# Multiscale Topography Analysis of Waterjet Pocketing of Silica Glass Surfaces

Antoine Brient, Romain Laniel, Mathieu Miroir, Gaëtan Le Goïc,
Jean-Christophe Sangleboeuf, Serge Samper

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Antoine Brient, Romain Laniel, Mathieu Miroir, Gaëtan Le Goïc, Jean-Christophe Sangleboeuf, et al.. Multiscale Topography Analysis of Waterjet Pocketing of Silica Glass Surfaces. 15th International Conference on Metrology and Properties of Engineering Surfaces, Mar 2015, Charlotte, United States. hal-01136081

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# Multiscale Topography Analysis of Waterjet Pocketing of Silica Glass Surfaces

Antoine Brient, Romain Laniel, Mathieu Miroir, Gaetan Le Goic, Jean-Christophe Sangleboeuf, Serge Samper

IPR, UMR 6251, Université de Rennes 1, Campus de Beaulieu, Bat. 10B, 35042 Rennes, France

LE2I, UMR 6306, Université de Bourgogne

E-mail: antoine.brient@univ-rennes1.fr

**Abstract.** Glass workpieces are mainly planar and obtained by diamond cutting however if free-form surfaces are required, manufacturing process is usually based on shaping grinding wheels. Multi-axis waterjet cutting, an other means of obtaining planar workpieces, could also be used to machine complex shapes with appropriate manufacturing strategies. Water jet pocketing could also be achieved but it brings challenging issues since the high pressure jet composed of water and abrasive particles must be contained inside the machined pocket. Water jet glass machining optimization requires understanding of numerous parameters such as interaction between the jet and the brittle material behavior or the identification of the jet himself. We focus our investigation on bottom pocket surfaces to study these parameters. Pocket bottom surfaces are characterized by multi-scale defects: shape defects influenced by the tool path and the manufacturing strategy, macro-craters at waviness scale due to the jet interactions, micro-craters at roughness scale due to particles impacts, sub-surface damages (SSD) at micro-roughness scale. This paper focuses on the study of macro and micro craters. We propose a decomposition of the multi-scale defects using modal filtering. Residual topography will then be analyzed to characterize the surface damages.

## 1. Introduction

Waterjet manufacturing process is used to achieve cutting of various materials by means of a high-pressure waterjet optionally mixed with abrasive grains. The waterjet flows from a pump to a cutting head where abrasive grains can be added in a mixing chamber before the abrasive waterjet is expelled through the nozzle. If abrasive waterjet can cut samples with a thickness of several tens of millimeters, it can also and paradoxically, achieve pocket milling by defining appropriate machining parameters that would allow the material not to be pierced through.

One of the advantages of waterjet machining, the lack of thermal distortion on the workpiece, as well as the machining versatility of this process has lead to investigate the industrial feasibility of metallic workpieces waterjet milling [2]. The manufacturing strategy as well as the cutting head speed are obviously key parameters to achieve pocketing but many other parameters also influence the quality of the surface finish [3] [4].

Abrasive waterjet is also widely used for brittle materials cutting however abrasive waterjet pocketing of glass has not yet been achieved. Brittleness of glass brings challenging issues when material removal process is involved (e.g. grinding [1]). Smooth surface finish, in particular, is
hard to obtained since material removal would induce surface damages as well as sub-surface
damages (SSD). Being able to shape a glass workpiece with the versatility of a 5-axis cutter
would bring innovative prospects for glass industry.

We propose to study the influence of the machining parameters on the surface finish of pockets. Abrasive waterjet machining induces different scales of damages that need to be characterize accordingly. Previous studies carried out on waterjet pocketing have mainly only used roughness average to characterize surface finish. We will discuss the relevancy of the roughness parameters with regards to the machining process and the workpiece material.

## 2. Manufacturing process parameters

A series of experiments has been achieved to investigate waterjet machining influence on surface finish using a Flow™ Mach3 waterjet machine with the following parameters :

* Water orifice diameter : 0.76 mm

* Stand-off distance : 20 mm

* Abrasive mass flow rate : 2218,4 g/min

* Abrasive material grain size : 120 mesh

* Abrasive material type : garnet

* Angle of impact : 0 rad (normal to the sample surface)

* Zig-zag machining strategy

* Pressure inside the pumping system : 35 MPa

* Traverse speed : 750 ; 1500 ; 3000 ; 4000 mm/min corresponding to samples 4 ; 3 ; 2 ; 1 respectively

Pockets of 90 mm width, 110 mm length and various depth have been machined on 110 × 130 × 7 mm³ Planilux™ glass samples. This material is characterized by a Vickers hardness Hv of 1,500 GPa, and a fracture toughness KIC of 0.71 MPa·m¹/².

## 3. Topography analysis

Glass samples pocket bottom surfaces topography has been acquired using an Alicona InfiniteFocus 3-D contactless measuring system. The measured area has been restricted to the pocket center to observe the surface finish resulting of a stabilized machining process. Aspect of surface finish is characterized by damages at different scales :

* form defect : at the largest scale, a slightly convex form defect

* textured waviness : an alternation of mounts and craters

* roughness : high $R_{vk}$, low $R_{pk}$ typical of machined brittle material

* SSD : sub surface damage is commonly observed on brittle material. They can induce cracking when the workpiece is loaded [1].

This study focuses on the roughness and waviness scales. Two methods have been used to identify the different scales of damages : a standard gaussian filter based approach and a modal approach.
## 4. Gaussian filter based approach

The complexity of the surface finish lead us to investigate the relevancy of the cut-off value to separate the damages scale. Figure 1 shows a surface finish profile waviness for two standard cut-off values: $\lambda_c = 2.5$ mm ; $\lambda_c = 0.8$ mm. The 2.5 mm cut-off roughness profile shows some waviness that still need to be filtered. A 0.8 mm cut-off gives better results where roughness and waviness are well separated without reducing significantly the roughness amplitude in one hand. In the other hand, the topographies of waviness and roughness is close to the observed macro-craters (waviness) and individual impact (roughness) shapes.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Roughness filtered for two different cut-off on a profile of sample 2.</figcaption></figure>

Additionally, depth distribution for different samples acquired with a Taylor Hobson mechanical profilometer has been plotted for $\lambda_c = 2.5$ mm and $\lambda_c = 0.8$ mm (c.f. figure 2). Depth distribution obtained after 0.8 mm cut-off high-pass filtering have a better correlation coefficient with a Gaussian fit. All results based on a Gaussian filter presented afterwards have been filtered with this value.

Surface finish characterization protocol is described on figure 3.

Characterization of the surface finish needs to be based on appropriate parameters to give relevant results. At roughness scale, machining of glass usually induces surface finishes characterized by a low amount of peaks broken by the cutting forces and the presence of cracks at roughness scale. Abbott-Firestone derived parameters $S_{pk}$, $S_k$ and $S_{vk}$ provide a good evaluation of these aspects [1]. Moreover, valleys depth is linked to SSD, so $S_{vk}$ parameter gives a good assumption of the SSD size [6].

Waterjet machined pocket bottom of the first series of experiments have been measured. 0.8 mm cut-off high-pass filtered surfaces roughness parameters $S_k$, $S_{pk}$ and $S_{vk}$ values are plotted on Figure 5. All parameters show a slight increase with regards to the transverse speed.

A watershed analysis of roughness has also been carried out. The valleys mean diameter is close to the size of damage area of an elementary impact (c.f. figure 4). This result supports our hypothesis of a cut-off value set at 0.8 mm.

At waviness scale, surface finish of the waterjet machined pockets shows an alternation of craters and mounts. We propose to evaluate the waviness surface obtained with a 0.8 mm cut-off low-pass filter with material and void volumes parameters obtained from the Abbott-Firestone curve $V_{mp}$, $V_{mc}$, $V_{vc}$, $V_{vv}$ [8]. Figure 5 shows the evolution of these parameters with regards to transverse speed. When speed increases, material volumes of peaks and core roughness as well as void volumes of valleys and core roughness tend to decrease. Interestingly, the decrease of the four parameters is very similar, and the ratio between material and void stays roughly the same. Waviness amplitude is assessed by summing $S_{pk}$, $S_k$ and $S_{vk}$ to filter outlier. It also
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Depth distribution for several profilometric data and for two different cut-off. The corelation coefficient with a Gaussian fit is given.</figcaption></figure>

tends to decrease with transverse speed. Overall this shows that the surface waviness amplitude decreases with transverse speed while keeping its "craters and mounts" aspect.

**5. Modal filter based approach**

The modal method [7], is a 3D topographic filtering method based on the dynamic modal shapes (natural eigen shapes) of surfaces. Here, we have used the modal shapes of a square surface. The modal eigen shapes of any structural object define a set of shapes that have very interesting properties applied to topography:

* First of all, this geometric basis of shapes is built automatically.

* All modal shapes are independent from each other.

* Globally, their shape complexity is sorted by their number (i.e. modal coefficients decrease according to the their number/order generally quickly in the same way than Fourier methods).

* All possible measured surface is fully decomposable in its corresponding modal basis.

* The initial surface is an addition of all filtered surfaces. Thus, non filtered (initial) surface is the addition of form, waviness and roughness surfaces.

In fig 6, the filtering process begins with the creation of a modal basis of the ideal (square here) surface. This preliminary operation is made only one time (modal database creation). Then we calculate the projection of the topography deviations in the modal basis (vectorial operation in a non orthonormal basis). The results are modal coordinates. The later can be observed as a list of values (coordinates in a n modal dimension space) or as a spectrum (Fourier like representation).
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Analysis approach of Gaussian filtered surfaces of sample 1.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Comparison of averaged width of valley $\bar{d}_{val} \simeq 160$ µm and size of damage area of elementary impact $\bar{d}_{imp} \simeq 100$ µm.</figcaption></figure>

We usually use the modal filtering to filter three surfaces, form, waviness and roughness, but it can be used to filter more or less levels. The separated shapes are subtracted to each other. Their addition give the initial surface. Thus the filtered process of surfaces are not dependents.
<figure><img src="image_6.png" /><figcaption>**Figure 6.** Analysis approach of Modal filtered surfaces of sample 1.</figcaption></figure>

<table><caption>**Table 1.** Comparison of waviness and roughness parameters for the Gaussian and the Modal filters.</caption><thead><tr><th rowspan="2">Filter</th><th rowspan="2">Sample</th><th colspan="4">Waviness parameters [µm]</th><th colspan="3">Roughness parameters [µm]</th></tr><tr><th>V<sub>mp</sub></th><th>V<sub>mc</sub></th><th>V<sub>vc</sub></th><th>V<sub>vv</sub></th><th>Amp.</th><th>S<sub>k</sub></th><th>S<sub>pk</sub></th><th>S<sub>vk</sub></th></tr></thead><tbody><tr><td rowspan="4">Gauss</td><td>1</td><td>1.2649</td><td>24.793</td><td>32.581</td><td>3.4009</td><td>126.648</td><td>25.262</td><td>8.6693</td><td>12.2</td></tr><tr><td>2</td><td>1.5537</td><td>28.108</td><td>38.489</td><td>3.3192</td><td>139.753</td><td>25.357</td><td>8.5298</td><td>12.439</td></tr><tr><td>3</td><td>1.5084</td><td>29.925</td><td>38.949</td><td>3.8901</td><td>147.587</td><td>22.744</td><td>8.091</td><td>10.627</td></tr><tr><td>4</td><td>1.5397</td><td>29.798</td><td>40.045</td><td>4.24</td><td>153.166</td><td>21.118</td><td>7.5195</td><td>9.203</td></tr><tr><td rowspan="4">Modal</td><td>1</td><td>0.944</td><td>22.3</td><td>30.6</td><td>2.99</td><td>107.4</td><td>30.8</td><td>9.95</td><td>14.7</td></tr><tr><td>2</td><td>1.29</td><td>23.0</td><td>30.3</td><td>3.06</td><td>116.4</td><td>30.2</td><td>9.96</td><td>15.5</td></tr><tr><td>3</td><td>1.19</td><td>27.0</td><td>35.6</td><td>3.25</td><td>126.8</td><td>27.4</td><td>9.37</td><td>14.3</td></tr><tr><td>4</td><td>1.27</td><td>26.8</td><td>35.5</td><td>3.09</td><td>125.3</td><td>22.7</td><td>7.81</td><td>13.0</td></tr></tbody></table>

scale damages. At roughness scale, $S_k$, $S_{vk}$, $S_{pk}$ give relevant informations of the surface characteristics. Cracks, peaks and core roughness tend to increase in the same proportions when transverse speed increases. At waviness scale the increase of transverse speed limits the material removal and therefore the amplitude of the waviness. The material and void volume ratio remains the same despite the waviness amplitude decrease. Both modal and Gaussian filtering methods provide relevant results. Influence of the machining parameters could be combined. A wider analysis based on design of experiments will be carried out in future work. It will also take into account others manufacturing parameters such as stand-off distance. Sub-surface damages
scale has not been presented here. However they have been observed (c.f. micrography in figure
7) and a further work will be to investigate the relationship between roughness, SSD, mechanical
toughness of machined part.

<figure><img src="image_7.png" /></figure>

**Figure 7.** In the case of grind milling process, the *S*<sub>vk</sub> parameter from the Abbott-Firestone curve can outcome the presence of sub surface damages. Is it the same in the case of water-jet pocketing ?

References

[1] A. Brient, M. Brissot, J.-C. Sangleboeuf, Service life of glass workpieces- influence of the grinding parameters on the surface roughness and the fracture strength

[2] G.A Escobar-Palafox, Characterisation of abrasive water-jet process for pocket milling in Inconel 718

[3] Hlavac et al, Experimental method for the investigation of the abrasive water jet cutting quality, Journal of Materials Processing Technology 209, pp. 6190-6195, 2009

[4] M.C. Kong, D. Axinte, W. Voice, An innovative method to perform maskless plain waterjet milling for pocket generation: a case study in Ti-based superalloys, IJMTM 51 (2011) 642648

[5] J. Folkes, Waterjet An innovative tool for manufacturing, Journal of Materials Processing Technology 209 (2009) 61816189

[6] Laheurte, R., Darnis, P., Darbois, N., Cahuc, O. and Neauport, J. (2012) Subsurface damage distribution characterization of ground surfaces using Abbott-Firestone curves, Optics Express, Vol. 20, No. 12, pp.1355113559.

[7] G. Le Goic, H. Favreliere, S. Samper, F. Formosa, Multi scale modal decomposition of primary form, waviness and roughness of surfaces, Scanning Vol. 33 pp 332-341, 2011

[8] F. Blateyron, Characterisation of areal surface texture, Edited by Richard Leach, 01/2013: chapter The Areal Field Parameters: pages 15-43; Springer., ISBN: 978-3-642-36457-0