叶片机器人百叶轮抛磨柔性适应性轨迹规划研究

doi:10.11996/JG.j.2095-302X.2025040874

图学学报 ›› 2025, Vol. 46 ›› Issue (4): 874-882.DOI: 10.11996/JG.j.2095-302X.2025040874

叶片机器人百叶轮抛磨柔性适应性轨迹规划研究

张晶晶¹(), 谷正钊¹, 王俊清¹, 刘佳²()

1.太原工业学院机械工程系，山西太原 030008
2.太原理工大学机械工程学院，山西太原 030024

收稿日期:2024-10-25 接受日期:2025-02-13 出版日期:2025-08-30 发布日期:2025-08-11
通讯作者:刘佳(1987-)，女，副教授，博士。主要研究方向为精密零件表面光整加工技术。E-mail：liujia@tyut.edu.cn
第一作者:张晶晶(1988-)，女，讲师，博士。主要研究方向为光整加工和制造过程数字化。E-mail：398956271@qq.com
基金资助:
国家自然科学基金(52105474);太原工业学院引进人才科研资助项目(2024KJ005)

Study on flexible adaptive trajectory planning for blade robot abrasive cloth wheel polishing

ZHANG Jingjing¹(), GU Zhengzhao¹, WANG Junqing¹, LIU Jia²()

1. Department of Mechanical Engineering, Taiyuan Institute of Technology, Taiyuan Shanxi 030008, China
2. School of Mechanical Engineering, Taiyuan University of Technology, Taiyuan Shanxi 030024, China

Received:2024-10-25 Accepted:2025-02-13 Published:2025-08-30 Online:2025-08-11
First author：ZHANG Jingjing (1988-), lecturer, Ph.D. Her main research interests cover finishing and digitalization of manufacturing processes. E-mail：398956271@qq.com
Supported by:
National Natural Science Foundation of China(52105474);Imported Talent Research Funding Program of Taiyuan Institute of Technology(2024KJ005)

摘要/Abstract

摘要：

在叶片复杂曲面零件的抛磨加工中，现有的轨迹规划方法主要将抛磨接触过程视为几何问题，未充分考虑抛磨工具的柔性变形和材料去除量的影响，导致轨迹规划产生误差，为提高叶片表面加工精度，研究百叶轮在抛磨接触过程中的柔性变形和接触区域的材料去除量对步长和行距的影响。首先，对接触区域进行分析，建立了材料去除量模型；接着，计算柔性适应性抛磨路径点的步长和行距，采用恒定进给速度进行插补；其次，提取叶片抛磨区域NURBS曲线，并离线仿真生成叶片表面抛磨轨迹点；最后，在搭建的抛磨平台上进行试验验证，叶背和叶盆的表面粗糙度R_a≤0.3 μm，前缘和后缘的表面粗糙度R_a≤0.2 μm，抛磨总效率提高约9.40%。证实了柔性适应性轨迹规划方法可有效提高表面加工精度和加工效率。

关键词: 轨迹规划, 百叶轮抛磨, NURBS曲线, 材料去除量, 柔性适应性

Abstract:

In the blade complex curved parts polishing processing, the existing trajectory planning methods mainly consider the polishing contact as a geometrical problem, and do not adequately consider the effects of the polishing tool flexible deformation and material removal, resulting in errors in trajectory planning. In order to improve the blade surface processing accuracy, the influence of abrasive cloth wheel flexible deformation and contact surface material removal on the step and line spacing was studied. Firstly, the contact area was analyzed and the material removal model was established. Then, the step length and row spacing for the flexible adaptive polishing path points were calculated, and the constant feed speed was employed for interpolation. Secondly, the NURBS curve of the blade polishing region was extracted, and the trajectory points of blade surface polishing were generated via offline simulation. Finally, the test verification was conducted on a constructed polishing platform, the surface roughness of blade concave and convex reached R_a≤0.3 μm, the leading and trailing edges reached R_a≤0.2 μm, and the total polishing efficiency increased by about 9.40%. It was proved that the flexible adaptive trajectory planning method could effectively improve the surface machining accuracy and machining efficiency.

Key words: trajectory planning, abrasive cloth wheel polishing, NURBS curve, material removal, flexible adaptation

中图分类号:

张晶晶, 谷正钊, 王俊清, 刘佳. 叶片机器人百叶轮抛磨柔性适应性轨迹规划研究[J]. 图学学报, 2025, 46(4): 874-882.

ZHANG Jingjing, GU Zhengzhao, WANG Junqing, LIU Jia. Study on flexible adaptive trajectory planning for blade robot abrasive cloth wheel polishing[J]. Journal of Graphics, 2025, 46(4): 874-882.

图/表 15

表1 百叶轮与叶片材料仿真参数

Table 1 Simulation parameters of abrasive cloth wheel and blade materials

参数	弹性模量/GPa	泊松比
百叶轮	0.03	0.04
叶片	220.00	0.30

图1 百叶轮和叶片接触区域应力分布

Fig. 1 Simulation of macroscopic contact between abrasive cloth wheel and blade

图2 微元A处接触示意图

Fig. 2 Contact diagram at element A

图3 步长计算示意图

Fig. 3 Step size calculation diagram

图4 改进的步长计算示意图

Fig. 4 Improved step size calculation diagram

图5 抛磨路径行距计算示意图

Fig. 5 Schematic diagram of line spacing calculation of polishing path

表2 抛磨工艺参数

Table 2 Polishing process parameters

参数	数值
叶片进给速度v_f	0.2 mm/min
快速进给速度v_k	1.0 mm/min
百叶轮主轴转速v_s	33.4 m/s
法向接触力F_n	30 N (叶盆/叶背) 10 N (前缘/后缘)
弦高误差εʹ	0.08 mm
残留高度	0.01 mm
Preston系数k_p	1

表3 步长/行距改进前后对比/mm

Table 3 Comparison of step size/line spacing before and after improvement/mm

参数	改进前	改进后
步长	9.254	13.087
行距	20	15

图6 叶背轨迹规划算法对比图((a) NURBS曲线轨迹仿真；(b) 柔性适应性NURBS曲线轨迹仿真)

Fig. 6 Comparison of blade back trajectory planning algorithms ((a) NURBS curve trajectory simulation; (b) Flexible adaptive NURBS curve trajectory simulation)

图7 改进前后抛磨时间和轨迹点数量对比((a) 改进前后抛磨时间对比；(b) 改进前后抛磨轨迹点数量)

Fig. 7 Comparison polishing time and track point before/after improvement (a) Improved comparison of polishing time before and after polishing; (b) Improving the number of track points before and after polishing)

图8 工业机器人抛磨叶片装置

Fig. 8 Industrial robot polishing blade device

图9 机器人砂带力控自适应磨削叶片((a) 磨削前；(b) 磨削后)[21]

Fig. 9 Robotic belt force-controlled adaptive grinding blades ((a) Before grinding; (b) After grinding)[21]

图10 机器人砂带磨抛轮廓误差逆向补偿轨迹法((a) 磨削整体叶盘；(b) 叶背三维表面形貌)[22]

Fig. 10 Robotic belt grinding for contour errors inverse compensation trajectory method ((a) Grinding integral discs; (b) Leaf back three-dimensional surface morphology) [22]

图11 叶片抛磨前后对比((a) 叶背抛磨前；(b) 叶背抛磨后；(c) 叶盆抛磨前；(d) 叶盆抛磨后；(e) 前缘抛磨后；(f) 后缘抛磨后)

Fig. 11 Comparison blades polishing before and after (a) Convex before polishing; (b) Convex after polishing; (c) Concave before polishing; (d) Concave after polishing; (e) After leading edge polishing; (f) After trailing edge polishing

图12 叶片表面粗糙度测量值对比((a) 叶背；(b) 叶盆；(c) 前缘；(d) 后缘)

Fig. 12 Comparison of blade surface roughness measurement values ((a) Convex; (b) Concave; (c) Leading edge; (d) Trailing edge)

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叶片机器人百叶轮抛磨柔性适应性轨迹规划研究

Study on flexible adaptive trajectory planning for blade robot abrasive cloth wheel polishing

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