数控铣削过程离线优化技术研究
|
摘要
数控加工技术在制造业中占有重要地位,是机械加工现代化的主要基础和关键技术,也是发展军事工业的重要战略技术。在数控加工中采用加工过程优化技术,不仅有利于提升数控加工设备的制造能力,而且能产生重大经济效益。传统的加工过程优化方法是采用自适应控制技术,尤其是约束型自适应控制技术。随着计算机技术的发展,国内外研究者开展了基于仿真技术的加工过程优化研究。相对于自适应控制的在线优化,这是一种具有离线性质的优化方法,具有成本低、符合绿色制造、无实时性要求的特点,拥有良好的发展前景。
虚拟加工技术是当前加工仿真技术发展的一个新阶段,不仅能提供逼真的加工环境仿真,而且在几何仿真和物理仿真过程中考虑了机床系统的运动特性和动态特性。本文开展了基于虚拟加工仿真的切削过程离线优化技术研究,对离线优化的原理和优化流程进行了分析,并对优化数学模型的建立、约束规则的选择进行了分析与研究。
加工过程离线优化的前提是实现准确的加工过程仿真,本文开展了利用实体仿真技术进行加工过程仿真的研究。分析了刀具扫描体生成过程中出现自相交现象的原因,并提出了解决方案。针对实体仿真中容易出现的错误,提出了基于空间扫描轮廓生成刀具扫描体的方法,保证了加工仿真结果的正确性。
在加工过程仿真与优化系统中,切削参数的获取对铣削力模型在加工过程中的应用、刀具寿命的预测以及切削参数的优化都具有重要意义。本文提出了采用“剖切法”获取切削参数,其实质是将刀具在进给方向上的半圆柱面代替刀具实体并与材料去除体进行布尔交运算,然后对布尔交结果进行处理来获取切削参数的过程。利用“剖切法”可正确地获得立铣加工中的切削深度、切削宽度以及切入角和切出角。相对于利用切屑几何体获取切削参数的方法,“剖切法”获取切削参数的过程不会增加工件复杂度,但显著降低了切削参数获取的计算量。铣削力预测值与测量值的较好吻合间接验证了切削参数获取方法的正确性。
针对加工过程优化的特点,本文选择粒子群优化算法优化切削参数。在标准粒子群优化算法基础上,引入粒子群平均距离对优化过程进行评价与控制。通过选择合适的粒子群平均距离阈值,改进型粒子群算法实现了优化成功率与优化效率的统一。
数控程序中的进给速度和主轴转速通常都未得到优化,针对切削参数优化研究较集中于优化进给速度而较少对主轴进行优化的现象,本文对同时实现进给速度和主轴转速优化进行了探索与研究。将主轴转速和进给速度与粒子群优化算法相结合,在粒子寻优过程中实现了对数控程序中的主轴转速和进给速度的同时优化。
在ACIS实体造型系统基础上,开发了具有实体仿真功能的铣削加工过程离线优化软件系统。利用该系统根据恒切削力和效率的组合目标对粗加工数控铣削程序进行了优化,并采用优化后的数控程序进行了加工实验。铣削实验验证了离线优化系统的有效性和可靠性。
Numerical control (NC) machining occupies an important place in the manufacturing industry. As one of the key technologies, NC machining is the basement for manufacturing modernization, and is strategically important to develop military industry. Using existing NC machining equipments, machining process optimization can increase efficiency and guarantee machining quality, which is important to improve the machineability of the equipments and produce great economic benefits. Traditionally, adaptive control (AC) technology, especially adaptive control constraints (ACC) was applied to optimize and control the machining process. With the development of computer technology, optimizing machining process based on machining process simulation technique becomes a more potential method, which is an off-line optimization method relative to the on-line optimization in AC, and shows the advantage of low cost, agreement with the trend of green manufacturing and without real-time requirement.
As a new stage of machining process simulation, virtual machining can supply vivid machining scene, and take full consideration of machine performance such as kinematic characteristics and dynamic characteristics in geometry simulation and physical simulation. In this paper, off-line machining process optimization technology, which based on virtual machining technique, is studied including off-line optimization principle and process, establishment of optimization mathematics model, selection for constraint rules.
Because machining simulation is the basement to the off-line optimization, this paper focus on the research on machining process simulation based on solid simulation technology. Depending on the analysis to the reasons of self-intersection in constructing tool swept volume, the solved method is proposed. To eliminate the wrong result in solid simulation, a sweeping method based on a 3-dimision swept profile is introduced.
In simulation and optimization to machining process, getting milling parameters is very important to apply cutting force model, to estimate tool life and to optimize cutting parameters. This paper presents a new method which is named“sliced method”, which replaces the tool by its half cylindrical face in feed direction, and treats the intersection geometry between the half cylindrical face and the removed material body of tool path to calculate the milling parameters including radial width, axial depth, cut-in angle and cut-out angle.“Sliced method”does not increase the complexity of workpiece, but is more efficient to calculate the parameters relative to the method according to the chip geometry. The validation of the“sliced method”is test by the good agreement between the measured forces and the predicted forces indirectly.
To fit the characteristic of machining process optimization, particle swarm optimization (PSO) algorithm was improved by introduced the particle average distance to the standard PSO algorithm. By controlling the threshold of particle average distance, improved PSO algorithm can achieve the optimal result with smaller iterations.
Because spindle revolutions and feed rates are not optimized in most NC file,but most optimization researches on federate optimization, this paper makes study on optimizing federates and spindle revolutions together. Combined with the PSO, feed rates and spindle revolutions in NC file are optimized during each“particle”seeking its optimal value.
Based on ACIS solid model system, an off-line optimization system of NC end milling process is developed which has the function of solid simulation. Using the optimization system, spindle revolutions and feed rates in NC file for rough machining are optimized according to the multiple objectives: constant machining forces and increasing machining efficiency. Using the optimal NC file, milling experiments are carried out and the experiment result shows the validity and reliability of off-line milling process optimization system.
虚拟加工技术是当前加工仿真技术发展的一个新阶段,不仅能提供逼真的加工环境仿真,而且在几何仿真和物理仿真过程中考虑了机床系统的运动特性和动态特性。本文开展了基于虚拟加工仿真的切削过程离线优化技术研究,对离线优化的原理和优化流程进行了分析,并对优化数学模型的建立、约束规则的选择进行了分析与研究。
加工过程离线优化的前提是实现准确的加工过程仿真,本文开展了利用实体仿真技术进行加工过程仿真的研究。分析了刀具扫描体生成过程中出现自相交现象的原因,并提出了解决方案。针对实体仿真中容易出现的错误,提出了基于空间扫描轮廓生成刀具扫描体的方法,保证了加工仿真结果的正确性。
在加工过程仿真与优化系统中,切削参数的获取对铣削力模型在加工过程中的应用、刀具寿命的预测以及切削参数的优化都具有重要意义。本文提出了采用“剖切法”获取切削参数,其实质是将刀具在进给方向上的半圆柱面代替刀具实体并与材料去除体进行布尔交运算,然后对布尔交结果进行处理来获取切削参数的过程。利用“剖切法”可正确地获得立铣加工中的切削深度、切削宽度以及切入角和切出角。相对于利用切屑几何体获取切削参数的方法,“剖切法”获取切削参数的过程不会增加工件复杂度,但显著降低了切削参数获取的计算量。铣削力预测值与测量值的较好吻合间接验证了切削参数获取方法的正确性。
针对加工过程优化的特点,本文选择粒子群优化算法优化切削参数。在标准粒子群优化算法基础上,引入粒子群平均距离对优化过程进行评价与控制。通过选择合适的粒子群平均距离阈值,改进型粒子群算法实现了优化成功率与优化效率的统一。
数控程序中的进给速度和主轴转速通常都未得到优化,针对切削参数优化研究较集中于优化进给速度而较少对主轴进行优化的现象,本文对同时实现进给速度和主轴转速优化进行了探索与研究。将主轴转速和进给速度与粒子群优化算法相结合,在粒子寻优过程中实现了对数控程序中的主轴转速和进给速度的同时优化。
在ACIS实体造型系统基础上,开发了具有实体仿真功能的铣削加工过程离线优化软件系统。利用该系统根据恒切削力和效率的组合目标对粗加工数控铣削程序进行了优化,并采用优化后的数控程序进行了加工实验。铣削实验验证了离线优化系统的有效性和可靠性。
Numerical control (NC) machining occupies an important place in the manufacturing industry. As one of the key technologies, NC machining is the basement for manufacturing modernization, and is strategically important to develop military industry. Using existing NC machining equipments, machining process optimization can increase efficiency and guarantee machining quality, which is important to improve the machineability of the equipments and produce great economic benefits. Traditionally, adaptive control (AC) technology, especially adaptive control constraints (ACC) was applied to optimize and control the machining process. With the development of computer technology, optimizing machining process based on machining process simulation technique becomes a more potential method, which is an off-line optimization method relative to the on-line optimization in AC, and shows the advantage of low cost, agreement with the trend of green manufacturing and without real-time requirement.
As a new stage of machining process simulation, virtual machining can supply vivid machining scene, and take full consideration of machine performance such as kinematic characteristics and dynamic characteristics in geometry simulation and physical simulation. In this paper, off-line machining process optimization technology, which based on virtual machining technique, is studied including off-line optimization principle and process, establishment of optimization mathematics model, selection for constraint rules.
Because machining simulation is the basement to the off-line optimization, this paper focus on the research on machining process simulation based on solid simulation technology. Depending on the analysis to the reasons of self-intersection in constructing tool swept volume, the solved method is proposed. To eliminate the wrong result in solid simulation, a sweeping method based on a 3-dimision swept profile is introduced.
In simulation and optimization to machining process, getting milling parameters is very important to apply cutting force model, to estimate tool life and to optimize cutting parameters. This paper presents a new method which is named“sliced method”, which replaces the tool by its half cylindrical face in feed direction, and treats the intersection geometry between the half cylindrical face and the removed material body of tool path to calculate the milling parameters including radial width, axial depth, cut-in angle and cut-out angle.“Sliced method”does not increase the complexity of workpiece, but is more efficient to calculate the parameters relative to the method according to the chip geometry. The validation of the“sliced method”is test by the good agreement between the measured forces and the predicted forces indirectly.
To fit the characteristic of machining process optimization, particle swarm optimization (PSO) algorithm was improved by introduced the particle average distance to the standard PSO algorithm. By controlling the threshold of particle average distance, improved PSO algorithm can achieve the optimal result with smaller iterations.
Because spindle revolutions and feed rates are not optimized in most NC file,but most optimization researches on federate optimization, this paper makes study on optimizing federates and spindle revolutions together. Combined with the PSO, feed rates and spindle revolutions in NC file are optimized during each“particle”seeking its optimal value.
Based on ACIS solid model system, an off-line optimization system of NC end milling process is developed which has the function of solid simulation. Using the optimization system, spindle revolutions and feed rates in NC file for rough machining are optimized according to the multiple objectives: constant machining forces and increasing machining efficiency. Using the optimal NC file, milling experiments are carried out and the experiment result shows the validity and reliability of off-line milling process optimization system.
引文
1 周济, 周艳红. 数控加工技术. 国防工业出版社, 2002,6～7
2 董丽华, 刘大昕, 赵彦玲. 网络化制造中加工过程仿真的研究. 工具技术. 2003, 37(112):21~23
3 A.д.马卡洛夫. 切削过程最优化. 杨锦华,等译 . 国防工业出版社, 1988:63~77
4 刘战强, 黄传真, 万熠, 艾兴. 切削数据库研究现状与发展. 计算机集成制造系统. 2003,9(11):37~43
5 王凤彪, 王秀伦, 段竹. 机加工用量选择专家系统. 电气技术与自动化. 2006,35(2):119~121
6 彭观, 陈统坚, 彭劲雄, 傅勇辉. 基于专家系统和神经网络的制造过程智能决策系统. 组合机床与自动化加工技术. 1999,(2):24~27
7 谢新民, 丁峰. 自适应控制系统. 清华大学出版社, 2002:2~4
8 李为民,黄田. 有约束数控铣削恒力控制. 天津大学学报, 1999, 32(3): 290～293
9 T.Y. Kim, J. Kim. Adaptive Cutting Force Control for a Machining Center by Using Indirect Cutting Gorce Measurements. International Journal of Machine Tools and Manufacture. 1996,36(8):925~937
10 M.Milfelner, F. Cus, J. Balic. An Overview of Data Acquisition System for Cutting Force Measuring and Optimization in Milling. Journal of Materials Processing Technology. 2005,164-165:1281~1288
11 李棠,于随然,王春,林宏韬. 数控切削自适应控制. 大连理工大学学报.1995,35(3):353~356
12 冯小军,朱华双,宁仲良. 数控铣削模糊自适应控制系统. 组合机床与自动化加工技术.2004,(7):73~76
13 韦彥成, 蔡志伟. 自适应控制在机床上的应用研究——自学习式建立数模. 北京航空航天大学学报.1988,14(1):67~72
14 Y. Altintas. Prediction of Cutting Forces and Tool Breakage in Milling from Feed Drive Current Measurements. ASME Journal of Engineering for Industry. 1992,114(4):386~392
15 郑华平, 李曦, 唐小琦. 基于自适应预测控制技术的数控铣削加工的研究与应用. 机床与液压. 2003,31(13):151~153
16 金仁成, 李水进,唐小琦,周云飞,童强,贾瑜. 智能自适应数控加工技术研究综述. 工具技术. 2000,34(11):3~5
17 陈统坚, 王卫平, 周泽华. 铣削过程的约束型智能控制研究. 华南理工大学学报. 1994, 22(4): 90～96
18 汪德才, 李从心. 数控加工自适应控制研究与应用状况及关键技术. 模具技术. 2001,(6):69~72
19 A. G. Ulsoy, Y. Koren. Applications of Adaptive Control to Machine Tool Process Control. IEEE Control Systems Magazine. 1989,9(4):33~37
20 Y. Koren. Control of Machine Tools. ASME Journal of Manufacturing Science and Engineering. 1997,119(11):749~755
21 冯勇. 现代计算机数控系统. 机械工业出版社, 2001:346~377
22 W. P. Wang, K. K. Wang. Real-time Verification of Multi-axis NC Programs with Raster Graphics. IEEE International Conference on Robotics and Automation Proceedings, San Francisco, California, 1986: 166~171
23 W. P. Wang. Solid Modeling for Optimization Metal Removal of Three-dimensional NC End Milling. Journal of Manufacturing Systems. 1988,7(1):57~65
24 K. Yamazaki, N. Kojima, C. Sakamoto, T. Saito. Real-time Model Reference Adaptive Control of 3D Sculptured Surface Machining. Annals of the CIRP. 1991, 40(1):479~482
25 S. Park, M. Y. Yang, C. W. Lee. Simulation of NC Machining Using a Ball End Mill. Computer Modelling and Simulation of Manufacturing Process, ASME. 1990,20:67~76
26 Z. Yazar, K. F. Koch, T. Merrick, et al. Feed Rate Optimization Based on Cutting Force Calculations in 3-Axis Milling of Dies and Molds with Sculptured Surfaces. International Journal of Machine Tools and Manufacture. 1994,34(3): 365 ~377
27 A. D. Spence, Y. Altintas. A Solid Modeler Based Milling Process Simulation and Planning System. ASME Journal of Engineering for Industry. 1994,116(1):61~69
28 Y. S. Tarng, S. T. Cheng. Fuzzy Control of Feed Rate in End MillingOperations. International Journal of Machine Tools and Manufacture. 1993,33(4):643~650
29 S. J. Kim, H. U. Lee, D. W. Cho. Feedrate Scheduling for Indexable End Milling Process Based on an Improved Cutting Force Model. International Journal of Machine Tools and Manufacture. 2006,46(12-13):1589~1597
30 J. H. Ko, W. S. Yun, D. W. Cho. Off-line Feed Rate Scheduling Using Virtual CNC Based on an Evaluation of Cutting Performance. Computer-Aided Design. 2003,35(4):383~393
31 H. U. Lee, D.W. Cho. Intelligent Feedrate Scheduling Based on Virtual Machining. International Journal of Advanced Manufacturing Technology. 2003,22(11-12): 873~882
32 K. K. Kim, M. C. Kang, J. S. Kim, et al. A Study on the Precision Machinability of Ball End Milling by Cutting Speed Optimization. Journal of Materials Processing Technology.2002,130-131:357~362
33 Z. Z. Li, M. Zheng, L. Zheng, et al. A Solid Model-Based Milling Process Simulation and Optimization System Integrated with CAD/CAM. Journal of Materials Processing Technology. 2003, 138: 513~517
34 倪其民,李从心,阮雪榆. 面向加工程序优化的铣削过程模拟. 模具技术. 2001,(1):65~69
35 刘强,尹力. 一种面向数控工艺参数优化的铣削过程动力学仿真系统研究. 中国机械工程. 2005,16(13):1146~1150
36 王太勇, 汪文津, 范胜波等. 基于自适应遗传算法的数控铣削过程参数优化仿真. 制造业自动化. 2004,26(8):28~30
37 张臣,周来水,余湛悦,安鲁陵,周儒荣. 基于仿真数据的数控铣削加工多目标变参数优化. 计算机辅助设计与图形学学报. 2005,17(5):1039~1045
38 T. V. Hook. Real-time Shaded NC Milling Display. ACM SIGGRPH, 1986, 20(4):15~20
39 R.B. Jerard, S.Z. Hussaini, R.L. Drysdale, B. Schaudt. Approximate Methods for Simulation and Verification of Numerically Controlled Machining Programs. The Visual Computer. 1989, 5(6):329~348
40 T. Saito, T. Takahashi. NC-machining With G-buffer Method. Computer Graphics. 1991,25(4):207~216
41 J. Crossman, D. Yoon. A Cutter Motion Simulation System. Transaction ofthe Society for Design and Process Science. 2000,4(1):25~35
42 汤幼宁, 魏生民, 杨海成. 基于 Dexel 模型的 NC 加工仿真和验证研究. 西北工业大学学报. 1997,15(4):629~633
43 Y. Huang, J. H. Oliver. NC-milling Error Assessment and Tool Path Correction. Computer Graphics Proceedings, SIGGRAPH, Florida, 1994:287~294
44 S. K. Lee, S. L. Ko. Development of Simulation System for Machining Process Using Enhanced Z Map Model. Journal of Material Processing Technology, 2002, 130-131: 608-617
45 罗亚波,陈定方,肖田元. 虚拟加工环境中的工件动态建模方法研究. 武汉大学学报(信息科学版). 2003, 28(2):238~241
46 G. Kedem, J. L.Ellis. The Ray-Casting Machine. Proc. ICCCD’84, 1984:533~538
47 W.P. Wang, K.K. Wang, Geometric Modeling for Swept Volume of Moving Solids. IEEE Computer Graphic Applications. 1986,6(12):8~17
48 Y. S. Tarng, C. I. Cheng, J. Y. Kao. Modeling of Three-dimensional Numerically Controlled End Milling Operations. International Journal of Machine Tools and Manufacture. 1995,35(7):939-950
49 B. K. Fussell, C Ersoy, R. B. Jerard. Computer Generated CNC Machining Feedrates. Proceedings of 1992 Japan-USA Symposium on Flexible Automation ASME, 1992,1(1):377~384
50 B. K. Fussell, R. B. Jerard, J. G. Hemmett. Robust Feedrate Selection for 3-Axis NC Machining Using Discrete Models. Journal of Manufacturing Science and Engineering. 2001,123(2):214~224
51 B. K. Fussell, R. B. Jerard, J. G. Hemmett. Modeling of Cutting Geometry and Forces for 5-axis Sculptured Surface Machining. Computer-Aided Design. 2003,35(4):333~346
52 K. Weinert, A. Enselmann, J. Friedhoff. Milling Simulation for Process Optimization in the Field of Die and Mould Manufacturing. Annals of the CIRP. 1997,46 (1):325~328
53 刘胤,郑力,刘大成,张智海. 铣削啮合几何参数提取方法的研究. 机械设计与制造. 2005,(9):89~91
54 A. Spence, Y. Altintas, D. Kirkpatrick. Direct Calculation of MachiningParameters from a Solid Model. Computers in Industry. 1990,14(4):271~280
55 Y.Altinas, A. Spence. End Milling Force Algorithms for CAD System.Annals of the CIRP. 1991,40(1):31～34
56 F. Gu, S.G. Kapoor, R.E. DeVor, P. Bantdyopadhyay. An Enhanced Cutting Force Model for Face Milling with Variable Cutter Feed Motion and Complex Workpiece Geometry. Journal of Manufacturing Science and Engineering.1997,119:467~475.
57 M. Dewaele, G. L. Kinzel. Speed Improvement for NC Program Verification Using Solid Modelling. Proceedings ASME International Computers in Engineering Conference and Exposition,1989,601~607
58 E. M. Lim, H. Y. Feng, C. H. Menq, Z.H. Lin.The Prediction of Dimensional Error for Sculptured Surface Productions Using the Ball-end Milling Process. Part 1: Chip Geometry Analysis and Cutting Force Prediction. International Journal of Machine Tools and Manufacture. 1995,35(8):1149~1169
59 E. M. Lim, H. Y. Feng, C. H. Menq, Z.H. Lin.The Prediction of Dimensional Error for Sculptured Surface Productions Using the Ball-end Milling Process. Part 2: Surface Generation Model and Experimental Verification. International Journal of Machine Tools and Manufacture. 1995,35(8):1171~1185
60 A. D. Spence, F. Abrari, M. A. Elbestawi. Integrated Solid Modeler Based Solutions for Machining. Computer-Aided design. 2000,32(8-9):553~568
61 P.V. Saturley, A. D. Spence. Integration of Milling Process Simulation with On-line Monitoring and Control. International Journal of Advanced Manufacturing. 2000,16(2):92~99
62 S. Takata, M. D. Tsai , M. Inui, et al. A Cutting Simulation System for Machinability Evaluation Using a Workpiece Model. Annals of the CIRP. 1989,38(1):417~420
63 李加种. 金属切削动力学. 浙江大学出版社. 1993:139
64 刘培德等. 切削力学新篇. 大连理工大学出版社. 1991:139～145
65 J. Tlusty, S. Smith, C, Zamudio. New NC Routines for Quality in Milling. Annals of the CIRP. 1990,39(1):517~521
66 徐安平, 曲云霞, 李为民, 等. 带再生反馈的柔性立铣刀铣削过程模型. 机械工程学报. 1999,35(5):31~36
67 V. Tandon, H. El-Mounayri. A Novel Artificial Neural Networks Force Model for End Milling. International Journal of Advanced Manufacturing Technology. 2001,18(10):693~700
68 T. Szecs. Cutting Force Modeling Using Artificial Neural Networks. Journal of Materials Processing Technology.1999,92-93: 344~349
69 丁同梅, 周正武, 王太勇. 切削参数多目标优化设计. 机械工程与自动化. 2006,(4):79~81
70 姜彬, 郑敏力, 徐鹿眉, 李振加. 数控铣削用量多目标优化. 哈尔滨理工大学学报. 2002,7(3):67~70
71 谢涛, 陈火旺. 多目标优化与决策问题的演化算法. 中国工程科学. 2002,4(2):59~68
72 C. A. Coello Coello, G. T. Pulido, M. S. Leehug. Handling multiple objectives with Particle Swarm Optimization. IEEE Trans. on Evolutionary Computation. 2004:8(3):256~279
73 X. Hu, R. C. Eberhart, Y. Shi.Particle Swarm with Extended Memory for Multiobjective Particle Swarm Optimization. Proc. IEEE Swarm Intelligence Symp..Indianapolis, IN, USA, 2003:193~197
74 张利彪, 周春光, 马铭, 刘小华. 基于粒子群算法求解多目标优化问题. 计算机研究与发展. 2004,41(7):1286~1291
75 李宁,邹彤,孙德宝,秦元庆. 基于粒子群的多目标优化算法. 计算机工程与应用. 2005,(23):43~46
76 张义民, 刘仁云, 于繁华. 基于多目标粒子群算法的可靠性稳健优化设计. 机械设计. 2006,23(1):3~5
77 吴志远,邵惠鹤,吴新余. 基于遗传算法的退火精确罚函数非线性约束优化方法. 控制与决策. 1998,13(2):136~140
78 蒋昇, 李爱平, 林献坤. 基于遗传算法的铣削加工参数模糊优化系统研究.机电一体化. 2006,(2):35~39
79 杨勇, 沈秀良, 邵华. 基于遗传算法的铣削参数优化. 机械设计与研究. 2001,17(2):59~61
80 P.V.S. Suresh, P. V. Rao, S. G. Deshmukh. A Genetic Algorithmic Approach for Optimization of Surface Roughness Prediction Model. International Journal of Machine Tools and Manufacture. 2002,42(6):675~680
81 Z. G. Wang, M. Rahman, Y. S. Wong, J Sun. Optimization of Multi-pass Milling Using Parallel Genetic Algorithm and Parallel Genetic Simulated Annealing. International Journal of Machine Tools and Manufacture. 2005, 45(15):1726~1734
82 倪其民, 李从心, 李祥等. 圆周铣削参数多目标模糊优化建模. 机械科学与技术. 2001,20(1):86~88
83 R. Salami, M.H. Sadeghi, B. Motakef. Feed Rate Optimization for 3-axis Ball-end Milling of Sculptured Surfaces. International Journal of Machine Tools and Manufacture. 2007,47(5):760~767
84 彭海涛, 雷毅, 周丹. 基于铣削力仿真模型的进给速率优化方法. 中国机械工程. 2005,16(18):1607~1609
85 Y. J. Cai, M. L. Wang, M. Qian, J. Zhang, C. J. Sun. A Feedrate Scheduling in Die-cavity Roughing Basde on Cutting Force Surface Model. Journal of Dalian University of Technology. 2006,46(7):516~522
86 D. K. Baek, T. J. Ko, H. S. Kim. Optimization of Federate in a Face Milling Operation Using a Surface Roughness Model. International Journal of Machine Tools and Manufacture. 2001,41(3):451~462
87 J. S. Chen, Y. K. Huang , M. S. Chen. Feedrate Optimization and Tool Profile Modification for the High-efficiency Ball-end Milling Process. International Journal of Machine Tools and Manufacture. 2005, 45(9):1070~1076
88 V. Tandon, H. E. Mounayri, H. Kishawy. NC End Milling Optimization Using Evolutionary Computation. International Journal of Machine Tools and Manufacture. 2002,42(5):595~605
89 A. Vidal, M. Alberti, J. Ciurana, M. Casadesús. A Decision Support System for Optimizing the Selection of Parameters When Planning Milling Operations. International Journal of Machine Tools and Manufacture. 2005,45(2):201~210
90 E. M. Lim, C. H. Menq, D. W. Yen. Integrated Planning for Precision Machining of Complex Surfaces, Part 1: Cutting path and Feedrate Optimization. International Journal of Machine Tools and Manufacture. 1997,37(1):61~75
91 H. Y. Feng, N. Su. Integrated Tool Path and Feed Rate Optimization for the Finishing Machining of 3D Plane Surfaces. International Journal of MachineTools and Manufacture. 2000,40(11):1557~1572
92 顾立志, 张惠丽, 袁哲俊. 基于刀具使用寿命的切削用量优化. 哈尔滨理工大学学报. 2000,5(2):62~65
93 N. K. Jha, K. Hornik. Integrated Computer-aided Optimal Design and Finite Element Analysis of a Plain Milling Cutter. Applied Mathematical Modeling. 1994,19(6):343~353
94 张世昌,李旦,高航. 机械制造技术基础. 高等教育出版社, 2001
95 M.Tolouei-Rad, I. M. Bidhendi. On the Optimization of Machining Parameters for Milling Operations. International Journal of Machine Tools and Manufacture. 1997,37(1):1~16
96 王永章等. 机床的数字控制技术. 哈尔滨工业大学出版,1995:187
97 B. M. Imani, M. A. Elbestawi. Geometric Simulation of Ball-End Milling Operations. Journal of Manufacturing Science and Engineering. 2001.123(5):177~184
98 K .Abdel-Malek, H. J.Yeh. Geometric Representation of the Swept Volume Using Jacobian Rank-deficiency Conditions. Computer-Aided Design. 1997,29(6):457~468
99 D. Blackmore, M. C. Leu. L. P.Wang. Sweep-envelope Differential Equation Algorithm and Its Application to NC Machining Verification. Computer-Aided Design. 1997,29 (9): 629~637
100 R. Martin, P. Stephenson. Sweeping of Three-dimensional Objects. Computer-Aided Design. 1990, 22(4):223~234
101 W. Schroeder, W. Lorensen, S. Linthicum. Implicit Modeling of Swept Surfaces and Volumes. Proceedings of the 1994 IEEE Visualization Conference, Washington, DC, USA,1994:40~45
102 张新宇. 基于网格的三维造型和处理技术研究. 浙江大学博士学位论文, 2004
103 S. Abrams, P. Allen. Swept Volumes and Their Use in Viewpoint Computation in Robot Work Cells. Proceedings of the 1995 International Symposium on Assembly and Task Planning,Pittsburgh, PA., 1995:188~193
104 何朝阳. 李际军. NURBS 曲面(实体)扫描体的逼近算法. 工程图学学报. 2006,27(3):84~91
105 J. Z. Yang, A. M. Karim. Approximate Swept Volumes of NURBS Surfacesor Solids. Computer Aided Geometric Design. 2005,22(1):1~26.
106 倪其民. 曲面加工过程切削负载自适应新策略及其关键技术研究. 上海交通大学博士学位论文.2001:18~19
107 盛亮. 基于实体的数控加工仿真关键技术的研究与实现. 南京航空航天大学博士学位论文. 2005
108 S.Engin, Y.Altintas. Mechanics and Dynamics of General Milling Cutters, Part I: Helical Rnd Mills. International Journal of Machine Tools and Manufacture.2001,41(15):2195~2212
109 肖田元. 虚拟制造. 清华大学出版社, 2004
110 荆怀靖.面向离线误差补偿的虚拟加工技术研究. 哈尔滨工业大学博士学位论文. 2005
111 X. Yan, K. Shirase, M. Hirao, T. Yasui. NC Program Evaluator for Higher Machining Productivity. International Journal of Machine Tools and Manufacture. 1999,39(10):1563~1573
112 W. A. Hunt, H. B. Voelcher. An Exploratory Study of Automatic Verification of Programs for Numerically Controlled Machine Tools. Technical Memorandum University of Rochester Production Automation Project. University of Rochester. 1982,34:61~68
113 刘胤. 实体法铣削力仿真中几何参数提取及算法优化的研究. 清华大学博士学位论文. 2005: 66~69
114 酒井英治著.切削磨削加工学.高希正,刘德忠译.机械工业出版社,1982:308
115 周泽华. 金属切削原理. 上海科学技术出版社, 1994:215~216
116 K. Shirase, Y. Altintas.Cutting Force and Dimensional Surface Error Generation in Peripheral Milling with Variable Pitch Helical End Mills. International Journal of Machine Tools and Manufacture. 2002,36(5):567~584
117 罗学科. 数控技术与制造自动化. 化学工业出版社, 2002:32~37
118 E. Budak, Y. Altintas, E. J. A. Armarego. Prediction of Milling Force Coefficents from Orthogonal Cutting Data. ASME Journal of Manufacturing Science and Engineering. 1996, 118:216~224
119 周明,孙树栋. 遗传算法原理及应用. 国防工业出版社,1999:168
120 J. H. Holland. Adaption in Natural and Artificial Systems. The University of Michigam Press, 1975
121 H. P. Schwefel. Numerical Optimization of Computer Models. John Wiley, 1981
122 L. J. Fogel, A. J. Owens, M. J. Walsh. Artificial Intelligence through Simulation Evolution. John Wiley, 1966
123 A. Colorni, M. Dorigo, V. Maniezzo. Distributed Optimization by Ant Colonies. In: Proc 1st European Conf Artificial Life, Pans, France,1991. Elsevier: 134~142
124 J. Kennedy, R. C. Eberhart. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neutral Networks, Perth, Australia, 1995:1942~1948
125 R.C. Eberhart, J. Kennedy. A New Optimizer Using Particle Swarm Theory. Proceedings of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995:39~43
126 C.W.Wilson. Sociobiology: The New synthesis. Belknap Press, 1975
127 Y. Shi, R. Eberhart. A Modified Particle Swarm Optimizer, Proceedings of IEEE International Conference on Evolutionary Computation, Archorage, Alaska, USA, 1998:69~73
128 Y. Shi, R. Eberhart. Parameter Selection in Particle Swarm Optimization. Proceeding of the 7th Annual Conference on Evolutionary Programming, New York,1998:591~600
2 董丽华, 刘大昕, 赵彦玲. 网络化制造中加工过程仿真的研究. 工具技术. 2003, 37(112):21~23
3 A.д.马卡洛夫. 切削过程最优化. 杨锦华,等译 . 国防工业出版社, 1988:63~77
4 刘战强, 黄传真, 万熠, 艾兴. 切削数据库研究现状与发展. 计算机集成制造系统. 2003,9(11):37~43
5 王凤彪, 王秀伦, 段竹. 机加工用量选择专家系统. 电气技术与自动化. 2006,35(2):119~121
6 彭观, 陈统坚, 彭劲雄, 傅勇辉. 基于专家系统和神经网络的制造过程智能决策系统. 组合机床与自动化加工技术. 1999,(2):24~27
7 谢新民, 丁峰. 自适应控制系统. 清华大学出版社, 2002:2~4
8 李为民,黄田. 有约束数控铣削恒力控制. 天津大学学报, 1999, 32(3): 290～293
9 T.Y. Kim, J. Kim. Adaptive Cutting Force Control for a Machining Center by Using Indirect Cutting Gorce Measurements. International Journal of Machine Tools and Manufacture. 1996,36(8):925~937
10 M.Milfelner, F. Cus, J. Balic. An Overview of Data Acquisition System for Cutting Force Measuring and Optimization in Milling. Journal of Materials Processing Technology. 2005,164-165:1281~1288
11 李棠,于随然,王春,林宏韬. 数控切削自适应控制. 大连理工大学学报.1995,35(3):353~356
12 冯小军,朱华双,宁仲良. 数控铣削模糊自适应控制系统. 组合机床与自动化加工技术.2004,(7):73~76
13 韦彥成, 蔡志伟. 自适应控制在机床上的应用研究——自学习式建立数模. 北京航空航天大学学报.1988,14(1):67~72
14 Y. Altintas. Prediction of Cutting Forces and Tool Breakage in Milling from Feed Drive Current Measurements. ASME Journal of Engineering for Industry. 1992,114(4):386~392
15 郑华平, 李曦, 唐小琦. 基于自适应预测控制技术的数控铣削加工的研究与应用. 机床与液压. 2003,31(13):151~153
16 金仁成, 李水进,唐小琦,周云飞,童强,贾瑜. 智能自适应数控加工技术研究综述. 工具技术. 2000,34(11):3~5
17 陈统坚, 王卫平, 周泽华. 铣削过程的约束型智能控制研究. 华南理工大学学报. 1994, 22(4): 90～96
18 汪德才, 李从心. 数控加工自适应控制研究与应用状况及关键技术. 模具技术. 2001,(6):69~72
19 A. G. Ulsoy, Y. Koren. Applications of Adaptive Control to Machine Tool Process Control. IEEE Control Systems Magazine. 1989,9(4):33~37
20 Y. Koren. Control of Machine Tools. ASME Journal of Manufacturing Science and Engineering. 1997,119(11):749~755
21 冯勇. 现代计算机数控系统. 机械工业出版社, 2001:346~377
22 W. P. Wang, K. K. Wang. Real-time Verification of Multi-axis NC Programs with Raster Graphics. IEEE International Conference on Robotics and Automation Proceedings, San Francisco, California, 1986: 166~171
23 W. P. Wang. Solid Modeling for Optimization Metal Removal of Three-dimensional NC End Milling. Journal of Manufacturing Systems. 1988,7(1):57~65
24 K. Yamazaki, N. Kojima, C. Sakamoto, T. Saito. Real-time Model Reference Adaptive Control of 3D Sculptured Surface Machining. Annals of the CIRP. 1991, 40(1):479~482
25 S. Park, M. Y. Yang, C. W. Lee. Simulation of NC Machining Using a Ball End Mill. Computer Modelling and Simulation of Manufacturing Process, ASME. 1990,20:67~76
26 Z. Yazar, K. F. Koch, T. Merrick, et al. Feed Rate Optimization Based on Cutting Force Calculations in 3-Axis Milling of Dies and Molds with Sculptured Surfaces. International Journal of Machine Tools and Manufacture. 1994,34(3): 365 ~377
27 A. D. Spence, Y. Altintas. A Solid Modeler Based Milling Process Simulation and Planning System. ASME Journal of Engineering for Industry. 1994,116(1):61~69
28 Y. S. Tarng, S. T. Cheng. Fuzzy Control of Feed Rate in End MillingOperations. International Journal of Machine Tools and Manufacture. 1993,33(4):643~650
29 S. J. Kim, H. U. Lee, D. W. Cho. Feedrate Scheduling for Indexable End Milling Process Based on an Improved Cutting Force Model. International Journal of Machine Tools and Manufacture. 2006,46(12-13):1589~1597
30 J. H. Ko, W. S. Yun, D. W. Cho. Off-line Feed Rate Scheduling Using Virtual CNC Based on an Evaluation of Cutting Performance. Computer-Aided Design. 2003,35(4):383~393
31 H. U. Lee, D.W. Cho. Intelligent Feedrate Scheduling Based on Virtual Machining. International Journal of Advanced Manufacturing Technology. 2003,22(11-12): 873~882
32 K. K. Kim, M. C. Kang, J. S. Kim, et al. A Study on the Precision Machinability of Ball End Milling by Cutting Speed Optimization. Journal of Materials Processing Technology.2002,130-131:357~362
33 Z. Z. Li, M. Zheng, L. Zheng, et al. A Solid Model-Based Milling Process Simulation and Optimization System Integrated with CAD/CAM. Journal of Materials Processing Technology. 2003, 138: 513~517
34 倪其民,李从心,阮雪榆. 面向加工程序优化的铣削过程模拟. 模具技术. 2001,(1):65~69
35 刘强,尹力. 一种面向数控工艺参数优化的铣削过程动力学仿真系统研究. 中国机械工程. 2005,16(13):1146~1150
36 王太勇, 汪文津, 范胜波等. 基于自适应遗传算法的数控铣削过程参数优化仿真. 制造业自动化. 2004,26(8):28~30
37 张臣,周来水,余湛悦,安鲁陵,周儒荣. 基于仿真数据的数控铣削加工多目标变参数优化. 计算机辅助设计与图形学学报. 2005,17(5):1039~1045
38 T. V. Hook. Real-time Shaded NC Milling Display. ACM SIGGRPH, 1986, 20(4):15~20
39 R.B. Jerard, S.Z. Hussaini, R.L. Drysdale, B. Schaudt. Approximate Methods for Simulation and Verification of Numerically Controlled Machining Programs. The Visual Computer. 1989, 5(6):329~348
40 T. Saito, T. Takahashi. NC-machining With G-buffer Method. Computer Graphics. 1991,25(4):207~216
41 J. Crossman, D. Yoon. A Cutter Motion Simulation System. Transaction ofthe Society for Design and Process Science. 2000,4(1):25~35
42 汤幼宁, 魏生民, 杨海成. 基于 Dexel 模型的 NC 加工仿真和验证研究. 西北工业大学学报. 1997,15(4):629~633
43 Y. Huang, J. H. Oliver. NC-milling Error Assessment and Tool Path Correction. Computer Graphics Proceedings, SIGGRAPH, Florida, 1994:287~294
44 S. K. Lee, S. L. Ko. Development of Simulation System for Machining Process Using Enhanced Z Map Model. Journal of Material Processing Technology, 2002, 130-131: 608-617
45 罗亚波,陈定方,肖田元. 虚拟加工环境中的工件动态建模方法研究. 武汉大学学报(信息科学版). 2003, 28(2):238~241
46 G. Kedem, J. L.Ellis. The Ray-Casting Machine. Proc. ICCCD’84, 1984:533~538
47 W.P. Wang, K.K. Wang, Geometric Modeling for Swept Volume of Moving Solids. IEEE Computer Graphic Applications. 1986,6(12):8~17
48 Y. S. Tarng, C. I. Cheng, J. Y. Kao. Modeling of Three-dimensional Numerically Controlled End Milling Operations. International Journal of Machine Tools and Manufacture. 1995,35(7):939-950
49 B. K. Fussell, C Ersoy, R. B. Jerard. Computer Generated CNC Machining Feedrates. Proceedings of 1992 Japan-USA Symposium on Flexible Automation ASME, 1992,1(1):377~384
50 B. K. Fussell, R. B. Jerard, J. G. Hemmett. Robust Feedrate Selection for 3-Axis NC Machining Using Discrete Models. Journal of Manufacturing Science and Engineering. 2001,123(2):214~224
51 B. K. Fussell, R. B. Jerard, J. G. Hemmett. Modeling of Cutting Geometry and Forces for 5-axis Sculptured Surface Machining. Computer-Aided Design. 2003,35(4):333~346
52 K. Weinert, A. Enselmann, J. Friedhoff. Milling Simulation for Process Optimization in the Field of Die and Mould Manufacturing. Annals of the CIRP. 1997,46 (1):325~328
53 刘胤,郑力,刘大成,张智海. 铣削啮合几何参数提取方法的研究. 机械设计与制造. 2005,(9):89~91
54 A. Spence, Y. Altintas, D. Kirkpatrick. Direct Calculation of MachiningParameters from a Solid Model. Computers in Industry. 1990,14(4):271~280
55 Y.Altinas, A. Spence. End Milling Force Algorithms for CAD System.Annals of the CIRP. 1991,40(1):31～34
56 F. Gu, S.G. Kapoor, R.E. DeVor, P. Bantdyopadhyay. An Enhanced Cutting Force Model for Face Milling with Variable Cutter Feed Motion and Complex Workpiece Geometry. Journal of Manufacturing Science and Engineering.1997,119:467~475.
57 M. Dewaele, G. L. Kinzel. Speed Improvement for NC Program Verification Using Solid Modelling. Proceedings ASME International Computers in Engineering Conference and Exposition,1989,601~607
58 E. M. Lim, H. Y. Feng, C. H. Menq, Z.H. Lin.The Prediction of Dimensional Error for Sculptured Surface Productions Using the Ball-end Milling Process. Part 1: Chip Geometry Analysis and Cutting Force Prediction. International Journal of Machine Tools and Manufacture. 1995,35(8):1149~1169
59 E. M. Lim, H. Y. Feng, C. H. Menq, Z.H. Lin.The Prediction of Dimensional Error for Sculptured Surface Productions Using the Ball-end Milling Process. Part 2: Surface Generation Model and Experimental Verification. International Journal of Machine Tools and Manufacture. 1995,35(8):1171~1185
60 A. D. Spence, F. Abrari, M. A. Elbestawi. Integrated Solid Modeler Based Solutions for Machining. Computer-Aided design. 2000,32(8-9):553~568
61 P.V. Saturley, A. D. Spence. Integration of Milling Process Simulation with On-line Monitoring and Control. International Journal of Advanced Manufacturing. 2000,16(2):92~99
62 S. Takata, M. D. Tsai , M. Inui, et al. A Cutting Simulation System for Machinability Evaluation Using a Workpiece Model. Annals of the CIRP. 1989,38(1):417~420
63 李加种. 金属切削动力学. 浙江大学出版社. 1993:139
64 刘培德等. 切削力学新篇. 大连理工大学出版社. 1991:139～145
65 J. Tlusty, S. Smith, C, Zamudio. New NC Routines for Quality in Milling. Annals of the CIRP. 1990,39(1):517~521
66 徐安平, 曲云霞, 李为民, 等. 带再生反馈的柔性立铣刀铣削过程模型. 机械工程学报. 1999,35(5):31~36
67 V. Tandon, H. El-Mounayri. A Novel Artificial Neural Networks Force Model for End Milling. International Journal of Advanced Manufacturing Technology. 2001,18(10):693~700
68 T. Szecs. Cutting Force Modeling Using Artificial Neural Networks. Journal of Materials Processing Technology.1999,92-93: 344~349
69 丁同梅, 周正武, 王太勇. 切削参数多目标优化设计. 机械工程与自动化. 2006,(4):79~81
70 姜彬, 郑敏力, 徐鹿眉, 李振加. 数控铣削用量多目标优化. 哈尔滨理工大学学报. 2002,7(3):67~70
71 谢涛, 陈火旺. 多目标优化与决策问题的演化算法. 中国工程科学. 2002,4(2):59~68
72 C. A. Coello Coello, G. T. Pulido, M. S. Leehug. Handling multiple objectives with Particle Swarm Optimization. IEEE Trans. on Evolutionary Computation. 2004:8(3):256~279
73 X. Hu, R. C. Eberhart, Y. Shi.Particle Swarm with Extended Memory for Multiobjective Particle Swarm Optimization. Proc. IEEE Swarm Intelligence Symp..Indianapolis, IN, USA, 2003:193~197
74 张利彪, 周春光, 马铭, 刘小华. 基于粒子群算法求解多目标优化问题. 计算机研究与发展. 2004,41(7):1286~1291
75 李宁,邹彤,孙德宝,秦元庆. 基于粒子群的多目标优化算法. 计算机工程与应用. 2005,(23):43~46
76 张义民, 刘仁云, 于繁华. 基于多目标粒子群算法的可靠性稳健优化设计. 机械设计. 2006,23(1):3~5
77 吴志远,邵惠鹤,吴新余. 基于遗传算法的退火精确罚函数非线性约束优化方法. 控制与决策. 1998,13(2):136~140
78 蒋昇, 李爱平, 林献坤. 基于遗传算法的铣削加工参数模糊优化系统研究.机电一体化. 2006,(2):35~39
79 杨勇, 沈秀良, 邵华. 基于遗传算法的铣削参数优化. 机械设计与研究. 2001,17(2):59~61
80 P.V.S. Suresh, P. V. Rao, S. G. Deshmukh. A Genetic Algorithmic Approach for Optimization of Surface Roughness Prediction Model. International Journal of Machine Tools and Manufacture. 2002,42(6):675~680
81 Z. G. Wang, M. Rahman, Y. S. Wong, J Sun. Optimization of Multi-pass Milling Using Parallel Genetic Algorithm and Parallel Genetic Simulated Annealing. International Journal of Machine Tools and Manufacture. 2005, 45(15):1726~1734
82 倪其民, 李从心, 李祥等. 圆周铣削参数多目标模糊优化建模. 机械科学与技术. 2001,20(1):86~88
83 R. Salami, M.H. Sadeghi, B. Motakef. Feed Rate Optimization for 3-axis Ball-end Milling of Sculptured Surfaces. International Journal of Machine Tools and Manufacture. 2007,47(5):760~767
84 彭海涛, 雷毅, 周丹. 基于铣削力仿真模型的进给速率优化方法. 中国机械工程. 2005,16(18):1607~1609
85 Y. J. Cai, M. L. Wang, M. Qian, J. Zhang, C. J. Sun. A Feedrate Scheduling in Die-cavity Roughing Basde on Cutting Force Surface Model. Journal of Dalian University of Technology. 2006,46(7):516~522
86 D. K. Baek, T. J. Ko, H. S. Kim. Optimization of Federate in a Face Milling Operation Using a Surface Roughness Model. International Journal of Machine Tools and Manufacture. 2001,41(3):451~462
87 J. S. Chen, Y. K. Huang , M. S. Chen. Feedrate Optimization and Tool Profile Modification for the High-efficiency Ball-end Milling Process. International Journal of Machine Tools and Manufacture. 2005, 45(9):1070~1076
88 V. Tandon, H. E. Mounayri, H. Kishawy. NC End Milling Optimization Using Evolutionary Computation. International Journal of Machine Tools and Manufacture. 2002,42(5):595~605
89 A. Vidal, M. Alberti, J. Ciurana, M. Casadesús. A Decision Support System for Optimizing the Selection of Parameters When Planning Milling Operations. International Journal of Machine Tools and Manufacture. 2005,45(2):201~210
90 E. M. Lim, C. H. Menq, D. W. Yen. Integrated Planning for Precision Machining of Complex Surfaces, Part 1: Cutting path and Feedrate Optimization. International Journal of Machine Tools and Manufacture. 1997,37(1):61~75
91 H. Y. Feng, N. Su. Integrated Tool Path and Feed Rate Optimization for the Finishing Machining of 3D Plane Surfaces. International Journal of MachineTools and Manufacture. 2000,40(11):1557~1572
92 顾立志, 张惠丽, 袁哲俊. 基于刀具使用寿命的切削用量优化. 哈尔滨理工大学学报. 2000,5(2):62~65
93 N. K. Jha, K. Hornik. Integrated Computer-aided Optimal Design and Finite Element Analysis of a Plain Milling Cutter. Applied Mathematical Modeling. 1994,19(6):343~353
94 张世昌,李旦,高航. 机械制造技术基础. 高等教育出版社, 2001
95 M.Tolouei-Rad, I. M. Bidhendi. On the Optimization of Machining Parameters for Milling Operations. International Journal of Machine Tools and Manufacture. 1997,37(1):1~16
96 王永章等. 机床的数字控制技术. 哈尔滨工业大学出版,1995:187
97 B. M. Imani, M. A. Elbestawi. Geometric Simulation of Ball-End Milling Operations. Journal of Manufacturing Science and Engineering. 2001.123(5):177~184
98 K .Abdel-Malek, H. J.Yeh. Geometric Representation of the Swept Volume Using Jacobian Rank-deficiency Conditions. Computer-Aided Design. 1997,29(6):457~468
99 D. Blackmore, M. C. Leu. L. P.Wang. Sweep-envelope Differential Equation Algorithm and Its Application to NC Machining Verification. Computer-Aided Design. 1997,29 (9): 629~637
100 R. Martin, P. Stephenson. Sweeping of Three-dimensional Objects. Computer-Aided Design. 1990, 22(4):223~234
101 W. Schroeder, W. Lorensen, S. Linthicum. Implicit Modeling of Swept Surfaces and Volumes. Proceedings of the 1994 IEEE Visualization Conference, Washington, DC, USA,1994:40~45
102 张新宇. 基于网格的三维造型和处理技术研究. 浙江大学博士学位论文, 2004
103 S. Abrams, P. Allen. Swept Volumes and Their Use in Viewpoint Computation in Robot Work Cells. Proceedings of the 1995 International Symposium on Assembly and Task Planning,Pittsburgh, PA., 1995:188~193
104 何朝阳. 李际军. NURBS 曲面(实体)扫描体的逼近算法. 工程图学学报. 2006,27(3):84~91
105 J. Z. Yang, A. M. Karim. Approximate Swept Volumes of NURBS Surfacesor Solids. Computer Aided Geometric Design. 2005,22(1):1~26.
106 倪其民. 曲面加工过程切削负载自适应新策略及其关键技术研究. 上海交通大学博士学位论文.2001:18~19
107 盛亮. 基于实体的数控加工仿真关键技术的研究与实现. 南京航空航天大学博士学位论文. 2005
108 S.Engin, Y.Altintas. Mechanics and Dynamics of General Milling Cutters, Part I: Helical Rnd Mills. International Journal of Machine Tools and Manufacture.2001,41(15):2195~2212
109 肖田元. 虚拟制造. 清华大学出版社, 2004
110 荆怀靖.面向离线误差补偿的虚拟加工技术研究. 哈尔滨工业大学博士学位论文. 2005
111 X. Yan, K. Shirase, M. Hirao, T. Yasui. NC Program Evaluator for Higher Machining Productivity. International Journal of Machine Tools and Manufacture. 1999,39(10):1563~1573
112 W. A. Hunt, H. B. Voelcher. An Exploratory Study of Automatic Verification of Programs for Numerically Controlled Machine Tools. Technical Memorandum University of Rochester Production Automation Project. University of Rochester. 1982,34:61~68
113 刘胤. 实体法铣削力仿真中几何参数提取及算法优化的研究. 清华大学博士学位论文. 2005: 66~69
114 酒井英治著.切削磨削加工学.高希正,刘德忠译.机械工业出版社,1982:308
115 周泽华. 金属切削原理. 上海科学技术出版社, 1994:215~216
116 K. Shirase, Y. Altintas.Cutting Force and Dimensional Surface Error Generation in Peripheral Milling with Variable Pitch Helical End Mills. International Journal of Machine Tools and Manufacture. 2002,36(5):567~584
117 罗学科. 数控技术与制造自动化. 化学工业出版社, 2002:32~37
118 E. Budak, Y. Altintas, E. J. A. Armarego. Prediction of Milling Force Coefficents from Orthogonal Cutting Data. ASME Journal of Manufacturing Science and Engineering. 1996, 118:216~224
119 周明,孙树栋. 遗传算法原理及应用. 国防工业出版社,1999:168
120 J. H. Holland. Adaption in Natural and Artificial Systems. The University of Michigam Press, 1975
121 H. P. Schwefel. Numerical Optimization of Computer Models. John Wiley, 1981
122 L. J. Fogel, A. J. Owens, M. J. Walsh. Artificial Intelligence through Simulation Evolution. John Wiley, 1966
123 A. Colorni, M. Dorigo, V. Maniezzo. Distributed Optimization by Ant Colonies. In: Proc 1st European Conf Artificial Life, Pans, France,1991. Elsevier: 134~142
124 J. Kennedy, R. C. Eberhart. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neutral Networks, Perth, Australia, 1995:1942~1948
125 R.C. Eberhart, J. Kennedy. A New Optimizer Using Particle Swarm Theory. Proceedings of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995:39~43
126 C.W.Wilson. Sociobiology: The New synthesis. Belknap Press, 1975
127 Y. Shi, R. Eberhart. A Modified Particle Swarm Optimizer, Proceedings of IEEE International Conference on Evolutionary Computation, Archorage, Alaska, USA, 1998:69~73
128 Y. Shi, R. Eberhart. Parameter Selection in Particle Swarm Optimization. Proceeding of the 7th Annual Conference on Evolutionary Programming, New York,1998:591~600