九轴联动叶片双刀铣削刀路平滑算法
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摘要
针对九轴联动叶片型面双刀对顶铣削方法,为保证加工轨迹的平滑性及双刀具的同步性,提出了一种基于几何约束的刀路平滑算法。首先,分析了九轴联动双刀加工机床中两把刀具的结构约束关系,通过旋转矩阵将切触点处法向矢量转化为表征双刀具姿态的刀轴矢量,并由刀轴矢量计算刀具的前倾角和侧偏角,确定满足双刀铣削要求的前倾角和侧偏角取值范围;然后,由残留高度和弦高误差定义切削宽度和步长对应的参数增量,对叶背、叶盆曲面沿行距方向上相邻切触点间参数增量Δu_(di)、Δu_(bi)和进给方向上相邻切触点间的参数增量Δv_(di)、Δv_(bi)进行等参数化求解;最后,根据叶背和叶盆曲面切削区域的范围设定自定义系数,研究双侧对顶铣削轨迹线的参数匹配算法,形成双刀铣削的刀路平滑算法。对典型汽轮机叶片规划了双刀对铣粗加工轨迹,并进行了加工仿真和实验验证,结果表明,叶片两侧对应加工区域可同时完成加工,且加工表面的轮廓误差满足该工序轮廓误差的公差要求。与考虑切削力抵消规划轨迹的算法相比,该算法的计算效率提高了56%,且在等效切削参数下,加工效率相对单刀提高了约41.5%。
Aiming at nine-axis twin-tool milling of blade profiles, a new path smoothing algorithm is proposed based on the geometric constraints in order to guarantee the smoothness of twin-tool paths and the synchronization of two cutters. Firstly, the structural constraint of two cutters in the nine-axis machine tool is analyzed, and the normal vector at cutting contact point is transformed into the cutter axis vector through rotation matrix for characterizing twin-tool pose. Meanwhile, the inclination angle and tilt angle of the cutter are calculated and the range of these two angles is determined to meet the twin-tool milling requirement. Secondly, the parameter increments in and between the cutting paths are calculated by iso-parametric solution on Δu_(di), Δu_(bi), Δv_(di) and Δv_(bi), here Δu_(di) and Δu_(bi) are the parameter increments between two adjacent cutting contact points, one is on the dorsal surface and another on the basin surface of the blade, along the cutting direction; Δv_(di) and Δv_(bi) are the parameter increments between two adjacent cutting contact points(on the same aforementioned two surfaces) along feed direction, respectively. Finally, the self-defined coefficient is defined according to the range of milling area on the dorsal and basin surfaces of the blade, and the matching algorithm and twin-tool path smoothing algorithm are proposed. The twin-tool paths of rough machining are planned for typical turbine blade. The results of simulation and experiments show that the two surfaces of the blade can be simultaneously and entirely machined, and the contour errors do not exceed the tolerance range. Compared with the path planning algorithm considering the cutting force offset,the computational efficiency of our method is enhanced by 56%. In addition, the machining efficiency can be increased by about 41.5% compared with the single-tool milling at equivalent cutting parameters.
Aiming at nine-axis twin-tool milling of blade profiles, a new path smoothing algorithm is proposed based on the geometric constraints in order to guarantee the smoothness of twin-tool paths and the synchronization of two cutters. Firstly, the structural constraint of two cutters in the nine-axis machine tool is analyzed, and the normal vector at cutting contact point is transformed into the cutter axis vector through rotation matrix for characterizing twin-tool pose. Meanwhile, the inclination angle and tilt angle of the cutter are calculated and the range of these two angles is determined to meet the twin-tool milling requirement. Secondly, the parameter increments in and between the cutting paths are calculated by iso-parametric solution on Δu_(di), Δu_(bi), Δv_(di) and Δv_(bi), here Δu_(di) and Δu_(bi) are the parameter increments between two adjacent cutting contact points, one is on the dorsal surface and another on the basin surface of the blade, along the cutting direction; Δv_(di) and Δv_(bi) are the parameter increments between two adjacent cutting contact points(on the same aforementioned two surfaces) along feed direction, respectively. Finally, the self-defined coefficient is defined according to the range of milling area on the dorsal and basin surfaces of the blade, and the matching algorithm and twin-tool path smoothing algorithm are proposed. The twin-tool paths of rough machining are planned for typical turbine blade. The results of simulation and experiments show that the two surfaces of the blade can be simultaneously and entirely machined, and the contour errors do not exceed the tolerance range. Compared with the path planning algorithm considering the cutting force offset,the computational efficiency of our method is enhanced by 56%. In addition, the machining efficiency can be increased by about 41.5% compared with the single-tool milling at equivalent cutting parameters.
引文
[1] WANG Hui, HUANG Lijiang, YAO Chao, et al. Integrated analysis method of thin-walled turbine blade precise machining [J]. International Journal of Precision Engineering and Manufacturing, 2015, 16(15): 1011-1019.
[2] CHEN Yueping, GAO Jian, DENG Haixiang, et al. Spatial statistical analysis and compensation of machining errors for complex surfaces [J]. Precision Engineering, 2013, 37(1): 203-212.
[3] DO M D, SON Y H, CHOI H J. Optimal workpiece positioning in flexible fixtures for thin-walled components [J]. Computer-Aided Design, 2018, 95: 14-23.
[4] FEI Jixiong, LIN Bin, XIAO Juliang, et al. Investigation of moving fixture on deformation suppression during milling process of thin-walled structures [J]. Journal of Manufacturing Processes, 2018, 32: 403-411.
[5] 付中涛, 杨文玉, 张彦辉, 等. 基于切削力预测模型的复杂曲面铣削进给速度优化 [J]. 中国科学: 技术科学, 2016, 46(7): 722-730. FU Zhongtao, YANG Wenyu, ZHANG Yanhui, et al. Feedrate optimization of complex surface milling based on predictive model of cutting force [J]. Scientia Sinica: Technologica, 2016, 46(7): 722-730.
[6] 陈志同, 张保国. 面向单元切削过程的切削参数优化模型 [J]. 机械工程学报, 2009, 45(5): 230-236. CHEN Zhitong, ZHANG Baoguo. Mathematic model on cutting parameter optimization for unit cutting process [J]. Journal of Mechanical Engineering, 2009, 45(5): 230-236.
[7] HUANG Tao, ZHANG Xiaoming, DING Han. Tool orientation optimization for reduction of vibration and deformation in ball-end milling of thin-walled impeller blades [J]. Procedia CIRP, 2017, 58: 210-215.
[8] WANG Minghai, SUN Yue. Error prediction and compensation based on interference-free tool paths in blade milling [J]. The International Journal of Advanced Manufacturing Technology, 2014, 71: 1309-1318.
[9] ZHANG Y, ZHANG D H, WU B H. An adaptive approach to error compensation by on-machine measurement for precision machining of thin-walled blade [C]//IEEE International Conference on Advanced Intelligent Mechatronics. Piscataway, NJ, USA: IEEE, 2015: 1356-1360.
[10] 徐金亭, 刘伟军, 邱晓杰, 等. 自由曲面加工中的等参数螺旋轨迹生成方法 [J]. 机械工程学报, 2010, 46(3): 148-151. XU Jinting, LIU Weijun, QIU Xiaojie, et al. Isoparametric and spiral toolpath for free-form surfaces machining [J]. Journal of Mechanical Engineering, 2010, 46(3): 148-151.
[11] DING Songlin, MANANN M A, POO A, et al. Adaptive iso-planar tool path generation for machining of free-form surfaces [J]. Computer-Aided Design, 2003, 35: 141-153.
[12] 蔡永林, 席光, 樊宏周, 等. 任意曲面叶轮五坐标数控加工刀具轨迹生成 [J]. 西安交通大学学报, 2003, 37(1): 77-80. CAI Yonglin, XI Guang, FAN Hongzhou, et al. Tool-path planning for 5-axis numerical control machining of arbitrary surface impeller [J]. Journal of Xi’an Jiaotong University, 2003, 37(1): 77-80.
[13] ZOU Qiang, ZHANG Juyong, DENG Bailin, et al. Iso-level tool path planning for free-form surfaces [J]. Computer-Aided Design, 2014, 53: 117-125.
[14] HU Pengchen, TANG Kai. Five-axis tool path generation based on machine-dependent potential field [J]. International Journal of Computer Integrated Manufacturing, 2016, 29(6): 636-651.
[15] ZHANG Ke, TANG Kai. Optimal five-axis tool path generation algorithm based on double scalar fields for freeform surfaces [J]. International Journal of Advanced Manufacturing Technology, 2016, 83: 1503-1514.
[16] DMG MORI Group. NT4300DCG/1500SZ technical information [EB/OL]. [2018-06-16]. http: //cn. dm gmori.com.
[17] DP Technology Corp. ESPRIT application case [EB/OL]. [2018-06-16]. https: //www.espritcam.com/solutions/technology/5-axis-pinch-milling.
[18] 王建录, 成冰, 赵万华, 等. 汽轮机长叶片型面双刀加工刀位轨迹优化算法 [J]. 西安交通大学学报, 2013, 47(9): 65-71. WANG Jianlu, CHENG Bing, ZHAO Wanhua, et al. New planning algorithm of tool path for long turbine blades machining with twin-cutters [J]. Journal of Xi’an Jiaotong University, 2013, 47(9): 65-71.
[19] LU Dun, LIU Jun, ZHAO Wanhua, et al. Tool path generation for turbine blades machining with twin tool [J]. Journal of Manufacturing Science and Engineering, 2017, 139: 1-10.
[20] LEE Y S. Mathematical modeling using different end-mills and tool placement problems for 4-and 5-axis NC complex surface machining [J]. International Journal of Production Research, 1998, 36(3): 785-814.
[2] CHEN Yueping, GAO Jian, DENG Haixiang, et al. Spatial statistical analysis and compensation of machining errors for complex surfaces [J]. Precision Engineering, 2013, 37(1): 203-212.
[3] DO M D, SON Y H, CHOI H J. Optimal workpiece positioning in flexible fixtures for thin-walled components [J]. Computer-Aided Design, 2018, 95: 14-23.
[4] FEI Jixiong, LIN Bin, XIAO Juliang, et al. Investigation of moving fixture on deformation suppression during milling process of thin-walled structures [J]. Journal of Manufacturing Processes, 2018, 32: 403-411.
[5] 付中涛, 杨文玉, 张彦辉, 等. 基于切削力预测模型的复杂曲面铣削进给速度优化 [J]. 中国科学: 技术科学, 2016, 46(7): 722-730. FU Zhongtao, YANG Wenyu, ZHANG Yanhui, et al. Feedrate optimization of complex surface milling based on predictive model of cutting force [J]. Scientia Sinica: Technologica, 2016, 46(7): 722-730.
[6] 陈志同, 张保国. 面向单元切削过程的切削参数优化模型 [J]. 机械工程学报, 2009, 45(5): 230-236. CHEN Zhitong, ZHANG Baoguo. Mathematic model on cutting parameter optimization for unit cutting process [J]. Journal of Mechanical Engineering, 2009, 45(5): 230-236.
[7] HUANG Tao, ZHANG Xiaoming, DING Han. Tool orientation optimization for reduction of vibration and deformation in ball-end milling of thin-walled impeller blades [J]. Procedia CIRP, 2017, 58: 210-215.
[8] WANG Minghai, SUN Yue. Error prediction and compensation based on interference-free tool paths in blade milling [J]. The International Journal of Advanced Manufacturing Technology, 2014, 71: 1309-1318.
[9] ZHANG Y, ZHANG D H, WU B H. An adaptive approach to error compensation by on-machine measurement for precision machining of thin-walled blade [C]//IEEE International Conference on Advanced Intelligent Mechatronics. Piscataway, NJ, USA: IEEE, 2015: 1356-1360.
[10] 徐金亭, 刘伟军, 邱晓杰, 等. 自由曲面加工中的等参数螺旋轨迹生成方法 [J]. 机械工程学报, 2010, 46(3): 148-151. XU Jinting, LIU Weijun, QIU Xiaojie, et al. Isoparametric and spiral toolpath for free-form surfaces machining [J]. Journal of Mechanical Engineering, 2010, 46(3): 148-151.
[11] DING Songlin, MANANN M A, POO A, et al. Adaptive iso-planar tool path generation for machining of free-form surfaces [J]. Computer-Aided Design, 2003, 35: 141-153.
[12] 蔡永林, 席光, 樊宏周, 等. 任意曲面叶轮五坐标数控加工刀具轨迹生成 [J]. 西安交通大学学报, 2003, 37(1): 77-80. CAI Yonglin, XI Guang, FAN Hongzhou, et al. Tool-path planning for 5-axis numerical control machining of arbitrary surface impeller [J]. Journal of Xi’an Jiaotong University, 2003, 37(1): 77-80.
[13] ZOU Qiang, ZHANG Juyong, DENG Bailin, et al. Iso-level tool path planning for free-form surfaces [J]. Computer-Aided Design, 2014, 53: 117-125.
[14] HU Pengchen, TANG Kai. Five-axis tool path generation based on machine-dependent potential field [J]. International Journal of Computer Integrated Manufacturing, 2016, 29(6): 636-651.
[15] ZHANG Ke, TANG Kai. Optimal five-axis tool path generation algorithm based on double scalar fields for freeform surfaces [J]. International Journal of Advanced Manufacturing Technology, 2016, 83: 1503-1514.
[16] DMG MORI Group. NT4300DCG/1500SZ technical information [EB/OL]. [2018-06-16]. http: //cn. dm gmori.com.
[17] DP Technology Corp. ESPRIT application case [EB/OL]. [2018-06-16]. https: //www.espritcam.com/solutions/technology/5-axis-pinch-milling.
[18] 王建录, 成冰, 赵万华, 等. 汽轮机长叶片型面双刀加工刀位轨迹优化算法 [J]. 西安交通大学学报, 2013, 47(9): 65-71. WANG Jianlu, CHENG Bing, ZHAO Wanhua, et al. New planning algorithm of tool path for long turbine blades machining with twin-cutters [J]. Journal of Xi’an Jiaotong University, 2013, 47(9): 65-71.
[19] LU Dun, LIU Jun, ZHAO Wanhua, et al. Tool path generation for turbine blades machining with twin tool [J]. Journal of Manufacturing Science and Engineering, 2017, 139: 1-10.
[20] LEE Y S. Mathematical modeling using different end-mills and tool placement problems for 4-and 5-axis NC complex surface machining [J]. International Journal of Production Research, 1998, 36(3): 785-814.
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