# 关于电缆卷绕过程的状态监测研究Study on State Monitoring of Cable Winding Process

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Cable winding is the final step of cable production, but in practice, there is no safe and efficient detection scheme. Therefore, if the cable is not neatly arranged during winding, the system cannot provide timely feedback. In order to solve this problem, a method of least square circle fitting based on radius constraint is proposed to realize the measurement of cable winding. At the same time, the influence of various factors on the fitting accuracy is analyzed in detail, and the simulation calculation is carried out.

1. 引言

(a) (b) (c)

Figure 1. Alignment of cables. (a) In alignment; (b) Misaligned1; (c) Misaligned 2

2. 国内外研究现状

3. 状态检测的算法设计

3.1. 基本原理

$x=\rho \cdot \mathrm{sin}\theta \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}y=\rho \cdot \mathrm{cos}\theta$ (1)

3.2. 算法设计

3.2.1. 数据预处理

3.2.2. 确定边界位置

${x}_{L}=\frac{1}{N}\underset{i=1}{\overset{N}{\sum }}{x}_{i}{x}_{R}=\frac{1}{N}\underset{j=1}{\overset{N}{\sum }}{x}_{j}$ (2)

3.2.3. 确定电缆位置

${\left(x-{x}_{0}\right)}^{2}+{\left(y-{y}_{0}\right)}^{2}={r}_{0}^{2}$ (3)

$\underset{i=1}{\overset{N}{\sum }}{\delta }_{i}^{2}={\left[{\left({x}_{i}-{x}_{0}\right)}^{2}+{\left({y}_{i}-{y}_{0}\right)}^{2}-{r}_{0}^{2}\right]}^{2}$ (4)

(a) (b)

Figure 2. The fitting process. (a) The process of fitting a line; (b) The process of fitting a circle

4. 拟合精度影响因素及扫描次数确定

4.1. 模型建立

Table 1. Parameters of sensor LMS400

Figure 3. Flow chart for determining the center of circles

4.2. 边界拟合

Figure 4. Boundary fitting error

4.3. 电缆圆心拟合

5. 相关要求

5.1. 电缆规格

$\frac{r}{\sqrt{{\left(\frac{D}{2}-r\right)}^{2}+{\left(h-r\right)}^{2}}}=\mathrm{sin}1.5\theta$ (5)

Figure 5. Fitting error of cable center

Figure 6. Schematic diagram of sensor detection range

5.2. 卷绕速度

Figure 7. Determination of cable specifications

$t>\frac{{T}_{2}}{f}$ (6)

5.3. 电缆盘规格

LMS400的检测范围如图6所示，考虑传感器的扫描范围充分覆盖电缆盘及电缆，所以适当缩小有效检测范围以确保检测的准确性。以角度范围60˚，长度范围0.8 m至2.9 m为例进行计算，实际应用中可对检测范围的取值做相应调整。

$1\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\text{\hspace{0.17em}}\text{m} (7)

$2\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.92\text{\hspace{0.17em}}\text{m} (8)

5.4. 安装要求

1) 电缆卷盘内宽最大值

$f\left(h\right)=\left\{\begin{array}{l}\frac{2\sqrt{3}}{3}h\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.8\text{\hspace{0.17em}}\text{m} (9)

2) 当 $0.8\text{\hspace{0.17em}}\text{m}

$f\left(h-H\right)=2\sqrt{3}\left(h-H\right)/3$ (10)

$g\left(h\right)=\left[f\left(h-H\right)-D\right]/5=\sqrt{3}\left(h-H\right)/3-D/2$ (11)

3) 当 $2.511\text{\hspace{0.17em}}\text{m}\le h<2.9\text{\hspace{0.17em}}\text{m}$$2.511\text{\hspace{0.17em}}\text{m}<\left(h-H\right)<2.9\text{\hspace{0.17em}}\text{m}$

$f\left(h\right)=2\sqrt{8.41-{h}^{2}}$ (12)

$g\left(h\right)=\left[f\left(h\right)-D\right]/2=\sqrt{8.41-{h}^{2}}-D/2$ (13)

4) 当 $0.8\text{\hspace{0.17em}}\text{m}<\left(h-H\right)<2.511\text{\hspace{0.17em}}\text{m}$$2.511\text{\hspace{0.17em}}\text{m}\le h<2.9\text{\hspace{0.17em}}\text{m}$

$f\left(h-H\right)=2\sqrt{3}\left(h-H\right)/3$ (14)

$f\left(h\right)=2\sqrt{8.41-{h}^{2}}$ (15)

$g\left(h\right)=\left(\mathrm{min}\left\{f\left(h-H\right),f\left(h\right)\right\}-D\right)/2$ (16)

6. 总结

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