# A New Approach to the Consideration and Analysis of Critical Factors in Robotic Machining

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## Abstract

**:**

## 1. Introduction

## 2. Factorial Procedure for Preliminary Study of Critical Factors in Robotic Machining

**Phase 1: Factorial design**

- Characterization of the robotic cell.

- 2.
- Machining parameters.

- 3.
- Machining strategies.

**Stage 1: Set initial data**

**Stage 2: Selection of the variables and parameters to study**

**Stage 3: Development of the test tables.**

**Phase 2: Methodology applied for determination of the simulated cutting tool path deviation**

**Stage 1: Characterization of the reduced equivalent model**

- -
- M
_{r}(${P}_{i},{\theta}_{1}\dots ,{\theta}_{i}$) is the equivalent matrix of the mass of the robot’s axes and machining head,$$\left[{M}_{r}\left({P}_{i},{\theta}_{1}\dots ,{\theta}_{i}\right)\right]=\frac{1}{{x}_{tcp}^{2}+{y}_{tcp}^{2}+{z}_{tcp}^{2}}{{\displaystyle \sum}}_{i=0}^{N}{m}_{i}\left[\begin{array}{ccc}{y}_{i}^{2}+{z}_{i}^{2}& -{x}_{i}{y}_{i}& -{x}_{i}{z}_{i}\\ -{x}_{i}{y}_{i}& {x}_{i}^{2}+{z}_{i}^{2}& -{y}_{i}{z}_{i}\\ -{x}_{i}{z}_{i}& -{y}_{i}{z}_{i}& {x}_{i}^{2}+{y}_{i}^{2}\end{array}\right]$$ - -
- K
_{r}(${P}_{i},{\theta}_{1}\dots ,{\theta}_{i}$) is the stiffness matrix equivalent to the mechanical structure of the robot for a point P_{i}of the space. The TCP deviations under the action of a known static force was measured with a deflection gauge.$$\left[{K}_{r}\left({P}_{i},{\theta}_{1}\dots ,{\theta}_{i}\right)\right]=\left[\begin{array}{ccc}{k}_{11}& {k}_{12}& {k}_{13}\\ {k}_{21}& {k}_{22}& {k}_{23}\\ {k}_{31}& {k}_{32}& {k}_{33}\end{array}\right]$$ - -
- C
_{r}(${P}_{i},{\theta}_{1}\dots ,{\theta}_{i}$) is the damping equivalent to the mechanical structure of the robot for a specific point P_{i}of the space. It was calculated through a hammer impact test and considering the Rayleigh equation.$$\left[{C}_{r}\left({P}_{i},{\theta}_{1}\dots ,{\theta}_{i}\right)\right]={a}_{0}\left[{M}_{r}\left({P}_{i},{\theta}_{1}\dots ,{\theta}_{i}\right)\right]+{a}_{1}\left[{K}_{r}\left({P}_{i},{\theta}_{1}\dots ,{\theta}_{i}\right)\right]$$

**Stage 2: Cutting force modeling**

**F**

_{xyz,tool}on the TCP is,

**Stage 3: Modeling of the interactions between the cutting forces and the robot mechanics**

**Stage 4: Evaluation and comparison of different structural configurations**

**Stage 5: Selection of the lowest-deviation structural configuration**

**Phase 3: Evaluation and identification of the most influential factors in robotic machining**

- Establish design criteria for the robotic cell, in cases where robot selection, location of external axes, machining head configuration or workpiece clamping methods are necessary.
- Determine whether a specific machining operation can be performed in the robotic cell, depending on the work material, machining operation, cutting tool and process parameters.
- Select the most convenient cutting strategy by defining the location and orientation of the part and determining the most favorable robot axis configuration, which guarantees the correct execution of the machining operation, complying with the required manufacturing tolerances of the part.

## 3. Experimental Validation of the Factorial Procedure

- Characterization of the robotic cell.

- 2.
- Machining parameters.Certain initial conditions are established:
- ○
- A grooving operation was chosen for its simple cutting force vector representation.
- ○
- To perform the machining tests, a KENDU hard metal burr-cutting tool with a 10 mm diameter, 150 mm length, two cutting edges, and a 30º helix angle was chosen.

- 3.
- Machining strategies.

- Characterization of the robotic cell.

- 2.
- Machining parameters.
- Selection of the workpiece material type: To evaluate the influence of the hardness of the material to be machined on the prediction of the robotic system, two materials with very different properties were selected: Aluminum EN AW—5083 (Al) and 300 kg/cm3 rigid polyurethane foam (PUR 300).
- Cutting parameter selection, based on the conventional machining manual for KENDU machine tool:

- ○
- To study the influence of cutting speed on path precision, two rotational tool speeds (n) were defined: 6000 rpm and 8000 rpm.
- ○
- To evaluate the influence of cutting depth on the tool’s path deviation, two values (a
_{p}) were defined: 1 mm and 1.5 mm.

- 3.
- Machining strategies.
- Selection of the relative workpiece position with respect to the robot’s coordinate origin: To assess the importance of the workpiece location with respect to the machining robot, two positions were evaluated, as shown in Figure 3, providing two different mechanical robot configurations: a workpiece position close to the robot’s base (A) and a position further from the base (B). Position A is 1.100 mm from the base of the robot in x axis and position B 1.600 mm.
- Cutting strategy definition:

## 4. Results through the Application of the Factorial Procedure

- The achieved precision depends fundamentally on the working material, becoming worse as its hardness increases. The most unfavorable results appear when machining tests are performed on Al.
- The workpiece location is an important variable to control because it directly influences the stiffness available for the robot to counter the cutting forces. Considering the same robot wrist configuration and the same cutting force vector for positions A and B, different trajectory deviation values are obtained due to the change in structural rigidity of the robotic arm.
- The milling head orientation with respect to the working direction (or the configuration of the robot’s axes) also modifies the robot’s stiffness and therefore influences the obtained precision.
- The cutting conditions, such as cutting speed (V
_{c}) or plunging depth (a_{p}), influence the result and must be adequate. - Acting on the previous conditions, the precision has been improved from an experimental deviation error of 0.685 mm to 0.352 mm for PUR 300 and from 0.982 mm to 0.607 mm for Al.

- Hardness of the material to be machined (HB)
- Workpiece position (B)
- Working direction or robot’s axes configuration (T)
- Plunging depth (a
_{p}) - Cutting speed (V
_{c})

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Orientation of the workpiece in L direction; (

**b**) orientation of the workpiece in T direction.

Factor | F_{1} | F_{2} | F_{3} | ….. | F_{j} |
---|---|---|---|---|---|

+ | f_{1}+ | f_{2}+ | f_{3}+ | ….. | f_{j}+ |

− | f_{1}− | f_{2}− | f_{3}− | ….. | f_{j}− |

Factor | Material (HB) | P (mm) | Direction (rad) | n (rpm) | a_{p} (mm) |
---|---|---|---|---|---|

+ | Al | A | L | 8000 | 1.5 |

- | PUR 300 | B | T | 6000 | 1 |

(a)Tests for Al. | |||||

Test | Material (HB) | P (mm) | D (rad) | N (rpm) | a_{p} (mm) |

E1 | Al | A | L | 8000 | 1.5 |

E2 | Al | A | L | 8000 | 1 |

E3 | Al | A | L | 6000 | 1.5 |

E4 | Al | A | L | 6000 | 1 |

E5 | Al | A | T | 8000 | 1.5 |

E6 | Al | A | T | 8000 | 1 |

E7 | Al | A | T | 6000 | 1.5 |

E8 | Al | A | T | 6000 | 1 |

E9 | Al | B | L | 8000 | 1.5 |

E10 | Al | B | L | 8000 | 1 |

E11 | Al | B | L | 6000 | 1.5 |

E12 | Al | B | L | 6000 | 1 |

E13 | Al | B | T | 8000 | 1.5 |

E14 | Al | B | T | 8000 | 1 |

E15 | Al | B | T | 6000 | 1.5 |

E16 | Al | B | T | 6000 | 1 |

(b) Tests for PUR 300 | |||||

Test | Material (HB) | P (mm) | D (rad) | N (rpm) | a_{p} (mm) |

E17 | PUR 300 | A | L | 8000 | 1.5 |

E18 | PUR 300 | A | L | 8000 | 1 |

E19 | PUR 300 | A | L | 6000 | 1.5 |

E20 | PUR 300 | A | L | 6000 | 1 |

E21 | PUR 300 | A | T | 8000 | 1.5 |

E22 | PUR 300 | A | T | 8000 | 1 |

E23 | PUR 300 | A | T | 6000 | 1.5 |

E24 | PUR 300 | A | T | 6000 | 1 |

E25 | PUR 300 | B | L | 8000 | 1.5 |

E26 | PUR 300 | B | L | 8000 | 1 |

E27 | PUR 300 | B | L | 6000 | 1.5 |

E28 | PUR 300 | B | L | 6000 | 1 |

E29 | PUR 300 | B | T | 8000 | 1.5 |

E30 | PUR 300 | B | T | 8000 | 1 |

E31 | PUR 300 | B | T | 6000 | 1.5 |

E32 | PUR 300 | B | T | 6000 | 1 |

Test | Experimental Max Deviation (mm) | Simulated Max Deviation (mm) | % Predictive Error |
---|---|---|---|

E01 | 0.614 | 0.559 | 9.0% |

E02 | 0.607 | 0.551 | 9.2% |

E03 | 0.791 | 0.713 | 9.9% |

E04 | 0.713 | 0.646 | 9.4% |

E05 | 0.696 | 0.630 | 9.5% |

E06 | 0.648 | 0.578 | 10.8% |

E07 | 0.971 | 0.883 | 9.1% |

E08 | 0.802 | 0.719 | 10.3% |

E09 | 0.699 | 0.631 | 9.7% |

E10 | 0.629 | 0.563 | 10.5% |

E11 | 0.889 | 0.801 | 9.9% |

E12 | 0.712 | 0.647 | 9.1% |

E13 | 0.705 | 0.640 | 9.2% |

E14 | 0.655 | 0.596 | 9.0% |

E15 | 0.982 | 0.894 | 9.0% |

E16 | 0.841 | 0.760 | 9.6% |

Test | Experimental Max Deviation (mm) | Simulated Max Deviation (mm) | % Predictive Error |
---|---|---|---|

E17 | 0.358 | 0.324 | 9.5% |

E18 | 0.352 | 0.325 | 7.7% |

E19 | 0.496 | 0.450 | 9.3% |

E20 | 0.456 | 0.416 | 8.8% |

E21 | 0.441 | 0.402 | 8.8% |

E22 | 0.394 | 0.348 | 11.7% |

E23 | 0.685 | 0.622 | 9.2% |

E24 | 0.544 | 0.499 | 8.3% |

E25 | 0.443 | 0.405 | 8.6% |

E26 | 0.374 | 0.349 | 6.7% |

E27 | 0.504 | 0.456 | 9.5% |

E28 | 0.457 | 0.422 | 7.7% |

E29 | 0.451 | 0.410 | 9.1% |

E30 | 0.399 | 0.363 | 9.0% |

E31 | 0.592 | 0.534 | 9.8% |

E32 | 0.585 | 0.541 | 7.5% |

Test | Material (HB) | P (mm) | D (rad) | n (rpm) | a_{p} (mm) |
---|---|---|---|---|---|

E2 | Al | A | L | 8000 | 1 |

E18 | PUR 300 | A | L | 8000 | 1 |

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**MDPI and ACS Style**

Iglesias Sánchez, I.; Ares, J.E.; González Gaya, C.; Rosales Prieto, V.
A New Approach to the Consideration and Analysis of Critical Factors in Robotic Machining. *Appl. Sci.* **2020**, *10*, 8885.
https://doi.org/10.3390/app10248885

**AMA Style**

Iglesias Sánchez I, Ares JE, González Gaya C, Rosales Prieto V.
A New Approach to the Consideration and Analysis of Critical Factors in Robotic Machining. *Applied Sciences*. 2020; 10(24):8885.
https://doi.org/10.3390/app10248885

**Chicago/Turabian Style**

Iglesias Sánchez, Iván, José Enrique Ares, Cristina González Gaya, and Victor Rosales Prieto.
2020. "A New Approach to the Consideration and Analysis of Critical Factors in Robotic Machining" *Applied Sciences* 10, no. 24: 8885.
https://doi.org/10.3390/app10248885