中文摘要：

针对现有的基于响应耦合子结构法（RCSA）的刀尖点频响函数预测方法需要辨识主轴-刀柄、刀柄-刀具结合面参数以及需要自制刀柄模型等引起的预测误差和预测过程复杂等问题，提出一种改进的基于RCSA的铣刀刀尖点频响函数预测方法。该方法首先改进已有的子结构划分方法，将机床-主轴-刀柄-刀具系统划分为机床-主轴-刀柄-部分刀杆、剩余刀杆和刀齿三个子结构；然后改进主轴-刀柄处转动频响函数的计算方法，通过铣刀的模态锤击实验采用反向RCSA和有限差分法计算机床-主轴-刀柄-部分刀杆结构的转动频响函数，并基于Euler梁模型计算出剩余刀杆、刀齿子结构的频响函数；最后将三个子结构的频响函数耦合确定刀尖点的预测频响函数。以一立式加工中心为研究对象，应用所提出的方法对铣刀刀尖点的频响函数进行了预测，并与其实测频响函数进行对比。对比结果表明：刀尖点的预测频响函数与实测频响函数符合程度较高，其预测、实测前三阶固有频率之间的误差在6．9％以内，所提出的方法可行有效、简单方便，且可直接基于铣刀的模态实验计算主轴一刀柄的频响函数，避免了相关结合面参数的辨识和刀柄模型的制作。

英文摘要：

The present predicting methods of tool point frequency response function （FRF） based on RCSA needed to identify the joint parameters of the spindle-holder and holder-tool joints and to manufacture the artificial tool-holder model, which will result in predicting errors and complexity, aiming at these problems, this paper presented an improved tool point FRF predicting method based on the RCSA. This method firstly improved the present substructure separating methods, and separated the machine-spindle-holder-tool structure into three parts： the machine-spindle-holder-partial tool bar, the remaining toolbar and the tool tooth; then improved the method for calculating the rotating FRFs of the machine-spindle-holder-partial tool bar through inverse RCSA and finite difference method by applying modal impact test on the toolbar, and calculated the FRFs of the remaining toolbar and tool tooth using Euler beam theory; finally the tool point FRF was predicted by coupling the three parts＇ FRFs. Experiments conducted on a machining center show that the predicted and measured tool point FRFs are in good agreement, the error between the first three order natural frequencies of the predicted and measured FRFs are within 6.9 %, the proposed method is feasible, effective and easy to carry out, it can compute the spindle-holder＇s rotating FRFs directly based on the tool modal experiments, avoiding the identification of the model. joint parameters and the manufacturing of the holder model.