In the current study, a factorial design is used to investigate the effect of total iron and silica on the metallurgical performance of different grades of manganese ores. The derived mathematical formulations are applied to estimate the reduction disintegration index (RDI_{+6.3}, RDI_{+3.15}, and RDI_{−0.5}), reduction index (total reduction index (RIT), manganese reduction index (RIM), and iron reduction index (RIF)), and softeningmelting property (start of softening (
Manganese is considered to be one of the most important alloying elements in different grades of steel and cast iron. Manganese improves the tensile strength, machinability, toughness, hardness, and abrasion resistance of steel. In addition, manganese has favourable influence on forging, welding, and grain refining properties in steel casting. Manganese can be used for production of less expensive austenitic steel grades by replacing the expensive alloying elements such as nickel [
The previous survey indicates that, in order to maintain a stable operation of ferromanganese production with lowest energy consumption, it is important to keep the metallurgical properties of the applied manganese ores at the optimum conditions. Although many experimental studies were carried out to estimate the effect of different parameters on the smelting reduction of manganese ores, few studies tried to estimate the magnitude’s effect of the individual and interaction parameters on the overall reduction process. The factorial design provides a novel approach to precisely estimate the effect of different parameters either individually or collectively on the process [
A 2^{2} factorial design is used to determine the main effect of total iron and silica and their interactions on the lowtemperature reduction disintegration index (RDI), reduction index (RI), and softeningmelting property (SMP) of different grades of manganese ores. The testing methods of the reduced manganese ores including RDI, RI, and SMP are reported by Zhang et al. elsewhere [
Chemical composition of different grades of manganese ores.
Ore description  T Fe  T Mn  SiO_{2}  Al_{2}O_{3}  CaO  MgO  P  LOI 

High Felow Si  23.48  34.73  6.75  0.56  0.38  0.16  0.051  8.29 
Low Felow Si  3.9  47.8  7.93  4.35  0.26  0.18  0.063  9.67 
Low Fehigh Si  2.72  36.66  27.26  2.49  1.97  0.26  0.062  8.88 
High Fehigh Si  33.24  13.67  16.32  1.32  0.2  0.06  0.12  10.03 
By convention, the total iron in manganese ores is denoted by “
Based on this concept, the effect of a factor is donated by a capital Latin letter. Thus “
Mathematical formulations are driven to estimate the effect of Fe, SiO_{2}, and their interaction (FeSiO_{2}) on the metallurgical properties of manganese ores. The effect of “
The complete analyses of the effect of Fe (
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


−1.1518  2.653286  2.653286  9.096124 

5.4581  59.58171  59.58171  204.2609 

−9.64705  186.1311  186.1311  638.1037 
Error  1.166777  0.291694  


Total  249.5329 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


1.765325  6.232745  6.232745  17.63527 

4.867275  47.38073  47.38073  134.0617 

−6.47918  83.95942  83.95942  237.5594 
Error  1.4137  0.353425  


Total  138.9866 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


0.185425  0.068765  0.068765  37.04831 

0.893125  1.595345  1.595345  859.5207 

2.370475  11.2383  11.2383  6054.839 
Error  0.007424  0.001856  


Total  12.90984 
In Table
The experimental results can be generally expressed in terms of regression model as given in (
Regression coefficient values for RDI_{+6.3}, RDI_{+3.15}, and







RDI_{+6.3}  76.18  −0.5759  2.729  −4.82353  ±0.419 
RDI_{+3.15}  83.96099  0.882662  2.433638  −3.23959  ±0.441 

5.95688  0.092713  0.446563  1.185238  ±0.0386 
The relation between the natural variables and the coded variable is given as follow: the coded variable is equal to [(natural variable − 1/2(variable at high level + variable at low level))/1/2(variable at high level − variable at low level)]. Consequently, the RDI_{+6.3}, RDI_{+3.15}, and RDI_{−0.5} can be predicted as a function of total iron and SiO_{2} as given in (
The RDI_{+6.3}, RDI_{+3.15}, and RDI_{−0.5} for the different grades of manganese ores (lowFe lowSi, highFe lowSi, lowFe highSi, and highFe highSi manganese ores) are calculated based on (
The experimental and predicted RDI_{+6.3} by using coded and actual variables.
The experimental and predicted RDI_{+3.15} by using coded and actual variables.
The experimental and predicted RDI_{−0.5} by using coded and actual variables.
The effect of total Fe and/or silica on the reduction index is calculated based on the total FeMn oxides (RIT), Mn oxide (RIM), and Fe oxide (RIF) as given in Tables
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


19.687  775.1559  775.1559  3994.748 

6.3685  81.11558  81.11558  418.0273 

6.268  78.57565  78.57565  404.9378 
Error  0.776175  0.194044  


Total  935.6233 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


−2.3  10.58  10.58  2116 

−0.3  0.18  0.18  36 

−1.4  3.92  3.92  784 
Error  0.02  0.005  


Total  14.7 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


21.4555  920.677  920.677  2537.032 

0.613  0.751538  0.751538  2.07095 

−2.603  13.55122  13.55122  37.34195 
Error  1.451581  0.362895  


Total  936.4313 
The results of experiments can be expressed in terms of regression models of RIT, RIM, and RIF as given in (
Regression coefficient values for RIT, RIM, and RIF.







RIT  61.24925  9.8435  3.18425  3.134  ±0.389 
RIM  98.15  −1.15  −0.15  −0.7  ±0.05 
RIF  84.39425  10.7277  0.3065  −1.3015  ±0.483 
The RIT, RIM, RIF can be predicted as a function of total iron and SiO_{2} as given in (
The experimental and predicted RIT by using coded and actual variables.
The experimental and predicted RIM by using coded and actual variables.
The experimental and predicted RIF by using coded and actual variables.
A mathematical regression model is derived to estimate the effect of total iron and/or silica on the softeningmelting property of manganese ores during reduction. The softening ranges can be estimated based on the determination of temperature at which the reduced ores start to soften (
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


−29.5  1740.5  1740.5  386.7778 

−47.5  4512.5  4512.5  1002.778 

−42.5  3612.5  3612.5  802.7778 
Error  18  4.5  


Total  9883.5 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


−8  128  128  10.24 

−64  8192  8192  655.36 

−10  200  200  16 
Error  50  12.5  


Total  8570 
The effect of iron and/or silica content on the melting property of manganese ores including
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


44  3872  3872  1936 

−79  12482  12482  6241 

22  968  968  484 
Error  8  2  


Total  17330 
Effect of total iron (
Source of variance  The average effect  Sum of square (SS)  Mean square (MS) 
Magnitude effect, 


−19  722  722  361 

−82  13448  13448  6724 

30  1800  1800  900 
Error  8  2  


Total  15978 
The relation between the natural variables and the coded variable for
Values of regression coefficient for




 


1123.25  −14.75  −23.75  −21.25  ±1.5 

1240.5  −4.0  −32.0  −5.0  ±2.5 

119.6888  11.65125  −8.33125  16.29125  ±0.7 

1229.5  22.0  −39.5  11.0  ±1.0 

1266.5  −9.5  −41.0  15.0  ±1.0 

36.66  −32.1825  −2.0175  3.51  ±0.37 
The
The experimental and predicted
The experimental and predicted
The softening range (
The experimental and predicted
Figures
The experimental and predicted
The melting range (
Based on the previous findings, it can be concluded that the factorial design is very useful approach to predict and precisely estimate the effect of different impurities such as Fe and/or Si which commonly contaminate the manganese ores and affect negatively the smelting reduction process. The derived mathematical regression models are able to predict the reduction disintegration index, reduction index, and the softeningmelting property of manganese ores as a function of the content of total iron and silica.
In the current study, a factorial design is built on the experimental data of four grades of manganese ores containing different percentages of iron and silica (lowFe highSi, highFe lowSi, lowFe highSi, and highFe highSi manganese ores). The main findings can be summarized as follow.
Regression formulations are derived to estimate the effect of total Fe and/or SiO_{2} on the reduction disintegration indexes (RDI_{+6.3}, RDI_{+3.15}, and RDI_{−0.5}) of manganese ores. The RDI_{+6.3} and RDI_{+3.15} increased with the individual effect of SiO_{2} and the interaction effect of FeSiO_{2} while they decreased as the total Fe increased. The RDI_{−0.5} increased with Fe and decreased with individual effect of silica and the interaction effect of FeSiO_{2} in the manganese ores.
The effect of total Fe and/or SiO_{2} on the reduction indexes (total reduction of manganese and iron oxides (RIT), manganese oxides reduction (RIM), and iron oxides reduction (RIF)) is developed. The RIT and RIF increased as the iron oxide content in manganese ore increased. The RIM was almost identical due to the simple conversion of MnO_{2} to MnO.
The effect of total iron and SiO_{2} on the softeningmelting property (start of softening (
The validation of regressions formulations was found to be in a good agreement with the experimental data which indicates the efficiency of the factorial design to predict the metallurgical properties of manganese ores under the influence of different impurities.
The authors declare that there is no conflict of interests regarding the publication of this paper.