Nano-finishing of BK7 optical glass using magnetic abrasive finishing process Farzad Pashmforoush and Abdolreza Rahimi* Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran *Corresponding author: [email protected] Received 9 December 2014; revised 1 February 2015; accepted 2 February 2015; posted 4 February 2015 (Doc. ID 229406); published 12 March 2015

BK7 is an optical glass extensively used in lens manufacturing. In this work, magnetic abrasive finishing (MAF) method was utilized for finishing of this hard-to-machine material and the effect of various process parameters on surface roughness was investigated using response surface methodology. The best surface roughness value achieved was 23 nm. Among various finishing parameters, the abrasive size was found to be the most significant parameter followed by machining gap, magnetic particles size, rotational speed, and percentage weight of binding agent. Also, the mechanisms of material removal were studied by using atomic force microscopy (AFM). The AFM observations revealed that both microcutting and microfracture mechanisms might exist during MAF of brittle materials depending on the finishing conditions. © 2015 Optical Society of America OCIS codes: (220.4610) Optical fabrication; (220.5450) Polishing; (120.6660) Surface measurements, roughness. http://dx.doi.org/10.1364/AO.54.002199

1. Introduction

Advanced engineering materials such as ceramics, composites, glasses, and so on are widely used in various high-tech industries. In this regard, BK7 optical glass is a hard-to-machine material extensively used in lens manufacturing. Due to the brittle nature of glass, conventional grinding and lapping processes are usually performed in brittle mode leading to surface and subsurface damages [1–3]. Hence, application of advanced finishing techniques is inevitable for efficient and precise finishing of this material. Magnetic abrasive finishing (MAF) is one of the advanced machining processes efficiently used for finishing of both magnetic and nonmagnetic materials. In this process, material removal takes place through nanoscale/microscale indentations in the presence of a controllable magnetic field generated via a permanent or an electronic magnet [4]. The cutting tool is a flexible magnetic abrasive brush formed 1559-128X/15/092199-09$15.00/0 © 2015 Optical Society of America

from magnetic abrasive particles (MAPs). MAPs themselves are made up of ferromagnetic particles such as iron powders and abrasive grains such as SiC, Al2 O3 , and so on. There are typically two types of MAPs, namely bonded and unbounded [5,6]. In unbounded type, a homogeneous mixture of iron powders and abrasive particles acts as the cutting tool. In bonded type, the mixture of iron powders and abrasive particles are sintered in furnace, followed by crushing and sieving. The sintering process leads to embedding of abrasives into iron particles [7]. According to [8] bonded type of MAPs results in better surface finish, while unbounded type yields higher material removal rate [8]. In MAF process, there are two kinds of forces that have direct effect on the creation of finished surface, namely normal force and cutting force. The normal force is responsible for nanoscale/microscale indentation of abrasives on the specimen surface, while cutting force is responsible for shearing off the peaks of the specimen top surface during rotation of magnetic brush. Due to the very low and controllable forces presented in MAF process, the technique is capable 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS

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of producing very smooth surface on the nanometer scale. This method has been successfully applied for finishing of different types of hard-to-machine materials such as ceramics, stainless steels, high-carbon steels, composites, and so on [9–13]. Also, a few studies have been performed toward polishing of glass using magnetic-field-assisted processes [14–17]. Hence, in this work the performance of MAF process as an efficient and cost-effective method was evaluated during finishing of BK7 optical glass. Also, the effect of process parameters on surface roughness was studied using response surface methodology (RSM) and an empirical model was developed to express surface roughness as a function of process parameters such as machining gap, rotational speed, abrasive size, MAP size, and percentage weight of binding agent. In the present work, in addition to statistical analysis and modeling of MAF process, the material removal mechanisms were also investigated during finishing of BK7 optical glass. In general, material removal mechanisms involved in finishing process of brittle materials can be classified as: brittle mode and ductile mode. In brittle (fracture) mode, chipping is accomplished through lateral cracking that initiate from the bottom of the plastic zone beneath the abrasive and propagate to the workpiece surface [18]. In contrast to brittle mode, ductile mode machining is associated with micro cutting mechanism which yields a high quality surface with less surface roughness and damages [19,20]. Therefore, it is of great importance to process brittle materials such as BK7 optical glass in ductile mode. According to the studies of [21], there is a critical depth of cut below which the machining of brittle materials is taken part in ductile manner. When the depth of cut is below the critical depth, the energy required for plastic deformation is less than the energy required for crack propagation and hence the plastic deformation is the dominant material removal mechanism. In addition to energy balance concept, there is another hypothesis that describes the machining mode of brittle materials from the view of stress field [22]. If the uncut chip thickness is sufficiently small, the critical stress field is small to suppress fracture [23]. The magnitude and state of the stress field induced in the workpiece are strongly dependent on the machining forces acting on the surface of the workpiece as well as the tool geometry. In MAF process, on one hand, the amount of machining forces is so low that the method is expected to produce a crack-free surface even in brittle materials. Furthermore, the negative rake angle of the abrasives provides sufficient hydrostatic pressure which facilitates plastic deformation. But on the other hand, due to the brittle nature of glass, finishing of this material has been usually accompanied by surface damages in conventional grinding and lapping processes. Hence, some part of this work was directed toward studying of the material removal 2200

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mechanisms during MAF of brittle materials. For this purpose, the specimens’ surfaces were inspected by using atomic force microscopy (AFM) and the prevailing mechanisms of material removal were investigated. 2. Experimental Setup

MAF experimental setup is shown in Fig. 1. The setup consists of three Nd–Fe–B permanent magnets, workpiece, and magnetic abrasive particles. The magnets were mounted on a holder and the holder was installed on the spindle of a vertical milling machine. The workpiece material was BK7 optical glass in the form of rectangular blocks with dimensions of 70 mm × 60 mm × 5 mm. Prior to MAF, all specimens were ground to surface roughness values in the range of 0.12–0.24 μm. The magnetic abrasive particles used in this work were composed of iron powders, Al2 O3 abrasives, and glass powder as a binder. The particles were first mixed homogenously and then were compressed into a cylindrical form followed by sintering in a vacuum furnace at 900°C for 1.5 h. After the sintering process, the MAPs were crushed and sieved in the dimensions shown in Table 1. Figure 2 shows a scanning electron microscopy (SEM) micrograph of sintered MAPs. The process variables considered in this work were: machining gap, rotational speed, abrasives size, MAPs size, and percentage weight of glass binder. These parameters were varied in three levels as given in Table 1. The feed rate and percentage

Fig. 1. Experimental setup of MAF process.

Table 1.

Process Parameters and Their Levels

Levels Process Parameters

Low

Medium

High

Machining gap (mm) Rotational speed (rpm) Abrasive size (μm) MAP size (μm) Percentage by weight of glass binder

1 800 1 50 25

1.5 1000 5 75 30

2 1250 10 100 35

4. Results and Discussion A. Empirical Modeling

Fig. 2. SEM micrograph of sintered MAPs.

weight of iron powders were kept constant. The experiments were conducted at a constant feed rate of 0.08 mm∕rev and 40% of iron powders. 3. Response Surface Methodology

In general, the main goal of experimental design is to study the relationship between output response and input variables (factors). Considering all the probable combinations of factors and levels (i.e., full factorial design), level factor (35 in this work) experiments are needed to be carried out which is very costly and time-consuming. Hence a well-designed experiment is essential to reduce the experimental cost and time. In this regard, RSM is one of the highly accepted methods for efficient design of experiments as well as studying the relationship between the response and process parameters [24–26]. The method is very useful for investigating not only the effects of individual parameters but also their interactions on output response. In this work, percentage change in rate of surface roughness was considered as response in order to take into account the variation of initial roughness of ground specimens as well as the finishing time effect. The response was defined as the ratio of change in surface roughness to the initial roughness divided by the finishing time as given by Eq. (1) :

The experiments were planned and carried out according to the RSM design and surface roughness was measured by using Mahr Perthometer M3 before and after MAF. Performing preliminary experiments, it was found that surface roughness decreased until 20 min and then settled to a steady level. Further increase of finishing time increased surface roughness slightly which might be due to the abrasives blunting and abrasives contamination by produced chips [9]. Figure 3 illustrates change of surface roughness with finishing time. _ are summarized in The obtained results for % ΔRa Table 2. In order to mathematically model the surface response as a function of process parameters, first of all the order of the polynomial equation had to be determined. For this purpose, analysis of variance (ANOVA) was performed by using the statistical software Design Expert and the highest polynomial order was obtained based on the statistical parameters of p-value and adjusted R2 . The results are listed in Table 3 for various polynomial orders. The obtained results show that the quadratic model has the lowest p-value and the highest adjusted R2 . A low p-value shows statistical significance on corresponding response and a high R2 value is an evaluation of the fit degree and good correlation between experimental and predicted results. These results recommended the quadratic polynomial as the best _ response surface for empirical modeling of % ΔRa. The detail of ANOVA results for quadratic response surface is given in Table 4. The ANOVA table represents the F-value and p-value for each of process parameters as well as for their interactions. These values show the significance degree of param_ The parameters with a p-value less eters on % ΔRa. than 0.05 (i.e., at confidence level of 95%) are _ important terms affecting % ΔRa. Among various

ΔRa∕Ra0  × 100 Δt   Initial roughness − Final roughness × 100;  Initial roughness × finishing time

%ΔRa 

(1) where ΔRa is the change of surface roughness, Ra0 is the initial roughness, and Δt is the finishing time.

Fig. 3. Variation of surface roughness with finishing time. Rotational speed, 800 rpm; abrasive size, 1 μm; MAP size, 50 μm; percentage weight of binder, 25%. 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS

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Table 2.

_ Design of Experiments and Obtained Results for % ΔRa

_ Standard Machining Rotational Abrasive MAP Percentage by Initial Final % ΔRa Order Gap (mm) Speed (rpm) Size (μm) Size (μm) Weight of Binder Roughness (nm) Roughness (nm) % ΔRa (min−1 ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 800 800 1250 1250 1000 1000 800 1250 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

1 1 1 1 10 10 10 10 1 1 1 1 10 10 10 10 1 1 1 1 10 10 10 10 1 1 1 1 10 10 10 10 5 5 5 5 1 10 5 5 5 5 5 5 5 5 5 5 5 5

50 50 50 50 50 50 50 50 100 100 100 100 100 100 100 100 50 50 50 50 50 50 50 50 100 100 100 100 100 100 100 100 75 75 75 75 75 75 50 100 75 75 75 75 75 75 75 75 75 75

machining parameters, the abrasive size is the most significant parameter having the lowest p-value and the highest F-value. Other important parameters are machining gap, MAP size, rotational speed, and percentage weight of binder, respectively. As shown in Table 4, there are many terms having a p-value more than 0.05 and hence are insignificant _ on % ΔRa. Therefore, another analysis was performed neglecting these insignificant terms in order to reduce the complexity of the empirical model. The 2202

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25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 30 30 30 30 30 30 30 30 25 35 30 30 30 30 30 30 30 30

205 196 183 162 218 144 155 220 225 193 181 178 221 201 211 208 201 134 122 121 166 180 243 179 209 192 203 187 233 197 229 231 183 133 176 162 224 144 173 164 198 155 191 190 201 192 178 169 191 206

87 112 76 101 116 118 96 133 104 159 140 77 161 194 148 188 109 110 96 73 150 156 122 110 128 142 128 94 188 187 176 192 79 87 36 23 92 101 41 72 42 53 32 36 40 38 32 30 36 39

57.561 42.857 58.469 37.654 46.789 18.055 38.064 39.545 53.778 17.616 22.652 56.741 27.149 3.482 29.858 9.615 45.771 17.910 21.311 39.669 9.638 13.333 49.794 38.547 38.756 26.042 36.946 49.733 19.313 5.076 23.144 16.883 56.831 34.586 79.545 85.802 58.928 29.861 76.300 56.097 78.788 65.806 83.246 81.053 80.099 80.208 82.022 82.248 81.152 81.068

2.878 2.143 2.923 1.883 2.339 0.903 1.903 1.977 2.688 0.880 1.132 2.837 1.357 0.174 1.493 0.480 2.288 0.895 1.065 1.983 0.482 0.666 2.489 1.927 1.938 1.302 1.847 2.486 0.965 0.254 1.157 0.844 2.841 1.729 3.977 4.290 2.946 1.493 3.815 2.805 3.939 3.290 4.162 4.052 4.005 4.010 4.101 4.112 4.057 4.053

ANOVA results for the new analysis are represented _ is in Table 5 and the regression equation for % ΔRa given by Eq. (2) :

%ΔRa  −2.41520  10.63195A − 0.00253055B  0.54276C − 0.00931682D − 0.035589E  0.00227479AB − 4.48526A2 − 0.057192C2 : (2)

Table 3.

ANOVA for Various Polynomial Orders

Sequential Model Sum of Squares Source

Sum of Squares

Mean versus total Linear versus mean 2FI versus linear Quadratic versus 2FI Cubic versus quadratic Residual Total

261.15 12.86 5.36 51.16 3.40 3.78 337.71

Degrees of Freedom

Mean Square

1 5 10 5 15 14 50

261.15 2.57 0.54 10.23 0.23 0.27 6.75

F-Value

p-Value

1.78 0.31 41.33 0.84

0.1374 0.9727

Nano-finishing of BK7 optical glass using magnetic abrasive finishing process.

BK7 is an optical glass extensively used in lens manufacturing. In this work, magnetic abrasive finishing (MAF) method was utilized for finishing of t...
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