element modelcan be used for more reliable predictions of the structural performance in the targetmechanical environment.
引文
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