The Integrated Energy Consumption Index for Energy Biomass Grinding Technology Assessment

: The assessment of engineering objects in terms of energy consumption is an important part of sustainable development. Many materials, including those from the energy sector, need to undergo earlier processing, e.g., grinding. Grinding processes still demand a signiﬁcant amount of energy, whereas current energy assessment methods do not take into account important parameters of the process, which makes it di ﬃ cult to choose their optimal values. The study presents the analysis, testing


Introduction
The simplest and the most common method of biomass utilization is its combustion, e.g., in the boilers of a power station [1]. There are also other forms of energy production that are increasing in popularity, including: gasification, biomethane production, esterification, the acquisition of bioethanol, etc. [2,3]. Depending on the energy purpose and type of biomass, the comminution process will vary-in particular, in terms of the desired final dimension of the comminution product [4,5]. In the case of anaerobic digestion, biomass is comminuted to several millimeter fractions [4]. Pellets are usually made of fibrous biomass ground to 2-4 mm or smaller, depending on the briquetting machine design, while briquettes, from particles smaller than 10 mm [6]. In the production of biofuels, in turn, biomass particles should be in the range of 100-500 µm, and for gasification and direct combustion processes, below 100 µm [4]. Previous research has shown that the smaller the biomass particles are used for energy purposes, the greater the efficiency and easier control of biomass thermochemical transformation processes [5]. Table 1. Energy assessment criteria of the grinding process presented in the literature.

Criterion Mathematical Model
Overall net energy for a grinding unit of dry mass [2] E T -Overall net energy for grinding unit of a dry biomass , kJ kg DM −1 ; P T -power consumed by the machine in time, t; W,-average power input of the grinder neutral gear , W; ∆P T -net power input for biomass grinding in time t, W; and m DM -mass of the ground dry feed mass, kg.
Specific grinding Energy [7] E spec = 1/m T 0 (P T − P 1 ) dt E spec -Specific energy of grinding, J·kg −1 ; P T -total power consumption, W; and P l -power consumed by the grinder without being loaded by the feed, W.
Specific energy of grinding [62] E r = (E c − E s )/m (5) E r -specific energy of grinding, J·kg −1 ; m-mass of the ground sample of material, kg; E c -overall energy consumption, J; and E s -neutral gear energy consumption, J.
Energy efficiency [58] EE = E m (SP)/E m (Mill)·100 (7) EE-energy efficiency, E m (SP)-specific energy used for grinding a single particle, and E m (Mill) -specific energy net energy used for production of a given product.
Target energy efficiency [58] EE = E m (SP)/E m (Mill)X 50 ·100 (8) EE-energy efficiency, E m (SP)-specific energy used to generate a product with a given average dimension X 50 , and E m (Mill)X 50 -net specific energy used to generate a product with average dimension X 50 .
Research problems were formulated in the form of questions in relation to the research goals established herein: 1.
Will the development of an adequate mathematical model of energy consumption considering basic parameters of the process such as the yield, fineness degree, unit energy consumption, and power input enable the integrated design of the structure, disc parameters, and hole movement in shearing culvert discs? 2.
What is the impact of deliberately changed characteristics and relations of the unit motion on the yield, fineness degree, power input, unit energy consumption, and integrated index of sustainable granular biomass grinding energy consumption in a multi-hole grinding unit?

Integrated Energy Consumption Index
The introduction of energy and pro-environment-based assessment into the construction-optimization process of the technology of energy biomass grinding leads to the creation of new, better structural and process solutions. In a sense, it is a driving force for biomass-processing competitiveness and innovativeness [66,67]. Paper [68] indicates that energy efficiency assessments make it possible to improve the grinder process motion parameters and indicates technologies which are the best for a given product. It has also been proven that the developed efficiency models can be used not only for process verification but also for verification of the whole structure of grinding, particularly the working unit.
Developing an adequate mathematical model and finding functional dependences between the variables are important elements of each assessment (structural-optimization efficiency) [69]. The first step should involve the identification of the assessed processes and subprocesses and the determination of criteria [68].
The assumption of the model of integrated energy consumption for grinding takes into account the most important grinding indexes, which are indirectly or directly connected with power and energy demand. First of all, the criteria for power consumption assessment, unambiguously characterizing the grinding device, were established. The following criteria were accepted as components of the model of integrated energy consumption, in accordance with the desired states of the grinding process [70,71]: • Yield of grinding K Qr : • Power demand K P : • Unit energy demand K Ej : • Fragmentation degree K i : where Q r -yield of grinding, kg·h −1 ; P r -average power consumption of grinding, kW; E j -unit of energy consumption, kWh·kg −1 ; and i 80 -80% fragmentation degree.
The yield of grinding is indirectly related to the power and energy consumption of grinding. Increasing the yield is usually associated with an increase in the grinder dimensions and, subsequently, an increase in the power of the drive unit, which involves a change of energy parameters. In the machine conditions, grinding yield Q r can be determined on the basis of a dependence of grinding product mass change ∆m in the intake hopper during the time of observation ∆t [19]: which can further be written: Power consumption for grinding changes in time, which is caused by an irregularity in the operation of the machine [72]. In the simplest way, it can be defined as a periodical occurrence of rises and falls in power consumption as a result of variable amounts of materials between the working Energies 2020, 13, 1417 6 of 26 elements, which causes momentary periods of the machine running idle during grinding (with no feed). In connection with this, the overall power consumption in time t P toti can be defined as [7,73]: where P ui -power consumption for the medium grinding in a given moment t, kW and P ii -power consumption of the idle gear in a given moment t, kW. Then, the total grinding power consumption P r in a certain time interval T is an average of the momentary power consumption, according to the equation: Grinding processes are characterized by the parameters of the unit energy demand; therefore, they were accepted to be a component of the integrated energy consumption index model. Generally, a unit energy demand is defined as the amount of energy per mass unit of the material (volume) [2,7,20,63,64]. For the grinding machine unit, demand E j is expressed as a ratio of average power consumed by the grinder P r to yield Q r [19,63,73]: The last criterion of the model of integrated energy consumption was accepted to be the fragmentation degree, being a determiner of the product quality and effectiveness of the grinding process [20,74]. Most generally, the fragmentation degree is defined as a ratio of the material mean dimensions before grinding to its mean dimensions after grinding [21,75]. So far, it has been proven that increasing the frequency of the machine element contact (by increasing the rotational, angular, and linear speeds of the grinding elements) and repetitions of grinding provides an output product with smaller dimensions-that is, with a higher fragmentation degree [72,76]. Unfortunately, it causes higher energy consumption [27,77,78]. The energy consumption model assumes a fragmentation degree of 80% i 80 , defined as [19]: where D 80 -dimension of the sieve hole through which 80% of the feed material passes and d 80 -dimension of the sieve hole through which 80% of the grinding product passes. The model of integrated energy consumption was constructed in the same way as the model of efficiency described in paper [68]. This made it possible to establish a quantitative relation between the most important grinding indexes in terms of energy consumption. Integrated energy consumption was described in the criteria-based approach proposed by J. Zawada in the following way [79]: Bearing in mind dependences (11)- (14) and (22), integrated energy consumption depends, in direct proportion, on the yield and fragmentation degree and, in an inverse proportion, to the power consumption and unit energy demand. Assuming that the state to be desired is that in which Q→ ∞, i 80 → ∞, P r → 0, and E j → 0, then E zint → ∞. In the sustainable approach, a better process will be the one with a higher integrated energy consumption index value (22).

Raw Materials
Rice and corn grains that are unsuitable for food purposes due to having been stored in inappropriate conditions that were used for the production of pellets underwent grinding in the experimental tests, verifying the correctness of the integrated energy consumption model. Both crops are extensively grown, and both of them have found applications in the energy sector due to their good energy characteristics, which make them suitable for the production of pellets whose calorific value is similar to that of a wooden biomass [80]. Grain moisture was determined on a moisture balance MAC 210/NP (RADWAG, Radom, Poland) by means of the weight method. Rice grains were characterized by moisture at the level of 13.47% ± 0.02%, whereas corn was at the level of 12.68% ± 0.02%. The characteristic dimension of grain D 80 for corn was 8.15 mm and, for rice, 2.14 mm (Figure 1). These values were obtained on the basis of a granulometric analysis carried out on a Camsizer (Retsch Technology GmbH, Haan, Germany) design according to the ISO norm 13322-2:2006 [81].
Energies 2020, 13, x FOR PEER REVIEW 7 of 27 value is similar to that of a wooden biomass [80]. Grain moisture was determined on a moisture balance MAC 210/NP (RADWAG, Radom, Poland) by means of the weight method. Rice grains were characterized by moisture at the level of 13.47%  0.02%, whereas corn was at the level of 12.68%  0.02%. The characteristic dimension of grain D80 for corn was 8.15 mm and, for rice, 2.14 mm (Figure  1.). These values were obtained on the basis of a granulometric analysis carried out on a Camsizer (Retsch Technology GmbH, Haan, Germany) design according to the ISO norm 13322-2:2006 [81].

Test Stand
Verification of the model of integrated energy consumption was performed on a test stand for the intelligent monitoring of performance characteristics of a multi-disc grinder. The test stand was composed of: a five-disc mill, a control panel with a performance monitoring system, and an integrated system for analysis of the grinding product's particle size ( Figure 2). Test stand for the intelligent monitoring of granular mass characteristics: 1-five-disc grinder, 2-worm feeder, 3-hopper, 4-control unit, 5-reception basket of the product of grinding, 6-weight of the product of grinding, and 7-integrated system for the analysis of the grinding product's particle size [28].
A five-disc mill was equipped with a special integrated system for feed-dosing with a screw conveyor feeder, which makes it possible to control the feeding of the grain material into the grinding chamber. The grinding unit consists of five multi-hole discs fixed on the grinder shaft ( Table 2). Each disc is powered individually by means of a dedicated motor which enables precise control of the

Test Stand
Verification of the model of integrated energy consumption was performed on a test stand for the intelligent monitoring of performance characteristics of a multi-disc grinder. The test stand was composed of: a five-disc mill, a control panel with a performance monitoring system, and an integrated system for analysis of the grinding product's particle size ( Figure 2). value is similar to that of a wooden biomass [80]. Grain moisture was determined on a moisture balance MAC 210/NP (RADWAG, Radom, Poland) by means of the weight method. Rice grains were characterized by moisture at the level of 13.47%  0.02%, whereas corn was at the level of 12.68%  0.02%. The characteristic dimension of grain D80 for corn was 8.15 mm and, for rice, 2.14 mm (Figure  1.). These values were obtained on the basis of a granulometric analysis carried out on a Camsizer (Retsch Technology GmbH, Haan, Germany) design according to the ISO norm 13322-2:2006 [81].

Test Stand
Verification of the model of integrated energy consumption was performed on a test stand for the intelligent monitoring of performance characteristics of a multi-disc grinder. The test stand was composed of: a five-disc mill, a control panel with a performance monitoring system, and an integrated system for analysis of the grinding product's particle size ( Figure 2). Test stand for the intelligent monitoring of granular mass characteristics: 1-five-disc grinder, 2-worm feeder, 3-hopper, 4-control unit, 5-reception basket of the product of grinding, 6-weight of the product of grinding, and 7-integrated system for the analysis of the grinding product's particle size [28].
A five-disc mill was equipped with a special integrated system for feed-dosing with a screw conveyor feeder, which makes it possible to control the feeding of the grain material into the grinding chamber. The grinding unit consists of five multi-hole discs fixed on the grinder shaft ( Table 2). Each disc is powered individually by means of a dedicated motor which enables precise control of the  Test stand for the intelligent monitoring of granular mass characteristics: 1-five-disc grinder, 2-worm feeder, 3-hopper, 4-control unit, 5-reception basket of the product of grinding, 6-weight of the product of grinding, and 7-integrated system for the analysis of the grinding product's particle size [28].
A five-disc mill was equipped with a special integrated system for feed-dosing with a screw conveyor feeder, which makes it possible to control the feeding of the grain material into the grinding chamber. The grinding unit consists of five multi-hole discs fixed on the grinder shaft ( Table 2). Each Energies 2020, 13, 1417 8 of 26 disc is powered individually by means of a dedicated motor which enables precise control of the angular speed of each disc. The final product is collected in the intake hopper with a scale fixed underneath, by means of which, the mass of the fragmented material is weighed. This makes it possible to determine the actual yield of the process. The integrated system of the particle size analysis makes it possible to assess the grinding product's granulometric composition and to determine the degree of fragmentation. The whole system is equipped with a set of sensors and archive modules. Control of the grinder and data reading is included in the control panel by means of the authors' own application (MŁYN, 2019).

Research Methodology
Verification of the integrated energy consumption index model was carried out consistently with the plan presented in Figure 3. angular speed of each disc. The final product is collected in the intake hopper with a scale fixed underneath, by means of which, the mass of the fragmented material is weighed. This makes it possible to determine the actual yield of the process. The integrated system of the particle size analysis makes it possible to assess the grinding product's granulometric composition and to determine the degree of fragmentation. The whole system is equipped with a set of sensors and archive modules. Control of the grinder and data reading is included in the control panel by means of the authors' own application (MŁYN, 2019).

Research Methodology
Verification of the integrated energy consumption index model was carried out consistently with the plan presented in Figure 3. Vp-feed dosing capacity, Pi-power consumption on the i-th disc, ∆m-mass increase in the intake hopper, d80-dimension of the sieve hole through which 80% of the grinding product passes, i80-80% fragmentation degree, Ej-unit energy consumption, Qr-yield of grinding, Pr-power consumed by the grinder, and Ezint-integrated energy consumption.
First, 20 one-kilogram samples of rice and corn were prepared. The moisture level was determined for each of them on a moisture balance MAC 210/NP (RADWAG, Radom, Poland) in accordance with ISO norm 1446 [82], and, additionally, average grain size before grinding on a CAMSIZER (Retsch Technology GmbH, Haan, Germany) device was also determined in accordance with ISO norm 13322-2:2006 [81]. Next, the prepared material was subjected to grinding on a fivedisc grinder for 20 different grinding disc angular speed settings in accordance with the accepted test program [28,79] in order to investigate the dependence of the integrated energy consumption index on the total increase in the grinder disc angular speed S∆ω ( Table 3). The minimal speed of the grinder discs accepted to be the point of reference was 20 rad•s −1 . The accepted settings of the disc angular  Research plan. V p -feed dosing capacity, P i -power consumption on the i-th disc, ∆m-mass increase in the intake hopper, d 80 -dimension of the sieve hole through which 80% of the grinding product passes, i 80 -80% fragmentation degree, E j -unit energy consumption, Q r -yield of grinding, P r -power consumed by the grinder, and E zint -integrated energy consumption.

No. of Configuration
The next step involved both statistical and substantive analyses. The values of the integrated energy consumption were determined for each setting of the grinder disc according to dependence (22). Statistical analysis of the results was carried out by means of MS EXCEL (Microsoft, Redmond, WA, USA) and Statistica software (TIBCO Software Inc., Palo Alto, CA, USA). A general statistical analysis of the results, including the determination of the characteristics of the integrated energy consumption distribution and its variable components, was performed. Tests of the distribution of the normality of the variables were conducted by means of a Shapiro-Wilk test. This test is used to assess the distribution of the results. The null hypothesis of this test is that the population is normally distributed [83]. Thus, if the p-value is less than the chosen alpha level (in this study, p > 0.05), then the null hypothesis is rejected, and it can be assumed that the data are not characterized by normal distribution. When the p-value is greater than the chosen alpha level, it cannot be rejected that the data are characterized by normal distribution [83]. A correlation analysis using the Pearson method was performed for variables whose distribution was close to normal, while a Spearman correlation analysis was applied for the remaining ones. Next, a regression analysis was used. The results of the statistical analyses were found to be significant for p < 0.05.

Results and Discussion
In this part of the study, the test results of the integrated energy consumption index variables are described along with an analysis of their relations with the independent variable: the increase in the grinder disc angular speed S∆ω. The results of the tests performed for the settings of the accepted grinder disc angular speed configurations for rice grinding are presented in Table S1 and, for corn, in Table S2.

Test Results of the Integrated Energy Consumption Model Variables and Their Analysis
The analysis included general descriptive characteristics of the resultant variables of power consumption, fragmentation degree, unit energy consumption, yield, the Shapiro-Wilk test for the normality of distribution, and correlation analysis with the Pearson method. Figure 4 shows the test results of the power consumption for rice and corn grinding on a five-disc grinder. The results indicate that the disc angular speed changes do affect power consumption. An increase in power consumption along with an increase in the grinder disc angular speed was observed. It can also be noticed that the power consumption for each disc setting was different depending on the material used ( Figure 4). The power consumption for rice grinding was lower than the power consumption for corn grinding for all cases, which is mostly connected with the differing properties and internal structures of these materials [34].

Power Consumption
Energies 2020, 13, x FOR PEER REVIEW 10 of 27 In this part of the study, the test results of the integrated energy consumption index variables are described along with an analysis of their relations with the independent variable: the increase in the grinder disc angular speed S∆ω. The results of the tests performed for the settings of the accepted grinder disc angular speed configurations for rice grinding are presented in Table S1 and, for corn, in Table S2.

Test Results of the Integrated Energy Consumption Model Variables and their Analysis
The analysis included general descriptive characteristics of the resultant variables of power consumption, fragmentation degree, unit energy consumption, yield, the Shapiro-Wilk test for the normality of distribution, and correlation analysis with the Pearson method. Figure 4 shows the test results of the power consumption for rice and corn grinding on a fivedisc grinder. The results indicate that the disc angular speed changes do affect power consumption. An increase in power consumption along with an increase in the grinder disc angular speed was observed. It can also be noticed that the power consumption for each disc setting was different depending on the material used ( Figure 4). The power consumption for rice grinding was lower than the power consumption for corn grinding for all cases, which is mostly connected with the differing properties and internal structures of these materials [34]. Earlier analyses of rice and corn strength indicated that higher forces are needed to grind corn grains, which is reflected by the power demand of grinding machines, due to the necessity of overcoming the higher resistance of moving elements [37]. An increased demand for power and energy in the case of a higher-strength grinding material was confirmed by [38][39][40], among others. An increased demand for power for corn grinding is also the effect of differences in the internal

Power Consumption
Power consumption, kW Configuration (Table 3) Rice Corn Earlier analyses of rice and corn strength indicated that higher forces are needed to grind corn grains, which is reflected by the power demand of grinding machines, due to the necessity of overcoming the higher resistance of moving elements [37]. An increased demand for power and energy in the case of a higher-strength grinding material was confirmed by [38][39][40], among others. An increased demand for power for corn grinding is also the effect of differences in the internal structure thereof [38][39][40]. Rice grains deprived of husks were used in the tests, whereas corn grains had the seed coat. Moreover, corn grains differ from rice grains in terms of endosperm structure. Grains with higher endosperm glassiness have been observed to need more energy and power in the process of grinding [36,41,42].
On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the power consumption test results, it was found that this distribution is approximately normal. Subsequently, the Pearson method was used for the analysis of correlation between the power consumption of grinding P R and total speed increase S∆ω. Correlation analysis revealed that there was a strong relation between the power consumption in grinding P R and a total speed increase S∆ω during both rice grinding (R = 0.9658, Appendix A, Table A5) and corn grinding (R = 0.9847, Appendix A, Table A6).
On the basis of the linear regression analysis, equations describing the dependence of power consumption as a function of total speed increase were determined. It was found that power consumption for grinding can be described by means of a linear model with a high match ( Figure 5). Both the coefficient in the equations and the regression models themselves were statistically significant (Tables 4 and 5).
Energies 2020, 13, x FOR PEER REVIEW 11 of 27 structure thereof [38][39][40]. Rice grains deprived of husks were used in the tests, whereas corn grains had the seed coat. Moreover, corn grains differ from rice grains in terms of endosperm structure. Grains with higher endosperm glassiness have been observed to need more energy and power in the process of grinding [36,41,42].
On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the power consumption test results, it was found that this distribution is approximately normal. Subsequently, the Pearson method was used for the analysis of correlation between the power consumption of grinding PR and total speed increase S∆ω. Correlation analysis revealed that there was a strong relation between the power consumption in grinding PR and a total speed increase S∆ω during both rice grinding (R = 0.9658, Appendix A, Table A5) and corn grinding (R = 0.9847, Appendix A, Table A6).
On the basis of the linear regression analysis, equations describing the dependence of power consumption as a function of total speed increase were determined. It was found that power consumption for grinding can be described by means of a linear model with a high match ( Figure 5). Both the coefficient in the equations and the regression models themselves were statistically significant (Tables 4 and 5).        Figure 6 shows the results of rice and corn grinding yield tests performed on a five-disc grinder. The results indicate that the disc angular speed changes have an impact on this parameter change. As in the case of power consumption, it was observed that grinding yields increased along with an increase in the disc angular speeds. It could also be observed that, for the settings of the grinder disc angular speeds at which the first disc speed was the lowest, the rice grinding yield was significantly higher than that of the corn (Figure 6). For the remaining settings, the yield was similar though slightly higher for corn. This might result from the relations between the structural characteristics of working discs, speed, and the size of the grain used. The average size of rice grains was definitely lower than that of corn; hence, more of them can be introduced into the open space of the grinding discs.
Energies 2020, 13, x FOR PEER REVIEW 12 of 27 3.1.2. Yield Figure 6 shows the results of rice and corn grinding yield tests performed on a five-disc grinder. The results indicate that the disc angular speed changes have an impact on this parameter change. As in the case of power consumption, it was observed that grinding yields increased along with an increase in the disc angular speeds. It could also be observed that, for the settings of the grinder disc angular speeds at which the first disc speed was the lowest, the rice grinding yield was significantly higher than that of the corn (Figure 6). For the remaining settings, the yield was similar though slightly higher for corn. This might result from the relations between the structural characteristics of working discs, speed, and the size of the grain used. The average size of rice grains was definitely lower than that of corn; hence, more of them can be introduced into the open space of the grinding discs. On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the performance test results, it was found that this distribution is approximately normal. Subsequently, the Pearson method was used in the analysis of correlation between grinding yield Qr and the total speed increase. A correlation analysis showed that the correlation between the yield of grinding Qr and the total speed increase S∆ω during both rice grinding (Appendix A, Table A5) and corn grinding was poor (Appendix A, Table A6).
Poor correlations between the disc total angular speed increased, and the yield might be the result of the grain strength properties and their relations and interactions with the grinding unit. The phenomena accompanying the flow of granular materials through the grinding chamber, the interhole space, and inter-disc space of the quasi-shearing unit are not without importance. There can occur, among other things, periods when the material lingers in the grinding chamber due to the adhesion of wet grains, which can be observed, e.g., in the case of corn and the poor results in the fourth test program. Production yield, kg·h -1 Configuration (Table 3) Rice Corn On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the performance test results, it was found that this distribution is approximately normal. Subsequently, the Pearson method was used in the analysis of correlation between grinding yield Q r and the total speed increase. A correlation analysis showed that the correlation between the yield of grinding Q r and the total speed increase S∆ω during both rice grinding (Appendix A, Table A5) and corn grinding was poor (Appendix A, Table A6).
Poor correlations between the disc total angular speed increased, and the yield might be the result of the grain strength properties and their relations and interactions with the grinding unit. The phenomena accompanying the flow of granular materials through the grinding chamber, the inter-hole space, and inter-disc space of the quasi-shearing unit are not without importance. There can occur, among other things, periods when the material lingers in the grinding chamber due to the adhesion of wet grains, which can be observed, e.g., in the case of corn and the poor results in the fourth test program.  Figure 7 shows the test results of the unit energy consumptions for rice and corn grain grinding. For all the considered settings of the five-disc grinder angular speeds, the unit energy demand was higher for corn grinding (Figure 7), which was mostly connected with a higher power consumption during corn grinding, which, in turn, results from the grain strength properties which are discussed in Section 3.1.1. Earlier research also indicated a higher unit energy consumption for corn grinding [19].
The results indicate that an increase in the angular speed of discs caused an increase in energy consumption (Figure 7).
Energies 2020, 13, x FOR PEER REVIEW 13 of 27 Figure 7 shows the test results of the unit energy consumptions for rice and corn grain grinding. For all the considered settings of the five-disc grinder angular speeds, the unit energy demand was higher for corn grinding (Figure 7), which was mostly connected with a higher power consumption during corn grinding, which, in turn, results from the grain strength properties which are discussed in Section 3.1.1. Earlier research also indicated a higher unit energy consumption for corn grinding [19]. The results indicate that an increase in the angular speed of discs caused an increase in energy consumption (Figure 7). On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the results of the unit energy consumption tests, it was found that this distribution is approximately normal for the grinding of rice, while for the grinding of corn, it deviated from normal. Subsequently, the Pearson method was used in an analysis of correlation between unit energy consumption Ej for rice grinding and total speed increase S∆ω; whereas, in the case of corn, the Spearman method was used to assess these relations. Correlation analysis showed that there was a very strong positive correlation between the unit energy consumption Ej and total speed increase S∆ω for rice grinding (R = 0.95332, Appendix A, Table A5). In the case of corn grinding, the correlation of these two variables was moderate (R = 0.5963, Appendix A, Table A8).

Unit Energy Consumption
An equation describing the dependence of the unit energy consumption for rice grinding as a function of the total speed increase was determined based on a linear regression analysis. It was found that the unit energy demand can be described by means of a linear model with a high match (Figure 8a).
In the case of the unit energy consumption involved in corn grinding, after the removal of outstanding values (results for settings IV3, IV4, and V1), it was the exponential model that provided the best match (Figure 8b) when compared to the others. This model was chosen on the basis of a ranking of the different nonlinear models. As a selection criterion, the value of the model match coefficient R 2 (the higher the value, the better the model) and the value of the standard error of the model coefficients (the lower the error, the better the model) were used. Unfortunately, the chosen model explained the variability of the unit energy consumption as a function of the total speed increase merely partially-slightly over 46% of the variability was explained by means of the chosen function. Both the coefficients in the equations and the regression models were statistically significant (Tables 6 and 7). The standard error of the coefficients in the equations did not exceed 12%.

Configuration
Corn Rice On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the results of the unit energy consumption tests, it was found that this distribution is approximately normal for the grinding of rice, while for the grinding of corn, it deviated from normal. Subsequently, the Pearson method was used in an analysis of correlation between unit energy consumption E j for rice grinding and total speed increase S∆ω; whereas, in the case of corn, the Spearman method was used to assess these relations. Correlation analysis showed that there was a very strong positive correlation between the unit energy consumption E j and total speed increase S∆ω for rice grinding (R = 0.95332, Appendix A, Table A5). In the case of corn grinding, the correlation of these two variables was moderate (R = 0.5963, Appendix A, Table A8).
An equation describing the dependence of the unit energy consumption for rice grinding as a function of the total speed increase was determined based on a linear regression analysis. It was found that the unit energy demand can be described by means of a linear model with a high match (Figure 8a).
In the case of the unit energy consumption involved in corn grinding, after the removal of outstanding values (results for settings IV3, IV4, and V1), it was the exponential model that provided the best match (Figure 8b) when compared to the others. This model was chosen on the basis of a ranking of the different nonlinear models. As a selection criterion, the value of the model match coefficient R 2 (the higher the value, the better the model) and the value of the standard error of the model coefficients (the lower the error, the better the model) were used. Unfortunately, the chosen model explained the variability of the unit energy consumption as a function of the total speed increase merely partially-slightly over 46% of the variability was explained by means of the chosen function.
Both the coefficients in the equations and the regression models were statistically significant (Tables 6  and 7). The standard error of the coefficients in the equations did not exceed 12%.
The unit (specific) energy consumption depend on two factors: the energy consumed for the grinding process and the mass of grinded material, and it described the amount of energy needed for grinding one kg of material. According to [19], the unit energy consumption can be expressed as the ratio of power demand and grinding yield. For grinded materials, the dependence between the yield and discs' total speed increase was not specified, and as it is one of the unit energy components, it influences the dependence between the unit energy consumption and the discs' total speed increase. For corn, the yield values spread was significant; that is why the fitting is very low. The problems with the yield in the case of corn grinding was presented in Section 3.1.2 and was also reported in the previous study [28].  Table 6. Test results of the significance of the coefficients of the unit energy consumption regression model.   Figure 9 shows the test results of rice and corn grain fragmentations at 80% after grinding on a five-disc mill. A higher fragmentation degree was found for corn grain grinding for all analyzed disc angular speed settings (Figure 9), which was connected with the ratio of the grain dimension and the inter-disc gap. The grains of rice and corn had similar average dimensions in all tests, and this value depended on the value of the inter-disc gap-the size of a particle after grinding will always be    The unit (specific) energy consumption depend on two factors: the energy consumed for the grinding process and the mass of grinded material, and it described the amount of energy needed for grinding one kg of material. According to [19], the unit energy consumption can be expressed as the ratio of power demand and grinding yield. For grinded materials, the dependence between the yield and discs' total speed increase was not specified, and as it is one of the unit energy components, it influences the dependence between the unit energy consumption and the discs' total speed increase. For corn, the yield values spread was significant; that is why the fitting is very low. The problems with the yield in the case of corn grinding was presented in Section 3.1.2 and was also reported in the previous study [28]. Figure 9 shows the test results of rice and corn grain fragmentations at 80% after grinding on a five-disc mill. A higher fragmentation degree was found for corn grain grinding for all analyzed disc angular speed settings (Figure 9), which was connected with the ratio of the grain dimension and the inter-disc gap. The grains of rice and corn had similar average dimensions in all tests, and this value depended on the value of the inter-disc gap-the size of a particle after grinding will always be smaller than the gap. Due to the fact that the characteristic size of corn grains was bigger before grinding than  (Table S1 and Table S2 in the Supplementary Materials) and their dimensions decreased down to those comparable to rice grains, the fragmentation degree of the corn grains was higher. It was observed, like in other studies [5,26], that for grinding bigger particles (corn has bigger particles than rice), the energy consumption is higher. It was also reported that the higher the disc speed (so the contacts between materials and cutting edges are more intensive), the grinding product has smaller particles [4,84]. On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of the skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the grinding results, it was found that this distribution is approximately normal for both rice and corn grinding. Subsequently, the Pearson method was used in an analysis of the correlation between the grain fragmentation degree i 80 and summary speed increase S∆ω. Correlation analysis showed that there was a very strong positive relation between the rice fragmentation degree i 80 and the total speed increase S∆ω (R = 0.93237, Appendix A, Table A5). In the case of corn grinding, the positive correlation between these two variables was moderate (R = 0.6893, Appendix A, Table A6).

Fragmentation Degree
smaller than the gap. Due to the fact that the characteristic size of corn grains was bigger before grinding than the size of rice grains (Tables S1 and S2 in the Supplementary Materials) and their dimensions decreased down to those comparable to rice grains, the fragmentation degree of the corn grains was higher. It was observed, like in other studies [5,26], that for grinding bigger particles (corn has bigger particles than rice), the energy consumption is higher. It was also reported that the higher the disc speed (so the contacts between materials and cutting edges are more intensive), the grinding product has smaller particles [4,84]. On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of the skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the grinding results, it was found that this distribution is approximately normal for both rice and corn grinding. Subsequently, the Pearson method was used in an analysis of the correlation between the grain fragmentation degree i80 and summary speed increase S∆ω. Correlation analysis showed that there was a very strong positive relation between the rice fragmentation degree i80 and the total speed increase S∆ω (R = 0.93237, Appendix A, Table A5). In the case of corn grinding, the positive correlation between these two variables was moderate (R = 0.6893, Appendix A, Table  A6).
The equation describing the dependence of an 80% degree of rice fragmentation as a function of the total speed increase was determined based on an analysis of linear regression. It was found that an 80% fragmentation degree can be described with a high match by means of a linear model ( Figure  10a). The obtained linear model was able to provide a 90% explanation of the fragmentation degree as a function of the total angular speed increase S∆ω.   The equation describing the dependence of an 80% degree of rice fragmentation as a function of the total speed increase was determined based on an analysis of linear regression. It was found that an 80% fragmentation degree can be described with a high match by means of a linear model (Figure 10a). The obtained linear model was able to provide a 90% explanation of the fragmentation degree as a function of the total angular speed increase S∆ω. For the case of the 80% fragmentation degree of corn, the linear model explained the fragmentation degree changes as a function of the total speed increase S∆ω only to a small extent (R 2 = 0.47513). Thus, the decision was made to check nonlinear models. As in the case of the unit energy demand, a ranking of models which took into account the value of the match coefficient R 2 and the For the case of the 80% fragmentation degree of corn, the linear model explained the fragmentation degree changes as a function of the total speed increase S∆ω only to a small extent (R 2 = 0.47513). Thus, the decision was made to check nonlinear models. As in the case of the unit energy demand, a ranking of models which took into account the value of the match coefficient R 2 and the value of the standard error of the model coefficients was used. It was the exponential model which best explained the highest percent of the 80% corn fragmentation degree variability as compared to the other models ( Figure 10b). Unfortunately, the chosen model did not sufficiently explain the variability of the 80% fragmentation degree as a function of the total speed increase. Both the coefficients in the equations and the regression models themselves were statistically significant (Tables 8 and 9). The standard error of the coefficients in the equations did not exceed 10%.

Analysis of the Integrated Energy Consumption Results
The next step of the tests involved an analysis of the integrated energy consumption for rice and corn grain comminution. Figure 11 shows the results of the integrated energy consumption tests for both grains. In the case of corn, the highest values of the integrated energy consumption were found for setting no. 4 with RP II and, next, for setting no. 1 with RP III and setting no. 1 with RP IV. For rice grinding, the highest values of the integrated energy consumption were found for setting no. 1 in RP IV and, next, for setting no. 1 in RP III, setting no. 4 in RP II, and setting no. 2 in RP IV.
An analysis of the relations between the integrated energy consumption made it possible to determine the yield ranges, power consumption, unit energy consumption, and fragmentation degree for which the integrated efficiency is the highest (Figures 12 and 13, red color). The integrated energy consumption for rice grinding on a five-disc grinder assumes values within the interval (928-1420) when the grinding yield is included in the range (25.2-30.6) kg·h −1 , unit energy consumption in the range (0.027-0.049) kWh·kg −1 , power consumption in the range (0.88-1.02) kW, and fragmentation degree in the range (1.04-1.13) (Figure 12). The integrated energy consumption of corn grinding on a five-disc grinder assumes values in the range (1592-2640) when the grinding yield is within (19.8-32.4) kg·h −1 , unit energy consumption within (0.037-0.061) kWh·kg −1 , power consumption within (0.91-1.31) kW, and fragmentation degree in the range (2.75-4.21) (Figure 13).
Energies 2020, 13, x FOR PEER REVIEW 17 of 27 rice grinding, the highest values of the integrated energy consumption were found for setting no. 1 in RP IV and, next, for setting no. 1 in RP III, setting no. 4 in RP II, and setting no. 2 in RP IV. Figure 11. Test results of the integrated energy consumption for rice and corn grinding.
An analysis of the relations between the integrated energy consumption made it possible to determine the yield ranges, power consumption, unit energy consumption, and fragmentation degree for which the integrated efficiency is the highest (Figures 12 and 13, red color). The integrated energy consumption for rice grinding on a five-disc grinder assumes values within the interval (928-1420) when the grinding yield is included in the range (25.2-30.6) kg·h −1 , unit energy consumption in the range (0.027-0.049) kWh·kg −1 , power consumption in the range (0.88-1.02) kW, and fragmentation degree in the range (1.04-1.13) (Figure 12). The integrated energy consumption of corn grinding on a five-disc grinder assumes values in the range (1592-2640) when the grinding yield is within (19.8-32.4) kg·h −1 , unit energy consumption within (0.037-0.061) kWh·kg −1 , power consumption within (0.91-1.31) kW, and fragmentation degree in the range (2.75-4.21) (Figure 13). The results of the integrated energy consumption tests are characterized by a higher value scatter for corn grinding, and the scatter of results for power consumption, yield, fragmentation degree, and unit energy consumption were also higher for corn grinding than for rice grinding (Figures 12 and 13). Thus, by knowing the components of the integrated energy consumption, its values can be predicted with a higher accuracy for rice grinding than for corn grinding.
Next, a basic statistical analysis of the variable was performed. On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of the skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the results, it was found that the distribution of the integrated energy consumption deviated from normal; therefore, in the correlation analysis, the Spearman coefficient was used to describe the monotonic relationships between the variables. Correlation analysis showed that there is a very strong negative correlation between the integrated energy consumption of rice grinding and total speed increase S∆ω (R = −0.95554, Appendix A, Table A7). In the case of corn grinding, the negative correlation of these two variables was moderate (R = −0.51131, Appendix A, Table A8).  An analysis of the relations between the integrated energy consumption made it possible to determine the yield ranges, power consumption, unit energy consumption, and fragmentation degree for which the integrated efficiency is the highest (Figures 12 and 13, red color). The integrated energy consumption for rice grinding on a five-disc grinder assumes values within the interval (928-1420) when the grinding yield is included in the range (25.2-30.6) kg·h −1 , unit energy consumption in the range (0.027-0.049) kWh·kg −1 , power consumption in the range (0.88-1.02) kW, and fragmentation degree in the range (1.04-1.13) (Figure 12). The integrated energy consumption of corn grinding on a five-disc grinder assumes values in the range (1592-2640) when the grinding yield is within (19.8-32.4) kg·h −1 , unit energy consumption within (0.037-0.061) kWh·kg −1 , power consumption within (0.91-1.31) kW, and fragmentation degree in the range (2.75-4.21) (Figure 13). The results of the integrated energy consumption tests are characterized by a higher value scatter for corn grinding, and the scatter of results for power consumption, yield, fragmentation degree, and unit energy consumption were also higher for corn grinding than for rice grinding (Figures 12 and  13). Thus, by knowing the components of the integrated energy consumption, its values can be predicted with a higher accuracy for rice grinding than for corn grinding. Nonlinear regression analysis was used to determine the equations describing the dependence of the rice and corn grinding's integrated energy consumption as a function of the total speed increase. In this case, the best-matched model was determined on the basis of the value of matching coefficient R 2 and the error values of the standard coefficients of the determined dependencies. It was found that the integrated energy consumption of rice grinding is best explained, nearly 77%, by an exponential model ( Figure 14a). As regards corn, the best match was an exponential model, though it accounted for only 46% of the integrated energy consumption variability (Figure 14b). Both coefficients in the equations and the regression models themselves were statistically significant (Tables 10 and 11). The standard error of coefficients did not exceed 11% in the rice grinding's integrated energy consumption equations, and, in the case of corn, it did not exceed 26%. The results of the integrated energy consumption tests are characterized by a higher value scatter for corn grinding, and the scatter of results for power consumption, yield, fragmentation degree, and unit energy consumption were also higher for corn grinding than for rice grinding (Figures 12 and  13). Thus, by knowing the components of the integrated energy consumption, its values can be predicted with a higher accuracy for rice grinding than for corn grinding. Next, a basic statistical analysis of the variable was performed. On the basis of the Shapiro-Wilk test (Appendix A, Tables A1 and A2) and the values of the skewness and kurtosis (Appendix A, Tables A3 and A4) of the distribution of the results, it was found that the distribution of the integrated energy consumption deviated from normal; therefore, in the correlation analysis, the Spearman coefficient was used to describe the monotonic relationships between the variables. Correlation analysis showed that there is a very strong negative correlation between the integrated energy consumption of rice grinding and total speed increase S∆ω (R = −0.95554, Appendix A, Table A7). In the case of corn grinding, the negative correlation of these two variables was moderate (R = −0.51131, Appendix A, Table A8).
Nonlinear regression analysis was used to determine the equations describing the dependence of the rice and corn grinding's integrated energy consumption as a function of the total speed increase. In this case, the best-matched model was determined on the basis of the value of matching coefficient R 2 and the error values of the standard coefficients of the determined dependencies. It was found that the integrated energy consumption of rice grinding is best explained, nearly 77%, by an exponential model (Figure 14a). As regards corn, the best match was an exponential model, though it accounted for only 46% of the integrated energy consumption variability (Figure 14b). Both coefficients in the equations and the regression models themselves were statistically significant (Tables 10 and 11). The standard error of coefficients did not exceed 11% in the rice grinding's integrated energy consumption equations, and, in the case of corn, it did not exceed 26%.   . 14a and 14b).  The results of the analyses indicate that the rice and corn grinding processes differ in terms of yield, power consumption, fragmentation degree, unit energy consumption, and integrated energy consumption. In the case of corn, the process of grinding has more of a random character, which is mostly the result of the large differentiation of the grains of one species, which was also observed in other tests [20,28,85]. Hence, the match of models of unit energy consumption, yield, and fragmentation degree as a function of corn grinding speed increases, and subsequently, the models of the integrated energy consumption, which include the above-listed components, is rather poor.  (Figure 14a,b). Analyzing the values of the integrated energy consumption for the two grain species considered herein, it can be said that, from the point of view of the accepted criterion, a smaller increase in the angular speeds in relation to the reference speed on each disc (20 rad·s −1 ) provides higher values of integrated energy consumption; e.g., the process of grinding is characterized by a low power consumption while maintaining the remaining parameters of grinding at a satisfactory level.
Verification of the integrated energy consumption model was performed for granular materials. It should be expected that, for a different type of biomass, e.g., wooden biomass, the value of the energy consumption index and its relations with the grinder disc total angular speeds would be different from the materials used in the study.
The proposed index of the integrated energy consumption can successfully be used to assess the grinding process and to select the grinder angular speeds to provide a low energy consumption, high yield, and a high fragmentation degree of the product. This index can find applications in automatic and control systems for industrial lines grinding energy materials, e.g., biomass, coal, and post-use polymer materials.

Summary and Conclusions
The aim of the study was achieved by developing and verifying the model of integrated energy consumption for grinding a biomass, which takes into account the fundamental parameters of the process: power consumption, unit energy consumption, yield, and the determination of the impact of changes in the grinding unit motion parameters on the values of the index developed herein.
The analyses of this study have proven that the index developed herein can be used successfully to assess a biomass grinding's energy consumption in an integrated approach-that is, one which includes not only energy consumption but also other parameters important from the point of view of the grinding process (yield, fragmentation degree, power consumption, and unit energy consumption). The verification of the model on a real object-a five-disc grinder-made it possible to determine the dependencies of the integrated energy consumption index and the motion parameters of the grinder discs for the total increase in disc annular speeds. Based on the analyses, it was found that the total speed increased, and thus, the increase in the disc angular speeds causes an increase in power consumption, in the fragmentation degree, and the unit energy consumption for both rice and corn grinding. In the case of rice grinding, these dependencies can be described with a high match by means of linear models. In the case of corn, a linear dependence was found only for power consumption. Nonlinear models were used for the unit energy consumption and fragmentation degree, though they accounted for only 60% of the studied parameter variability. The yield did not correlate with the total increase in angular disc speeds for either rice or corn grinding. This results mainly from physical mechanical properties of the grains and grain-grinding unit relations and confirms the variety and variability of grains observed so far within one type of grain and, in addition, confirms the randomness of the grinding process.
The test results prove that integrated energy consumption is negatively correlated with a total increase in the grinder angular speeds. The models which best represent the variability of the integrated energy consumption were exponential models; though, in the case of corn, this model was characterized by a lower matching coefficient (R 2 = 0.45896) than the energy consumption model for rice grinding (R 2 = 0.76749). Upon analyzing the values of the integrated energy consumption for two grain species, it can be observed that, in terms of the criterion accepted herein, a smaller angular speed increase in relation to the reference speed on each disc of the grinder (20 rad·s −1 ) causes higher values of integrated energy consumption; that is, the process of grinding is characterized by a low power consumption while sustaining the remaining parameters of grinding at a satisfactory level.
The model of integrated energy consumption considered in this study can be a useful tool for integrated design and to select structural and process grinding parameters in preimplementation tests for grinders. Moreover, it can find an application in the automation and control systems of industrial lines' grinding energy materials, such as biomass, coal, and post-use polymers.
Further research on the structures and operations of biomass grinders in terms of their energy consumptions should be focused on finding the relations between selected structural characteristics of the grinding unit and negative environmental factors such as CO 2 emissions and natural resource depletion, as well as operation potentials.
Supplementary Materials: The following are available online at http://www.mdpi.com/1996-1073/13/6/1417/s1: Table S1: The test results of rice grinding's integrated energy consumption and particular components of the model. Table S2: Test results of the integrated energy consumption for rice grinding and particular components of the model

Conflicts of Interest:
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.   P r -power consumption for grinding, kW; Q r -yield of grinding, kg·h −1 ; E j -unit energy consumption, kWh·h −1 ; i 80 -80% fragmentation degree; E zint -integrated energy consumption; and S∆ω -total increase in angular speeds, rad·s −1 . P r -power consumption for grinding, kW; Q r -yield of grinding, kg·h −1 ; E j -unit energy consumption, kWh·h −1 ; i 80 -80% fragmentation degree; E zint -integrated energy consumption; and S∆ω-total increase in angular speeds, rad·s −1 . Two-tailed test of significance is used and * correlation is significant at the 0.05 level. P r -power consumption for grinding, kW; Q r -yield of grinding, kg·h −1 ; E j -unit energy consumption, kWh·h −1 ; i 80 -80% fragmentation degree; and S∆ω-total angular speed increase, rad·s −1 . Two-tailed test of significance is used and * correlation is significant at the 0.05 level. P r -power consumption for grinding, kW; Q r -yield of grinding, kg·h −1 ; i 80 -80% fragmentation degree; and S∆ω-total angular speed increase, rad·s −1 . Two-tailed test of significance is used and * correlation is significant at the 0.05 level. E zint -integrated energy consumption and S∆ω-total angular speed increase, rad·s −1 . Two-tailed test of significance is used and * correlation is significant at the 0.05 level. E j -unit energy consumption, kWh·h −1 ; E zint -integrated energy consumption; and S∆ω-total angular speed increase, rad·s −1 .