THE POSSIBILITIES OF WHEAT ROLLER MILLING OPTIMIZATION USING THE RESPONSE SURFACE METHODOLOGY

Roller mills are one of the most frequently used grinding machines especially for cereal milling. Magnitude and type of the forces acting on particle depend on the set of roll parameters. Particle size distribution (PSD) resulting from milling a particular feed size critically depends on the ratio of roll-gap to input particle size. Box-Behnken experimental design was applied in order to optimize roll-gap adjustments and desired PSD of the milling output obtained by subsequent grinding of wheat on three pair of rollers. Adequate models, which allow the optimization of the milling process, were obtained by regression analysis. Values that define the PSD of the output, i.e. weight fractions of the milling output size fractions, were set to minimum, maximum or values within a certain interval. The examples of optimization which set the roll-gap values to ensure the desired PSD of the output, were obtained with a high level of desirability.


INTRODUCTION
Size reduction is a unit operation included in many industrial processes.Different types of comminution equipment are distinguished by the design and working principle or the maximum size of the product (Haque, 1991).Roller mills are one of the most frequently used grinding machines especially for milling of cereals.The best example of roller mills application is probably the wheat flour milling process.Nowadays the grinding of cereals or other diet ingredients by roller mills, for the purpose of animal feed production, is getting more attention (Vukmirović et al., 2016a;Vukmirović et al., 2016b).
In roller milling the material is passed between two counterrotating rolls separated by a small gap.The rolls are with either a corrugated or smooth finish and for most grain grinding operations the two rolls run at different speeds.Degree of particle size reduction depend on the interaction between its structural characteristics and set of roll parameters (roll gap, roll velocities, differential, roll surface etc.).They influence the magnitude and the relative contributions of compressive and shearing forces acting on the particle (Haque, 1991).During the milling process in industrial conditions, only the roll gap and feed rate (to a limited degree) can be adjusted, while the other roll parameters remain the same (Fistes et al., 2008).As roll gap decreases, greater stresses are imposed, increasing the number of fractures and the degree of particle size reduction (Scanlon et al., 1988;Fang and Campbell, 2002).In addition, by decreasing the gap the grinding zone size increases and grinding action is prolonged (Haque, 1991).Campbell and Webb (2001) and Campbell et al. (2001) stated that PSD of the milling output critically depends on the ratio of roll gap to input particle size.So, in order to achieve successful roller milling operation it is imperative to find an optimum gap setting for a particular feed stock and product.
Particle size distribution (PSD) of solids is often an important quality factor (Fistes et al., 2013).For example, each break passage in the flour milling flow has a predetermined target break release in order to keep the mill in balance (Wilson, 2001).Break releases determine the distribution and PSD of intermediate stocks throughout the rest of the milling process and in this way it is assured that subsequent equipment in the process is being feed by the appropriate amount of stock (Bojanić et al., 2016).PSD of wheat flour is also of interest since the flour particles of different sizes have different characteristics (Tarjan et al., 2009).In recent years there is a growing interest in PSD of animal feed since it is closely related with the utilization of nutrients and production efficiency (Amerah et al., 2008;Svihus, 2011;Vukmirović et al., 2016b).
Control of any milling process is based on ability to relate the PSDs of input and output material in a milling operation.Different approaches were used for modeling particle size reduction such as population balance models, breakage matrix approach, etc. (for details refer to Bilgili and Capece, 2012).Population balance type of modeling requires continual intraprocess sampling (difficult or impossible) in order to monitor the evolution of PSDs over time.In breakage matrix approach the relationship between the input and output PSDs is described by the matrix equation , B f o ⋅ =where f and o are column vectors of the PSD in the input and output material from a milling operation, and B is the breakage matrix.By determing the B for any PSD of input material, PSD of output can be predicted.Reverse problem in the breakage matrix context (Fistes et al., 2013(Fistes et al., , 2014) ) aims to calculate the input PSD in a milling operation, in order to obtain the desired output PSD.
The most efficient way to influence the outlet PSD is by changing the process parameters, such as gap considering the roller milling.Experimental design method, and response surface method (RSM) within it, simultaneously monitors the changes of input factors and analyzes the significance of their influence to the output.In that sense, Box-Behnken experimental design was applied in order to optimize the milling of wheat by subsequent grinding on three pair of rolls.The goal was to investigate the possibilities of using the RSM to optimize the roll-gap adjustments and the desired PSD of the milling output.More precisely, the major objective was to find the optimal combination of roll gap settings (input factors) such that desired PSD of the stock (output factors) is obtained.Values that define the PSD of the output, that are the weight fractions of the milling output size fractions, were set to minimum, maximum or values within a certain interval.

Methods
Wheat samples were milled using a roller mill equipped with three pairs of rolls (ROSKAMP TP650-9, California pellet mill, USA).Fluted rolls are 165 mm in diameter and 230 mm long with 1.77, 4.33 and 5.51 corrugations per cm from the first (upper) to the third (lower) pair of rolls, respectively.A differential of 1.5 was employed relative to a fast roll speed of 750 rpm for the 1 st roll and 850 rpm for the 2 nd and 3 rd rolls.The roller mill is equipped with dosing system and samples were feed at the rate of 26 kg/cm h.The roll gaps were set to: 1 st (upper) rolls: 1.2, 1.4 and 1.6 mm; 2 nd (middle) rolls: 0.8, 1.0 and 1.2 mm and 3 rd (lower) rolls: 0.4, 0.6 and 0.8 mm.Roll gap combinations were set according to Box-Behnken experimental design (Table 1).Sieve analysis was performed on the Bühler laboratory sifter operating at 220 rpm (MLU-300, Switzerland) using the entire milled stock.Samples were sieved for 3 min and separated into five fractions using square aperture sieves of size 1500, 1000, 450 and 150 µm, along with a bottom collecting pan.Rubber balls were used as sieve cleaners.The stock held on each sieve and pan was weighed to 0.1 g using a Sartorius Precision balance (Sartorius AG, Germany) and PSD is given as weight fractions of the milling output size fractions.

Experimental design, statistical analysis and optimization
The Box-Behnken experimental design with 3 input factors arranged at 3 levels and three central points (which is 15 runs in total) (Myers et al., 2009) was used to reduce number of experimental runs and to evaluate the influence of roll gap settings and their interactions on PSD of the stock following the grinding on three pairs of rolls.The regression analysis is performed and model is described by the polynomial of second order: where, R is a measured response (weight fractions of the milling output size fractions); β 0 is an intercept; β 1 to β 33 are regression coefficients; A, B and C are the coded levels of input factors.The terms AB, AC and BC represent interactions of input factors, while A 2 , B 2 and C 2 represent quadratic terms.Model adequacy checking is done by calculating the R 2 value and graphically by predicted versus actual plot.In addition, within the residual analysis a normal probability plot of the residuals and residual versus predicted plot are checked.Optimization is carried out using constrained optimization problem where numerical calculation is performed by nonlinear programming methods (Myers et al., 2009).This procedure maximizes desirability function: where d i , i ∈ {1,2, … , n} are individual desirability functions associated to constrains on responses R i .The analyses were carried out using Statistica 12 (Stratosoft, USA) and Design-Expert 10 (trial version) (Anderson and Whitcomb, 2007).

RESULTS AND DISCUSSION
A total of 15 experimental runs were determined by the Box-Behnken design.Recommended order of roll gap combinations and the obtained responses, i.e.PSD of the milling output given as weight fraction of the milling output size fractions are presented in Table 1.
Mean values, standard deviation, range of results for the analyzed responses and the ratio between maximum and minimum values are shown in Table 2. Regresion equation coeficients for responses together with R 2 values are shown in Table 3.
Positive or negative sign of the obtained regression equation coefficients for the depended responses indicates that the response increases or decreases with the corresponding input factor.As it was mentioned earlier in the text model adequacy checking is done by plotting a normal probability plot of the residuals and residual versus predicted plot (not shown in the paper), as well as, actual versus predicted plot (Fig. 1).Since the points on normal probability plot of the residuals and actual versus predicted plot are distributed close to the straight lines the normality assumption and adequacy of obtained model are confirmed (Montgomery, 2001).In a real manufacturing process it is usually necessary to coordinate few responses in order to achieve the best solution.
Optimization of controllable parameters determines the levels at which the system achieve optimal conditions.In this method, each of identified responses is transformed to the value called the single function of satisfaction which can range from 0 to 1.The closer the value to 1, the response is closer to the desired value.Combination of individual satisfaction functions produces the total satisfaction function which should also be close to 1.In this way, a compromise solution for the harmonization of the conditions given for responses, which often conflict with each other, is obtained.Model determined by regression analyses is used to perform the optimization of rollgap adjustments in order to find the optimal combination of gap settings (input factors) such that desired PSD of the stock is obtained.The responses, that is the weight fractions of the milling output size fractions, were set to minimum or maximum value (Example 1), within certain (narrow) interval (Example 2) or combination of extreme and interval values (Example 3) (Table 4).
The recommended roll gap settings and obtained weight fractions of the milling output size fractions together with the obtained desirability functions (D) are given in the Tables 5, 6 and 7 for examples 1, 2 and 3 respectively.
As can be seen from tables 5-7 the obtained desirability ranges from almost 90 % (example 3) to even 100 % (example 2) proving that the approach of using RSM can be successfully used for this purpose.Complete solution of the problem (desirability 100 %) was obtained in example 2 where the weight fractions were set out in intervals, although these intervals were set to a relatively narrow range.For example, the weight fraction of the size fraction >1500 μm range in interval of almost 50 % (from 6.7 % to 55.1 %) while the weight fraction of fraction <150 μm range between only 2-8 %.For both size fractions the targeted weight fraction was set within only 2 % (20-22 %).On the other hand, it needs to be pointed out that practically there is no difference in the proposed solutions, i.e. there is no difference in combinations of roll gap settings as well as obtained weight fractions in five recommended solutions.In example 1 the weight fractions were set to either a minimum or maximum value while desirability ranged from 90 % to almost 97 %.
Considering the proposed roll gap settings it can be noticed that all solutions propose the same roll gap at 3 rd roll while differences exist in roll gap settings on first two rolls.The lowest desirability was obtained in example 3, which combines min/max and interval target for weight fractions.However, with almost 90 % this desirability can also be classified as high.In this example the variability of suggested roll gap settings is highest, but again for the upper and middle pair of rolls, while the gap setting for the lower pair of rolls varies to a relatively small extent.It needs to be emphasized that this approach was evaluated as general principle and the results would be different if the range for the roll gap settings or the output size classes were different.Nevertheless, the possibility of obtaining such high desirability values indicates usefulness of this approach in optimization of the milling process.

CONCLUSION
Control of the milling process essentially involves finding the optimal combination of grinding parameters which would, relative to the characteristics of the input material, result in desired PSD of the milling output.Characteristics of input material are often not under control so the control of the grinding parameters is most efficient way to influence the output PSD.The RSM proved to be applicable for the optimization of wheat roller milling.By defining the range of variation for roll gap settings, through the model obtained by regression analysis, it is possible, with a high level of desirability, to find the optimal combination of roll-gap settings which would lead to the targeted PSD of the milling output.

Table 1 .
The Box-Behnken experimental design and obtained responses

Table 2 .
Descriptive statistics for responses

Table 3 .
Regression equation coefficients for responses

Table 4 .
Targets and limits for input factors and responses

Table 5 .
Roll gap settings, weight fractions of the milling output size fractions and desirability (Example 1)

Table 6 .
Roll gap settings, weight fractions of the milling output size fractions and desirability (Example 2)

Table 7 .
Roll gap settings, weight fractions of the milling output size fractions and desirability (Example 3)