Surface roughness model in experiment of grinding engineering glass-ceramics

Abstract

The grinding experiment of mica glass-ceramics was conducted on the GM-D300-type surface grinder. The article investigated the influence of surface roughness on grinding wheel velocity, table feed speed, and grinding depth. The results indicated that surface roughness decreased with the increasing grinding wheel velocity and grinding depth in overall trend, and decreased with increasing table feed speed. Moreover, a modified surface roughness model, which introduced the maximum undeformed chip thickness, was developed based on Snoeys’ empirical formula. The modified model was in good agreement with the experimental data in most cases. The disparity between experimental data and predicted results of surface roughness was attributed to the organization of pores randomly distributed within the mica glass-ceramics.

Keywords

Plane grinding surface roughness empirical model chip thickness engineering ceramics

Introduction

Surface roughness is an important factor to describe the surface quality of the component and the assemble accuracy for mechanical processing such as cutting, grinding, and so on. The reliability of the components was improved based on good surface roughness. Precision or super-precision grinding is one of the mechanical processes to achieve better surface performance.^1,2 Ceramic grinding is one of the advanced objectives in mechanical manufacture. Bandyoupadhyay³ investigated the effect of the process parameters on the strength and the surface integrity of silicon nitride through grinding experiments. Ali and Zhang⁴ proposed the prediction model of surface roughness based on the fuzzy theory. Hecker and Liang⁵ showed the relationship between undeformed cutting chip thickness and surface roughness using the topology data of the grinding wheel and the interaction of the wheel–workpiece. It was found that the predicted results were in good agreement with the cylindrical grinding experimental data. Chen et al.⁶ obtained the critical condition of the transition from brittle to ductile by means of the indention experiments with different loads. The influenced factors on the surface performance were analyzed with the theory of super-precision grinding. The grain size of the grinding wheel had a significant effect on the ground surface. The actual critical condition was also provided by the grinding experiments.

The removal process of the brittle material was different with the shear of the metal. The removal mechanism of brittle fracture was affected by the material property, the micro-defects, and so on. Thus, there were certain random factors. Since the machined mechanism of brittle material was not very clear, the removal process was uncontrollable. An important parameter of mechanical processing was surface roughness which was seen as the difference between good finish and poor finish. Thus, it was necessary to further investigate the surface roughness of the difficult-to-machine materials. Engineering ceramic of hard-brittle material was studied in the article.

Removal mechanism of engineering ceramic

Material-removal mode of engineering ceramic

Figure 1 shows a sketch of the indentation test. The median crack was gradually generated below the plastic zone, while the normal force increased in the loading procedure. The lateral crack emerged by the effect of the stress field formed by the plastic deformation and the median crack in the unloading procedure. The lateral crack extended to the material surface layer to form some exfoliations surrounded by micro-cracks, while the actual cutting depth and load were greater than their critical values. The chip appeared while the loose material broke away from the workpiece under the external forces. The internal material can prevent the expansion of the current cracks through consumption of the energy by plastic deformation. It can be concluded that the removal forms of the brittle material are collapsed blocks and powder blocks.

Figure 1.

Micro-crack formation process.

So far, there were three material-removal modes of engineering ceramic: brittle removal,^7,8 pulverization removal^7–9 and ductile deformation.^10–12 In the brittle removal mode, lateral and radial cracks propagated result in material crushing. In the pulverization removal mode, the hydrostatic stress of the abrasive results in local shear stress field which causes micro-crushing between intergranular and transgranular ceramic material in the grinding process. The study of ductile regime grinding showed that the removal mode of brittle material was ductile deformation in the case of small grinding depth. The removal modes were determined by the characteristics of workpiece and wheel, grinding process conditions, and so on.

Fracture model of engineering ceramic

The theoretical fracture strength was mainly determined by the interatomic force, while the removal mode of the ceramic¹³ composed of ideal crystals was total brittle fracture. The practical strength was less than two orders of magnitude than the theoretical strength

σ_{th} = \frac{2 E r_{0}}{π a_{0}}

(1)

where $σ_{th}$ is the theoretical fracture stress, $E$ is the elastic modulus, $r_{0}$ is the spacing increment in the maximum interatomic force, and $a_{0}$ is the space between two neighboring atoms.

Griffith¹⁴ showed that ceramic material can be led to an entire fracture with the spread of an internal micro-crack under some special circumstances. In fact, the material fracture was much easier than the damage of the atomic bond. According to the energy criterion, the fracture stress given by Griffith is

σ_{c} = \sqrt{\frac{2 E' r^{s}}{π c}}

(2)

where $σ_{c}$ is the Griffith fracture stress, $r^{s}$ is the surface energy of the refresh surface, $c$ is half of the crack length, $ν$ is the Poisson ratio, and $E'$ is the elastic modulus which can be calculated as

E' = {\begin{matrix} E (plane stress) \\ \frac{E}{1 - ν^{2}} (plane strain) \end{matrix}

Equation (2) indicated the fracture principle of ceramic material to conduct the research of material removal, and it was usually called Griffith equation. It was also clarified by Griffith that the actual fracture stress was influenced by material property, crack size, and so on. Kies et al.¹⁵ discussed the process of micro-crack generation and expansion through the contrastive grinding experiments for several brittle or ductile materials. It was found that the current theory cannot explain the fracture of brittle material clearly. The evolutive Griffith equation was given by Irwin¹⁶ as

σ_{f} = \frac{1}{Y} \sqrt{\frac{2 E' r^{*}}{c}}

(3)

where $σ_{f}$ is the Irwin fracture stress, $Y$ is the geometrical factor, and $r^{*}$ is the generated surface energy by the loosen stress.

Model of surface roughness for engineering ceramic

Uncut chip thickness

A sketch of grinding model is shown in Figure 2. The cutting edge came into contact with the workpiece at $F'$ to reach $A'$ . The cutting trajectory $F' B' C' A'$ was a cycloid curve formed by the grinding wheel velocity and the workpiece velocity. The displacement $A A'$ is the distance s moved on two neighboring cutting edges, and it can be given as

s = \frac{L ν_{w}}{ν_{s}}

(4)

where $s$ is the moving distance of the grinding wheel on two neighboring cutting edges, $ν_{s}$ is the grinding wheel tangential speed, $ν_{w}$ is the workpiece velocity, and $L$ is the space of two neighboring working cutting edges

l_{k} = (1 + \frac{ν_{s}}{ν_{w}}) • \sqrt{a_{p} d_{s}} + \frac{s}{2}

where $a_{p}$ is the uncut chip thickness, $d_{s}$ is the wheel diameter, and $ν_{w}$ is the workpiece velocity.

Figure 2.

The interference trajectory of the wheel–workpiece.

Generally, let

l_{k} = l_{c} = \sqrt{a_{p} d_{s}}

(5)

h_{m} = O' C - O' A = \frac{d_{s}}{2} - O' A

(6)

O' A = \sqrt{{(\frac{d_{s}}{2})}^{2} + s^{2} - s d_{s} \cos γ}

O' A = \sqrt{{(\frac{d_{s}}{2})}^{2} + s^{2} - s d_{s} \sqrt{1 + \cos^{2} θ}}

(7)

because $γ + θ = (π / 2)$ , $\cos θ = 1 - 2 a_{p} / d_{s}$ when simplified gives

h_{m} = 2 s \sqrt{\frac{a_{p}}{d_{s}}} \sqrt{1 - \frac{a_{p}}{d_{s}}} - \frac{s^{2}}{d_{s}}

Because $a_{p} / d_{s} << 1$

h_{m} = 2 s \sqrt{\frac{a_{p}}{d_{s}}} - \frac{s^{2}}{d_{s}}

(8)

which when put into equation (4) gives

h_{m} = 2 \frac{L ν_{w}}{ν_{s}} \sqrt{\frac{a_{p}}{d_{s}}} - \frac{{(\frac{L ν_{w}}{ν_{s}})}^{2}}{d_{s}}

(9)

where $h_{m}$ is the uncut chip thickness, $d_{s}$ is the wheel diameter, and $d_{w}$ is the workpiece diameter.

Mathematical model of surface roughness

Snoeys empirical model R_a1

The grinding wheel topology was too irregular to be characterized by random cutting edge’s spacing and protrusion height in the grinding process. Snoeys et al.¹⁷ and Kedrov¹⁸ proposed the empirical model of surface roughness using the cylindrical plunge grinding experiments; it is given as

R_{a 1} = R_{1} {(\frac{ν_{w} a_{p}}{ν_{s}})}^{x}

(10)

where $R_{1}$ was determined by a series of experimental data. Snoeys et al.¹⁷ showed that surface roughness was related through empirical constants $R_{1}$ and $x$ to the expression $ν_{w} a_{p} / ν_{s}$ for a given dressing condition. The coefficients $R_{1}$ and $x$ of the Snoeys model were determined by a series of grinding experiments. $x$ is one coefficient to be chosen in [0.15, 0.6]. However, the model had certain limitations in predicting grinding forces because the constants depend on the particular wheel, workpiece, grinding fluid, and dressing conditions, as well as on the accumulated stock removal. The Snoeys model not only correlated fairly well with the surface roughness and wheel wear but also with other performance characteristics, including the grinding forces and energy. Therefore, the modified model was proposed based on the Snoeys model in this article. The determination coefficients $R_{1}$ and $x$ of the modified model was the same as those of the Snoeys model, that is, the least-squares method was used to determine the parameters $R_{1}$ and $x$ by a series of grinding experiments in this article.

Empirical model R_a2 about uncut chip thickness

A new model of surface roughness was proposed in this article based on the Snoeys empirical model in which the equivalent cutting depth was equal to the uncut chip thickness

R_{a 2} = R_{1} {(\frac{ν_{w} h_{m}}{ν_{s}})}^{x}

(11)

that is

R_{a 2} = R_{1} {(\frac{ν_{w} 2 s \sqrt{\frac{a_{p}}{d_{s}}} \sqrt{1 - \frac{a_{p}}{d_{s}}} - \frac{s^{2}}{d_{s}}}{ν_{s}})}^{x}

The two models of surface roughness, Snoeys model, and modified model (shown in equations (10) and (11), respectively), were considered to assess the following experimental results.

Experiment

The relationship between surface roughness $R_{a}$ and process parameters in grinding engineering ceramic was studied in this article. Surface roughness was calculated by Snoeys’ empirical model and chip thickness model. These theoretical calculations were compared with experimental data in order to verify the accuracy of those models.

Experimental equipments and methods

The grinding experiment was carried out on the GM-D300-type surface grinder. The cubic boron nitride (CBN) grinding wheel was used to machine the mica glass-ceramic, drying. The wheel diameter is $d_{g} = 180 mm$ ; the ceramic material parameters are listed as follows: density $ρ = 2.65 g / c m^{3}$ , thermal conductivity $k = 2.1 W / (mK)$ , bending strength $σ = 108 MPa$ , and Vickers hardness $HV = 1.02 GPa$ . Surface roughness was measured on the MICROMEASURE 2–type surface profilometer (made in France) after grinding, surface profile was measured in terms of area sampling 0.1 mm × 0.1 mm and length sampling $1 μm$ . Surface morphology was observed on the VHX-10000 three-dimensional (3D) optical microscopy system. In addition, the average surface roughness of the ceramic material was gained from three specimens under the same conditions.

Surface roughness was studied based on the simple single factor test, that is, single factors such as the grinding wheel velocity $ν_{s}$ , the table feed speed $ν_{w}$ , or the grinding depth $a_{p}$ were changed with other process parameters remaining unchanged. The test conditions of simple single factor are shown in Table 1.

Table 1.

The test conditions of simple single factor.

Group no.	$ν_{s}$	$ν_{w}$	$a_{p}$
	m/s	mm/min	mm
1	29.5–62.5	40	0.15
2	62.5	10–75	0.15
3	62.5	40	0.05–0.3

Micro-surface in grinding glass-ceramic

Many pores randomly distributed within mica glass-ceramic were observed by mean of the software SPIP with Micromeasure 2 surface profilometer. In measurement, machined surface roughness will be a substantial deviation from the actual contour because of the pore composition of the surface material. Thus, the surface roughness of theoretical derivation was different from the experimental one.

The mica glass-ceramic, which contains a considerable number of pores with random distribution, is made by powder consolidation and sintering. Thus, the quantitative analysis was only studied on the influence of pores on the roughness measurements. As shown in Figure 3, the surface roughness of three measurement positions on the same grinding surface was compared. The results indicated that surface roughness varied greatly with the different pore organizations of the material surface. When the porosity was small within the material, the surface quality was better and the roughness measurements were lower, $R_{a} = 0.061 μm$ (Figure 3(a) and (b)). The roughness measurements were increased, $R_{a} = 0.394 μm$ (Figure 3(c) and (d)), with the increase in the porosity within the material. When the porosity was large within the material, the surface quality was poor and the roughness measurements were the largest, $R_{a} = 0.437 μm$ (Figure 3(e) and (f)).

Figure 3.

The pore organization of material affects the surface roughness. (a) V3D profilometer at position 1; (b) Random pores distributions; (c) V3D profilometer at position 2; (d) Random pores distributions; (e) V3D profilometer at position 3 and (f) Random pores distributions.

Results and discussions

The experimental results for simple single factor tests were shown in Figures 5 –7. The experimental data were recorded as $R_{a 0}$ . The reduplicative tests at the same condition were conducted three times. Two surface roughness models $R_{a 1}$ and $R_{a 2}$ (equations (10) and (11)) were used to predict the above experimental results. Now $d_{s} = 180 mm$ and $d_{w} = 30 mm$ are known; $R_{1}$ , $x$ , and $L$ are the three unknown coefficients. According to wheel micromorphology (Figure 4), the average distance $L$ was measured between two random continuous cutting grains, namely, $L = 0.035 mm$ . According to the above experimental results, the coefficients $R_{1}$ and $x$ were obtained by means of the least-squares method, that is, $R_{1} = 1.5$ and $x = 0.25$ . The predicted results of the Snoeys model $R_{a 1}$ and the grinding thickness model $R_{a 2}$ were shown in Figures 5 –7.

Figure 4.

The micromorphology of wheel surface.

Figure 5.

The influence of grinding wheel speed $ν_{s}$ on the arithmetic mean deviation of the surface roughness profile $R_{a}$ .

Figure 6.

The influence of table feed speed $ν_{w}$ on the arithmetic mean deviation of the surface roughness profile $R_{a}$ .

Figure 7.

The influence of grinding depth $a_{p}$ on the arithmetic mean deviation of the surface roughness profile $R_{a}$ .

Grinding wheel speed

The influence of wheel speed on surface roughness was shown in Figure 4 for simple single factor tests. It was found that the average surface roughness for engineering glass-ceramics was gained from 15 specimens at 5 different grinding wheel speeds (29.5, 38, 47, 57, and 67 m/s, respectively). It was shown from Figure 4 that the surface roughness decreased with the increasing wheel speed and surface quality was improved. It was found that the predicted results of grinding thickness model $R_{a 2}$ were in more agreement with the experimental data than those of Snoeys model $R_{a 1}$ . The contact rate between grains and workpiece surface increased and decreased residues on the grinding path with the increasing wheel speed whether other conditions were unchanged.

Table feed speed

Figure 6 showed the influence of table feed speed on surface roughness in grinding mica glass-ceramic. The results indicated that surface roughness increased with the increasing table feed speed $ν_{w}$ and surface quality was deteriorated. Theoretically, the contact zone was formed due to relative motion between the grinding wheel and the workpiece surface, the interference path was a wavy-line. The spacing between adjacent peaks (or adjacent trough) will increase and the residues on the grinding path will decrease with the increase in table feed speed whether other conditions are changed or not.

As shown in Figures 5 and 6, the experimental data were compared with, Snoeys empirical model $R_{a 1}$ and grinding thickness model $R_{a 2}$ if grinding wheel speed $ν_{s}$ (or table feed speed $ν_{w}$ ) was seen as the single factor, that is, independent variable. It was found that their trends were almost identical. Two models had the same effect if one of two models could become closer with the experimental data by adjusting the coefficient value $R_{1}$ .

Grinding depth

Figure 7 shows that the average surface roughness for engineering glass-ceramics was gained from 15 specimens at 6 different grinding depths, namely, 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3 mm, respectively. Figure 7 showed the influence of grinding depth on surface roughness. The results indicated that surface roughness decreased with the increase of grinding depth. But there was a great fluctuation which was observed by the surface roughness curve. It indicated the relationship between surface roughness and grinding depth. The minimum value and maximum value appeared, respectively, at $a_{p} = 0.15 mm$ and $a_{p} = 0.2 mm$ .

As shown in Figure 7, the predicted trends of the model $R_{a 1}$ and model $R_{a 2}$ were different. The slope of the model $R_{a 1}$ was greater than that of the model $R_{a 2}$ ; the distribution of predicted results did not match with the experimental data. The predicted trends of the model $R_{a 2}$ were closer with the experimental data. The predicted trends of the model $R_{a 1}$ were unchanged through adjusting coefficient $R_{1}$ . The results showed that the influence of grinding thickness on surface roughness was larger than that of grinding wheel speed and table feed speed.

Conclusion

In the article, the grinding experiment of mica glass-ceramic, which considered the influence of surface roughness on only simple single factor, such as grinding wheel velocity, table feed speed, or grinding depth, was conducted by a GM-D300-type surface grinder. It was found that surface roughness decreased with the increasing wheel speed and grinding depth, and increased with the increasing table feed speed. The results indicated that the influence of grinding depth on the surface roughness was larger than that of grinding wheel velocity and table feed speed in grinding mica glass-ceramic.

The modified model was proposed in this article, namely, the undeformed chip thickness was introduced into Snoeys’ empirical formula. In general, the modified model was well consistent with the experimental data. It was further verified that surface roughness was relatively more seriously affected by grinding thickness. Sometimes, a certain disparity, which was attributed to the pores organization randomly deviating from the actual contour of the machined surface distributed within the mica glass-ceramic, was found between the experimental data of surface roughness and predicted results.

Footnotes

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

The funding for this work was provided by the National Natural Science Foundation of China (No. 51275083).

References

Ahearne

Byrne

. Ultraprecision grinding technologies in silicon semiconductor processing. Proc IMechE, Part B: J Engineering Manufacture 2004; 218(3): 253–267.

Thiagarajan

Sivaramakrishnan

Somasundaram

. Experimental evaluation of grinding forces and surface finish in cylindrical grinding of Al/SiC metal matrix composites. Proc IMechE, Part B: J Engineering Manufacture 2011; 225(9): 1606–1614.

Bandyoupadhyay

. The effects of grinding parameters on the strength and surface finish of two silicon nitride ceramics. J Mater Process Tech 1995; 53(3–4): 533–543.

Ali

Zhang

. Surface roughness prediction of ground components using fuzzy logic approach. J Mater Process Tech 1999; 89(19): 561–568.

Hecker

Liang

. Predictive modeling of surface roughness in grinding. Int J Mach Tool Manu 2003; 43(8): 755–761.

Chen

Zhao

Dong

. The critical conditions of brittle–ductile transition and the factors influencing the surface quality of brittle materials in ultra-precision grinding. J Mater Process Tech 2005; 168(1): 75–82.

Zhang

Zheng

Tokura

. Grinding induced damage in ceramics. J Mater Process Tech 2002; 132: 353–364.

Regiani

Fortulan

Purquerio

. Abrasive machining of advance ceramics. Ind Diamond Rev 2000; l: 37–42.

Zhang

. Surface integrity in machining hard-brittle materials. J Jpn Soc Abras Tech 2003; 47(3): 131–134.

10.

Malkin

Hwang

. Grinding mechanisms for ceramics. CIRP Ann: Manuf Techn 1996; 45(2): 569–580.

11.

Lawn

. Fracture of brittle solids. 2nd ed. Cambridge University Press, 1993, pp.249–306.

12.

Subramanian

Ramanath

Tricard

. Mechanisms of material removal in the precision production grinding of ceramics. J Manuf Sci E: T ASME 1997; 119(11): 509–519.

13.

Orowan

. Fracture and strength of solids. Rep Prog Phys 1949; 12: 185–232.

14.

Griffith

. The phenomena of rupture and flow in solids. Philos T Roy Soc A 1920; 221: 163–198.

15.

Kies

Sullivan

Irwin

. Interpretation of fracture markings. J Appl Phys 1950; 21(7): 716–720.

16.

Irwin

. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 1957; 24: 361–364.

17.

Snoeys

Peters

Decneut

. The significance of chip thickness in grinding. CIRP Ann: Manuf Techn 1974; 23(2): 227–237.

18.

Kedrov

. Investigation of surface finish in cylindrical grinding operations. Mach Tool 1980; 51(1): 40–45.

Surface roughness model in experiment of grinding engineering glass-ceramics

Abstract

Keywords

Introduction

Removal mechanism of engineering ceramic

Material-removal mode of engineering ceramic

Fracture model of engineering ceramic

Model of surface roughness for engineering ceramic

Uncut chip thickness

Mathematical model of surface roughness

Snoeys empirical model Ra1

Empirical model Ra2 about uncut chip thickness

Experiment

Experimental equipments and methods

Micro-surface in grinding glass-ceramic

Results and discussions

Grinding wheel speed

Table feed speed

Grinding depth

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References

Snoeys empirical model R_a1

Empirical model R_a2 about uncut chip thickness