Chatter stability analysis for milling with single-delay and multi-delay using combined high-order full-discretization m
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ORIGINAL ARTICLE
Chatter stability analysis for milling with single-delay and multi-delay using combined high-order full-discretization method Zhenghu Yan 1 & Changfu Zhang 1 & Xingguang Jiang 1 & Baoji Ma 1 Received: 13 October 2019 / Accepted: 23 September 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Regenerative chatter limits the surface finish and machining efficiency of the products. The demand for milling stability prediction and chatter suppression has been increasing. This paper presents a combined high-order full-discretization method (CHFDM) to analyze the milling stability of the system with single-delay and then extends it to calculate the stability lobe diagram (SLD) of milling with multi-delay. Firstly, the dynamic model of the milling with single-delay is represented by delay differential equation (DDE). Both the free vibration process and the forced vibration process are considered in the calculating process. The state transition matrix of the milling system is obtained by directly constructing the mapping relationship between the dynamic responses for current and previous periods. The comparisons between the CHFDM and the benchmark methods are carried out from the aspect of the rate of convergence and computational time. It is indicated that the CHFDM is applicable for obtaining the stability boundary of milling with both large and small radial immersion ratios accurately. Meanwhile, the computational efficiency of the CHFDM is verified to be good through comparison. Then, the CHFDM is extended to obtain the SLD of milling with multi-delay. The effectiveness of the extended CHFDM is validated by comparing it with two existing methods. The comparison results indicate that the CHFDM can be extended to obtain the SLD of milling with multi-delay reliably and efficiently. Keywords Chatter stability . Full-discretization method . Single-delay . Multi-delay
1 Introduction Milling operation is usually adopted in the machining process for many precision products. Regenerative chatter is a common phenomenon during milling operations. It is pointed out that the surface finish and machining efficiency of the products are still limited by chatter [1]. Moreover, chatter may accelerate tool wear and even shorten the lifetime of the machine tool. Therefore, the demand for stability prediction and chatter suppression has been increasing. Chatter-free parameters determined by using the SLD should be adopted to optimize the milling process. The milling dynamics considering the regenerative mechanism can be mathematically modeled by time-periodic DDEs
* Zhenghu Yan [email protected] 1
School of Mechatronic Engineering, Xi’an Technological University, Xi’an 710021, China
[2]. The stability lobe diagram (SLD), which illustrates the boundary of milling stability, can be obtained through the numerical solution of the DDE. According to the SLD, the parameter combinations in the stable region can be adopted for achieving high-efficiency and high-quality milling processes. Therefore, many
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