Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model
Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model
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DOI：
10.1007/s00170-014-5703-0
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发表时间：
2014-06
期刊：
影响因子：
--
通讯作者：
Yiqing Yang;Qiang Liu;Bin Zhang
中科院分区：
文献类型：
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作者：
Yiqing Yang;Qiang Liu;Bin Zhang
稳定叶被广泛用于避免限制加工质量和生产率的颤振。为了快速、准确地预报稳定波瓣，人们做了大量的工作。然而，大多数的颤振稳定性研究都是基于线性力模型，且颤振稳定性极限与进给速度无关，这与实际加工情况不符。参考零阶解，研究了基于指数力模型的颤振稳定性预报问题。聚焦于具有导程角的刀具（即，对于容易产生Z向颤振的三种刀具（镶齿面铣刀、球头铣刀和外圆角铣刀），将稳定性模型扩展到三维。在计算方向系数时，利用泰勒方程对指数表达式进行线性化，以作为线性力模型解析求解稳定极限。仿真结果表明，指数力模型和线性力模型预测的切削力与实测值吻合较好，能够反映进给速度对稳定极限的影响。时域仿真结果表明，随着进给速度的增加，系统的稳定极限也随之增加。最后进行了切削试验，验证了稳定性模型的正确性。通过进一步简化，该模型可以简化为X/Y维或线性力模型稳定性模型。
Stability lobes are widely used to avoid chatter which restricts the machining quality and productivity. A lot of work has been done to predict the stability lobes fast and accurately. However, most of them are based on the linear force model, and the chatter stability limit is formulated as independent on the feed rate, which is inconsistent with the machining practice. By referencing with the zero-order solution, this paper investigates the chatter stability prediction based on the exponential force model. Focusing on the cutters with a lead angle (i.e., inserted face mill, the ball-end mill, and bull-nose end mill) where chatter is likely to be brought up inZdirection, the stability model is extended to three-dimensional. Taylor equation is utilized to linearize the exponential expressions when computing the directional coefficients in order to solve the stability limit analytically as the linear force model. Simulation results show that the exponential force model agrees with the measurements as well as the linear force model in the cutting force prediction, and it is able to demonstrate the feed rate effect on the stability limit. The stability limit is found to be increased as the feed rate increases, which is evidenced by the time domain simulation. Cutting tests are performed in the end to verify the stability model. The proposed model could be reduced to eitherX/Ydimensional or linear force model-based stability model by further simplifications.