# Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Measurement System and Principle

#### 2.1. Principle of the Run-Out Measurement of the Microdrill Bit

_{Edge}(θ), is employed to measure the two margins. θ represents the angular position of the microdrill bit along its circumference. The measurement principle is shown in Figure 5. The microdrill bit is being rotated by the concentricity gauge, and the measurement output on Margin 1 is referred to as T

_{Edge}(θ

_{j}), in which T

_{Edge}(θ

_{j}) is the minimum measurement output of the top edge segment in the first half of the rotation of the microdrill bit. j is the sampling interval in the circumference direction. Hence, the measurement output on Margin 2 is referred to as T

_{Edge}(θ

_{j}+ π). Based on the definition, the run-out, which is the absolute value of the output difference on the two margins, can then be calculated as:

_{Spindle_}

_{1,2}. Then, the run-out influenced by e

_{Spindle_}

_{1,2}can be written as:

_{Spindle_}

_{1,2}directly determines the measurement accuracy of the run-out. For achieving satisfied measurement accuracy, the spindle error motion of the concentricity gauge must be separated. As expressed above—that one revolution of the microdrill bit corresponds to a portion of one revolution of the concentricity gauge—the microdrill bit can be measured accurately at a fine position of the concentricity gauge, where the spindle error motion reaches the minimum. An accurate measurement of the spindle error motion of the concentricity gauge of the measurement system is a pre-condition in order to locate the fine position.

#### 2.2. Spindle Error Motion Measurement Using the Laser Scan Micrometer

_{Spindle}(θ

_{M}). θ

_{M}represents the angular position of the main rollers along its circumference, which is provided by the attached scale on the drive handle. A pin gauge with a small diameter is used as the measurement artifact. It is rotationally supported by the concentricity gauge. The upper surface and the lower surface of the pin gauge are simultaneously measured by the top edge segment and the bottom edge segment of the LSM, in which the top edge segment and the bottom edge segment are denoted as T

_{Edge}and B

_{Edge}, respectively. The spindle error motion of the concentricity gauge is measured before and after a 180-degree reversal operation of the pin gauge, as shown in Figure 8. Before the reversal operation of the pin gauge, the pin gauge is driven by the two main rollers, and the outputs of the top edge segment T

_{Edge_Before}and the bottom edge segment B

_{Edge_Before}are respectively expressed as:

_{Form}(θ

_{p}) is the form error of the pin gauge, including an out-of-roundness error component and a straightness error component. θ

_{p}represents the angular position of the pin gauge along its circumference. After the pin gauge is rotated by 180 degrees with respect to the angular position of the two main rollers, the same measurement is conducted again, and the measurement outputs of the two edge segments are expressed as:

_{Spindle}(θ

_{M}) can then be evaluated without the influence of e

_{Form}(θ

_{p}) as:

## 3. Experiments

#### 3.1. Experimental Result of the Spindle Error Motion Measurement

_{Spindle}(θ

_{M}) of the concentricity gauge was evaluated based on the proposed measurement method, as shown in Figure 8. The concentricity gauge was driven manually, and the angular position was provided by the scale attached to the drive handle. The measurement sampling interval of e

_{Spindle}(θ

_{M}) was 5.625°. The measurement of e

_{Spindle}(θ

_{M}) was repeated by three revolutions, and the measurement outputs of T

_{Edge}and B

_{Edge}before and after the reversal operation are shown in Figure 11. Based on Equation (7), the measurement results of e

_{Spindle}(θ

_{M}) were calculated, and are shown in Figure 12. The average PV value of e

_{Spindle}(θ

_{M}) of the repeated measurement result was 7.10 μm, and the measurement repeatability was 2.54 μm. The repeatability error was mainly caused by the rotation accuracy of the concentricity gauge, since the concentricity gauge was driven manually. Also, the non-repeatable rotation errors of the two main rollers were also a factor that induced the repeatability error.

_{Spindle}(θ

_{M}), which was 1.86 μm (PV). The fine position corresponds to a 0.111 revolution of the concentricity gauge. Since the diameter of the shank part of the microdrill bit and the diameter of the main rollers are 3 mm and 22 mm, one revolution of the microdrill bit corresponded to 0.136 revolution of the concentricity gauge. The range of the fine position of the concentricity gauge satisfied the required range for the measurement of the run-out of the microdrill bit.

#### 3.2. Experimental Result of the Run-Out Measurement

_{Spindle}(θ

_{M}) out of the concentricity gauge to meet the required measurement accuracy, the microdrill bit was measured at the identified fine position of the concentricity gauge. The microdrill bit was gripped at the beginning of the fine position of the concentricity, as shown in Figure 12b, and rotated one revolution to measure the two margins by the top segment of the LSM. Then, the microdrill bit was rotated back to the beginning of the fine position for the second measurement. This set of measurements was repeated 10 times, and the measurement outputs on the two margins are shown in Figure 13a. The measurement repeatability on Margin 1 and Margin 2 was 0.51 μm and 0.96 μm, respectively. By utilizing Equation (1) and the measurement outputs in Figure 13a, the average of the measured run-out of the microdrill bit was 13.57 μm, with a measurement repeatability of 1.16 μm, as shown in Figure 13b. The standard deviation of the measurement results was 0.40 μm. The repeatability error was mainly caused by the uneven rotational speed and the drift of the scanning beam of the LSM during the measurement.

## 4. Uncertainty of the Run-Out Measurement

_{Margin}, can be evaluated based on the following equation:

_{Margin}of the two margins and the uncertainty u

_{Spindle}of the spindle error motion of the concentricity gauge, as well as the uncertainty u

_{Reading}of the measurement repeatability of the run-out, in which u

_{Spindle}is the spindle error motion at the fine position of the concentricity gauge. The combined measurement uncertainty of the run-out, which is referred to as u

_{Run-out}, can be expressed as:

_{Margin}was evaluated to be 0.34 μm. The combined uncertainty of u

_{Run-out}based on Equation (9) was evaluated to be 0.61 μm. The expanded uncertainty with a coverage factor of k = 2 for the measurements of the run-out was evaluated to be 1.22 μm, in which the evaluated uncertainty had a level of confidence of approximately 95%. The measurement results and the measurement uncertainty confirmed that the proposed error separation method is reliable for the measurement of the run-out with sub-micrometric accuracy.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- LaDou, J. Printed circuit board industry. Int. J. Hyg. Environ. Health
**2006**, 209, 211–219. [Google Scholar] [CrossRef] [PubMed] - Nguyen, N.T.; Huang, X. Miniature valveless pumps based on printed circuit board technique. Sens. Actuators A Phys.
**2001**, 88, 104–111. [Google Scholar] [CrossRef] - Gower, M.C. Industrial applications of laser micromachining. Opt. Express
**2000**, 7, 56–67. [Google Scholar] [CrossRef] - Gan, E.K.; Zheng, H.Y.; Lim, G.C. Laser drilling of micro-vias in PCB substrates. In Proceedings of the 3rd Electronics Packaging Technology Conference (EPTC 2000), Sheraton Towers, Singapore, 5–7 December 2000. [Google Scholar]
- Sen, M.; Shan, H.S. A review of electrochemical macro-to micro-hole drilling processes. Int. J. Mach. Tools Manuf.
**2005**, 45, 137–152. [Google Scholar] [CrossRef] - Rajurkar, K.P.; Sundaram, M.M.; Malshe, A.P. Review of electrochemical and electrodischarge machining. Procedia CIRP
**2013**, 6, 13–26. [Google Scholar] [CrossRef] - Cheong, M.S.; Cho, D.W.; Ehmann, K.F. Identification and control for micro-drilling productivity enhancement. Int. J. Mach. Tools Manuf.
**1999**, 39, 1539–1561. [Google Scholar] [CrossRef] - Yoon, H.S.; Wu, R.; Lee, T.M.; Ahn, S.H. Geometric optimization of micro drills using Taguchi methods and response surface methodology. Int. J. Precis. Eng. Manuf.
**2011**, 12, 871–875. [Google Scholar] [CrossRef] - Chyan, H.C.; Ehmann, K.F. Development of curved helical micro-drill point technology for micro-hole drilling. Mechatronics
**1998**, 8, 337–358. [Google Scholar] [CrossRef] - Fu, L.; Guo, Q. Development of an ultra-small micro drill bit for packaging substrates. Circuit World
**2010**, 36, 23–27. [Google Scholar] [CrossRef] - Wang, X.; Wang, L.J.; Tao, J.P. Investigation on thrust in vibration drilling of fiber-reinforced plastics. J. Mater. Process. Technol.
**2004**, 148, 239–244. [Google Scholar] [CrossRef] - Fu, L.; Li, X.; Guo, Q. Development of a micro drill bit with a high aspect ratio. Circuit World
**2010**, 36, 30–34. [Google Scholar] [CrossRef] - Ancău, M. The optimization of printed circuit board manufacturing by improving the drilling process productivity. Comput. Ind. Eng.
**2008**, 55, 279–294. [Google Scholar] [CrossRef] - Bhandari, B.; Hong, Y.S.; Yoon, H.S.; Moon, J.S.; Pham, M.Q.; Lee, G.B.; Huang, Y.; Linke, B.S.; Dornfeld, D.A.; Ahn, S.H. Development of a micro-drilling burr-control chart for PCB drilling. Precis. Eng.
**2014**, 38, 221–229. [Google Scholar] [CrossRef] - Huang, C.K.; Wang, L.G.; Tang, H.C.; Tarng, Y.S. Automatic laser inspection of outer diameter, run-out and taper of micro-drills. J. Mater. Process. Technol.
**2006**, 171, 306–313. [Google Scholar] [CrossRef] - Watanabe, H.; Tsuzaka, H.; Masuda, M. Microdrilling for printed circuit boards (PCBs)—influence of radial run-out of microdrills on hole quality. Precis. Eng.
**2008**, 32, 329–335. [Google Scholar] [CrossRef] - Suganthi, X.H.; Natarajan, U.; Ramasubbu, N. A review of accuracy enhancement in microdrilling operations. Int. J. Adv. Manuf. Technol.
**2015**, 81, 199–217. [Google Scholar] [CrossRef] - Williams, K.L. Concentricity Gage. U.S. Patent 4,679,330, 14 July 1987. [Google Scholar]
- Laser Scan Micrometer-Mitutoyo. Available online: http://www.mitutoyo.com/wp-content/uploads/2013/07/2101_Laser-Scan-Mic.pdf (accessed on 5 October 2017).
- Evans, C.J.; Hocken, R.J.; Estler, W.T. Self-calibration: Reversal, redundancy, error separation, and ‘absolute testing’. CIRP Ann.-Manuf. Technol.
**1996**, 45, 617–634. [Google Scholar] [CrossRef] - Gao, W.; Lee, J.C.; Arai, Y.; Noh, Y.J.; Hwang, J.H.; Park, C.H. Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece. Int. J. Mach. Tools Manuf.
**2010**, 50, 404–410. [Google Scholar] [CrossRef] - Lee, J.; Gao, W.; Shimizu, Y.; Hwang, J.; Oh, J.S.; Park, C.H. Spindle error motion measurement of a large precision roll lathe. Int. J. Precis. Eng. Manuf.
**2012**, 13, 861–867. [Google Scholar] [CrossRef] - Niu, Z.; Chen, Y.L.; Matsuura, D.; Lee, J.C.; Kobayashi, R.; Shimizu, Y.; Ito, S.; Wei, G.; Oh, J.S.; Park, C.H. Precision measurement of Z-slide vertical error motion of an ultra-precision lathe by using three-probe method. Int. J. Precis. Eng. Manuf.
**2017**, 18, 651–660. [Google Scholar] [CrossRef] - Chen, Y.L.; Niu, Z.; Matsuura, D.; Lee, J.C.; Shimizu, Y.; Gao, W.; Oh, J.S.; Park, C.H. Implementation and verification of a four-probe motion error measurement system for a large-scale roll lathe used in hybrid manufacturing. Meas. Sci. Technol.
**2017**, 28. [Google Scholar] [CrossRef] - BIPM; IEC; IFCC; ILAC; ISO; IUPAC; IUPAP; OIML. Evaluation of Measurement Data—Guide for the Expression of Uncertainty in Measurement (GUM); International Bureau of Weight and Measures: Sèvres, France, 2008. [Google Scholar]

**Figure 12.**(

**a**) Measurement result of the spindle error motion and (

**b**) the fine position for the run-out measurement.

**Figure 13.**(

**a**) Measurement outputs on the two margins and (

**b**) the measurement result of the run-out at the fine position of the concentricity gauge.

Uncertainty Source | Type | Standard Uncertainty (μm) | |
---|---|---|---|

LSM | Resolution | B | 2.89 × 10^{−4} |

Linearity | B | 0.02 | |

Thermal drift | B | 0.16 | |

Mechanical vibration | A | 0.04 | |

Combined uncertainty u_{Margin} | 0.17 | ||

Spindle error motion | B | 0.54 | |

Reading repeatability | A | 0.13 | |

Combined uncertainty u_{Run-out} | 0.61 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Niu, Z.; Chen, Y.-L.; Shimizu, Y.; Matsukuma, H.; Gao, W.
Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System. *J. Manuf. Mater. Process.* **2018**, *2*, 4.
https://doi.org/10.3390/jmmp2010004

**AMA Style**

Niu Z, Chen Y-L, Shimizu Y, Matsukuma H, Gao W.
Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System. *Journal of Manufacturing and Materials Processing*. 2018; 2(1):4.
https://doi.org/10.3390/jmmp2010004

**Chicago/Turabian Style**

Niu, Zengyuan, Yuan-Liu Chen, Yuki Shimizu, Hiraku Matsukuma, and Wei Gao.
2018. "Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System" *Journal of Manufacturing and Materials Processing* 2, no. 1: 4.
https://doi.org/10.3390/jmmp2010004