# Optimization of the Polishing Efficiency and Torque by Using Taguchi Method and ANOVA in Robotic Polishing

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### 2.1. Workpiece and Polishing Tool

#### 2.2. Experimental Setup

#### 2.3. Taguchi Method and Polishing Parameters

#### 2.4. Analysis of Variance (ANOVA)

#### 2.5. Regression

## 3. Results and Discussion

#### 3.1. Analysis of the Means and S/N Ratios of the Results

#### 3.2. Analysis of ANOVA

#### 3.3. Regression Analysis of Polishing Efficiency and Torque

#### 3.4. Confirmatory Test

## 4. Conclusions

- (a)
- Robot polishing is a challenging task that requires precision, as well as the consideration of polishing surface coverage, controlled polishing force, and best polishing parameters. The presented polishing system with optimal polishing parameters is effective and finishes the polishing job in a short time with precision.
- (b)
- The S/N ratios analysis from the Taguchi method shows the best levels of the control factors for highest polishing efficiency (PE = 0.943) as: start-up torque of rotatory gripper = 0.019 Nm (S/N = −2.451), wheel speed = 4500 rpm (S/N = −2.066), normal contact force = 16 N (S/N = −1.312), and gripper velocity = 5 mm/s (S/N = −2.642). Similarly, the best levels of the control factors for the minimum torque (T = 0.47 Nm) as: start-up torque of rotatory gripper = 0.019 Nm (S/N = 9.049), wheel speed = 4500 rpm (S/N = 9.398), normal contact force = 16 N (S/N = 12.278), and gripper velocity = 5 mm/s (S/N = 9.160).
- (c)
- According to the ANOVA statistical model, selected optimal levels for each control factors are same as in Taguchi method. It further determines the ranks and % contributions of the control factors for polishing efficiency (${F}_{z}$: rank = 1 and % = 71.56, ω: rank = 2 and % = 19.96, ${T}_{g}$: rank = 3 and % = 3.93, and ${V}_{f}$: rank = 4 and % = 0.57) and torque (${F}_{z}$: rank = 1 and % = 90.54, ω: rank = 2 and % = 3.01, ${V}_{f}$: rank = 3 and % = 1.12, and ${T}_{g}$: rank = 4 and % = 0.66).
- (d)
- Polishing efficiency is given higher preference over polishing torque, therefore the overall system input parameters for good polishing efficiency and torque are as: startup torque of rotatory gripper = 0.019 Nm, wheel speed = 4500 rpm, normal contact force = 16 N, and gripper velocity = 5 mm/s.
- (e)
- The most significant control factor which contributes more to the polishing process in this system is the normal contact force applied by the polishing wheel following the wheel speed, gripper torque, and gripper vibratory velocity. Gripper velocity is comparatively less significant factor in achieving the good polishing surface in a short time but it is useful in a way that it uniformly distributes the polishing effect on the surface area and safe the polishing wheel from damage and shape deformation by avoiding lingering it at one point for a long time. Therefore, the correct combination of the force, speed, and gripper torque can achieve the desired level of the surface quality in a short time.
- (f)
- Robotic polishing is an advantageous process which offers productivity, error minimization, product consist quality. Additionally, it can protect humans from the unhealthy environment of the polishing workplace. With the optimization of the process parameters, robotic polishing can further improve the polishing process. This study used some important but limited number of input polishing parameters and their levels to shows the effect on the polishing process. In the future, some other factors will be included, such as polishing time, different polishing tools, etc.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Polishing wheel and workpiece: (

**a**) Top view of the polishing wheel and workpiece interaction; (

**b**) isometric view of the workpiece (watch bezel).

**Figure 3.**Equipment used in experiments: (

**a**) surface roughness tester (Mitutoyo, SJ-210); (

**b**) torque sensor (Forsentek, FY02); (

**c**) tachometer.

**Figure 8.**Predicted results against experimental results: (

**a**) for polishing efficiency; (

**b**) for torque.

Input Polishing Parameters | Symbol | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|

Gripper start-up torque (Nm) | ${T}_{g}$ | 0.019 | 0.020 | - |

Wheel rotational speed (rpm) | ω | 3500 | 4000 | 4500 |

Normal contact force (N) | ${F}_{z}$ | 8 | 12 | 16 |

Gripper vibratory motion velocity (mm/s) | ${V}_{f}$ | 5 | 10 | 15 |

Exp. No. | ${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | Exp. No. | ${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ |
---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 10 | 2 | 1 | 1 | 3 |

2 | 1 | 1 | 2 | 2 | 11 | 2 | 1 | 2 | 1 |

3 | 1 | 1 | 3 | 3 | 12 | 2 | 1 | 3 | 2 |

4 | 1 | 2 | 1 | 1 | 13 | 2 | 2 | 1 | 2 |

5 | 1 | 2 | 2 | 2 | 14 | 2 | 2 | 2 | 3 |

6 | 1 | 2 | 3 | 3 | 15 | 2 | 2 | 3 | 1 |

7 | 1 | 3 | 1 | 2 | 16 | 2 | 3 | 1 | 3 |

8 | 1 | 3 | 2 | 3 | 17 | 2 | 3 | 2 | 1 |

9 | 1 | 3 | 3 | 1 | 18 | 2 | 3 | 3 | 2 |

**Table 3.**Experimental results ${L}_{18}({2}^{1}\times {3}^{3})$ for polishing efficiency, and torque.

Exp. No. | ${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | Mean PE | Calculated S/N for PE | Mean T | Calculated S/N for T |
---|---|---|---|---|---|---|---|---|

1 | 0.019 | 3500 | 8 | 5 | 0.572 | −4.848 | 0.24 | 12.396 |

2 | 0.019 | 3500 | 12 | 10 | 0.719 | −2.863 | 0.37 | 8.636 |

3 | 0.019 | 3500 | 16 | 15 | 0.829 | −1.629 | 0.38 | 8.404 |

4 | 0.019 | 4000 | 8 | 5 | 0.634 | −3.956 | 0.24 | 12.396 |

5 | 0.019 | 4000 | 12 | 10 | 0.804 | −1.892 | 0.38 | 8.404 |

6 | 0.019 | 4000 | 16 | 15 | 0.913 | −0.795 | 0.51 | 5.849 |

7 | 0.019 | 4500 | 8 | 10 | 0.588 | −4.616 | 0.25 | 12.041 |

8 | 0.019 | 4500 | 12 | 15 | 0.882 | −1.095 | 0.40 | 7.959 |

9 | 0.019 | 4500 | 16 | 5 | 0.959 | −0.364 | 0.54 | 5.352 |

10 | 0.020 | 3500 | 8 | 15 | 0.449 | −6.964 | 0.24 | 12.396 |

11 | 0.020 | 3500 | 12 | 5 | 0.650 | −3.747 | 0.39 | 8.179 |

12 | 0.020 | 3500 | 16 | 10 | 0.710 | −2.976 | 0.48 | 6.375 |

13 | 0.020 | 4000 | 8 | 10 | 0.616 | −4.214 | 0.25 | 12.041 |

14 | 0.020 | 4000 | 12 | 15 | 0.742 | −2.587 | 0.40 | 7.959 |

15 | 0.020 | 4000 | 16 | 5 | 0.857 | −1.342 | 0.54 | 5.352 |

16 | 0.020 | 4500 | 8 | 15 | 0.634 | −3.956 | 0.24 | 12.396 |

17 | 0.020 | 4500 | 12 | 5 | 0.832 | −1.596 | 0.39 | 8.179 |

18 | 0.020 | 4500 | 16 | 10 | 0.916 | −0.766 | 0.54 | 5.352 |

Levels | Polishing Efficiency (PE) | Torque (T) | ||||||
---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | ${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | |

1 | −2.451 * | −3.838 | −4.759 | −2.642 * | 9.049 * | 9.398 * | 12.278 * | 8.642 |

2 | −3.128 | −2.464 | −2.297 | −2.888 | 8.692 | 8.667 | 8.219 | 8.808 |

3 | − | −2.066 * | −1.312 * | −2.838 | − | 8.546 | 6.114 | 9.160 * |

Delta | 0.677 | 1.772 | 3.447 | 0.246 | 0.357 | 0.851 | 6.164 | 0.518 |

Rank | 3 | 2 | 1 | 4 | 4 | 2 | 1 | 3 |

Sources | DF | Adj SS | Adj MS | F Ratio | p-value | % Contribution |
---|---|---|---|---|---|---|

${T}_{g}$ | 1 | 0.0136 | 0.0136 | 9.5600 | 0.0110 * | 3.93 |

ω | 2 | 0.0691 | 0.0345 | 24.2500 | 0.0000 * | 19.96 |

${F}_{z}$ | 2 | 0.2476 | 0.1238 | 86.9400 | 0.0000 * | 71.56 |

${V}_{f}$ | 2 | 0.0020 | 0.0010 | 0.6900 | 0.5250 | 0.57 |

Error | 10 | 0.0142 | 0.0014 | 4.12 | ||

Total | 17 | 0.3465 |

Sources | DF | Adj SS | Adj MS | F Ratio | p Value | % Contribution |
---|---|---|---|---|---|---|

${T}_{g}$ | 1 | 0.0014 | 0.0014 | 1.4100 | 0.2630 | 0.66 |

ω | 2 | 0.0065 | 0.0033 | 3.2300 | 0.0830 | 3.01 |

${F}_{z}$ | 2 | 0.1963 | 0.0982 | 97.0700 | 0.0000 * | 90.54 |

${V}_{f}$ | 2 | 0.0024 | 0.0012 | 1.2000 | 0.3400 | 1.12 |

Error | 10 | 0.0101 | 0.0010 | 4.66 | ||

Total | 17 | 0.2168 |

Levels | Polishing Efficiency (PE) | Torque (T) | ||||||
---|---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | ${\mathit{T}}_{\mathit{g}}$ | ω | ${\mathit{F}}_{\mathit{z}}$ | ${\mathit{V}}_{\mathit{f}}$ | |

1 | 0.767 * | 0.655 | 0.582 | 0.751 * | 0.368 * | 0.350 * | 0.243 * | 0.390 |

2 | 0.712 | 0.761 | 0.772 | 0.725 | 0.386 | 0.387 | 0.388 | 0.379 |

3 | − | 0.802 * | 0.864 * | 0.741 | − | 0.393 | 0.498 | 0.366 * |

Predicted Results | Experimental Results | ||
---|---|---|---|

Input optimal parameters | Gripper startup torque (${T}_{g}$) | 0.019 Nm | 0.019 Nm |

Wheel speed (ω) | 4500 rpm | 4500 rpm | |

Normal contact force (${F}_{z}$) | 16 N | 16 N | |

Gripper velocity (${V}_{f}$) | 5 mm/s | 5 mm/s | |

Polishing efficiency $\left(PE={A\Delta R}_{a}/T\right)$ | 0.976 | 0.943 | |

Polishing Torque (T) | 0.50 Nm | 0.47 Nm |

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## Share and Cite

**MDPI and ACS Style**

Mohsin, I.; He, K.; Li, Z.; Zhang, F.; Du, R.
Optimization of the Polishing Efficiency and Torque by Using Taguchi Method and ANOVA in Robotic Polishing. *Appl. Sci.* **2020**, *10*, 824.
https://doi.org/10.3390/app10030824

**AMA Style**

Mohsin I, He K, Li Z, Zhang F, Du R.
Optimization of the Polishing Efficiency and Torque by Using Taguchi Method and ANOVA in Robotic Polishing. *Applied Sciences*. 2020; 10(3):824.
https://doi.org/10.3390/app10030824

**Chicago/Turabian Style**

Mohsin, Imran, Kai He, Zheng Li, Feifei Zhang, and Ruxu Du.
2020. "Optimization of the Polishing Efficiency and Torque by Using Taguchi Method and ANOVA in Robotic Polishing" *Applied Sciences* 10, no. 3: 824.
https://doi.org/10.3390/app10030824