﻿ 介观尺度铣削刀具偏心参数在位识别方法
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 哈尔滨工程大学学报  2021, Vol. 42 Issue (2): 253-258  DOI: 10.11990/jheu.201905079 0

### 引用本文

ZHANG Xiang, PAN Xudong, WANG Guanglin. In-position measuring of tool runout parameters in micro-milling[J]. Journal of Harbin Engineering University, 2021, 42(2): 253-258. DOI: 10.11990/jheu.201905079.

### 文章历史

In-position measuring of tool runout parameters in micro-milling
ZHANG Xiang , PAN Xudong , WANG Guanglin
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China
Abstract: In micro-milling, tool runout caused by manufacturing and clamping errors has a great influence on milling force, surface topography, tool life, etc. In this paper, the influence of tool runout parameters on actual cutting radius in mesoscopic scale is analyzed. A new method for in-position identification of tool runout parameters is then proposed. First, the formula for the actual cutting radius of the cutting edge of the considered tool runout is deduced and then used to analyze the influence of tool runout on the actual cutting radius. On this basis, an analytical model for tool runout parameters is established, and the model parameters are obtained by displacement measurement. Finally, tool runout parameters are identified and analyzed by an iterative algorithm, and the obtained result is verified by the milling experiment. The results show that the proposed method of the tool runout length based on displacement measurement is simple and easy to operate and has high resolution and efficiency. It can also be applied to the identification of tool runout parameters in conventional milling.
Keywords: micro-milling    tool runout length    tool runout angle    analytic model    actual cutting radius    displacement measurement    in-position measuring    iterative algorithm

1 刀具偏心参数定义及影响

 ${R_1} = \overline {{O_{\rm{s}}}{T_{\rm{1}}}} = \sqrt {{{(R + r\cos \theta )}^2} + {r^2}{{\sin }^2}\theta }$ (1)

 ${R_k} = \overline {{O_{\rm{s}}}{T_k}} = \sqrt {{R^2} + {r^2} + 2Rr\cos [2{\rm{ \mathsf{ π} }}(k - 1)/K - \theta ]}$ (2)

 Download: 图 2 刀具1各切削齿实际切削半径 Fig. 2 The actual radius of each cutting edge of the first cutter

 Download: 图 3 刀具2各切削齿实际切削半径 Fig. 3 The actual radius of each cutting edge of the second cutter
2 刀具偏心参数识别 2.1 刀具偏心参数解析模型

 $\left\{ \begin{array}{l} \Delta {R_k} = {R_k} - {R_{k + 1}} = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sqrt {{R^2} + {r^2} + 2Rr\cos [2{\rm{ \mathsf{ π} }}(k - 1)/K - \theta ]} - \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sqrt {{R^2} + {r^2} + 2Rr\cos (2{\rm{ \mathsf{ π} }} k/K - \theta )} \\ \Delta {R_K} = {R_K} - {R_1} = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sqrt {{R^2} + {r^2} + 2Rr\cos (2{\rm{ \mathsf{ π} }} /K + \theta )} - \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sqrt {{R^2} + {r^2} + 2Rr\cos \theta } \end{array} \right.$ (3)

 $\begin{array}{l} \Delta {R_1} = - \Delta {R_2} = {R_1} - {R_2} = \sqrt {{R^2} + {r^2} + 2Rr\cos \theta } - \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sqrt {{R^2} + {r^2} - 2Rr\cos \theta } \end{array}$ (4)

2.2 刀具偏心量测量

 $\Delta r({z_1}) = \Delta L({z_1})/2 = [L{({z_1})_{\max }} - L{({z_1})_{\min }}]/2$ (5)

 $\begin{array}{l} r = \bar r(z) - \bar z\sum\limits_{i = 1}^n {{{[r({z_i}) - \bar r(z)]}^2}} /\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{i = 1}^n {[r({z_i}) - \bar r(z)]({z_i} - \bar z)} \end{array}$ (6)
 $\bar r(z) = \sum\limits_{i = 1}^n {r({z_i})} /n,\bar z = \sum\limits_{i = 1}^n {{z_i}} /n$ (7)
2.3 实际切削半径差测量

 $\left\{ \begin{array}{l} \Delta {R_k} = {R_k} - {R_{k + 1}} = {P_k} - {P_{k{\rm{ + }}1}}\\ \Delta {R_K} = {R_K} - {R_1} = {P_K} - {P_1} \end{array} \right.$ (8)
2.4 测量误差分析

 $\delta = \Delta L - \Delta L' = \Delta L(1 - {\rm{sec}}\alpha )$ (9)

3 参数识别实验

3.1 刀具参数测量

 Download: 图 6 刀具位移参数测量结果 Fig. 6 Displacement measurement results of the cutter
3.2 刀具偏心参数识别

 Download: 图 7 刀具偏心参数迭代识别流程 Fig. 7 Iterative identification process for tool runout parameters

3.3 实验验证

4 结论

（1）刀具偏心导致铣削刀具各切削齿实际切削半径差别较大，且刀具偏心量越大，两切削齿实际切削半径相差越大。

（2）建立了刀具偏心参数识别模型，通过高精度激光位移传感器对模型中参数进行了精确测量，分析了测量误差。

（3）通过铣孔实验验证了本文提出的刀具偏心参数识别方法，该方法操作简便，识别效率优于基于切削力的识别算法。

（4）本文提出的刀具偏心参数识别方法可应用于常规尺度铣削刀具偏心参数的识别。

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