Abstract
Chatter is one of the significant limitations in the milling process, which may cause poor surface quality, reduced productivity, and accelerated tool wear. Variable pitch and variable helix tools can be used to suppress regenerative chatter. This study extends the high-order full-discretization methods (FDMs) to predict the stability of milling with variable pitch and variable helix tools. The time-periodic delay-differential equation (DDE) with multiple delays is used to model the milling process using variable pitch and variable helix tools. Then, the DDE with multiple delays is reexpressed by the state-space equation. Meanwhile, the spindle rotational period is divided into many small-time intervals, and the state space equation is integrated on the small-time interval. Then, the high-order interpolation polynomials are used to approximate the state term, and the weights related to the time delay are employed to approximate the time-delay term. The second-order, third-order, and fourth-order extended FDMs (2nd EFDM, 3rd EFDM, and 4th EFDM) are compared with the benchmark in terms of the rate of convergence. It is found that the 2nd EFDM, 3rd EFDM, and 4th EFDM converge faster than the benchmark method. The difference between the curves obtained by different EFDMs and the reference curve is very small. There is no need to extend hypersecond FDMs to analyze the stability of milling with variable pitch and variable helix tools.
Highlights
High precision products machined by using high-speed milling technology have an increasing demand in various industries
Regenerative chatter can be modeled by time-periodic DDE. e mapping relations of the dynamic responses between two consecutive periods can be obtained by solving the DDE. en, the stability lobe diagrams can be determined according to the obtained mapping relations
E computational time consumed by the 2nd EFDM, 3rd EFDM, and 4th EFDM is compared with that consumed by enhanced multistage homotopy perturbation method (EMHPM) [22] and to illustrate the efficiencies of the extended FDMs
Summary
High precision products machined by using high-speed milling technology have an increasing demand in various industries. Based on the ZOA method, Altintas et al [19] presented an analytical model for stability prediction in milling with variable pitch cutters. Regarding the mechanics model for nonuniform milling tools, Chen et al [33] proposed a unified analytical cutting force model based on a predictive machining theory for variable helix end mill considering cutter runout.
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