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Milling stability analysis using the spectral method

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Abstract

This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral term. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ye Ding, LiMin Zhu & Han Ding

  2. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    XiaoJian Zhang

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  1. Ye Ding
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  2. LiMin Zhu
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  3. XiaoJian Zhang
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  4. Han Ding
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Correspondence to Han Ding.

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Ding, Y., Zhu, L., Zhang, X. et al. Milling stability analysis using the spectral method. Sci. China Technol. Sci. 54, 3130–3136 (2011). https://doi.org/10.1007/s11431-011-4611-x

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