机床的动态特性可以衡量机床抵抗动载荷的能力，对机床切削性能有着重要影响。该文以一种具有平行四边形结构的3自由度并联主轴头为研究对象，研究其动力学建模方法及其分析动态特性。该主轴头运动学支链中的杆件具有变截面特点，基于有限元思想该文提出了一种求解变截面杆件质量矩阵的方法，并考虑铰链的影响，建立了铰链的质量矩阵，进一步推导了并联主轴头的动力学模型。基于动力学模型，研究了并联主轴头在工作空间内的固有频率分布规律及其振型。通过在并联主轴头样机上的实验，验证了动力学模型和动态特性分析的准确性和有效性，为并联主轴头的工程应用奠定了坚实基础。
The dynamic characteristics of a machine tool are related to the ability of the tool to resist the dynamic loads which has an important influence on the machine tool cutting performance. This paper presents a model of the dynamic characteristics of a 3-DOF spindle with a parallel linkage mechanism. The valuable cross-section of the link in the spindle complicates an accurate defination of the mass matrix. This paper presents an approach to derive the mass matrix of a link with an arbitrarily shaped cross-section based on the finite-element method. The joint mass matrix is also considered in the model. The dynamic model is then used to investigate the natural frequencies and the vibration modes in the workspace. Tests on a prototype with the parallel linkage validate the model for accurate dynamic modeling of 3-DOF spindles with parallel linkages. This work is very useful for development of the 3-DOF spindle with parallel mechanism.
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