This study demonstrated the strength of a theoretical model founded on the Box-Behnken experimental design method to determine the surface roughness (Ra parameter) of solid Oriental beech (Fagus orientalis Lipsky) wood. The working parameters (sanding belt grit size of 60 to 100, feeding speed of 4 m/min to 10 m/min, and sanding cutting depth of 0.1 mm to 0.3 mm) of a wide belt sanding machine were determined. The Ra of the samples was experimentally described so that the experimental results were also remodeled with the Box-Behnken method to find the optimum parameters for the lowest Ra. An adjusted correlation factor of 93.6% for the Ra confirmed the compatibility between the experimental and theoretical findings. The high correlation (strength) allowed for a more detailed discussion of the effect of the working parameters on the Ra. The theoretical approach showed that the grit size factor had the largest effect on the Ra compared with the other factors. The optimum parameters were found to be a grit size of 100, feed speed of 4 m/min, and sanding depth of 0.1 mm for a minimum Ra for Oriental beech wood. The experimental data supported these parameters.
Determination of Surface Roughness Based on the Sanding Parameters of Oriental Beech Wood
Abdullah Cemil İlçe *
This study demonstrated the strength of a theoretical model founded on the Box-Behnken experimental design method to determine the surface roughness (Ra parameter) of solid Oriental beech (Fagus orientalis Lipsky) wood. The working parameters (sanding belt grit size of 60 to 100, feeding speed of 4 m/min to 10 m/min, and sanding cutting depth of 0.1 mm to 0.3 mm) of a wide belt sanding machine were determined. The Ra of the samples was experimentally described so that the experimental results were also remodeled with the Box-Behnken method to find the optimum parameters for the lowest Ra. An adjusted correlation factor of 93.6% for the Ra confirmed the compatibility between the experimental and theoretical findings. The high correlation (strength) allowed for a more detailed discussion of the effect of the working parameters on the Ra. The theoretical approach showed that the grit size factor had the largest effect on the Racompared with the other factors. The optimum parameters were found to be a grit size of 100, feed speed of 4 m/min, and sanding depth of 0.1 mm for a minimum Ra for Oriental beech wood. The experimental data supported these parameters.
Keywords: Surface roughness; Box-Behnken design; Grit size; Feed speed; Sanding thickness
Contact information: Department of Industrial Engineering, Engineering Architecture Faculty, Bolu Abant Izzet Baysal University, Bolu, Turkey; *Corresponding author: firstname.lastname@example.org
Surface roughness (Ra parameter) in wood materials is one of the most important factors that affects the finishing operations with regards to the bonding quality, especially the painting characteristics. A material surface should be as smooth as possible before starting finishing operations. It is not possible to obtain a completely smooth surface, even in wood materials processed with proper techniques, by reason of cell size. However, the roughness can be reduced before finishing operations are conducted. The factors affecting the surface smoothness of a wood material may be summed under three groups, including the properties of the wood material, cutters, and machines (Kilic et al. 2006; Malkoçoğlu 2007; Aslan et al. 2008; Magoss 2008).
In much more detail, there are several quantity factors affecting the surface roughness (arithmetic average of surface irregularities with regard to a mean line). The factors can largely be classified into four main groups: (I) the machining parameters including the feed rate, cutting speed, and depth of cut; (II) the cutting tool parameters as regards the wear, geometry, material, and coating of tools used; (III) the machining and machine tool conditions regarding the dry or wet turning, cutting fluid type, fluid applications, machine tool rigidity, and vibration of chatter; and (IV) the workpiece material properties (hardness, microstructure, grain size, and inclusions) (Ratnam 2017).
Researchers have studied such properties in detail and searched for ways to obtain smoother surfaces. Taylor et al. (1999) and Fujiwara et al. (2001) found that high quality wood material surfaces may be obtained if the proper feeding speed and grit size are determined in the sanding process (Tan et al. 2012), which established that the grit size and feed speed are effective at reducing the Ra.
Budakçı et al. (2011) reported that a quality surface is also dependent on the chip thickness and cutting velocity, as well as the rake angle. Örs and Baykan (1999) found that when the number of cutters and grit size in the sanding process are higher, then the values of the Ra are lower. According to the studies mentioned above, the sanding operation, which depends on the textural features, anatomical or cell structure, annual ring differentiation, ratio between early wood and latewood, moisture, and density, also plays an important role in understanding how or why the surface quality changes during processing (Ratnasingam and Scholz 2006; Hiziroglu et al. 2013; Hazir et al. 2017). Similarly, the research shows a preference for the optimum sanding operation parameters (including the grit size, feed speed, and sanding depth) for a wide belt sanding machine with respect to the wood properties, such as the anisotropic nature and heterogeneous texture (Saloni et al. 2010).
Additionally, different researchers have indicated that tangential cutting results in a softer surface than radial cutting, but the interaction among the cutting destination and sort of cutter is not significant (Örs and Baykan 1999; Örs and Gürleyen 2002; Efe and Gürleyen 2003; Söğütlü 2005; Malkoçoğlu 2007). Studies in which the Ra was optimized with an experimental design method (response surface design) have frequently been conducted in recent years and mostly in different areas (Kant and Sangwan 2014; Luo et al. 2014; López et al. 2016; Nguyen and Hsu 2016; Sofuoglu 2017).
Scientists can also classify attractive properties, such as changes, permanent variances, and conformity for locking, with the assistance of statistical analyses and response surface designs (Box et al. 1978). In this regard, the classic quadratic designs are sorted into two main groups, including the Box-Wilson central composite and Box-Behnken designs. Classic models have allowed the researchers to determine the optimum locations in the industry, technology, and engineering application fields for several years (Box and Behnken 1960; Ayodele and Cheng 2015; Ba-Abbad et al. 2015; Shahri and Niazi 2015; Montgomery 2017). The Box-Behnken design is a free (rotatable) quadratic design because of the lack of a buried or fractional factorial design. Therefore, the Box-Behnken design combined with rarer cure alternatives limits the ability for orthogonal locking in proportion with the central composite designs. Additionally, the Box-Behnken design shows benefits in rarer cure alternatives in the literature. In the present work, the preparation conditions, including the grit size, feed speed, and sanding depth, were determined with the Box-Behnken design to optimize the Ra of oriental beech materials.
Oriental beech wood was selected because it is frequently used in the furniture industry in Turkey, easily accessible, has a reasonable price, and the processing methods are familiar. A total of 15 Oriental beech air-dried samples for 15 main groups (totally 225 samples), measuring 18 mm × 110 mm × 350 mm, were designed according to TS 2470 (2005). The annual rings were on the surfaces vertically. The wood was a high grade, finely fibrous, knotless, crack-free, and had no differences in the color or density. Subsequently, they were stored at 20 °C ± 2 °C and 65% ± 5% relative humidity in a conditioning cabinet until they reached a constant weight. The experimental materials (air-dry density of 0.69±0.03 and moisture content levels of 9±1 %) were sanded with a wide belt sanding machine (Version 1100 Melkuç Machine Company, Ankara, Turkey). The machine and sanding belt properties are shown in Table 1.
Table 1. Machine and Sanding Characteristics
Surface Roughness Test
The Ra of the samples was defined according to ISO 4287 (1997) using a stylus profilometer (TIME TR200, Time Group Inc., Beijing City, China). The measurements were made parallel to the fibers at five different points on each sample. The mean line between the profile valleys and ridges was the average Ra value in micrometers (Fig. 1).
Fig. 1. Graphical representation of the Ra (Nguyen and Hsu 2016)
Experimental Design and Statistical Method
The three factor Box-Behnken experimental design method was preferred in this study. The Box-Behnken design is an independent quadratic model. It does not include a full or partial factorial design. The testing points were located on the mid points of the edges and on the center. These models are rotatable and need three levels for each factor. The center of the design has a limited capability for orthogonal blocking compared with composite designs. When the same number of factors exist, this design is more economical because it includes a lower number of points compared with central composite designs. The three factor Box-Behnken design necessitates 15 tests and the four-factor design necessitates 27 tests (Winer et al. 1991; Myers et al. 2016).
In the Box-Behnken experimental design, each experimental factor must identify the minimum or lower level (-1), central or medium level (0), and higher or maximum level (+1). The independent variables of this study were the grit size, feed speed, and sanding depth, while the dependent variable was the Ra. The specified experimental points are given in Table 2. The experiments were repeated in triplicate to represent the mid points and were repeated to estimate the errors.
Table 2. Experimental Points Used in the Box-Behnken Experimental Design Method
The following response surface function was used to correlate the Ra (Y) with the independent variables (X1, X2, and X3) (Eq. 1):
where Y is the Ra, b0 is the value taken by Y in case the effect of all of the independent variables is zero, X1, X2, and X3 are the grit size, feed speed, and sanding depth, respectively, b1, b2, and b3 are linear coefficients, b12, b13, and b23 are interaction coefficients among the independent variables, and b11, b22, and b33 are second degree coefficients.
The MINITAB statistical software program (Minitab Inc., State College, PA, USA) was used to perform the experimental design, determine the coefficients, perform the data analysis, and generate the graphs. The validity checks of the obtained model were made by comparing the experimental data and estimated values.
RESULTS AND DISCUSSION
The Ra values obtained as a result of the Box-Benkhen experimental design and experiments are given in Table 2. The values given in the chart indicate both the 3-level structure used in the surface response method and the experimental values corresponding to these levels. The highest Ra value (12.87 µm) was obtained with a 60-grit sanding belt size, 10-m/min feeding speed, and 0.20-mm sanding depth. The lowest Ra (7.05 µm) was acquired with a 100-grit sanding belt, 4-m/min feeding speed, and 0.2-mm sanding depth (Table 3).
The effects of the feed speed and sanding depth parameters on the Ra were tested with two different models (linear and square) and an analysis of variance (ANOVA), and the results are shown in Table 4. The independent effects of the parameters were seen in the linear model, while the effectiveness of the squares of the parameters was determined in the square model. Accordingly, the correlation of the grit size and speed parameters with the Ra was found to be important for the linear model (P < 0.050). The correlation of the grit size square with the Ra was found to be important for the square model (P < 0.050). It was concluded based on the results that the grit size had the largest effect on the Ra.
Table 3. Experimental Design and Results
Table 4. Results of the ANOVA of the Ra
Fig. 2. Surface plots and counter plot charts of the parameters
The combined effect of the three parameters on the Ra was interpreted with the surface plots and counter plot graphs, which are given in Fig. 2. The sanding depth was kept at 0.2 mm in Figs. 2a (surface plot) and 2b (counter plot). According to Fig. 2a, when the grit size increased, the Ra slightly increased, even though the feed speed increased. If the grit size increased and the feed speed decreased, the Ra was reduced. The same correlation was seen in the counter plot graph (Fig. 2b), where a 100-grit sanding belt size and feed speed below 7.5 m/min were required to obtain a Rabelow 8 µm. The feed speed was kept at 0.7 m/min in Figs. 2c (surface plot) and 2d (counter plot). Figure 2c shows that the Rawas reduced when the grit size increased and the sanding depth decreased. The Ra increased slightly when the grit size increased, even though the sanding depth increased. Figure 2d shows that a 100-grit sanding belt size and sanding depth below 0.21 mm was required to obtain an Ra value below 8 µm. According to Fig. 2e (surface plot) and 2f (counter plot), the grit size was kept at 80. The Ra was reduced when the feed speed and sanding depth decreased. The Ra increased slightly when the feed speed increased, even though the sanding depth increased (Fig. 2e). According to the counter plot graph (Fig. 2f) a sanding depth below 0.21 mm and feed speed below 5 m/min were required for an Ra value below 8 µm.
The mathematical method obtained from the experimental data analyzed with the surface response method is given below (Eq. 2):
Ra = -2.63 + 0.2960Grit size + 1.069Feed speed + 3.4Sanding depth – 0.002196Grit size × Grit size – 0.0120Feed speed × Feed speed + 2.4Sanding depth × Sanding depth – 0.00609Grit size × Feed speed + 0.070Grit size × Sanding depth – 0.95Feed speed × Sanding depth (2)
The mathematical model founded on the experimental measurement results was used to determine the lowest Ra, which is seen in Fig. 3. It was apparent from the graphs that the lowest Rawas 6.765 when the sanding parameters were a 100-grit sanding belt size, 4-m/min feed speed, and 0.1-mm sanding depth.
Fig. 3. Optimum parameters for the minimum Ra
Additionally, the correlation between the experimental results and estimations can be seen in Fig. 4.
Fig. 4. Test results and estimated Ra values
It was determined from Fig. 4 that the R2 was 0.9410 and the adjusted R2 was 0.9360. This indicates there was good compatibility between the computed theoretical values and experimental measurement results. The values obtained with the Raestimation model explained 93.6% of the experimental variation. Moreover, the compatibility of the R2 and adjusted R2 showed that the model functions chosen during this study were suitable for the determination of Ra parameters for Oriental beech wood.
The surface roughness value resulting from the sanding of solid beech surfaces was found to be correlated with feed speed, sanding depth quantity and the grit size, and successfully remodeled with regard to the Box Benkhen experimental design method. According to regression between model results and experiment values for the working parameters on the surface roughness, the adjusted correlation factor was computed to be 93.6%, presenting the perfect compatibility, operation and superiority of the theoretical model used in this work. Accordingly;
- It was found that the factors of feed speed and the grit size were statistically important and significant regarding the surface roughness value, while the sanding depth parameter was not statistically significant. In the square model, only the grit size was found to be statistically important and significant. This was attributed to the fact that the most effective factor on surface roughness value is the grit size depending on the low surface roughness. In other words, the higher the grit size, the lower the surface roughness.
- To the best of our knowledge, there are several studies on the working parameters of the sanding machine in regards to feed speed (Magoss 2008); feed speed and the grit size (Taylor et al. 1999; Fujiwara et al. 2001); grit size and feed speed (Tan et al. 2012); and grit size, feed rate, depth of cut, and cutting speed (Hazir et al. 2017). In these studies, the researchers produced rather smoother surface for wood production. The present work endeavored to optimize the working parameters such as feed speed, the grit size and sanding depth for the minimum surface roughness of beech wood.
- According to the results deduced from the model, the combination of 100 grit sanding belt, 4 m/min feed speed, and 0.1 sanding depth was corrected by both the experimental evidence and theoretical results for the lowest surface roughness on solid beech surfaces. Consequently, the present results confirm that effective optimization can be achieved by means of a Box Benkhen experimental design model using a low number of experimental measurements points.
- The theoretical model correctly selected for the specific work enables the researchers to easily and economically decide the optimum working parameters for the smoothest surface roughness.
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Article submitted: April 18, 2018; Peer review completed: June 5, 2018; Revised version received and accepted: June 8, 2018; Published: June 13, 2018.