Study on the effects of smooth roll grinding conditions on reduction of wheat middlings using response surface methodology

Abstract

Influence of the milling parameters on the reduction process of the wheat middlings by the smooth rolls was investigated. Three level and four variables Box–Behnken experimental design with response surface methodology was applied in order to evaluate effects of milling parameters and to optimize grinding conditions for various responses. As independent variables roll gap (0.04–0.1 mm), differential (1.1.–1.9), roll speed (300–500 rpm) and feed rate (0.2–0.4 kg/cm min) were employed. Responsive variables were flour yield, ash content and energy consumption. In order to optimize milling process adequate models were obtained by regression analysis. Possibilities of the optimization of the milling parameters in order to obtain different combination of the desired outputs are illustrated by four examples.

Introduction

Wheat kernel is constituted of three main anatomic parts: endosperm, bran and germ. The main goals of wheat flour milling process are to separate aforementioned anatomic parts and to obtain maximum yield of flour consisted of purified endosperm particles with the lowest contamination of bran and germ which increase the flour ash content (Antoine et al. 2004). Therefore, it is required for grinding action to be highly selective in its nature. The roller mills are the principal grinding machines used in commercial flour milling because of their range of selective grinding and economy of operation (Posner and Hibbs 2005). Wheat flour milling is a gradual reduction process consisted of repeated size reduction (roller milling) and separation (sifting) and after every grinding step the ground material is sieved and the undersize material removed before regrinding. The grinding process is divided into different systems (break, sizing, reduction) and each of the system contains a number of grinding steps known as grinding passages. Break system aims to separate the endosperm from bran and germ, sizing system separates the small bran pieces from larger endosperm particles, and finally reduction system reduces the endosperm to flour.

The effectiveness of wheat flour milling process could be observed by three groups of indicators. The first ones are related to quantity measurements such are break release, flour yield, particle size distribution (PSD) of the output etc. The second ones indicate the effectiveness of achieved dissociation between endosperm and bran and they are measured by ash content of flour and intermediate streams, flour color or bran speck counts (Sakhare and Inamdar 2011; Kim and Flores 1999). Finally, the economy of the process is indicated by the energy requirements relative to the amount of flour produced.

In order to achieve these tasks two aspects of the milling process have to be considered. First are the properties of the milled material. Secondly, control of milling parameters such as roll gap, roll speed, feed rate, differential, roll surface, etc. due to their influence on the magnitude and the relative contributions of compressive and shearing forces acting on the particles in the grinding zone (Haque 1991). Both, change of the milling material properties and milling parameters, influence on these indicators (Campbell et al. 2001).

Thus, many researches have been conducted in order to define previously mentioned impact and to find optimum conditions for wheat flour milling. However, each of the milling system and even each of the grinding passages need to be examined separately, since the particles in different grinding steps vary in size and composition. This particularly applies to the break system, since the corrugated steel rolls are used while the roll surface characteristics vary from head break to tail break passages. The majority of the researches considering the effect of grinding parameters on the milling results are focusing on the break system (Hareland 1998; Manthey and Hareland 2001; Fang and Campbell 2002a, b, 2003; Niernberger and Farrell 1970; Schumacher 1966; McCorkle 1973; Creason 1975; Hsieh et al. 1980; Mateos-Salvador et al. 2011, 2013). On the other hand, a relatively small number of studies dealt with the effect of smooth roll grinding conditions in the reduction system. Scanlon and Dexter (1986) examined the effects of the roll velocity, roll differential and feed rate on the reduction of hard red spring wheat farina. All of the parameters were varied on the three levels: roll velocity (460, 550, 780 rpm), differential (1.19:1, 1.41:1, 2.0:1) and feed rate (5.9, 7.1, 10.0 kg/m⁻¹ min⁻¹). As output parameters particle size distribution, milling energy requirements, flour starch damage, ash content in flour fraction and flour color were observed. It has been shown that increase of roll velocity led to higher flour release with improvement of flour quality, while milling energy consumption rose. With decrease of the feed rate similar trend of output parameters change has been observed. Elevated roll differential increased flour starch damage, flour water absorption and milling energy consumption. The same author in his later work (Scanlon et al. 1988) investigated impact of roll gap and differential on particle size distribution of a milled stock. It has been shown that as roll gap decreases, greater stresses are imposed, increasing the number of fractures and the degree of particle size reduction. Moreover, it has been observed that with elevated differential the starch damage has increased. Similar influence of higher differential on the starch damage recognized Evers et al. (1984). In their work, authors varied differential in range from 1:1 to 1:31, and investigated impact of this change on flour yield and starch damage. It has been observed that increase of differential from 1:1 to 1:1.25 led to an increased flour yield while further increasing the magnitude of the shear forces imparted by the differential had little effect on flour release. Furthermore, elevated differential resulted with the production of increased levels of starch damage.

Response surface methodology (RSM) is well established method in scientific practice which simultaneously monitors the changes of input factors and it is able to analyze and quantify the significance of their influence (together with the influence of their interaction) to the output. In that sense it could be suitable tool for giving clearer insight in the wheat flour milling process. Fang et al. (1998, 2000) employed aforementioned methodology in order to collect experimental data, which was later on used for modeling of the grinding process on the first break passage using artificial neural networks (ANN). In similar manner, Dal-Pastro et al. (2016, 2017) applied RSM in their research to obtain data from roller mills and plansifters, which was thereafter used for modeling via different mathematical models (principal component analysis (PCA), partial least-square regression method (PLS) and Joint Y PLS (JY-PLS)). Although experiments were carried out for nine different passages, in their work authors reported results from second breakage passage and first reduction passage, as a representative for modeling of the breakage and reduction operation. Fišteš et al. (2017) investigated the possibility of optimization of the wheat roller milling operation using RSM. This work intended to find the best combination of the roll gaps on three consecutive pairs of rollers in order to obtain desired particle size distribution of the milled stock. Author showed that it is possible to optimize wheat grinding using RSM, and defined adequate model which provided combination of roll-gap settings that leaded to the targeted PSD of the milling outputs.

However, to our best knowledge no researches have been conducted on using RSM in order to investigate combined impact of milling parameters on the wheat flour milling process effectiveness. Therefore, the aim of this work was to investigate effects that roll gap, roll speed, feed rate and the differential have on the milling results obtained by the smooth roll grinding of middlings (intermediate stocks) in the reduction system of the flour milling process. More precisely the goal was to inspect impact of aforementioned parameters and their interactions on flour yield (fraction < 150 µm), flour ash content and energy consumption. For that purpose, response surface methodology was used and the Box-Behnken experimental design was applied.

Materials and methods

Material

The sample was obtained from local industrial mill (300 t/day) by intercepting cleaned middlings from the purification system, which normally would have gone to the reduction system of the flour milling process. This material can also be regarded as fine semolina. Total mass of the sample was 50 kg. Sample was firstly characterized in terms of granulation, moisture content and ash content. Granulation of sample has been determined using sieve analysis, and following percentage of the fractions was obtained: fraction > 450 µm–38.79%, 450/350 µm–46.69%, 350/250 µm–10.06% and fraction < 250 µm–1.35%. Ash content and moisture content have been determined according to ICC standard methods (No. 104/1 and 110/1, respectively), and results were: 0.43% (calculated on dry matter basis) and 12.26%, respectively. After that, material was homogenized and then separated using the automatic sampler divider (Gompper–Maschinen KG) into 1 kg batches.

Milling of wheat middlings

For each experiment, 1000 ± 0.01 g of cleaned wheat middlings were milled on the laboratory roll stand Variostühl, model C Ex 2 (Miag, Braunschweig, Germany), equipped with smooth rolls (100 mm length and 250 mm diameter) having a frosted finish. Smooth rolls used in the reduction system of the wheat flour milling process usually have roll surface roughness of approximately 2.5 to 3.5 µm (Posner and Hibbs 2005; Inauen 2018). All operating parameters of the mill were varied at three levels according to experimental plan. Roll gap (0.04, 0.07 and 0.1 mm), differential (1.1., 1.5. and 1.9), roll speed (300, 400 and 500 rpm) and feed rate (0.2, 0.3 and 0.4 kg/cm min) were employed as independent variables. The upper and lower levels for input parameters were chosen based on the previous research associated with the investigated topic (Scanlon and Dexter 1986 and Scanlon et al. 1988) and chosen to be near the ranges that are likely to occur in commercially milling. The responsive variables were: R1: flour yield (%), R2: flour ash (%)_dm, R3: energy consumption in relation to milled material (kJ/kg) and R4: energy consumption in relation to obtained flour (kJ/kg).

Flour analysis

Sieve analysis of milled stock was performed on the Bühler laboratory sifter (gyratory in a horizontal plane), model MLU-300 (Uzwil, Switzerland) using the entire milled stock (10 batches of 100 g). Samples were sieved for 3 min in order to obtain flour (< 150 µm). The stock held on a bottom collecting pan was weighed to 0.01 g using a Sartorius Precision balance (Sartorius AG, Germany) and flour yield is given relative to the mass of input material. Ash content in flour was determined according to ICC standard method No. 104/1.

Energy consumption

Integral part of laboratory roll stand is an instrument for measuring the power (kW) required for roll stand to operate without and/or with material flow. This instrument was used to obtain data for calculation of total energy consumption during the milling operation according to the following equations:

$$E=\frac{P_w}{m}·t$$ 1

$$E=\frac{P_w}{M}·t$$ 2

Equation (1) was used to calculate total energy consumption in relation to the mass of the obtained flour. Here, P_w (kW) represents the power reading corresponding to the operation of the roll stand with the material flow. Time of the grinding run determined by the chronometer is denoted by t (s), while m (kg) stands for the weight of the obtained flour. Total energy consumption in relation to the mass of the milled sample was calculated by Eq. (2), where M (kg) stands for weight of the native feed, while P_w (kW) and t (s) have same connotation as in Eq. (1).

Statistical analysis

Experimental runs were performed according to Box-Behnken experimental design (BBD) with four independent process parameters at three levels and with three replicates at the central point. This design reduces the number of runs from 81 (full factorial design) to 27, with sufficient information for testing of the lack of fit, since three central point are included. Four independent process parameters were: A—roll gap, B—roll speed, C—differential and D—feed rate. Flour yield, ash content in flour, energy consumption in relation to milled material and energy consumption in relation to obtained flour have been observed as a responses, R1–R4, respectively. The regression analysis is performed and model is described by the polynomial of second order:

$$\begin{array}{cc}\hfill \text{R}& ={\beta }_0+{\beta }_1\text{A}+{\beta }_2\text{B}+{\beta }_3\text{C}+{\beta }_4\text{D}+{\beta }_{12}\text{AB}+{\beta }_{13}\text{AC}+{\beta }_{14}\text{AD}+{\beta }_{23}\text{BC}\hfill \\ \hfill & +{\beta }_{24}\text{BD}+{\beta }_{34}\text{CD}+{\beta }_{11}{\text{A}}^2+{\beta }_{22}{\text{B}}^2+{\beta }_{33}{\text{C}}^2+{\beta }_{44}{\text{D}}^2\hfill \\ \hfill \end{array}$$ 3

where, R is a measured response; β₀ is an intercept; β₁ to β₄₄ are regression coefficients; A, B, C and D are the coded levels of input factors. The terms AB, AC, AD, BC, BD and CD represent interactions of input factors, while A², B², C² and D² represent quadratic terms.

Model adequacy checking is done by calculating the R² and “Lack of Fit” (LoF) coefficients. Significance of input factors and their interactions in the observed model are determined by statistical method of analysis of variance (ANOVA). Using 5% level of significance, a factor is considered as statistically significant if the p value is less than 0.05. Sum of squares obtained by ANOVA are used to calculate the corresponding contributions. The analysis was carried out using Statistica 13.5 and Design-Expert 11 (Anderson and Whitcomb 2007).

Results and discussion

A total of 27 experimental runs were determined by the Box-Behnken design. Recommended order of milling parameters combinations and the obtained responses, i.e. flour yield, ash content and energy consumption are presented in Table 1.

Table 1.

The Box-Behnken experimental design and obtained responses

Grinding	A	B	C	D	R1	R2	R3	R4
Run
1	0.1	500	1.5	0.3	10.26	0.43	35.87	349.74
2	0.07	400	1.5	0.3	14.49	0.41	33.64	232.21
3	0.07	500	1.5	0.2	21.33	0.39	55.6	260.65
4	0.07	400	1.1	0.2	10.48	0.36	36.85	351.62
5	0.07	500	1.5	0.4	13.66	0.37	34.74	254.32
6	0.04	500	1.5	0.3	17.85	0.39	42.98	240.81
7	0.07	400	1.9	0.4	11.8	0.42	37.77	320.21
8	0.07	400	1.5	0.3	14.19	0.39	34.44	242.73
9	0.04	400	1.5	0.4	12.05	0.41	33.45	277.73
10	0.07	300	1.9	0.3	11.01	0.42	36.84	334.78
11	0.07	400	1.9	0.2	16.83	0.42	53.07	315.21
12	0.04	400	1.5	0.2	21.76	0.39	53.63	246.46
13	0.07	500	1.1	0.3	10.52	0.38	31.75	301.77
14	0.1	400	1.9	0.3	9.3	0.43	36.02	387.34
15	0.1	400	1.1	0.3	6.23	0.42	22.85	367.04
16	0.07	400	1.5	0.3	12.94	0.41	33.76	260.86
17	0.04	400	1.1	0.3	10.19	0.41	26.26	257.67
18	0.07	300	1.5	0.4	10.06	0.37	24.96	248.2
19	0.07	400	1.1	0.4	6.45	0.4	19.69	305.51
20	0.04	400	1.9	0.3	14.07	0.42	45.15	320.9
21	0.1	400	1.5	0.4	9.61	0.39	26.35	274.36
22	0.1	400	1.5	0.2	10.26	0.43	40.6	395.9
23	0.04	300	1.5	0.3	12.91	0.4	31.38	243.08
24	0.07	300	1.5	0.2	14.63	0.39	38.31	261.93
25	0.07	300	1.1	0.3	5.56	0.45	22.08	397.43
26	0.07	500	1.9	0.3	15.38	0.41	49.28	320.38
27	0.1	300	1.5	0.3	9.17	0.42	25.09	273.72

Regression coefficients are represented in Table 2 where by star are denoted input factors, their interactions and their quadratic terms which expressed statistically significant influence on the observed responses, according to p values from ANOVA table (p < 0.05). Coefficient of determination (R²) was used to check if applied model provides proper representation of experimental data. Lack of fit testing confirmed adequacy of fitting experimental data to a second-order polynomial model since p-values for lack of fit were insignificant (p > 0.05).

Table 2.

Regression equation coefficients for responses

	Responses
	R1	R2	R3	R4
Intercept
β0	13.84	0.4006	33.28	259.07
Linear
β1	− 2.83*	0.0083	− 3.84*	38.45*
β2	2.14*	− 0.007	5.96*	− 2.62
β3	2.41*	0.0069	8.22*	1.48
β4	− 2.64*	− 0.0037	− 8.42*	− 12.62
Interaction
β12	− 0.9625*	0.0054		19.58
β13			− 1.43*
β14	2.27*	− 0.0134	1.48*	− 38.2*
β23		0.0165		20.32
β24	− 0.775		− 1.88*
β34				12.78
Quadratic
β11	− 1.11*	0.0102		22.09
β22			1.03
β33	− 3.09*	0.0107		65.23*
β44		− 0.0138	4.3*
Lack of fit	0.533	0.2544	0.0942	0.2246
R2	0.9689	0.615	0.9881	0.8294

*Statistically significant at p < 0.05

Contribution plots of the milling parameters influencing investigated responses and trend of influence of following parameters on responses are represented by Figs. 1 and 2.

Fig. 1.

Contribution plot of milling parameters influencing: a flour yield; b energy consumption in relation to milled material; c energy consumption in relation to obtained flour

Fig. 2.

Influence of the milling parameters on the: (1) flour yield; (2) flour ash content; (3) energy consumption in relation to milled material; (4) energy consumption in relation to obtained flour

Influence of milling parameters on the flour yield

Flour yield values ranged from 5.56% up to 21.76% (Table 1), while p values from ANOVA table suggested that all linear terms of selected milling parameters and quadratic term of the differential and roll gap had significant impact on the observed response. Moreover, it is suggested that interactions of the roll gap and roll speed as well as roll gap and feed rate significantly influenced flour yield. Contribution plot of the milling parameters influencing flour yield is represented by Fig. 1a, while high value of coefficient of determination represented in Table 2 (R² = 0.9689) suggests that proposed model adequately represents observed experimental data.

Decrease of the roll gap resulted with higher flour yield (Fig. 21a). Probably the most adequate representation of the dominant influence of the roll gap on the flour yield could be illustrated by runs 12 and 22. In these runs roll speed, differential and feed rate were held at the same levels (400 r/min, 1.5 and 0.2 kg/cm min, respectively) while roll gap was increased from 0.04 mm to 0.1 mm. This change decreased flour yield from 21.76 to 10.62%, which is a relative decrease of 52.84%. Negative contribution of the enlargement of the roll gap on the flour yield is rather expected, since with the increase of the roll gap, particles are less exposed to stress and compression forces, which leads to decreased number of fractures and the degree of particle size reduction. Moreover, narrower roll gap as a consequence has increase of the grinding zone, causing prolonged grinding action. These results are in accordance with earlier researches related to influence of the roll gap on the flour yield (Scanlon et al. 1988; Fistes et al. 2008; Fistes and Rakić 2015). On the other hand, increase of the roll speed had positive impact on the flour release (Fig. 21b), since the transmission of the deformation forces from rolls to particles of the grinded material is improved with higher roll velocities. Scanlon and Dexter (1986) also reported that with increase of the roll velocity particles are drawn through grinding zone more quickly, which enhance their brittleness, leading to increased flour production. Observed trend of influence of the roll velocity on the flour yield was in concordance with the ribbon theory for flour production, presented by Perry and Chilton (1973). The ribbon theory predicts that grinding action is proportional to the ratio of the roll velocity and the feed rate. When roll velocity is increased the feed ribbon spreads out, reducing the load in the grinding zone. The increased grinding action on particles resulting from reduced ribbon width causes greater flour release as roll velocity increases.

Furthermore, according to the ribbon theory, increased feed rate reduces the amount of grinding any given particles receives, thus influencing negatively on the flour yield (Fig. 21d). With the increment of the feed rate, more material needs to be comminuted in the same period of time. Therefore, intensity of the grinding action was dispersed on the higher number of particles and every single particle was less exposed to deformation forces, which led to reduced flour yield.

Differential was the only parameter that expressed double-natured influence on the flour yield. With the raise of the differential from the 1.1 to 1.65 flour yield increased, after which elevation of the differential had negative impact on the flour release (Fig. 21c). This kind of trend is suggested with high contribution of quadratic term of parameter C (Fig. 1a). Aforementioned phenomenon was noticed and described in earlier researches addressing influence of the differential on the flour yield. However, certain differences exist between previously reported values of the differential at which change of the trend occurs (i = 1.4—Scanlon and Dexter 1986; i = 1.5—Scanlon et al. 1988; i = 1.25 - Evers et al. 1984). When roll differential is set at the values closer to 1, dominant forces in grinding zone are compressive forces. With the elevation of the differential, greater shear stresses are imposed, which alters relative contribution of compressive and shearing forces. In this study, samples are composed primarily from endosperm, and for the disintegration of such material compressive forces are more effective compared to shear forces. Thus, milling efficiency as measured by flour release is higher in the region of small roll differentials.

Interaction of the roll gap and feed rate contributed relatively significantly (approximately 5%) on the flour yield. This interaction would probably be more influent in cases of combination of extremely small roll gap and high feed rate. In that case material affect roll gap by expanding it, which is followed by the decrease of the degree of particle size reduction, and later on influences on the reduction of the flour release.

Highest flour yield was registered in experimental runs 12 (21.76%) and 3 (21.33%). In both of these runs differential and feed rate were set at the same value (1.5 and 0.2 kg/cm min, respectively), while roll gap and roll speed had different values. As it can be noticed, flour yield was maximized when feed rate was set at minimum value and roll differential was set close to the value at which change of the influence of the differential on the flour yield was observed (1.65—Fig. 21c). In run 12, roll gap was set to lowest value (0.04 mm) with roll speed of 400 r/min, while in run 3 roll gap and roll speed were 0.07 mm and 500 r/min, respectively. It could be observed that raise of the roll speed from 400 r/min in run 12, to 500 r/min in run 3 refunded expected reduction of the flour yield induced by enlarged roll gap. This could be attributed to a fact that with higher roll speed transmission of the deformation forces from rolls to a grinded material is faster. In that manner, decrease of the deformation forces produced by larger roll gap was compensated, and flour yield remained closely equal.

Influence of milling parameters on the ash content

As it can be observed from Table 1, flour ash content varied in relatively narrow range from 0.36 to 0.45%_dm. Statistically insignificant impact of the main input factors or factor interactions and squared terms of factors on the observed responses was suggested by p values from ANOVA table. Moreover, relatively low value of coefficient of determination represented in Table 2 (R² = 0.615) indicated inadequacy of the applied model. Aforementioned could be attributed to the very low ash content in the milled samples. As it was mentioned, milled samples are cleaned middlings from the purification system, which is mostly constituted of the endosperm particles. Thus, the lack of the outer parts of the wheat kernel in the samples contributed to the low ash content in obtained wheat flour, regardless of flour release. Certain differences exist in the amount of the flour, but not in its composition.

Trend of the influence of the operating parameters on the observed response was shown in Fig. 22, where it could be observed similar impact of the roll gap and differential on the ash content in wheat flour (Fig. 22a, 2c). Firstly, ash content was decreased with increase of observed parameters to the certain value, after which ash content went higher with further increase of the parameters A and C. Similar influence of the differential on the ash content was noticed in previous researches (Scanlon and Dexter 1986; Scanlon et al. 1988).

Feed rate expressed opposite trend, and with its increase ash content in milled samples raised to a maximum point, while, afterwards, elevated feed rate led to decrease of the ash flour content (Fig. 22d). Scanlon and Dexter (1986) also investigated impact of the feed rate on the ash content, but in different range (from 0.5 to 1 kg/cm·min). Authors noticed that percentage of the ash in flour samples gradually rose with increase of the feed rate. Same authors observed that with elevated roll speed ash content in obtained flour decreased. The trend of influence of the roll speed on the ash content in the obtained flour, registered in this paper, was in accordance with the observations made by Scanlon and Dexter (1986) (Fig. 22b).

Influence of milling parameters on the energy consumption in relation to milled material

Although every linear term expressed statistically significant influence on the observed response (Table 2) it could be suggested that feed rate exhibited most dominant impact (approximately 40% in the sum of linear and quadratic term) on the total energy consumption in relation to the milled material (Fig. 1b). The basic assumption was that with the higher feed rate energy consumption will raise, since the mass flow of milled material is going to be higher. Nevertheless, Fig. 23d showed that the trend of the influence of the feed rate on the energy consumption was opposite. The cause of contradictory trend of impact could be explained by Eq. 2 which was used for calculation of the observed response. Since, in mentioned equation, mass of material (M) was constant (1000 ± 0.01 g), factors influencing energy consumption were power during operation of the roll stand with the material flow (P_w) and milling time (t). Values for power ranged from 0.99 to 2.11 kW, and it was observed that elevation of the feed rate resulted with higher values of power. This was expected, since more power is required to overcome higher mass flow of material. However, with the increase of the feed rate from 0.2 kg/cm min to 0.4 kg/cm min, milling time significantly shortened (approximately from 33 s to 17 s, respectively) for all observed runs. Thus, difference of milling time in runs with different levels of feed rate influenced more significantly on energy consumption than roll stand power requirements during milling operation. Therefore, increase of the feed rate required higher power consumption, but exhibited negative influence on the overall energy consumption in relation to milled material (Fig. 23d).

Enhancement of the roll velocity and increase of the differential led to higher energy consumption. This kind of positive influence of observed factors on the response (Fig. 23b, 3c) was rather expected, since for maintaining the elevated levels of roll velocities and differential requires higher driving power. The most economical way is to run the rolls at the lowest rpm necessary to handle the capacity (Posner and Hibbs 2005). Similar trend of influence of roll velocity and differential on energy consumption was observed in previous works of authors investigating featured topic(Scanlon and Dexter1986; Scanlon et al. 1988; Wanzenreid 1970; Zwingelberg et al. 1983). On the other hand, enlargement of the roll gap, influenced on the reduction of the energy consumption (Fig. 23a). This is explained by the fact that when roll gap is set to higher levels, power required for overcoming particle resistance during milling process is decreased. Therefore, increased roll gap influenced negatively on the energy consumption. This observation was in accordance with previous works investigating similar theme (Scanlon et al. 1988; Fišteš and Tanović 2007).

Influence of milling parameters on the energy consumption in relation to obtained flour

Energy consumption in relation to obtained flour is a responsive variable that was directly related to a R1 (flour yield), and it could be observed as a consequence of the obtained flour in featuring run (Eq. 1). From ANOVA table it could be concluded that linear term of roll gap, interaction of roll gap and feed rate and quadratic term of differential expressed statistically significant impact on energy consumption. Considering Figs. 21, 4 it could be suggested that trend of influence of milling parameters on flour yield and energy consumption was opposite for all parameters except feed rate. This kind of trend was rather expected and suggested with Eq. 1. From Figs. 24a, 4b it could be observed that with the decrease of the roll gap and increase of the roll speed less energy in relation to obtained flour was required, which is direct consequence of the higher flour yield. On the other hand, as in a case of the flour yield, differential exhibited double-natured influence on the observed parameter (Fig. 24c), which was also suggested by the contribution plot (Fig. 1c), where quadratic term of parameter C contributed with 45.54%. Firstly, with the increase of the differential from 1.1 to 1.50 energy consumption reduced, while with further increase of the differential energy consumption requirements rose. This kind of trend was directly connected to the influence of the differential on the flour yield. As described in Sect. 3.1, with higher differential flour yield increased to the value of 1.65, and this increase in the flour yield influenced on the decrease of the energy consumption. Afterwards trend of influence of the differential changed, which resulted in higher energy requirements. It is notable that change of influence of differential on flour yield and energy consumption occurred at the relatively similar values (1.65 and 1.50, respectively). Feed rate was only parameter which expressed similar (negative) trend of the influence on the flour yield and on energy consumption (Figs. 21d, 4d). Explanation of this phenomenon is, as in Sect. 3.3, in a fact that with higher feed rate less time was needed to mill sample material, which later on resulted in reduced energy consumption.

RSM optimization

One of the main advantages of RSM is possibility of simultaneous optimization of multiple responses in investigated experimental domain. Aforementioned requires obtaining of the adequate response surface model for each response and afterwards finding a set of process parameters at which responses are on the optimal levels or at least kept in desired interval (Myers et al. 2009). Models obtained in this work were used to perform the optimization of the process parameters in order to find optimal combination of the milling settings (roll gap, roll speed, differential and the feed rate) which would provide targeted levels for responses (flour yield, ash content and energy consumption). Four different systems were observed, depending on target responses, and for all cases input parameters were held within experimental range (Table 3). Suggested milling settings and thus obtained responses together with desirability functions are represented in the Table 4. It needs to be emphasized that Table 4 represents only one of the recommended solutions for every of four different examples. Reason for this is that practically there was no difference between proposed sets of the milling parameters and thus obtained results.

Table 3.

Targets and limits for input factors and responses

Input factors	Target	Limit value
		Lower	Upper
A: Roll gap [mm]	in range	0.04	0.1
B: Fast roll speed [r/min]	in range	300	500
C: Differential	in range	1.1	1.9
D: Feed rate [kg/cm min]	in range	0.2	0.4

Example	Responses	Target	Limit value
			Lower	Upper
1	R1: flour yield [%]	Maximize	5.56	21.76
	R2: flour ash [%]dm	Minimize	0.36	0.45
	R3: energy consumption (kJ/kg) in relation to milled material	Minimize	19.69	55.6
2	R2: flour ash [%]dm	Minimize	0.36	0.45
	R3: energy consumption (kJ/kg) in relation to milled material	Minimize	19.69	55.6
	R4: energy consumption (kJ/kg) in relation to obtained flour	Minimize	232.21	397.43
3	R1: flour yield [%]	Maximize	5.56	21.76
	R2: flour ash [%]dm	Minimize	0.36	0.45
	R4: energy consumption (kJ/kg) in relation to obtained flour	Minimize	232.21	397.43
4	R1: flour yield [%]	Maximize	5.56	21.76
	R2: flour ash [%]dm	Minimize	0.36	0.45
	R3: energy consumption (kJ/kg) in relation to milled material	Minimize	19.69	55.6
	R4: energy consumption (kJ/kg) in relation to obtained flour	Minimize	232.21	397.43

Table 4.

Milling parameters, responses and desirability for all investigated examples

Example	Input factors				Responses				Desirability [%]
Example 1	A	B	C	D	R1	R2		R3	63.11
	0.05	500	1.27	0.31	15.65	0.38		36.86
Example 2	A	B	C	D	R2	R3		R4	84.69
	0.07	500	1.22	0.4	0.37	28.64		249.80
Example 3	A	B	C	D	R1	R2		R4	100
	0.04	495.27	1.3	0.2	21.91	0.36		213.98
Example 4	A	B	C	D	R1	R2	R3	R4	70.66
	0.05	500	1.3	0.3	16.25	0.38	37.79	232.21

In the first example (Table 4), investigated parameters were set to meet requirements for maximum flour yield (R1) and minimum flour ash content (R2) and energy consumption in relation to milled material (R3). Relatively low desirability (63.11%) for all suggested solutions indicates that observed responses conflicts one another, thus preventing higher level of satisfaction. In this particular case, for maximization of the flour yield roll gap and feed rate needs to be set at lower levels, while differential should be higher, as well as roll speed (Fig. 21a, 1d). Such combination of the input parameters influences on the increase of the energy consumption (Fig. 23a, 3d), thus making it impossible to achieve maximum satisfaction for both requirement.

Aforementioned is further corroborated with example 2 where responses were ash content, energy consumption in relation to milled material and energy consumption in relation to obtained flour. Parameters were set to minimize energy requirements and since these two responses do not affect each other as dominantly as responses in example 1, achieved desirability of suggested solutions was higher (84.69%). However, considering that difference between featuring set of parameters and combination from example 1 is increased roll gap and feed rate it is reasonable to assume that with these solutions obtained flour yield would probably be on lower levels. This assumption is suggested by negative influence of increase of the roll gap and the feed rate on flour yield (Fig. 21a, 1d).

Example 3 illustrates case where maximum desirability (100%) was achieved. In following example it was possible to set process parameters in that manner to obtain maximum flour yield and simultaneously not to influence on the elevation of the energy requirements. This was rather expected since it has been shown that energy consumption in relation to obtained flour is a responsive variable that is directly related to a flour yield. Change of the milling conditions that leads to the increase in flour yield affects decrease of the energy requirements.

In last example four responses were observed together with same level of the importance for all responses. As expected, desirability of the proposed solutions decreased (70.66%), since responsive variables conflicted with each other, especially in case of flour yield (R1) and energy consumption in relation to the milled material (R3). In this case in order to obtain higher flour yield it is necessary to modify milling parameters so that energy requirements increase. Consequently, energy consumption in relation to the milled material increases. However, it should be noted that flour yield does not conflict with energy consumption in relation to obtained flour (R4). This difference between interactions of the responses is explained by the equations for calculation of the both energy consumptions (Eqs. 1 and 2). Higher flour yield implies increase in the flour mass (factor M from the Eq. 2), which results in reduce of the energy consumption in relation to the obtained flour. On the other hand, flour mass is not implemented in the Eq. 1 for calculation of the energy consumption in relation to milled material. Therefore, set of milling parameters for obtaining higher flour yield (R1) conflicts only with energy consumption in relation to the milled material (R3), but not with energy consumption in relation to obtained flour (R4).

Conclusion

RSM was successfully utilized in order to evaluate effects of the milling parameters on the flour yield, ash content and on energy consumption. It has been shown that all investigated milling parameters influenced flour yield and energy consumption in relation to the milled material. Roll gap together with differential crucially affected energy consumption in relation to the obtained flour. Ash content in the flour fraction did not drastically changed with the differences in the operating parameters, which was explained by high purity of the milled samples and their low ash content. Optimization of the milling process via smooth rolls has been conducted. Obtained set of parameters by which maximum flour yield with low ash content and minimum energy consumption will be achieved was as follows: roll gap 0.05 mm, differential 1.3, roll speed 500 rpm and feed rate 0.3 kg/cm min. According to predicted values for the responses, at aforementioned milling conditions expected flour yield would be 16%, while other responsive variables would be as follows: ash content 0.38%, energy consumption in relation to milled material 37.8 kJ/kg and energy consumption in relation to obtained flour 232.2 kJ/kg. It is demonstrated that RSM could be successfully utilized for optimization of the milling process in cases where investigated responses do not conflict each other. Thus, in cases when optimized responses were flour yield and energy efficiency of the process expressed as energy consumption in relation to the obtained flour, maximum desirability of 100% was achievable.