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摘要: 微细铣刀在主轴上存在装夹偏角时，会加剧刀刃磨损，降低刀具使用寿命。为了精确观测微细铣刀在机倾斜状态，提出了基于景深的微细铣刀三维位姿重建方法。利用激光同轴数字全息实验装置得到微细铣刀全息图，并通过菲涅尔再现算法获得再现像。在再现像中提取刀具边缘点作为关键点，采用小波变换局部方差算子求出关键点的聚焦程度，确定铣刀对应的轴向位置。利用最小二乘法对关键点拟合修正重建误差，实现微细铣刀的三维位姿重建。实验结果表明,基于景深的微细铣刀三维位姿重建方法获得的微细铣刀重建误差优于0.1°。该方法能够精确测量微细铣刀三维位姿，可为后续的微细铣刀装夹精度修正提供参考依据。Abstract: When a micro-milling tool has a clamping angle on its spindle, the wear of the tool edge will accelerate and shorten the tool’s lifespan. In order to accurately observe the inclination state of the micro-milling tool on the machine, a three-dimensional pose reconstruction method based on the depth of field of a micro-milling tool is proposed. The laser coaxial digital holographic experimental device is used to obtain the micro-milling tool hologram, and the reconstruction image is obtained through the Fresnel reconstruction algorithm. The tool edge points are extracted as the key points in the reconstruction image, the wavelet transform local variance operator is used to obtain the degree of focus of the key points, and then the axial position corresponding to the milling tool is determined. The least square method is used to fit the key points and correct the reconstruction error, from which the three-dimensional pose reconstruction of the micro-milling tool is realized. The experimental results show that the reconstruction error of the micro-milling tool obtained by the three-dimensional pose reconstruction method is better than 0.1°. This method can accurately measure a three-dimensional pose of a micro-milling tool, which can provide a reference for the subsequent correction of micro-milling tool clamping accuracy.
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图 1 数字全息记录过程示意图
Figure 1. Schematic diagram of the recording process of the digital holography
图 2 数字全息再现过程示意图
Figure 2. Schematic diagram of the reconstruction process of the digital holography
图 3 刀具三维位姿重构流程图。(a)刀具全息图；(b) n张再现像；(c)滤波后的n张再现像；(d)点(i, j)的最佳再现距离；(e)刀具三维位姿示意图
Figure 3. Flow diagram of three-dimensional pose reconstruction of the tool. (a) Tool hologram; (b) reconstruction images; (c) reconstruction images after filtering; (d) best reconstruction distance for point (i, j); (e) schematic diagram of the tool’s three-dimensional pose
图 4 数字全息实验装置示意图
Figure 4. Schematic diagram of the digital holography experimental device
图 5 铅芯数字全息实验装置示意图。（a）摆正状态；（b）倾斜指定角度
Figure 5. Schematic diagram of the digital holographic experimental device for the lead core as simulated sample. (a) Straightened; (b) incline at a specified angle
图 6 铅芯数字全息图及再现像。(a)数字全息图；（b）再现像（左）及计算区域放大图（右）
Figure 6. Digital hologram and reconstruction image of the lead-core. (a) Digital hologram; (b) reconstruction image (left) and calculation area magnification (right)
图 7 (a)小波变换局部方差算子及 (b)局部灰度方差算子对应的的整体轴向位置分布
Figure 7. Overall axial position distribution corresponding to (a) the local variance operator of wavelet transform and (b) local gray-scale variance operator
图 8 (a)小波变换局部方差算子对应的低频点的聚焦评价曲线; (b)小波变换局部方差算子对应的边缘点的聚焦评价曲线; (c)局部灰度方差算子对应的低频点聚焦评价曲线; (d)局部灰度方差算子对应的边缘点聚焦评价曲线
Figure 8. (a) Focus evaluation curve of low frequency points corresponding to the local variance operator of the wavelet transform; (b) focus evaluation curve of the edge points corresponding to the local variance operator of the wavelet transform; (c) focus evaluation curve of the low frequency points corresponding to the local gray-scale variance operator; (d) focus evaluation curve of the edge points corresponding to the local gray-scale variance operator
图 9 铅芯的三维重建结果。（a）小波变换局部方差算子的三维重建结果；（b）局部灰度方差算子的三维重建结果
Figure 9. Three-dimensional reconstruction results of lead core. (a) Three-dimensional reconstruction results calculated by local variance operator of the wavelet transform; (b) three-dimensional reconstruction results calculated by local gray-scale variance operator
图 10 像素坐标下铅芯三维重建结果。（a）小波变换局部方差算子的三维重建结果；（b）局部灰度方差算子的三维重建结果
Figure 10. Three-dimensional reconstruction results of the lead core in pixel coordinates. (a) Three-dimensional reconstruction results calculated by local variance operator of wavelet transform; (b) three-dimensional reconstruction result calculated by local gray-level variance operator
图 11 距离坐标下铅芯三维重建结果。（a）小波变换局部方差算子的三维重建结果；（b）局部灰度方差算子的三维重建结果
Figure 11. Three-dimensional reconstruction results of the lead core in the distance coordinates. (a) Three-dimensional reconstruction result calculated by local variance operator of the wavelet transform; (b) three-dimensional reconstruction results calculated by local gray-level variance operator
图 12 (a)待测铣刀及其(b)数字全息图和(c)再现像
Figure 12. (a) Tested tool and its (b) digital hologram and (c) reconstruction image
图 13 (a)铣刀再现像低频点的聚焦评价曲线;(b)铣刀再现像边缘点的聚焦评价曲线
Figure 13. (a) Focus evaluation curve of the low-frequency point of the milling tool′s reconstruction image; (b) focus evaluation curve of the edge point of the milling tool’s reconstruction image
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