# Variation of Grain Height Characteristics of Electroplated cBN Grinding-Wheel Active Surfaces Associated with Their Wear

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment

#### 2.2. Examination of Surface Texture

- 35 parameters of texture joined to the SPIP 6.4.2 software library using own developed procedures (scripts):
- –
- –
- Smc(mr)—the height of surface (elevation value) for a bearing area value mr, for $mr$ obtaining values from $5\%$ to $95\%$ with step $5\%$ (computed according to the ISO 25178-2:2012 standard [36]);
- –
- Smc(mr1_mr2)—average value of elevation between two bearing area values mr1 and mr2 (expressed with Formula (1)): Smc(0_5), Smc(0_10), Smc(0_15), Smc(0_20), Smc(0_30), Smc(0_40);$$Smc(mr1\_mr2)=\frac{{\sum}_{i=1}^{n}{h}_{i}}{n}$$
- –
- dSmc(mr1_mr2)—relative average value of elevation between two bearing area values mr1 i mr2 (where $\mathit{mr}2>\mathit{mr}1$), assuming elevation value equal 0 on the level associated with Smc(mr2) (expressed with Formula (2)): dSmc(0_5), dSmc(0_10), dSmc(0_15), dSmc(0_20), dSmc(0_30), dSmc(0_40).$$dSmc(mr1\_mr2)=\frac{{\sum}_{i=1}^{n}{h}_{i}-Smc\left(mr2\right)}{n}$$

- the base area of the islands: mean value $\mathit{Am}$, standard deviation $\mathit{Asd}$, the percentage of islands in the entire area of analysis $\mathit{A}\%$;
- the volume of the islands V: sum value $\mathit{Vsum}$, mean value $\mathit{Vm}$, standard deviation $\mathit{Vsd}$;
- the maximum height of the island $\mathit{Zmax}$: average value for all islands $\mathit{Zmax}\_\mathit{m}$, standard deviation value of all islands $\mathit{Zmax}\_\mathit{sd}$;
- the average altitude of the island $\mathit{Zmean}$: average value for all islands $\mathit{Zmean}\_\mathit{m}$, standard deviation value of all islands $\mathit{Zmean}\_\mathit{sd}$;
- equivalent diameter of the islands $\mathit{dD}$ (diameter of a circle with the same surface area as the island): average value $\mathit{dDm}$, standard deviation $\mathit{dDsd}$;
- the largest Ferret diameter of the islands $\mathit{dF}$: mean value $\mathit{dFm}$, standard deviation $\mathit{dFsd}$;
- the length of the islands L defined in [45]: mean value $\mathit{Lm}$, standard deviation $\mathit{Lsd}$;
- the width of the islands B defined in [45]: mean value $\mathit{Bm}$, standard deviation $\mathit{Bsd}$;
- the circumference of the islands P: mean value $\mathit{Pm}$, standard deviation $\mathit{Psd}$;
- the distance to the nearest island $\mathit{ND}$: mean value $\mathit{NDm}$, standard deviation $\mathit{NDsd}$;
- the number of islands Lw.

## 3. Results and Discussion

#### 3.1. Forms of Grinding Wheel as Wear

- grain crushing,
- grain grinding,
- breaking grains from the binder.

#### 3.2. The Selection of Parameters Sensitive to Wear of Grinding-Wheel AS

- Fisher testem (F test),
- Greenhouse–Geisser test (G-G test).

#### 3.3. Model Relations Concerning Wear Depending on Adjustable Process Parameters

- 4 main linear effects: ${v}_{s}$, ${v}_{w}$, ${a}_{e}$ and ${V}^{\prime}$;
- 3 effects, related to squares of variables: ${v}_{w}\xb7{v}_{w}$, ${v}_{s}\xb7{v}_{s}$ and ${V}^{\prime}\xb7{V}^{\prime}$;
- 2 interaction effects: ${v}_{w}\xb7{v}_{s}$ and ${v}_{w}\xb7{a}_{e}$.

- grinding speed ${v}_{s}$ decreased,
- grinding depth ${a}_{e}$ increased,
- feed ${v}_{w}$ increased,
- specific material loss ${V}^{\prime}$ increased.

## 4. Conclusions

- In the conducted tests, the highest sensitivity to changes in grinding-wheel AS caused by wear was shown by the average value of the mean island heights Zmean_m (Table 3).
- This decrease in Zmean_m and Spk was related to the loss of abrasive resulting from various types of wear processes. In the presented studies, the above-mentioned parameters changed mainly due to grain breaking and, to a lesser extent, due to tearing them out of the binder (Section 3.1).
- As wheel wear increased, the Spk parameter, compared to Zmean_m, became less susceptible to grinding-wheel AS changes (Figure 7). The analysis of grinding-wheel AS state based on Spk with high wear is therefore more error-prone than would be the case with the value of the parameter Zmean_m.
- The Zmean_m parameter turned out to be a better measure of wear than Spk (Table 4), especially in the case of large sticking areas (Section 3.2, p. 11).
- Without taking into account the grinding wheel on which very large areas of sticking were observed, the average relative change Zmean_m on a given grinding wheel was almost 11% greater than the change in parameter Spk (Section 3.2, p. 11).
- The developed polynomial models of the response surface linking Zmean_m and Spk with the process parameters and the specific material loss were very well suited to the empirical data (${R}^{2}=0.95$ and 0.94).
- The developed polynomial models linking textitZmean_m and Spk with the process parameters and the specific material loss were well suited to the empirical data (${R}^{2}=0.74$ and 0.70).
- The tendencies of the influence of the adjustable process parameters on the grinding-wheel wear predicted by the models can be explained in the context of physics of the grinding process. They are consistent with the general grinding theory. Reducing ${v}_{s}$ and increasing ${v}_{w}$ and ${a}_{e}$ lead to a greater load operating on the wheel. In turn, the bigger forces acting on the abrasive grains contribute to their faster wear (Section 3.3).
- The effect of the specific material loss ${V}^{\prime}$ on the parameters Zmean_sr and Spk is greater for its small values. This effect results from the greater wear intensity in the initial phase of the grinding wheel’s work (Figure 8).

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AS | Active surface |

EXP | Exponential |

SD | Second-degree |

SLGW | Single-layer grinding wheel |

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**Figure 1.**Grains on a new grinding wheel (

**top**) and after grinding using that wheel (

**bottom**): visible wear due to breaking grains from the binder (views of 3D texture maps).

**Figure 2.**Abrasive grain on the grinding-wheel AS before grinding (

**top**) and after grinding using that wheel (

**bottom**): visible wear due to grain crushing (views obtained from replicas).

**Figure 4.**Abrasive grain before grinding (

**top**) and after grinding (

**bottom**): visible wear due to grain grinding and grain crushing (view obtained from replica).

**Figure 7.**Graphical representation of a linear regression equation for individual grinding wheels (${R}^{2}=0.79$) showing the change in $\delta $Zmean_m$-\delta $Spk depending on the specific material loss ${V}^{\prime}$.

**Figure 8.**Dependence of Zmean_m and Spk on grinding speed ${v}_{s}$ as well as specific material loss ${V}^{\prime}$ with ${a}_{e}=18\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{m}$ and ${v}_{w}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{m}/\mathrm{min}$.

Grinding conditions | |
---|---|

Grinder | Fortis firmy Michael Deckel |

Type of process | plane grinding |

Processing liquid | grinding oil |

Grinding speed ($d=100\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$) | ${v}_{s}=20$–$40\phantom{\rule{0.166667em}{0ex}}\mathrm{m}/\mathrm{s}$ |

Feed speed | ${v}_{w}=1$–$7.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m}/\mathrm{min}$ |

Grinding depth | ${a}_{e}=7$–$30\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{m}$ |

Grinding wheel | |

Shape | conical |

Cone angle | ${140}^{\circ}$ |

Max. diameter d | 100 mm |

Binder | electroplated (Ni) |

Abrasive | cBN |

Grain number | B35 |

Workpiece | |

Material | Pyrowear 53 |

Treatment | thermo-chemical treatment |

Hardness | 81 HRA |

Material of replicas | RepliSet-F5 by Struers |

Resolution of replicas | $0.1\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{m}$ |

Measurement microscope | InfiniteFocus G4 by Alicona |

Lens | $\times 20$ |

Measurement area | 2.35 mm × 2.59 mm |

Vertical resolution | 5 $\mathsf{\mu}\mathrm{m}$ |

Horizontal resolution | 3.91 $\mathsf{\mu}\mathrm{m}$ |

Pixel size | 0.44 $\mathsf{\mu}\mathrm{m}$ × 0.44 $\mathsf{\mu}\mathrm{m}$ |

**Table 3.**Mean values of ranks assigned to surface texture parameters, islands and pores for which the null hypothesis ${\mathrm{H}}_{0}$ was rejected. The sign (−) next to the parameter name means that its value decreased with the wear of the grinding wheel. The sign (+) indicates the opposite relationship.

Parameter AS | Mean of Ranks | Parameter AS | Mean of Ranks | Parameter AS | Mean of Ranks | |||
---|---|---|---|---|---|---|---|---|

Zmean_m | (−) | 1.5 | Sa | (−) | 36.5 | $\mathit{dDsd}\left(\mathit{p}\right)$ | (−) | 62 |

$\mathit{Zmean}\_\mathit{sd}$ | (−) | 1.5 | Zmean_sd(p) | (+) | 37 | $\mathit{Lsr}\left(\mathit{p}\right)$ | (−) | 62.5 |

$\mathit{Zmax}\_\mathit{m}$ | (−) | 3 | Svi | (+) | 37.5 | $\mathit{dFsr}\left(\mathit{p}\right)$ | (−) | 63 |

Vsr | (−) | 4 | Sq | (−) | 38 | Ssc | (−) | 65 |

dSmc(0_30) | (−) | 7.5 | Smc(_40) | (+) | 39 | Sfd | (−) | 67.5 |

Smc(0_5) | (−) | 7.5 | Smr1 | (−) | 40 | Bsr | (−) | 68.5 |

Smc(_60) | (+) | 8.5 | Sk | (−) | 40.5 | Vsr(p) | (+) | 69 |

dSmc(0_20) | (−) | 9 | Vsum | (−) | 41 | Asr(p) | (−) | 69 |

dSmc(0_15) | (−) | 10 | Smc(_15) | (−) | 41.5 | Smc(_25) | (−) | 72 |

Smc(_65) | (+) | 10 | Zmax_sd | (−) | 43.5 | NDsr | (+) | 73 |

Smc(_55) | (+) | 10.5 | Sdc5_10 | (−) | 44 | Bsr(p) | (−) | 73 |

dSmc(0_40) | (−) | 11.5 | Smc(_85) | (+) | 44.5 | Asd(p) | (−) | 74 |

Smc(0_10) | (−) | 13 | Zmax_sd(p) | (+) | 45 | dDsr(p) | (−) | 74.5 |

Smc(_70) | (+) | 15.5 | Zmean_m(p) | (+) | 45 | S10z | (−) | 75 |

Vsd | (−) | 15.5 | Zmax_m(p) | (+) | 46 | Str37 | (−) | 75.5 |

Smc(_50) | (+) | 16.5 | Sp | (−) | 46.5 | Sz_tph | (−) | 76 |

Spk | (−) | 16.5 | Vmc | (−) | 47.5 | St | (−) | 77 |

Smc(0_15) | (−) | 17 | Sdq6 | (−) | 48 | Vvv | (+) | 77 |

dSmc(0_10) | (−) | 20 | Sdq | (−) | 49.5 | Zmean_m(s) | (−) | 78 |

Smc(0_20) | (−) | 20.5 | S3A | (−) | 50.5 | dDsr | (−) | 79 |

Vmp | (−) | 21 | Sdr | (−) | 51.5 | Vsum(p) | (+) | 81 |

Smc(_75) | (+) | 22.5 | Smc(_20) | (−) | 52.5 | A%(p) | (−) | 81.5 |

dSmc(0_5) | (−) | 23 | Sci | (−) | 54 | NDsd | (+) | 82 |

Sdc10_50 | (−) | 25 | Smr2 | (−) | 54 | Sds | (−) | 84.5 |

Smc(0_30) | (−) | 25.5 | Sdc0_5 | (−) | 56 | Str20 | (−) | 85 |

Smc(_45) | (+) | 26.5 | Smc(_90) | (+) | 57 | dFsr | (−) | 87 |

Vvc | (−) | 27 | Sbi | (+) | 57 | Asr | (−) | 88 |

Smc(_5) | (−) | 28.5 | Zmax_(s) | (−) | 58 | Lsr | (−) | 88.5 |

Smc(0_40) | (−) | 29.5 | Svk | (+) | 58.5 | Sv | (+) | 90.5 |

Ssk | (−) | 31.5 | Psd(p) | (−) | 59 | Smc(_95) | (+) | 92 |

A% | (−) | 31.5 | Psr(p) | (−) | 59 | Zmax_sd(s) | (−) | 93 |

Smc(_80) | (+) | 32.5 | dFsd(p) | (−) | 60 | Psr | (−) | 94 |

Lw | (−) | 32.5 | Lsd(p) | (−) | 60.5 | Shw | (+) | 94.5 |

Smc(_10) | (−) | 34.5 | Smc(_35) | (+) | 61 | Scl37 | (+) | 96 |

**Table 4.**Selected statistical characteristics of the relative change of parameters Zmean_m and Spk as well as differences between them.

Relative Change | Mean | Min | Max |
---|---|---|---|

$\delta $Zmean_m [%] | 50.6 | 22.3 | 73.5 |

$\delta $Spk [%] | 39.7 | 19.8 | 56.4 |

$\delta $Zmean_m$-\delta $Spk [%] | 12.4 | 2.5 | 34.7 |

**Table 5.**The adjustable process parameters with which the grinding wheels worked, excluded from the regression analysis, and the specific volume of the material they ground.

Lp. | ${\mathit{v}}_{\mathit{s}}$ [m/s] | ${\mathit{v}}_{\mathit{w}}$ [m/min] | ${\mathit{a}}_{\mathit{e}}$ [$\mathsf{\mu}$m] | ${\mathit{V}}^{\prime}$ [mm${}^{3}$/mm] |
---|---|---|---|---|

1 | 20 | 7.50 | 20 | 5 |

2 | 20 | 4.25 | 20 | 58 |

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**MDPI and ACS Style**

Bazan, A.; Kawalec, A.; Rydzak, T.; Kubik, P.
Variation of Grain Height Characteristics of Electroplated cBN Grinding-Wheel Active Surfaces Associated with Their Wear. *Metals* **2020**, *10*, 1479.
https://doi.org/10.3390/met10111479

**AMA Style**

Bazan A, Kawalec A, Rydzak T, Kubik P.
Variation of Grain Height Characteristics of Electroplated cBN Grinding-Wheel Active Surfaces Associated with Their Wear. *Metals*. 2020; 10(11):1479.
https://doi.org/10.3390/met10111479

**Chicago/Turabian Style**

Bazan, Anna, Andrzej Kawalec, Tomasz Rydzak, and Pawel Kubik.
2020. "Variation of Grain Height Characteristics of Electroplated cBN Grinding-Wheel Active Surfaces Associated with Their Wear" *Metals* 10, no. 11: 1479.
https://doi.org/10.3390/met10111479