An implicit exponentially fitted method for chatter stability prediction of milling processes

Chatter stability prediction is an important technique for obtaining chatter-free cutting parameters to enhance product quality and achieve better cutting performance. Based on the exponential fitting multistep algorithms and Fibonacci search, this paper presents an implicit exponentially fitted method to efficiently and accurately determine the chatter stability limits. The dynamic model with consideration of the regeneration effect for milling processes can be expressed as delay-differential equations (DDEs) with time-periodic coefficients. The tooth-passing period can be subdivided into two distinct phases according to whether the cutting tool is contacting the machined parts. On the basis that the forced vibration phase can be discretized into time intervals of identical duration, a three-step implicit exponentially fitted method is developed to estimate the state term. Subsequently, the milling stability boundary can be obtained by using the Fibonacci search to substitute traditional sequential search, which can remarkably reduce the computational time. The effectiveness of the implicit exponentially fitted method is validated through making comparisons with the other two benchmark methods. Simulation results indicate that the implicit exponentially fitted method exhibits excellent accuracy and efficiency. Furthermore, the experimental verification was performed to further demonstrate the availability and validity of the implicit exponentially fitted method. On this basis, we extend the implicit exponentially fitted method to the variable pitch cutters case. Furthermore, a benchmark example is provided to evaluate the feasibility of the extended implicit exponentially fitted method. The results indicate that the implicit exponentially fitted method can achieve significantly better computational efficiency and accuracy.