针对目前航空发动机叶片进排气边加工精度和表面质量较差的问题，提出了一种基于机床运动学约束球头刀多轴加工刀轴矢量优化方法。建立刀位优化变量与刀位数据之间的关系方程，同时建立刀位数据与机床回转轴角度之间的运动变换方程，从而推导出刀位优化变量与机床回转轴角度之间的关系方程。通过求解上述方程得到球头刀多轴加工复杂曲面的刀轴矢量计算公式。在此基础上，给出球头刀多轴加工刀轴矢量优化方法和刀轨生成方法。同时，以某航空发动机叶片为例，分析了本文算法和Sturz算法对机床回转轴角度的影响。分别利用本文算法和Sturz算法生成该叶片进气边加工的刀轨，并在五轴数控机床上进行加工试验。试验结果表明，该算法能够避免加工过程中机床回转轴的大幅波动，使机床轴运动更加平稳和光滑，从而提高曲面的加工质量和加工效率，具有一定的实际应用价值。
徐汝锋
,
陈志同
,
孟凡军
,
张云
,
吴献珍
. 基于机床运动学约束球头刀多轴加工刀轴矢量优化方法[J]. 机械工程学报, 2015
, 51(23)
: 160
-167
.
DOI: 10.3901/JME.2015.23.160
In order to solve the problem of the poor machining quality of the leading and trailing edge surface of the aero engine blade, a tool orientation optimization method based on the kinematics constraints of the machine tool in multi-axis machining with a ball-end cutter is presented. A relation equation between the design variables of tool position and cutter location (CL) data is established, and a coordinate transformation equation between CL data and rotary axes of the machine tool is established. From the above two equations, a relation equation between the design variables of tool position and rotary axes of the machine tool is derived. Through solving the above relation equation, formulas for calculating tool position and tool orientation during the machining of sculptured surfaces with a ball-end cutter are derived. On this basis, a tool orientation optimization method and a tool path generation method for multi-axis machining with a ball-end cutter is presented. Besides, analyze the influence of the proposed method and Sturz method on rotary axes of the machine tool. Tool paths of the leading edge surface of an aero engine blade are generated by the proposed method and the Sturz method, respectively, and cutting trials are carried out on a five-axis machine tool. Experimental results show that the proposed method can avoid abrupt change of rotary axes of the machine tool and make the movement of machine axes more stable and smoother, and further obtain better machining quality and higher machining efficiency. Consequently, the proposed method will have important practical value.
[1] JUN C，CHA K，LEE Y. Optimizing tool orientations for 5-axis machining by configuration-space search method[J]. Computer-Aided Design，2003，35(6)：549-566.
[2] 冯俊然. 基于UG二次开发的自由曲面高效刀具路径方法研究[D]. 武汉：华中科技大学，2011.FENG Junran. Study of efficient tool path planning for machining free form surface Based on UG customization[D]. Wuhan：Huazhong University of Science and Technology，2011.
[3] HO M，HWANG Y，HU C. Five-axis tool orientation smoothing using quaternion interpolation algorithm[J]. International Journal of Machine Tools and Manufacture，2003，43(12)：1259-1267.
[4] 陈鼎宁，王乾廷，陈文哲. 汽车玻璃钢化风栅成形器五轴加工刀轴矢量插值[J]. 中国机械工程，2006，17(20)：2113-2117.CHEN Dingning，WANG Qianting，CHEN Wenzhe. Five-axis Tool orientation interpolation in windshield mold of automobile toughened glass machining[J]. China Mechanical Engineering，2006，17(20)：2113-2117.
[5] 姬俊锋，周来水，安鲁陵，等. 一类开式整体叶轮五坐标数控加工刀轴矢量生成及其光顺方法的研究[J]. 中国机械工程，2009，20(2)：202-206.JI Junfeng，ZHOU Laishui，AN Luling，et al. Generation and the smoothing method of 5-axis nc machining tool orientation for the open integrated impeller[J]. China Mechanical Engineering，2009，20(2)：202-206.
[6] 樊留群，齐党进，沈斌，等. 五轴联动刀轴矢量平面插补算法[J]. 机械工程学报，2011，47(19)：158-162. FAN Liuqun，QI Dangjin，SHEN Bin，et al. Plane interpolation of tool orientation algorithm for 5-axis circumference milling[J]. Journal of Mechanical Engineering，2011，47(19)：158-162.
[7] 周波，赵吉宾，刘伟军. 复杂曲面五轴数控加工刀轴矢量优化方法研究[J]. 机械工程学报，2013，49(7)：184-192. ZHOU Bo，ZHAO Jibin，LIU Weijun. Method study on optimization of tool axis vector for complex surface of 5-axis CNC[J]. Journal of Mechanical Engineering，2013，49(7)：184-192.
[8] 毕庆贞，王宇晗，朱利民，等. 刀触点网格上整体光顺五轴数控加工刀轴方向的模型与算法[J]. 中国科学：技术科学，2010，40(10)：1159-1168. BI Qingzhen，WANG Yuhan，ZHU Limin，et al. Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh[J]. Sci. China Tech. Sci.，2010，40(10)：1159-1168.
[9] 任军学，何卿功，姚倡锋，等. 闭式整体叶盘通道五坐标分行定轴加工刀轴矢量规划方法[J]. 航空学报，2012，33(10)：1923-1930. REN Junxue，HE Qinggong，YAO Changfeng，et al. Tool axis orientation planning method of fixed axis in each cutting line for closed blisk tunnel five-axis machining[J]. Acta Aeronautica et Astronautica Sinica，2012，33(10)：1923-1930.
[10] 王晶，张定华，罗明，等. 复杂曲面零件五轴加工刀轴整体优化方法[J]. 航空学报，2013，34(6)：1452-1462. WANG Jing，ZHANG Dinghua，LUO Ming，et al. A global tool orientation optimization method for five-axis CNC machining of sculptured surfaces[J]. Acta Aeronautica et Astronautica Sinica，2013，34(6)：1452-1462.
[11] 耿聪，于东，张函. 五轴联动刀轴矢量平滑插补算法[J]. 机械工程学报，2013，49(3)：180-185. GENG Cong，YU Dong，ZHANG Han. Tool orientation smooth interpolation algorithm for five-axis cnc machining [J]. Journal of Mechanical Engineering，2013，49(3)：180-185.
[12] 罗明，吴宝海，李山，等. 自由曲面五轴加工刀轴矢量的运动学优化方法[J]. 机械工程学报，2009，45(9)：158-163. LUO Ming，WU Baohai，LI Shan，et al. Five-axis tool orientation optimization based on kinematical method[J]. Journal of Mechanical Engineering，2009，45(9)：158-163.
[13] KIM T，SARMA S. Toolpath generation along directions of maximum kinematic performance：A first cut at machine-optimal paths[J]. Computer-Aided Design，2002，34(6)：453-468.
[14] WANG N，TANG K. Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath[J]. Computer-Aided Design，2007，39(10)：841-852.
[15] 徐汝锋. 宽行加工刀位误差求解与刀轨规划技术研究[D]. 北京：北京航空航天大学，2010.XU Rufeng. Research on tool position error calculation and tool path planning methods in 5-axis machining of sculptured surfaces[D]. Beijing：Beihang University，2010.
[16] 付敏，郑敏利，姜彬. 球头铣刀加工倾角对切削力的影响[J]. 工具技术，2005，39(6)：17-19.FU Min，ZHENG Minli，JIANG Bin. Influence of inclination angle of ball-end cutter on cutting force[J]. Tool Engineering，2005，39(6)：17-19.
