在航空发动机多级转子装配过程中，优化的转子堆叠装配方案对提高转子装配质量及安全运行有着重要的意义。为了提高转子安装相位优化效率和装配质量，基于几何代数理论并结合多目标优化方法提出了一种高效求解最优堆叠装配方案的方法。首先，对几何代数和齐次矩阵的计算效率进行对比验证，并基于几何代数理论改进多级转子堆叠装配误差传递模型；其次，针对航空发动机转子安装相位角度的装配要求，建立转子同心度和初始不平衡量的多目标优化模型；最后，采用非支配排序遗传算法求解该堆叠装配多目标优化问题，获得符合工艺要求的最优装配方案。算例结果表明，优化后的转子装配方案比随机装配方案同心度降低65.10%，初始不平衡量降低97.88%。
In the assembly process of aero-engine multi-stage rotors, the optimized rotor stacking assembly plan is of particular significance in improving the rotor assembly quality and safe operation. To enhance the optimization efficiency of rotor installation phase and assembly quality, a method for efficient solution of the optimal stacking assembly scheme is proposed based on the geometric algebra theory combined with the multi-objective optimization method. The computational efficiency of the geometric algebra and homogeneous matrix is first compared and verified, and the multi-stage rotor stack assembly error propagation model improved based on the geometric algebra theory. Secondly, according to the assembly requirements of the aero-engine rotor installation phase angle, a multi-objective optimization model of rotor concentricity and initial unbalance is established. The non-dominated sorting genetic algorithm II is finally used to solve the multi-objective optimization problem of the stack assembly, obtaining the optimal assembly scheme that satisfies the process requirements. Results show that the concentricity of the rotor and the initial unbalance are reduced by 65.10% and 97.88%, respectively, compared with the random assembly scheme.
[1] 刘君, 吴法勇, 王娟. 航空发动机转子装配优化技术[J]. 航空发动机, 2014, 40(3):75-78. LIU J, WU F Y, WANG J. Optimization technique of aeroengine rotor assembly[J]. Aeroengine, 2014, 40(3):75-78(in Chinese).
[2] HUSSAIN T, YANG Z, POPOV A A, et al. Straight-build assembly optimization:A method to minimize stage-by-stage eccentricity error in the assembly of axisymmetric rigid components (two-dimensional case study)[J]. Journal of Manufacturing Science and Engineering, 2011, 133(3):031014.
[3] YANG Z, HUSSAIN T, POPOV A A, et al. Novel optimization technique for variation propagation control in an aero-engine assembly[J]. Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2011, 225(1):100-111.
[4] MARZIALE M, POLINI W. A review of two models for tolerance analysis of an assembly:Vector loop and matrix[J]. The International Journal of Advanced Manufacturing Technology, 2009, 43(11-12):1106-1123.
[5] YANG Z, POPOV A A, MCWILLIAM S. Variation propagation control in mechanical assembly of cylindrical components[J]. Journal of Manufacturing Systems, 2012, 31(2):162-176.
[6] WHITNEY D E, GILBERT O L, JASTRZEBSKI M. Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies[J]. Research in Engineering Design, 1994, 6(4):191-210.
[7] ZHANG Z Q, ZHANG Z J, JIN X, et al. A novel modelling method of geometric errors for precision assembly[J]. The International Journal of Advanced Manufacturing Technology, 2018, 94(1-4):1139-1160.
[8] MANTRIPRAGADA R, WHITNEY D E. Modeling and controlling variation propagation in mechanical assemblies using state transition models[J]. IEEE Transactions on Robotics and Automation, 1999, 15(1):124-140.
[9] 曹茂国. 多级盘结构转子的工艺装配优化设计方法[J]. 航空发动机, 1994,20(3):48-52. CAO M G. Process assembly optimization design method of multi-disk structure rotor[J]. Journal of Aeroengine, 1994,20(3):48-52(in Chinese)..
[10] 李立新, 艾延廷, 王志, 等. 基于遗传算法的多级盘转子平衡方案优化设计[J]. 振动、测试与诊断, 2008, 28(2):139-142, 182. LI L X, AI Y T, WANG Z, et al. Optimum design for balance in multi-disk rotor installation based on genetic algorithm[J]. Journal of Vibration, Measurement & Diagnosis, 2008, 28(2):139-142, 182(in Chinese).
[11] 琚奕鹏, 吴法勇, 金彬, 等. 基于转子跳动和初始不平衡量优化的多级盘转子结构装配工艺[J]. 航空发动机, 2018, 44(6):83-90. JU Y P, WU F Y, JIN B, et al. Structure assembly technique of multi-stage disc rotor based on rotor runout and unbalance optimization[J]. Aeroengine, 2018, 44(6):83-90(in Chinese).
[12] 李洪波. 共形几何代数:几何代数的新理论和计算框架[J]. 计算机辅助设计与图形学学报, 2005, 17(11):2383-2393. LI H B. Conformal geometric algebra:A new framework for computational geometry[J]. Journal of Computer-Aided Design & Computer Graphics, 2005, 17(11):2383-2393(in Chinese).
[13] FU Z T, YANG W, YANG Z. Solution of inverse kinematics for 6R robot manipulators with offset wrist based on geometric algebra[J]. Journal of Mechanisms and Robotics, 2013, 5(3):310081-310087.
[14] HUO X M, SUN T, SONG Y M. A geometric algebra approach to determine motion/constraint, mobility and singularity of parallel mechanism[J]. Mechanism and Machine Theory, 2017, 116:273-293.
[15] LI Q C, CHAI X X, XIANG J N. Mobility analysis of limited-degrees-of-freedom parallel mechanisms in the framework of geometric algebra[J]. Journal of Mechanisms and Robotics, 2016, 8(4):041005.
[16] SELIG J M. Clifford algebra of points, lines and planes[J]. Robotica, 2000, 18(5):545-556.
[17] 李洪波. Clifford代数与几何定理机器证明[J]. 世界科技研究与发展, 2001, 23(3):41-47. LI H B. Clifford algebra and automated geometric theorem proving[J]. World Sci-Tech R & D, 2001, 23(3):41-47(in Chinese).
[18] CRILLY T. Geometric algebra for physicists[J]. The Mathematical Gazette, 2005, 89(514):180-181.
[19] CAI M, YANG J X, WU Z T. Mathematical model of cylindrical form tolerance[J]. Journal of Zhejiang University-SCIENCE A, 2004, 5(7):890-895.
[20] CHEN G Y, LI J H. A diversity ranking based evolutionary algorithm for multi-objective and many-objective optimization[J]. Swarm and Evolutionary Computation, 2019, 48:274-287.
[21] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[22] 李泽林. 基于轴向预载的转子装配方法研究[D]. 哈尔滨:哈尔滨工业大学, 2018:10-11. LI Z L. Research on rotor assembly method based on axial compression[D]. Harbin:Harbin Institute of Technology, 2018:10-11(in Chinese).
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