# Process Parameter Effects on Biocompatible Thermoplastic Sheets Produced by Incremental Forming

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometry and Materials

- varying wall angle along the part’s depth.
- 105 mm in length.
- 45° for the initial wall angle
- 80 mm generatrix radius.

^{3}sheets. The PCL sheets were produced in our laboratory by compression molding. Around 55 g of PCL pellets (Sigma Aldrich, Saint Louis, MO, USA, ≈3 mm, average Mn = 80,000) were positioned into the cavity (150 × 150 × 2 mm

^{3}) of a stainless-steel cast which was previously warmed to a set temperature between 60 and 80 °C inside a heating hydraulic press. A low load was applied for a fixed time to guarantee the melt of the material. Subsequently, the load was increased, thus keeping the sheet in place for a few more minutes to complete the final compaction of the fused polymer. The pressure was then retired, and the cast cooled to room temperature by placing it in a cooling press.

#### 2.2. Experimental Setup

^{®}HS1000 3-axis milling machine (Kondia, Elgoibar, Spain). The details of the clamping system (Figure 1b) and the setup are described in detail in previous works [10]. The forming forces were measured by a table-type dynamometer Kistler

^{®}9257B (Kistler ibérica SL, Granollers, Spain); surface roughness was determined by means of a Mitutoyo Surftest SV-2000 profilometer (Sariki, Cerdanyola del Vallès, Spain) (Figure 1c) and the maximum depth was recorded by a direct reading off the Kondia milling machine (Kondia, Elgoibar, Spain).

#### 2.3. Design of Experiments

- Dt: Tool diameter (6, 10, 14 mm)
- S: Spindle speed (Free*, 1000, 2000 rpm)
- F: Feed rate (1500, 2250, 3000 mm/min)
- Δz: Step down (0.2, 0.35, 0.5 mm).

#### 2.4. Analysis Procedure

- Estimation of the full model with first order, two-way interactions and pure quadratic terms.
- Sequentially removal of the non-significant terms based on the tests on individual regression and groups of coefficients. Each model was evaluated in terms of the fit statistics: R
^{2}, R^{2}-adjusted, R^{2}-predicted and RMSE. In addition, the test for significance of regression (p-value associated to Model in the ANOVA table) was observed: a p-value < α indicated that the regression was significant. The lack of fit test was also examined as an indicator of the tentative model satisfactorily describing the data when its p-value was high. - Model adequacy checking: last squares regression assumptions.

^{2}, adj-R

^{2}, pred-R

^{2}and low RMSE) together with an appropriate model adequacy. The reason for using a subset of explanatory variables, rather than all of them, is that the estimates of the coefficients will have smaller variance and the predictions will be more precise. The Shapiro Wilk normality test (SWNT) was used to check the normality of the residuals.

## 3. Results and Discussion

#### 3.1. Maximum Axial Force (Fz Max)

#### 3.1.1. PCL

^{2}of 92%. The residuals of the model are homoscedastic, independent and identically normally distributed (SWNT p-value = 0.06).

#### 3.1.2. UHMWPE

^{2}= 96%). The residuals of the retained model are i.i.d. distributed (SWNT p-value = 0.3303).

#### 3.2. Surface Roughness (Ra)

#### 3.2.1. PCL

^{2}of 74%. Residuals are independent, homoscedastic and normally distributed (SWNT p-value = 0.3082). The model is complex because of the high numbers of terms included in it, but the surface plots shown in Table 4 can help in interpreting it.

#### 3.2.2. UHMWPE

^{2}. It was decided to keep F in the model to achieve a non-significant lack-of-fit test. The general regression test is significant. Residuals are normally distributed (SWNT p-value = 0.87).

#### 3.3. Maximum Achieved Depth (Zmax)

#### 3.3.1. PCL

^{0.95}= 2.59) as the multiplicative effects of the hazard. That is, increasing Dt one level (e.g., from −1 to 0) increases the danger of breaking by, on average, a factor of 2.59. The overall tests of significance p-value (likelihood ratio, Wald and logrank) are significant, indicating that the model is appropriate.

^{−0.70}= 0.50. Note, however, that the interaction between Dt and S is not significant. More experiments should be carried out in order to confirm the significance of S in the survival function.

#### 3.3.2. UHMWPE

^{3.38}= 29.49.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Test geometry (

**b**) Dynamometer with tooling (

**c**) Experimental setup (

**d**) Roughness measurement on ultra-high molecular weight polyethylene (UHWMPE) (

**e**) UHMWPE part (

**f**) polycaprolactone (PCL) part.

**Figure 3.**(

**a**) Effect of different tool diameters, Dt, on surface roughness, Ra (

**b**) Effect of different step down, Δz, on surface roughness, Ra.

Material | Vicat Softening Temperature (°C) | Tensile Strength (MPa) | Elastic Modulus (MPa) |
---|---|---|---|

PCL | 44.3 | 15.2 | 375 |

UHMWPE | 80 | 19 | 700 |

ID | Tool Diameter, Dt (mm) | Spindle Speed, S (rpm) | Feed Rate, F (mm/min) | Step Down, Δz (mm) | PCL | UHMWPE | ||||
---|---|---|---|---|---|---|---|---|---|---|

Fz Max (N) | Ra (μm) | Zmax * (mm) | Fz max (N) | ΔRa (μm) | Zmax * (mm) | |||||

1 | 6 | Free | 2250 | 0.35 | 208.72 | 0.498 | 27.7 (0) | 485.33 | 0.437 | 42.7 (1) |

2 | 14 | Free | 2250 | 0.35 | 439.14 | 0.627 | 29.1 (0) | 1027.50 | 0.750 | 42.7 (1) |

3 | 6 | 2000 | 2250 | 0.35 | 190.95 | 0.41 | 42.7 (1) | 414.58 | 0.916 | 42.0 (0) |

4 | 14 | 2000 | 2250 | 0.35 | 329.64 | 2.23 | 43.0 (1) | 697.15 | −0.194 | 35.7 (0) |

5 | 10 | 1000 | 1500 | 0.20 | 314.38 | 0.608 | 41.4 (0) | 635.68 | 0.511 | 43.0 (1) |

6 | 10 | 1000 | 3000 | 0.20 | 309.16 | 0.622 | 43.0 (1) | 596.08 | 0.242 | 43.0 (1) |

7 | 10 | 1000 | 1500 | 0.50 | 293.05 | 1.393 | 42.0 (0) | 636.66 | 0.391 | 43.0 (1) |

8 | 10 | 1000 | 3000 | 0.50 | 291.63 | 0.509 | 43.0 (1) | 591.00 | 0.324 | 43.0 (1) |

9 | 10 | 1000 | 2250 | 0.35 | 325.57 | 0.585 | 38.2 (0) | 643.44 | 0.477 | 42.7 (1) |

10 | 6 | 1000 | 2250 | 0.20 | 214.14 | 0.453 | 43.0 (1) | 491.68 | 0.508 | 43.0 (1) |

11 | 14 | 1000 | 2250 | 0.20 | 425.94 | 1.114 | 39.0 (0) | 765.37 | 0.739 | 43.0 (1) |

12 | 6 | 1000 | 2250 | 0.50 | 197.63 | 0.484 | 37.0 (0) | 399.84 | 0.373 | 43.0 (1) |

13 | 14 | 1000 | 2250 | 0.50 | 390.87 | 1.549 | 24.0 (0) | 858.88 | 0.635 | 43.0 (1) |

14 | 10 | Free | 1500 | 0.35 | 320.78 | 1.023 | 40.6 (0) | 818.05 | 0.332 | 42.7 (1) |

15 | 10 | 2000 | 1500 | 0.35 | 275.32 | 1.880 | 41.3 (0) | 581.63 | 0.230 | 38.5 (0) |

16 | 10 | Free | 3000 | 0.35 | 343.10 | 0.716 | 40.3 (0) | 747.58 | 0.198 | 42.7 (1) |

17 | 10 | 2000 | 3000 | 0.35 | 282.30 | 1.735 | 40.6 (0) | 558.92 | 0.420 | 39.2 (0) |

18 | 10 | 1000 | 2250 | 0.35 | 296.22 | 0.464 | 42.7 (1) | 595.00 | 0.524 | 42.7 (1) |

19 | 6 | 1000 | 1500 | 0.35 | 227.42 | 0.527 | 42.7 (1) | 486.95 | 0.354 | 42.7 (1) |

20 | 14 | 1000 | 1500 | 0.35 | 418.57 | 1.385 | 30.1 (0) | 802.43 | 0.863 | 42.7 (1) |

21 | 6 | 1000 | 3000 | 0.35 | 240.99 | 0.330 | 42.7 (1) | 449.30 | 0.231 | 42.7 (1) |

22 | 14 | 1000 | 3000 | 0.35 | 381.09 | 0.902 | 31.5 (0) | 830.85 | 0.956 | 42.7 (1) |

23 | 10 | Free | 2250 | 0.20 | 330.25 | 0.859 | 36.0 (0) | 727.72 | 0.115 | 42.8 (0) |

24 | 10 | 2000 | 2250 | 0.20 | 281.23 | 1.775 | 37.0 (0) | 554.77 | 0.549 | 38.8 (0) |

25 | 10 | Free | 2250 | 0.50 | 355.89 | 0.579 | 43.0 (1) | 774.19 | 0.801 | 43.0 (1) |

26 | 10 | 2000 | 2250 | 0.50 | 266.34 | 2.102 | 43.0 (1) | 587.48 | 0.407 | 36.5 (0) |

27 | 10 | 1000 | 2250 | 0.35 | 280.30 | 0.598 | 42.7 (1) | 611.80 | 0.440 | 42.7 (1) |

PCL | UHWMPE | ||||||||||

Parameter estimates | Parameter estimates | ||||||||||

Coefficient | p-value | Coefficient | Pr (>|t|) | ||||||||

(Intercept) | 304.84 | <0.001 | (Intercept) | 626.33 | <0.001 | ||||||

Dt | 92.12 | <0.001 | Dt | 187.88 | <0.001 | ||||||

S | −31.01 | <0.001 | S | −98.82 | <0.001 | ||||||

Dt·S | −22.93 | 0.009 | F | −15.64 | 0.033 | ||||||

Δz | 6.40 | 0.359 | |||||||||

Dt·S | −64.90 | <0.001 | |||||||||

Dt·Δz | 46.34 | <0.001 | |||||||||

S^{2} | 38.24 | <0.001 | |||||||||

Analysis of variance | Analysis of variance | ||||||||||

Df | Sum Sq | Mean Sq | F value | p-value | Df | Sum Sq | Mean Sq | F value | p-value | ||

Model | 3 | 115,468 | 38,489 | 149.76 | <0.001 | Model | 7 | 579,363 | 82,766 | 148.86 | <0.001 |

Residuals | 23 | 5918 | 257 | Residuals | 19 | 10,570 | 556 | ||||

Lack of fit | 5 | 1185 | 237 | 0.90 | 0.502 | Lack of fit | 17 | 9360 | 551 | 0.91 | 0.644 |

Pure Error | 18 | 4733 | 263 | Pure Error | 2 | 1210 | 605 | ||||

Summary of fit | Summary of fit | ||||||||||

R^{2} | 0.95 | RMSE | 16.04 | R^{2} | 0.98 | RMSE | 23.59 | ||||

Adj, R^{2} | 0.94 | Pred. R^{2} | 0.93 | Adj, R^{2} | 0.98 | Pred. R^{2} | 0.96 | ||||

PCL | UHWMPE | ||||||||||

Parameter estimates | Parameter estimates | ||||||||||

Coefficient | p-value | Coefficient | p-value | ||||||||

(Intercept) | 0.57 | <0.001 | (Intercept) | 0.46 | <0.001 | ||||||

Dt | 0.43 | <0.001 | Dt | 0.08 | 0.259 | ||||||

S | 0.49 | <0.001 | S | −0.03 | 0.707 | ||||||

F | −0.17 | 0.010 | F | −0.03 | 0.703 | ||||||

Δz | 0.10 | 0.105 | Dt·S | −0.36 | 0.006 | ||||||

Dt·S | 0.42 | 0.001 | |||||||||

F· Δz | −0.22 | 0.038 | |||||||||

S^{2} | 0.51 | <0.001 | |||||||||

F^{2} | 0.16 | 0.070 | |||||||||

Δz ^{2} | 0.21 | 0.020 | |||||||||

Analysis of variance | Analysis of variance | ||||||||||

Df | Sum Sq | Mean Sq | F value | p-value | Df | Sum Sq | Mean Sq | F value | p-value | ||

Model | 9 | 7.97 | 0.89 | 22.24 | <0.001 | Model | 4 | 0.59 | 0.15 | 2.77 | <0.001 |

Residuals | 17 | 0.68 | 0.04 | Residuals | 22 | 1.18 | 0.05 | ||||

Lack of fit | 15 | 0.67 | 0.04 | 8.14 | 0.115 | Lack of fit | 14 | 0.91 | 0.06 | 1.89 | 0.184 |

Pure Error | 2 | 0.01 | 0.01 | Pure Error | 8 | 0.27 | 0.03 | ||||

Summary of fit | Summary of fit | ||||||||||

R^{2} | 0.92 | RMSE | 0.20 | R^{2} | 0.33 | RMSE | 0.23 | ||||

Adj, R^{2} | 0.88 | Pred. R^{2} | 0.74 | Adj, R^{2} | 0.21 | Pred. R^{2} | −0.33 | ||||

**Table 5.**Summary of the coefficients of the selected models (bold indicates significance (α = 0.05)).

Intercept | Dt | S | F | Δz | $\mathbf{D}\mathbf{t}\xb7\mathbf{S}$ | $\mathbf{D}\mathbf{t}\xb7\Delta \mathbf{z}$ | $\mathbf{F}\xb7\Delta \mathbf{z}$ | S^{2} | F2 | Δz^{2} | |
---|---|---|---|---|---|---|---|---|---|---|---|

Fz max | |||||||||||

PCL | $\mathbf{304.84}$ | $\mathbf{92.12}$ | $\mathbf{-}\mathbf{31.01}$ | $\mathbf{-}\mathbf{22.93}$ | |||||||

UHMWPE | $\mathbf{626.33}$ | $\mathbf{187.88}$ | $\mathbf{-}\mathbf{98.82}$ | $\mathbf{-}\mathbf{15.64}$ | $6.40$ | $-64.90$ | $\mathbf{+}\mathbf{46.34}$ | $\mathbf{38.24}$ | |||

Ra | |||||||||||

PCL | $\mathbf{0.57}$ | $\mathbf{0.43}$ | $\mathbf{0.49}$ | $\mathbf{-}\mathbf{0.17}$ | $0.1$ | $\mathbf{0.42}$ | $\mathbf{-}\mathbf{0.22}$ | $\mathbf{0.51}$ | $0.16$ | $\mathbf{0.21}$ | |

UHMWPE (ΔRa) | $\mathbf{0.46}$ | $0.08$ | $-0.03$ | $-0.03$ | $\mathbf{-}\mathbf{0.36}$ | ||||||

Z max (Survival analysis) | |||||||||||

PCL | × | ||||||||||

UHMWPE | × |

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## Share and Cite

**MDPI and ACS Style**

Sabater, M.; Garcia-Romeu, M.L.; Vives-Mestres, M.; Ferrer, I.; Bagudanch, I.
Process Parameter Effects on Biocompatible Thermoplastic Sheets Produced by Incremental Forming. *Materials* **2018**, *11*, 1377.
https://doi.org/10.3390/ma11081377

**AMA Style**

Sabater M, Garcia-Romeu ML, Vives-Mestres M, Ferrer I, Bagudanch I.
Process Parameter Effects on Biocompatible Thermoplastic Sheets Produced by Incremental Forming. *Materials*. 2018; 11(8):1377.
https://doi.org/10.3390/ma11081377

**Chicago/Turabian Style**

Sabater, Marc, M. Luisa Garcia-Romeu, Marina Vives-Mestres, Ines Ferrer, and Isabel Bagudanch.
2018. "Process Parameter Effects on Biocompatible Thermoplastic Sheets Produced by Incremental Forming" *Materials* 11, no. 8: 1377.
https://doi.org/10.3390/ma11081377