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Response Sensitivity Analysis of the Dynamic Milling Process Based on the numerical integration method

Chinese Journal of Mechanical Engineering 2012年第5期25卷 940-946页

作者： DING Ye ZHU Limin ZHANG Xiaojian DING Han State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 China

As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.

关键词： milling stability sensitivity of the stability boundary numerical integration method

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numerical simulation of a cabin ventilation subsystem in a space station oriented real-time system

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Chinese Journal of Aeronautics 2017年第6期30卷 1809-1817页

作者： Zezheng QIU Liping PANG Guoxiang LI Helin ZHANG School of Aeronautic Science and Engineering Beihang UniversityBeijing 100083China Aviation Key Laboratory of Science and Technology on Aero Electromechanical System integration Nanjing Engineering Institute of Aircraft SystemsNanjing 211102China

An environment control and life support system（ECLSS） is an important system in a space station. The ECLSS is a typical complex system, and the real-time simulation technology can help to accelerate its research process by using distributed hardware in a loop simulation system. An implicit fixed time step numerical integration method is recommended for a real-time simulation system with time-varying parameters. However, its computational efficiency is too low to satisfy the real-time data interaction, especially for the complex ECLSS system running on a PC cluster. The instability problem of an explicit method strongly limits its application in the ECLSS real-time simulation although it has a high computational efficiency. This paper proposes an improved numerical simulation method to overcome the instability problem based on the explicit Euler method. A temperature and humidity control subsystem（THCS） is firstly established, and its numerical stability is analyzed by using the eigenvalue estimation theory. Furthermore, an adaptive operator is proposed to avoid the potential instability problem. The stability and accuracy of the proposed method are investigated carefully. Simulation results show that this proposed method can provide a good way for some complex time-variant systems to run their real-time simulation on a PC cluster.

关键词： numerical integration method Real-time simulation Stability THCS Time-variant system

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Fast and accurate adaptive collocation iteration method for orbit dynamic problems

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Chinese Journal of Aeronautics 2023年第9期36卷 231-242页

作者： Honghua DAI Zhe ZHANG Xuechuan WANG Haoyang FENG Changtao WANG Xiaokui YUE National Key Laboratory of Aerospace Flight Dynamics(AFDL) Northwestern Polytechnical UniversityXi’an 710072China School of Astronautics Northwestern Polytechnical UniversityXi’an 710072China

For over half a century,numerical integration methods based on finite difference,such as the Runge-Kutta method and the Euler method,have been popular and widely used for solving orbit dynamic *** general,a small integration step size is always required to suppress the increase of the accumulated computation error,which leads to a relatively slow computation ***,a collocation iteration method,approximating the solutions of orbit dynamic problems iteratively,has been *** method achieves high computation accuracy with extremely large step *** efficient,the collocation iteration method suffers from two limitations:(A)the computational error limit of the approximate solution is not clear;(B)extensive trials and errors are always required in tuning *** overcome these problems,the influence mechanism of how the dynamic problems and parameters affect the error limit of the collocation iteration method is *** this basis,a parameter adjustment method known as the“polishing method”is proposed to improve the computation *** method proposed is demonstrated in three typical orbit dynamic problems in aerospace engineering:a low Earth orbit propagation problem,a Molniya orbit propagation problem,and a geostationary orbit propagation *** simulations show that the proposed polishing method is faster and more accurate than the finite-difference-based method and the most advanced collocation iteration method.

关键词： Collocation iteration method numerical integration method Orbit dynamics Parameter adjustment method Polishing method

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Variable-step integration method for milling chatter stability prediction with multiple delays

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Science China(Technological Sciences) 2011年第12期54卷 3137-3154页

作者： ZHANG XiaoJian XIONG CaiHua DING Ye XIONG YouLun State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China

This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.

关键词： variable-step numerical integration method milling chatter stability prediction multiple delays variable pitch cutter cutter runout

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An accurate RLGC circuit model for dual tapered TSV structure

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Journal of Semiconductors 2014年第9期35卷 136-142页

作者：魏祯李晓春毛军发 Key Laboratory of Ministry of Education of Design and Electromagnetic Compatibility of High-Speed Electronic Systems Shanghai Jiao Tong University

A fast RLGC circuit model with analytical expression is proposed for the dual tapered through-silicon via （TSV） structure in three-dimensional integrated circuits under different slope angles at the wide frequency region. By describing the electrical characteristics of the dual tapered TSV structure, the RLGC parameters are extracted based on the numerical integration method. The RLGC model includes metal resistance, metal inductance, substrate resistance, outer inductance with skin effect and eddy effect taken into account. The proposed analytical model is verified to be nearly as accurate as the Q3D extractor but more efficient.

关键词： tapered TSV RLGC circuit model numerical integration method current continuity eddy effect

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