# In-Process Error-Matching Measurement and Compensation Method for Complex Mating

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Selection of Key Nodes

#### 2.2. Measurement Method

#### 2.3. Fitting Method

_{1}, Y

_{1}), (X

_{2}, Y

_{2})… (X

_{N}, Y

_{N}) and curve-fitted line. For a given coordinate, such as (X

_{i}, Y

_{i}), a deviation D

_{i}exists between the corresponding value on the Y-axis and the Y value on the curve C. This deviation value can be positive, negative, or zero. The maximum order of the polynomial is dictated by the number of data points used to generate it, and can be calculated as m = N − 1. The polynomial can be created passing through all the points when the polynomial of the degree is N − 1. On the other hand, if the polynomial of the degree is less than N − 1, the polynomial does not pass through any of the points, but overall approximates the data. The general form of polynomials function can be written as Equation (3).

#### 2.4. Error Comparison

#### 2.5. Error Conversion

#### 2.6. Autogeneration of an Error-Compensated NC Program

## 3. Mating Error Compensation System

#### 3.1. Human–Machine Interface Setup

#### 3.2. HMI On-Line Error Compesation

## 4. Experiment and Verification

#### 4.1. Experiment Preparation

#### 4.2. Verification of Curve Mating

#### 4.3. Verification of Complex Mating

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the mating area that consists of straight line, triangle, and curve shapes. (

**a**) keypoints to measure straight line, (

**b**) keypoints to measure triangle, and (

**c**) keypoints to measure curve.

**Figure 6.**(

**a**) Part shape, (

**b**) counterpart shape, (

**c**) assembly matching without compensation, (

**d**) assembly matching with compensation.

**Figure 18.**Error comparison between counterpart w/o compensation vs. counterpart w/ compensation for complex mating.

Subject | Curve | Complex |
---|---|---|

Tool diameter (mm) | 6 | 6 |

Spindle speed (rpm) | 6000 | 6000 |

Feed rate (mm/min) | 500 | 500 |

Material | Aluminum | Aluminum |

Tool material | Tungsten Carbide | Tungsten Carbide |

Tool flutes | 3 | 3 |

Width of Cut (mm) | 0.1 | 0.2 |

Depth of Cut (mm) | 13.5 | 13.5 |

Point | X (mm) | Y (mm) |
---|---|---|

1 | 0.883 | −2.819 |

2 | 2.281 | −8.381 |

3 | 0.790 | −15.772 |

4 | 1.803 | −25.847 |

5 | 2.490 | −35.824 |

6 | 2.290 | −43.426 |

7 | 1.311 | −51.845 |

8 | 0.812 | −61.008 |

9 | 1.663 | −68.944 |

10 | 1.510 | −73.454 |

Point | Measured Coordinate | Converted Coordinate | ||
---|---|---|---|---|

X (mm) | Y (mm) | X (mm) | Y (mm) | |

1 | 1.193 | −2.818 | −2.006 | −2.768 |

2 | 2.591 | −8.382 | −0.655 | −8.332 |

3 | 1.100 | −15.769 | −2.176 | −15.719 |

4 | 2.113 | −25.866 | −1.191 | −25.816 |

5 | 2.810 | −35.823 | −0.542 | −35.773 |

6 | 2.600 | −43.425 | −0.766 | −43.375 |

7 | 1.621 | −51.843 | −1.799 | −51.793 |

8 | 1.112 | −61.007 | −2.304 | −60.957 |

9 | 1.933 | −68.943 | −1.445 | −68.893 |

10 | 1.710 | −73.453 | −1.567 | −73.403 |

Point | Measured Coordinate | Converted Coordinate | ||
---|---|---|---|---|

X (mm) | Y (mm) | X (mm) | Y (mm) | |

1 | 0.835 | −2.818 | −2.217 | −2.719 |

2 | 2.236 | −8.380 | −0.964 | −8.383 |

3 | 0.779 | −15.769 | −2.421 | −15.779 |

4 | 1.808 | −25.846 | −1.181 | −25.843 |

5 | 2.533 | −35.822 | −0.377 | −35.824 |

6 | 2.335 | −43.425 | −0.535 | −43.426 |

7 | 1.439 | −51.843 | −1.361 | −51.847 |

8 | 0.851 | −61.007 | −1.751 | −61.008 |

9 | 1.688 | −68.943 | −0.808 | −68.944 |

10 | 1.558 | −73.452 | −0.995 | −73.468 |

Point | X (mm) | Y (mm) | Angle (Deg) | Distance (mm) |
---|---|---|---|---|

1 | −32.067 | 76.005 | 17.649 | |

2 | −32.372 | 58.359 | 118.948 | |

3 | −45.769 | 49.020 | 63.948 | |

4 | −32.266 | 37.782 | ||

5 | −32.280 | 33.047 | ||

6 | −33.943 | 28.052 | ||

7 | −35.924 | 22.701 | ||

8 | −36.626 | 19.804 | ||

9 | −36.827 | 17.891 | ||

10 | −36.812 | 16.453 | ||

11 | −36.217 | 12.695 | ||

12 | −35.332 | 9.749 | ||

13 | −33.811 | 5.734 | ||

14 | −32.311 | 1.794 |

**Table 6.**The measured coordinates and conversion coordinates of complex counterpart without compensation.

Point | Measured Coordinates | Converted Coordinates | ||||||
---|---|---|---|---|---|---|---|---|

X (mm) | Y (mm) | Angle (Deg) | Distance (mm) | X (mm) | Y (mm) | Angle (Deg) | Distance (mm) | |

1 | −31.691 | 76.003 | 17.308 | −32.443 | 76.003 | 17.308 | ||

2 | −32.524 | 58.715 | 119.542 | −32.220 | 58.715 | 119.542 | ||

3 | −45.345 | 49.027 | 64.878 | −46.193 | 49.027 | 64.878 | ||

4 | −31.895 | 37.792 | −32.637 | 37.792 | ||||

5 | −32.206 | 33.064 | −32.354 | 33.064 | ||||

6 | −33.853 | 28.066 | −34.033 | 28.066 | ||||

7 | −35.955 | 22.716 | −35.893 | 22.716 | ||||

8 | −36.712 | 19.803 | −36.540 | 19.803 | ||||

9 | −36.878 | 17.888 | −36.776 | 17.888 | ||||

10 | −36.862 | 16.455 | −36.762 | 16.455 | ||||

11 | −36.27 | 12.696 | −36.164 | 12.696 | ||||

12 | −35.396 | 9.746 | −35.268 | 9.746 | ||||

13 | −33.907 | 5.733 | −33.715 | 5.733 | ||||

14 | −32.448 | 1.792 | −34.033 | 1.792 |

**Table 7.**The measured coordinates and conversion coordinates of complex counterpart with compensation.

Point | Measured Coordinates | Converted Coordinates | ||||||
---|---|---|---|---|---|---|---|---|

X (mm) | Y (mm) | Angle (Deg) | Distance (mm) | X (mm) | Y (mm) | Angle (Deg) | Distance (mm) | |

1 | −32.101 | 76.006 | 17.592 | −32.033 | 76.006 | 17.562 | ||

2 | −32.367 | 58.446 | 119.061 | −32.377 | 58.446 | 119.061 | ||

3 | −45.365 | 49.027 | 63.83 | −46.173 | 49.027 | 63.83 | ||

4 | −31.875 | 37.792 | −32.657 | 37.792 | ||||

5 | −32.224 | 33.054 | −32.336 | 33.064 | ||||

6 | −33.918 | 28.066 | −33.968 | 28.066 | ||||

7 | −35.947 | 22.716 | −35.901 | 22.716 | ||||

8 | −36.64 | 19.803 | −36.612 | 19.803 | ||||

9 | −36.853 | 17.888 | −36.801 | 17.888 | ||||

10 | −36.841 | 16.455 | −36.783 | 16.455 | ||||

11 | −36.234 | 12.696 | −36.200 | 12.696 | ||||

12 | −35.353 | 9.746 | −35.311 | 9.746 | ||||

13 | −33.827 | 5.731 | −33.795 | 5.733 | ||||

14 | −32.34 | 1.791 | −32.282 | 1.792 |

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**MDPI and ACS Style**

Wang, S.-M.; Tu, R.-Q.; Gunawan, H.
In-Process Error-Matching Measurement and Compensation Method for Complex Mating. *Sensors* **2021**, *21*, 7660.
https://doi.org/10.3390/s21227660

**AMA Style**

Wang S-M, Tu R-Q, Gunawan H.
In-Process Error-Matching Measurement and Compensation Method for Complex Mating. *Sensors*. 2021; 21(22):7660.
https://doi.org/10.3390/s21227660

**Chicago/Turabian Style**

Wang, Shih-Ming, Ren-Qi Tu, and Hariyanto Gunawan.
2021. "In-Process Error-Matching Measurement and Compensation Method for Complex Mating" *Sensors* 21, no. 22: 7660.
https://doi.org/10.3390/s21227660