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A lightweight design scheme for a heavy-duty planetary gear three-stage transmission system based on the sqp algorithm and the response surface method

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ENGINEERING RESEARCH EXPRESS 2025年第2期7卷 025508-025508页

作者： Li, Jubo Zhang, Huijie Ren, Yanbo Yang, Jianjun Xin, Wen Jiang, Chuang Henan Univ Sci & Technol Sch Mechatron Engn Luoyang 471000 Henan Peoples R China CITIC Heavy Ind Co Ltd Luoyang 471039 Henan Peoples R China

Within a certain range of total transmission ratios, the heavy-duty planetary gear multi-stage transmission system faces challenges such as difficulty in coordinating transmission ratios, balancing lightweight design with load-carrying capacity, and low space utilization. To address these issues, this study proposes an optimized design for a heavy-duty planetary gear three-stage transmission system, with the volume of the gearing system as the optimization objective. Firstly, based on the sequential quadratic programming algorithm, eight kinds of transmission ratio preferential assignments are made for the heavy-duty planetary gear three-stage transmission system. By analyzing the results of the volume optimization, the preliminary transmission scheme for the heavy-duty planetary gear three-stage transmission system, in which the ratios of the first two stages are both reduced and the ratio of the tertiary stage is increased, is preferred. Secondly, on this basis, and in combination with the response surface method, the second-order response model for the relationship between the transmission ratios of all stages of the heavy-duty planetary gear three-stage transmission system and the total volume of the system is established. The reasonableness of the initial selection scheme is verified by solving the response surface objective function, and the optimal allocation result is obtained. This result is allocated as follows: The primary transmission ratio is 1.5635, the secondary transmission ratio is 5.7158, and the tertiary transmission ratio is 4.8800. The volume under this allocation is 5.32573 x 108 mm3, which decreases by 7.75% compared to the maximum volume of 5.77307 x 108 mm3 among all lightweighting schemes. The lightweight design of the heavy-duty planetary gear three-stage transmission system is realized. The results of the study provide helpful references for the lightweight design and optimization of transmission systems, the coordinated distribution of t

关键词： heavy-duty planetary gear three-stage transmission system sqp algorithm optimized design scheme response surface method

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An improved sqp algorithm for solving minimax problems

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APPLIED MATHEMATICS LETTERS 2009年第4期22卷 464-469页

作者： Zhu, Zhibin Cai, Xiang Jian, Jinbao Guilin Univ Elect Technol Coll Math & Comp Sci Guilin 541004 Peoples R China Guangxi Univ Coll Math & Informat Sci Nanning 510004 Peoples R China

in this work, an improved sqp method is proposed for solving minimax problems, and a new method with small computational cost is proposed to avoid the Maratos effect. In addition, its global and superlinear convergenc... 详细信息

关键词： Minimax problem sqp algorithm Global convergence Superlinear convergence rate

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A New Superlinearly Convergent sqp algorithm for Nonlinear Minimax Problems

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Acta Mathematicae Applicatae Sinica 2007年第3期23卷 395-410页

作者： Jin-bao Jian Ran Quan Qing-jie Hu College of Mathematics and Information Science Guangxi University Nanning 530004 China College of Electrical Engineering Guangxi University Nanning 530004 Chin Department of Information Hunan Business College Changsha 410205 China

In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （sqp）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.

关键词： Minimax problems sqp algorithm global convergence superlinear convergence

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A superlinearly convergent sqp algorithm for mathematical programs with linear complementarity constraints

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期172卷 222-244页

作者： Zhu, ZB Zhang, KC Guilin Inst Elect Technol Dept Computat Sci & Math Guilin 541004 Peoples R China Xian Jiaotong Univ Fac Sci Xian 710049 Shaanxi Peoples R China

In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer-Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation. The smooth optimization is solved by sqp algorithm for standard constrained optimization. Global convergence and superlinear convergence rate are established under some suitable assumptions. Moreover, we conclude that the current iterate point is an exact stationary point of the MPEC problem when the proposed algorithm stops in finite iteration. (c) 2005 Elsevier Inc. All rights reserved.

关键词： mathematical programs with equilibrium constraints sqp algorithm successive approximation system of linear equations global convergence superlinear convergence rate

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A NEW NONMONOTONE LINESEARCH sqp algorithm FOR UNCONSTRAINED MINIMAX PROBLEM

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2014年第4期35卷 487-508页

作者： Wang, Fu-Sheng Jian, Jin-Bao Taiyuan Normal Univ Dept Math Taiyuan 030012 Peoples R China Yulin Normal Univ Coll Math & Informat Sci Yulin Guangxi Peoples R China

In this article, unconstrained minimax problems are discussed, and a sequential quadratic programming (sqp) algorithm with a new nonmonotone linesearch is presented. At each iteration, a search direction of descent is obtained by solving a quadratic programming (QP). To circumvent the Maratos effect, a high-order correction direction is achieved by solving another QP and a new nonmonotone linesearch is performed. Under reasonable conditions, the global convergence and the rate of superlinear convergence are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

关键词： Linesearch method Minimax problem Nonmonotone technique Nonsmooth optimization sqp algorithm 90C47 90C30 65K05 49K35

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Smoothing sqp algorithm for semismooth equations with box constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第2期55卷 399-425页

作者： Wang, Changyu Liu, Qian Ma, Cheng Qufu Normal Univ Inst Operat Res Qufu Peoples R China Shandong Normal Univ Dept Math Jinan Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, in order to solve semismooth equations with box constraints, we present a class of smoothing sqp algorithms using the regularized-smooth techniques. The main difference of our algorithm from some related literature is that the correspondent objective function arising from the equation system is not required to be continuously differentiable. Under the appropriate conditions, we prove the global convergence theorem, in other words, any accumulation point of the iteration point sequence generated by the proposed algorithm is a KKT point of the corresponding optimization problem with box constraints. Particularly, if an accumulation point of the iteration sequence is a vertex of box constraints and additionally, its corresponding KKT multipliers satisfy strictly complementary conditions, the gradient projection of the iteration sequence finitely terminates at this vertex. Furthermore, under local error bound conditions which are weaker than BD-regular conditions, we show that the proposed algorithm converges superlinearly. Finally, the promising numerical results demonstrate that the proposed smoothing sqp algorithm is an effective method.

关键词： Semismooth equations with box constraints sqp algorithm Global convergence Finite termination Superlinear convergence rate

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An improved Z-MAP method based on the sqp algorithm for fast surface topography simulation of ball-end milling

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2023年第3-4期128卷 1863-1878页

作者： Xiao, Yukun Ge, Guangyan Zeng, Zhilin Feng, Xiaobing Du, Zhengchun Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Ningbo SKYNC F Axis Numer Control Technol Co Ltd Ningbo 315000 Peoples R China

Products with complex free-form surfaces, such as aerospace impellers and automotive engines, are typically manufactured with ball-end milling. The machined surface topography is critical to these key components' performance in harsh environments. Accurate prediction of the machined surface topography is essential to obtaining the optimized process parameters to achieve the best possible surface quality. An improved Z-MAP method based on the sequential quadratic programming (sqp) algorithm is proposed for efficient ball-end milling surface topography simulation in this paper. Compared to the traditional Z-MAP method, this improved method does not discretize the cutter edge and does not require a strict time-step limit. At each simulation time interval, the workpiece surface grid points falling into the cutting-edge instantaneous sweep polygon are searched to reduce the computation scale. An optimization problem, which combines these grid points' coordinates with the cutting-edge trajectory model, is established for the accurate cutting time and cutting-edge element. The sqp algorithm is used to solve this optimization problem due to its global search capability. The surface topography is then updated by comparing the height of the cutting-edge element with the corresponding grid point. Experimental results indicate that the simulated surface topography is consistent with the measured surface topography. The proposed method achieves the same level of accuracy as the traditional method while requiring less computing time. The proposed method for fast surface topography in ball-end milling shows potential in optimizing process parameters to guarantee the surface quality of critical components.

关键词： Ball-end milling Surface topography Improved Z-MAP method sqp algorithm

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An sqp algorithm for mathematical programs with nonlinear complementarity constraints

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Applied Mathematics and Mechanics(English Edition) 2009年第5期30卷 659-668页

作者：朱志斌简金宝张聪 School of Mathematics & Computational Science Guilin University of Electronic Technology College of Mathematics and Information Science Guangxi University

In this paper, we describe a successive approximation and smooth sequential quadratic programming （sqp） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.

关键词： mathematical programs with equilibrium constraints (MPEC) sqp algorithm successive approximation global convergence superlinear convergence rate

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An sqp algorithm with Cautious Updating Criteria for Nonlinear Degenerate Problems

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 33-42页

作者： Tao-wen Liu Jin-ping Zeng College of Mathematics and Econometrics Hunan University Changsha 410082 China College of Software Dongguan University of Technology Dongguan 523808 China

An efficient sqp algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions.

关键词： Degenerate problem exact penalty function sqp algorithm cautious update criteria globalconvergence

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A superlinearly convergent implicit smooth sqp algorithm for mathematical programs with nonlinear complementarity constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第3期31卷 335-361页

作者： Jian, JB Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China

This paper discusses a special class of mathematical programs with nonlinear complementarity constraints, its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. We first reformulate the complementarity constraints as a standard nonlinear equality and inequality constraints by making use of a class of generalized smoothing complementarity functions, then present a new sqp algorithm for the discussed problems. At each iteration, with the help of a pivoting operation, a master search direction is yielded by solving a quadratic program, and a correction search direction for avoiding the Maratos effect is generated by an explicit formula. Under suitable assumptions, without the strict complementarity on the upper-level inequality constraints, the proposed algorithm converges globally to a B-stationary point of the problems, and its convergence rate is superlinear.

关键词： nonlinear complementarity constraints mathematical programs sqp algorithm superlinear convergence

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