# Comprehensive Areal Geometric Quality Characterisation of Injection Moulded Thermoplastic Gears

^{*}

## Abstract

**:**

## 1. Introduction

- Development and evaluation of novel injection quality parameters and areal surface quality parameters.
- Investigation of the influence of injection moulding process parameters on the introduced novel quality parameters.
- Enhancement of the gear quality assessment using the developed analysis procedure.
- A method for rapid refinement of the injection moulding process parameters in order to achieve the required precision of the produced gears.

## 2. Methodology

#### 2.1. Polymer Gear Manufacturing

#### 2.2. Optical Measurement

#### 2.3. Data Processing

#### 2.3.1. Moulding Runout Quality Parameter ${F}_{\mathrm{mr}}$

#### 2.3.2. Novel Areal Parameters

#### 2.4. Post-Processing

## 3. Results and Discussion

#### 3.1. Parameter ${F}_{\mathrm{mr}}$

#### 3.2. Areal Parameter Results

## 4. Conclusions

- The developed parameter ${F}_{\mathrm{mr}}$ proved to be effective in evaluating the shrinkage that can occur in the injection moulding process, whereas the standard quality parameters are incapable of determining it. The average value of parameter ${F}_{\mathrm{r}}$ of all the gears was 29.4 $\mathsf{\mu}$m, whereas the average value of ${F}_{\mathrm{mr}}$ was −21.8 $\mathsf{\mu}$m. Here, the negative value of the parameter is directly associated with moulding shrinkages. The developed areal parameters ${F}_{\mathrm{S}}$, ${f}_{\mathrm{f},\mathrm{S}}$, ${f}_{\mathrm{H},\alpha ,\mathrm{S}}$, and ${f}_{\mathrm{H},\beta ,\mathrm{S}}$ proved to be advantageous in characterising the deviations on the teeth more comprehensively.
- The influence of the moulding process parameters on the new quality parameters was investigated. The rate of cooling was determined to be the most influential factor for the shrinkage of the gears, which we were able to determine through the parameter ${F}_{\mathrm{mr}}$. The study also determined the linear regression coefficients for the new quality parameters, based on Spearman’s correlation coefficient. The results and coefficients are valid for the investigated range of the process parameters and the used material, outside this range further testing should be carried out to confirm their validity.
- The developed analysis will contribute to an enhanced quality assessment of gears and a refinement of the injection moulding process parameters.
- The introduced quality parameters and evaluation methods are useful for both gear manufacturers and developers in R&D departments. With this method, we can quickly characterise the geometrical quality using commercially available scanners while considering surface deviations and shrinkages typical of injection moulded gears. The method also offers many possibilities for automating measuring procedures, which could allow measurements to be performed not only on a pair of samples from a batch but on a much larger number by means of automated in-process control.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Parameter | Symbol | Unit |

gear width | b | (mm) |

specific heat | ${c}_{\mathrm{p}}$ | (J/(kgK)) |

reference circle diameter | d | (mm) |

base diameter | ${d}_{\mathrm{b}}$ | (mm) |

nominal gear hole diameter | ${d}_{\mathrm{h}}$ | (mm) |

elastic modulus | E | (MPa) |

moulding runout quality parameter | ${F}_{\mathrm{mr}}$ | (µm) |

cumulative pitch deviation | ${F}_{\mathrm{p}}$ | (µm) |

runout deviation | ${F}_{\mathrm{r}}$ | (µm) |

flank surface deviation | ${F}_{\mathrm{S}}$ | (µm) |

profile deviation | ${F}_{\alpha}$ | (µm) |

lead profile deviation | ${F}_{\beta}$ | (µm) |

surface form deviation | ${f}_{\mathrm{f},\mathrm{S}}$ | (µm) |

profile form deviation | ${f}_{\mathrm{f}\alpha}$ | (µm) |

lead profile form deviation | ${f}_{\mathrm{f}\beta}$ | (µm) |

profile slope deviation | ${f}_{\mathrm{H}\alpha}$ | (µm) |

surface profile slope deviation | ${f}_{\mathrm{H},\alpha ,\mathrm{S}}$ | (µm) |

lead profile slope deviation | ${f}_{\mathrm{H}\beta}$ | (µm) |

surface lead profile slope deviation | ${f}_{\mathrm{H},\beta ,\mathrm{S}}$ | (µm) |

single pitch deviation | ${f}_{\mathrm{p}}$ | (µm) |

thermal conductivity | k | (W/(mK)) |

normal gear module | ${m}_{\mathrm{n}}$ | (mm) |

packing pressure | ${P}_{\mathrm{p}}$ | (Bar) |

tensile yield strength | ${R}_{\mathrm{m}}$ | (MPa) |

injection T | ${T}_{\mathrm{inj}}$ | (${}^{\circ}$C) |

melting temperature | ${T}_{\mathrm{m}}$ | (${}^{\circ}$C) |

recommended moulding temperature | ${T}_{\mathrm{r},\mathrm{inj}}$ | (${}^{\circ}$C) |

water (mould) T | ${T}_{\mathrm{wi}}$ | (${}^{\circ}$C) |

cooling time | ${t}_{\mathrm{c}}$ | (s) |

packing pressure time | ${t}_{\mathrm{Pp}}$ | (s) |

injection speed | ${v}_{\mathrm{inj}}$ | (mm/s) |

number of teeth | Z | (/) |

linear thermal expansion | $\alpha $ | (K${}^{-1}$) |

normal pressure angle | ${\alpha}_{\mathrm{n}}$ | (°) |

displacement of the runout probing body | $\Delta $ | (mm) |

Poisson’s ratio | $\nu $ | (/) |

density | $\rho $ | (kg/m${}^{3}$) |

## Appendix A

**Table A1.**Results of the evaluation of standard parameters for gear metrology. The results for the parameters are shown for the left flank.

Smpl. | ${\mathit{f}}_{\mathbf{p}}$ ($\mathsf{\mu}$m) | Q(${\mathit{f}}_{\mathbf{p}}$) (/) | ${\mathit{F}}_{\mathbf{p}}$ ($\mathsf{\mu}$m) | Q(${\mathit{F}}_{\mathbf{p}}$) (/) | Q(${\mathit{F}}_{\mathit{\alpha}}$) (/) | Q(${\mathit{f}}_{\mathbf{f}\mathit{\alpha}}$) (/) | Q(${\mathit{f}}_{\mathbf{H}\mathit{\alpha}}$) (/) | Q(${\mathit{F}}_{\mathit{\beta}}$) (/) | Q(${\mathit{f}}_{\mathbf{f}\mathit{\beta}}$) (/) | Q(${\mathit{f}}_{\mathbf{H}\mathit{\beta}}$) (/) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 6.4 | 6 | 35.1 | 8 | 10 | 8 | 11 | 10 | 8 | 11 |

2 | 6.5 | 6 | 41.8 | 9 | 9 | 8 | 10 | 11 | 9 | 11 |

3 | 6.1 | 6 | 33.7 | 8 | 8 | 7 | 8 | 10 | 9 | 11 |

4 | 6.0 | 6 | 41.7 | 9 | 12 | 10 | 13 | 10 | 9 | 11 |

5 | 5.2 | 6 | 34.5 | 8 | 10 | 8 | 11 | 10 | 9 | 10 |

6 | 15.2 | 9 | 30.9 | 8 | 9 | 10 | 10 | 10 | 9 | 10 |

7 | 7.4 | 7 | 35.2 | 8 | 13 | 11 | 13 | 12 | 8 | 13 |

8 | 5.6 | 6 | 33.8 | 8 | 11 | 6 | 13 | 11 | 8 | 12 |

9 | 11.7 | 8 | 49.5 | 9 | 9 | 8 | 10 | 13 | 10 | 13 |

10 | 6.3 | 6 | 44.0 | 9 | 8 | 7 | 8 | 10 | 8 | 11 |

11 | 5.2 | 6 | 16.3 | 6 | 8 | 7 | 9 | 10 | 8 | 10 |

12 | 9.9 | 7 | 40.7 | 8 | 9 | 9 | 10 | 11 | 10 | 12 |

13 | 6.3 | 6 | 39.8 | 8 | 11 | 8 | 12 | 9 | 8 | 10 |

14 | 6.7 | 6 | 34.3 | 8 | 10 | 8 | 12 | 10 | 9 | 11 |

15 | 5.2 | 6 | 21.1 | 7 | 11 | 10 | 13 | 11 | 12 | 10 |

16 | 8.2 | 7 | 17.5 | 6 | 12 | 7 | 13 | 9 | 8 | 9 |

17 | 4.0 | 5 | 18.3 | 6 | 11 | 7 | 12 | 9 | 8 | 9 |

18 | 10.3 | 8 | 28.3 | 7 | 12 | 9 | 13 | 12 | 9 | 13 |

19 | 7.0 | 6 | 27.3 | 7 | 8 | 8 | 8 | 10 | 9 | 11 |

20 | 5.9 | 6 | 35.0 | 8 | 9 | 10 | 10 | 10 | 8 | 11 |

21 | 5.3 | 6 | 23.5 | 7 | 9 | 8 | 9 | 10 | 8 | 10 |

22 | 2.8 | 4 | 13.3 | 5 | 9 | 8 | 10 | 9 | 9 | 9 |

23 | 38.4 | 11 | 87.7 | 11 | 10 | 9 | 12 | 12 | 10 | 13 |

24 | 7.7 | 7 | 43.6 | 9 | 10 | 9 | 12 | 13 | 10 | 13 |

25 | 6.4 | 6 | 41.2 | 9 | 12 | 8 | 13 | 10 | 8 | 11 |

26 | 5.7 | 6 | 38.6 | 8 | 13 | 7 | 13 | 11 | 8 | 12 |

27 | 5.8 | 6 | 39.3 | 8 | 12 | 7 | 13 | 11 | 8 | 12 |

28 | 6.7 | 6 | 21.7 | 7 | 10 | 8 | 11 | 10 | 9 | 11 |

29 | 12.3 | 8 | 27.1 | 7 | 11 | 9 | 12 | 12 | 10 | 13 |

**Table A2.**Results of the evaluation of areal parameters for gear metrology. The arithmetic mean and the standard deviation of the parameter on all of the teeth.

${\mathit{F}}_{\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{f},\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{H},\mathit{\alpha},\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{H},\mathit{\beta},\mathbf{S},\mathbf{left}}$ | |||||
---|---|---|---|---|---|---|---|---|

Smpl. | $\overline{\mathsf{x}}$ | $\mathsf{\sigma}$ | $\overline{\mathsf{x}}$ | $\mathsf{\sigma}$ | $\overline{\mathsf{x}}$ | $\mathsf{\sigma}$ | $\overline{\mathsf{x}}$ | $\mathsf{\sigma}$ |

1 | 31.5 | 8.1 | 9.9 | 4.5 | −14.3 | 4.2 | −9.6 | 8.8 |

2 | 29.2 | 6.9 | 10.8 | 4.3 | −10.6 | 3.9 | 9.9 | 9.1 |

3 | 21.8 | 7.1 | 11.5 | 4.1 | −3.3 | 2.1 | 7.5 | 10.0 |

4 | 49.6 | 9.3 | 9.3 | 4.8 | −33.5 | 4.3 | 10.1 | 8.2 |

5 | 32.8 | 6.4 | 7.4 | 2.9 | −18.5 | 3.5 | −7.1 | 8.9 |

6 | 25.3 | 5.5 | 12.5 | 6.1 | −8.4 | 2.7 | −7.2 | 8.0 |

7 | 76.8 | 11.6 | 9.3 | 7.5 | −64.0 | 5.0 | −14.3 | 17.8 |

8 | 54.2 | 9.0 | 6.9 | 2.9 | −36.6 | 3.9 | 10.6 | 13.7 |

9 | 59.4 | 21.4 | 19.0 | 6.1 | −7.7 | 4.8 | 39.2 | 21.5 |

10 | 21.0 | 6.6 | 10.1 | 2.2 | −3.6 | 3.3 | 8.6 | 8.3 |

11 | 22.0 | 8.6 | 12.3 | 9.6 | 5.4 | 2.9 | −9.6 | 4.9 |

12 | 37.8 | 8.0 | 27.4 | 9.4 | 3.3 | 3.6 | 4.4 | 16.1 |

13 | 44.5 | 7.1 | 9.4 | 2.8 | −27.5 | 4.5 | −10.9 | 6.3 |

14 | 42.0 | 5.7 | 8.9 | 3.1 | −22.5 | 3.1 | −12.9 | 9.3 |

15 | 54.2 | 11.3 | 20.2 | 16.3 | −32.6 | 2.9 | −9.3 | 4.0 |

16 | 57.1 | 6.8 | 8.7 | 5.6 | −49.2 | 3.1 | −7.0 | 5.7 |

17 | 44.9 | 13.3 | 11.2 | 11.7 | −32.2 | 3.2 | −5.0 | 3.0 |

18 | 62.4 | 14.3 | 17.8 | 16.8 | −32.7 | 5.0 | −18.8 | 17.6 |

19 | 24.7 | 7.9 | 12.2 | 4.4 | −3.9 | 2.3 | −10.9 | 9.9 |

20 | 26.7 | 7.2 | 10.4 | 4.1 | −8.6 | 4.1 | −9.9 | 8.4 |

21 | 25.3 | 5.4 | 11.2 | 3.6 | −6.8 | 3.6 | −9.1 | 8.5 |

22 | 28.2 | 4.9 | 11.6 | 4.7 | −11.4 | 2.0 | −7.3 | 3.8 |

23 | 63.5 | 18.8 | 22.1 | 10.2 | 17.6 | 9.0 | −42.7 | 13.8 |

24 | 67.4 | 27.7 | 14.1 | 9.2 | 15.7 | 4.1 | 12.2 | 51.8 |

25 | 56.3 | 8.2 | 6.2 | 2.9 | −43.2 | 4.2 | −11.9 | 8.2 |

26 | 72.8 | 8.8 | 6.1 | 3.4 | −67.9 | 4.3 | −11.7 | 11.9 |

27 | 62.1 | 10.0 | 6.7 | 2.6 | −44.1 | 3.7 | 16.2 | 9.6 |

28 | 45.1 | 9.8 | 14.7 | 11.1 | −18.9 | 5.8 | −16.1 | 4.8 |

29 | 54.0 | 18.2 | 22.5 | 15.6 | −26.6 | 4.1 | −9.6 | 20.6 |

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**Figure 4.**Parameter ${F}_{\mathrm{mr}}$ determination procedure, using the maximum, minimum, and ideal values of the displacement of the probing body.

**Figure 5.**The process of determining the areal parameters for the characterisation of the surface flank deviation. (

**a**) The evaluation area of the teeth. (

**b**) Transformation of the data to the roll length for evaluation of the parameters.

**Figure 6.**The parameters and relations used for the transformation to the roll length distance. M—measured points, A—points on the ideal involute, T—points on the base circle and the formed tangent.

**Figure 7.**Flank surface deviation ${F}_{\mathrm{S}}$, surface form deviation ${f}_{\mathrm{f},\mathrm{S}}$, surface profile slope deviation ${f}_{\mathrm{H},\alpha ,\mathrm{S}}$, and surface lead profile slope deviation ${f}_{\mathrm{H},\beta ,\mathrm{S}}$ determined on measured data.

**Figure 9.**(

**a**) Dependency of the parameter ${F}_{\mathrm{S},\mathrm{left}}$ on the water (mould) temperature. (

**b**) Dependency of the parameter ${f}_{\mathrm{f},\mathrm{S},\mathrm{left}}$ on the packing pressure time. (

**c**) Dependency of the parameter ${f}_{\mathrm{H},\alpha ,\mathrm{S},\mathrm{left}}$ on the water (mould) temperature. (

**d**) Dependency of the parameter ${f}_{\mathrm{H},\beta ,\mathrm{S},\mathrm{left}}$ on the injection temperature.

Parameter (Standard) | Symbol (Unit) | Delrin 100 NC010 |
---|---|---|

Density (ISO 1183) | $\rho $ (kg/m${}^{3}$) | 1420 |

Elastic modulus (ISO 527) | E (MPa) | 2900 |

Tensile yield strength (ISO 527) | ${R}_{\mathrm{m}}$ (MPa) | ≈71 |

Poisson’s ratio (ISO 527) | $\nu $ (/) | 0.37 |

Specific heat | ${c}_{\mathrm{p}}$ (J/(kgK)) | ≈3000 |

Thermal conductivity | k (W/(mK)) | ≈0.36 |

Melting temperature (ISO 11357) | ${T}_{\mathrm{m}}$ (${}^{\circ}$C) | 178 |

Lin. therm. expansion (ISO 11359) | $\alpha $ (K${}^{-1}$) | 110 × 10${}^{-6}$ |

Recommended moulding temperature | ${T}_{\mathrm{r},\mathrm{inj}}$ (${}^{\circ}$C) | 215 ± 5 |

Gear Characteristic | Symbol (Unit) | Value |
---|---|---|

Number of teeth | Z (/) | 39 |

Reference circle diameter | d (mm) | 39 |

Gear width | b (mm) | 6 |

Nominal gear hole diameter | ${d}_{\mathrm{h}}$ (mm) | 6.5 |

Normal gear module | ${m}_{\mathrm{n}}$ (mm) | 1 |

Base diameter | ${d}_{\mathrm{b}}$ (mm) | 36.648 |

Normal pressure angle | ${\alpha}_{\mathrm{n}}$ (°) | 20 |

Type of profile | / | Involute; ISO 53.2:1997 |

**Table 3.**Measured manufactured gears and the corresponding injection moulding process parameters—injection temperature, water (mould) temperature, injection speed, packing pressure, packing pressure time, and cooling time.

Sample | ${\mathit{T}}_{\mathbf{inj}}$ (${}^{\circ}$C) | ${\mathit{T}}_{\mathbf{wi}}$ (${}^{\circ}$C) | ${\mathit{v}}_{\mathbf{inj}}$ (mm/s) | ${\mathit{P}}_{\mathbf{p}}$ (Bar) | ${\mathit{t}}_{\mathbf{Pp}}$ (s) | ${\mathit{t}}_{\mathbf{c}}$ (s) |
---|---|---|---|---|---|---|

1 | 210 | 90 | 10 | 800 | 5 | 30 |

2 | 210 | 90 | 10 | 800 | 6 | 40 |

3 | 210 | 90 | 10 | 800 | 7 | 50 |

4 | 210 | 110 | 20 | 1000 | 5 | 30 |

5 | 210 | 110 | 20 | 1000 | 6 | 40 |

6 | 210 | 110 | 20 | 1000 | 7 | 50 |

7 | 210 | 130 | 40 | 1200 | 5 | 30 |

8 | 210 | 130 | 40 | 1200 | 6 | 40 |

9 | 210 | 130 | 40 | 1200 | 7 | 50 |

10 | 215 | 90 | 20 | 1200 | 5 | 40 |

11 | 215 | 90 | 20 | 1200 | 6 | 50 |

12 | 215 | 90 | 20 | 1200 | 7 | 30 |

13 | 215 | 110 | 40 | 800 | 5 | 40 |

14 | 215 | 110 | 40 | 800 | 6 | 50 |

15 | 215 | 110 | 40 | 800 | 7 | 30 |

16 | 215 | 130 | 10 | 1000 | 5 | 40 |

17 | 215 | 130 | 10 | 1000 | 6 | 50 |

18 | 215 | 130 | 10 | 1000 | 7 | 30 |

19 | 220 | 90 | 40 | 1000 | 5 | 50 |

20 | 220 | 90 | 40 | 1000 | 6 | 30 |

21 | 220 | 90 | 40 | 1000 | 7 | 40 |

22 | 220 | 110 | 10 | 1200 | 5 | 50 |

23 | 220 | 110 | 10 | 1200 | 6 | 30 |

24 | 220 | 110 | 10 | 1200 | 7 | 40 |

25 | 220 | 130 | 20 | 800 | 5 | 50 |

26 | 220 | 130 | 20 | 800 | 6 | 30 |

27 | 220 | 130 | 20 | 800 | 7 | 40 |

28 | 215 | 110 | 20 | 1000 | 6 | 40 |

29 | 220 | 130 | 40 | 1200 | 7 | 50 |

**Table 4.**Results of the evaluation of ${F}_{\mathrm{r}}$ and new parameters for the upgraded geometric characterisation of injection moulded gears. The results for the areal parameters are shown for the left flank.

Smpl. | ${\mathit{F}}_{\mathbf{r}}$ ($\mathsf{\mu}$m) | ${\mathit{F}}_{\mathbf{mr}}$ ($\mathsf{\mu}$m) | Q(${\mathit{F}}_{\mathbf{r}}$) (/) | Q(${\mathit{F}}_{\mathbf{mr}}$) (/) | ${\mathit{F}}_{\mathbf{S}}$ ($\mathsf{\mu}$m) | Q(${\mathit{F}}_{\mathbf{S}}$) (/) | ${\mathit{f}}_{\mathbf{f},\mathbf{S}}$ ($\mathsf{\mu}$m) | Q(${\mathit{f}}_{\mathbf{f},\mathbf{S}}$) (/) | ${\mathit{f}}_{\mathbf{H},\mathit{\alpha},\mathbf{S}}$ ($\mathsf{\mu}$m) | Q(${\mathit{f}}_{\mathbf{H},\mathit{\alpha},\mathbf{S}}$) (/) | ${\mathit{f}}_{\mathbf{H},\mathit{\beta},\mathbf{S}}$ ($\mathsf{\mu}$m) | Q(${\mathit{f}}_{\mathbf{H},\mathit{\beta},\mathbf{S}}$) (/) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 38.0 | 7.9 | 9 | 4 | 49.2 | 12 | 29.3 | 11 | −22.1 | 11 | −26.8 | 11 |

2 | 37.9 | 21.6 | 9 | 7 | 46.0 | 12 | 28.4 | 11 | −17.1 | 10 | 27.6 | 11 |

3 | 27.0 | 42.0 | 8 | 9 | 44.1 | 12 | 34.3 | 12 | −7.7 | 8 | 26.0 | 10 |

4 | 34.1 | −71.5 | 9 | 11 | 68.6 | 13 | 26.2 | 11 | −43.1 | 13 | 23.7 | 10 |

5 | 35.1 | −11.0 | 9 | 5 | 46.8 | 12 | 16.2 | 10 | −24.2 | 11 | −21.3 | 10 |

6 | 32.7 | 21.7 | 9 | 7 | 39.2 | 11 | 39.7 | 12 | −13.0 | 10 | −20.2 | 10 |

7 | 34.6 | −158.6 | 9 | 13 | 103.4 | 13 | 40.7 | 12 | −74.1 | 13 | −47.9 | 12 |

8 | 26.8 | −95.0 | 8 | 12 | 75.6 | 13 | 15.4 | 9 | −43.5 | 13 | 34.5 | 11 |

9 | 35.0 | 5.6 | 9 | 4 | 92.4 | 13 | 42.6 | 12 | −19.0 | 10 | 71.5 | 13 |

10 | 33.7 | 38.2 | 9 | 9 | 34.8 | 11 | 15.1 | 9 | −9.9 | 9 | 25.8 | 10 |

11 | 9.2 | 65.6 | 5 | 11 | 44.7 | 12 | 39.1 | 12 | 10.7 | 9 | −18.3 | 10 |

12 | 18.6 | 54.6 | 7 | 10 | 58.8 | 13 | 46.2 | 13 | 10.1 | 9 | 34.3 | 11 |

13 | 40.1 | −52.9 | 9 | 10 | 61.2 | 13 | 15.0 | 9 | −35.2 | 12 | −22.5 | 10 |

14 | 31.5 | −25.6 | 8 | 8 | 54.3 | 12 | 19.7 | 10 | −26.8 | 12 | −26.1 | 11 |

15 | 22.4 | −45.5 | 7 | 9 | 83.8 | 13 | 68.1 | 13 | −39.8 | 13 | −17.8 | 9 |

16 | 33.7 | −129.1 | 9 | 12 | 74.3 | 13 | 22.9 | 11 | −55.5 | 13 | −17.8 | 9 |

17 | 18.5 | −85.1 | 7 | 11 | 85.5 | 13 | 47.2 | 13 | −36.1 | 12 | −13.6 | 9 |

18 | 27.8 | −69.3 | 8 | 11 | 92.6 | 13 | 91.0 | 13 | −45.9 | 13 | −47.3 | 12 |

19 | 31.3 | 33.6 | 8 | 9 | 39.0 | 11 | 32.2 | 12 | −8.6 | 8 | −27.1 | 11 |

20 | 30.9 | 24.9 | 8 | 8 | 38.5 | 11 | 29.7 | 11 | −17.3 | 10 | −23.3 | 10 |

21 | 33.3 | 32.3 | 9 | 9 | 38.9 | 11 | 19.6 | 10 | −12.2 | 9 | −21.9 | 10 |

22 | 17.3 | −6.3 | 7 | 4 | 45.8 | 12 | 30.5 | 11 | −15.3 | 10 | −12.8 | 8 |

23 | 27.4 | 106.9 | 8 | 12 | 90.0 | 13 | 36.3 | 12 | 28.1 | 12 | −59.6 | 13 |

24 | 33.5 | 94.3 | 9 | 12 | 136.0 | 13 | 39.1 | 12 | 23.6 | 11 | −111.5 | 13 |

25 | 32.7 | −103.2 | 9 | 12 | 74.1 | 13 | 11.6 | 9 | −51.4 | 13 | −24.0 | 10 |

26 | 35.5 | −158.1 | 9 | 13 | 88.9 | 13 | 12.2 | 9 | −75.1 | 13 | −31.5 | 11 |

27 | 35.5 | −101.0 | 9 | 12 | 87.3 | 13 | 14.0 | 9 | −50.7 | 13 | 35.7 | 11 |

28 | 21.7 | −16.1 | 7 | 7 | 73.4 | 13 | 45.6 | 13 | −23.8 | 11 | −23.8 | 10 |

29 | 16.2 | −51.8 | 7 | 10 | 90.0 | 13 | 68.9 | 13 | −33.9 | 12 | −56.5 | 13 |

**Table 5.**Spearman correlation for the target parameter ${F}_{\mathrm{mr}}$. The greatest correlation is to the water (mould) temperature.

Process Parameter | Symbol | Spearman Correlation Coefficient (/) |
---|---|---|

Water (mould) T | ${T}_{\mathrm{wi}}$ (${}^{\circ}$C) | −0.791 |

Packing pressure | ${P}_{\mathrm{p}}$ (Bar) | +0.317 |

Packing pressure time | ${t}_{\mathrm{Pp}}$ (s) | +0.270 |

Injection speed | ${v}_{\mathrm{inj}}$ (mm/s) | −0.167 |

Cooling time | ${t}_{\mathrm{c}}$ (s) | +0.113 |

Injection T | ${T}_{\mathrm{inj}}$ (${}^{\circ}$C) | +0.087 |

**Table 6.**Spearman correlation for the target areal parameters. Water (mould) temperature has a generally high impact on the quality parameter values.

Spearman Correlation for Areal Parameters | ||||
---|---|---|---|---|

Process Parameter | ${\mathit{F}}_{\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{f},\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{H},\mathbf{\alpha},\mathbf{S},\mathbf{left}}$ | ${\mathit{f}}_{\mathbf{H},\mathbf{\beta},\mathbf{S},\mathbf{left}}$ |

Water (mould) T | +0.789 | +0.030 | −0.756 | −0.104 |

Cooling time | −0.238 | +0.002 | +0.219 | +0.185 |

Packing pressure time | +0.230 | +0.455 | +0.229 | +0.123 |

Packing pressure | +0.162 | +0.395 | +0.373 | −0.019 |

Injection speed | −0.074 | −0.088 | −0.183 | −0.013 |

Injection T | +0.066 | −0.116 | +0.098 | −0.414 |

Regression Coefficients | ||||||
---|---|---|---|---|---|---|

Areal Parameter | A (µm/${}^{\circ}$C) | B (µm/${}^{\circ}$C) | C (s/10^{3}) | D (µm/Bar) | E (µm/s) | F (µm/s) |

${F}_{\mathrm{S},\mathrm{left}}$ | −0.315 | 1.032 | −0.205 | 0.024 | 6.276 | −0.885 |

${f}_{\mathrm{f},\mathrm{S},\mathrm{left}}$ | −0.264 | 0.131 | −0.108 | 0.027 | 10.800 | −0.329 |

${f}_{\mathrm{H},\alpha ,\mathrm{S},\mathrm{left}}$ | −0.117 | −1.093 | −0.462 | 0.062 | 7.956 | 0.550 |

${f}_{\mathrm{H},\beta ,\mathrm{S},\mathrm{left}}$ | −0.249 | −0.117 | 0.270 | −0.010 | 4.300 | 0.740 |

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## Share and Cite

**MDPI and ACS Style**

Urbas, U.; Zorko, D.; Vukašinović, N.; Černe, B.
Comprehensive Areal Geometric Quality Characterisation of Injection Moulded Thermoplastic Gears. *Polymers* **2022**, *14*, 705.
https://doi.org/10.3390/polym14040705

**AMA Style**

Urbas U, Zorko D, Vukašinović N, Černe B.
Comprehensive Areal Geometric Quality Characterisation of Injection Moulded Thermoplastic Gears. *Polymers*. 2022; 14(4):705.
https://doi.org/10.3390/polym14040705

**Chicago/Turabian Style**

Urbas, Uroš, Damijan Zorko, Nikola Vukašinović, and Borut Černe.
2022. "Comprehensive Areal Geometric Quality Characterisation of Injection Moulded Thermoplastic Gears" *Polymers* 14, no. 4: 705.
https://doi.org/10.3390/polym14040705