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Effects of composition and process variables on core loss and hardness of low carbon electrical steels
Journal of Magnetism and Magnetic Materials 92 (1990) 109-115 North-Holland
109
Effects of composition and process variables on core loss and hardness of low carbon electrical steels C.K. Hou Steel and Aluminum Research and Development Department, China Steel Corporation, Hsiao Kang, Kaohsiung 81233, Taiwan
and P.C. Wang Graduate Institute of Statistics, National Central University, Chung-Li 32054, Taiwan Received 2 March 1990; in revised form 29 May 1990
The effects of chemical composition and process variables on core loss and hardness of continuous annealed low carbon electrical steels have been studied i~ an experiment of statistical design. After data were collected from the experiment, statistical analyses were carded out for finding the dominant factors. Factors that influence the core loss, hardness, grain size and texture of low carbon electrical steels are found. Additionally, two regression equations are established to represent quantitative relationships between those dominant factors and two characteristics, the core loss and hardness, of the electrical steels.
1. Introduction Low c a r b o n electrical steels are commonly used to m a k e lamination cores of fractional horsepower m o t o r s for economic reasons. Their chemical compositions contain smaller a m o u n t s of alloy elements, such as silicon and a l u m i n u m , than nonoriented electrical steels. However, one must keep the c a r b o n content and other impurities as low as possible to enhance magnetic properties, and increase the phosphorus to increase the hardness. Moreover, in order to avoid the detrimental effects of a l u m i n u m nitride on grain growth and magnetic properties, low c a r b o n electrical steel is often killed with silicon instead of aluminum during steelmaking. M o d e r n steelmaking technology has reduced carbon content to less than 50 p p m through vacuum-degasser treatment. Recently, continuous annealing lines have been widely installed all over the world for the obvious ad-
vantages of shortening annealing time, improving sheet flatness a n d saving energy. W i t h these advances, it becomes possible for the steel mill to produce low c a r b o n electrical steels. T h e effects of factors, such as chemical composition, thickness, texture and microstructure, on the magnetic properties of low c a r b o n electrical steels and nonoriented electrical steels have been studied by many researchers [1-11]. Some of them adopted factorial design m e t h o d s to conduct their experiments [10,11]. S o m e of them a d o p t e d nonfactor/al desi~,.l m e t h o d s to conduct the~l" experiments [5,6,8]. Some of them designed their experiments with factorial m e t h o d s in certain variables but not in others [7,9]. However, there are no papers using the orthogonal statistical design m e t h o d to investigate the effects of composition and process variables on the core loss of low c a r b o n electrical steels. The orthogonal statistical design that can be established by the method of orthogonal array
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
1 iO
C.K. Hou, P.C. Wang / Core loss and hardness of low carbon electrical steels
has the advantage to study the effects of many factors and some of their interactions with a few tests in an experiment. In fact, the methods of orthogonal array have been widely used in Japanese industry for quality improvements, and recently in the industry of the United States [12,13]. In this work, we set up an experiment using the method of orthogonal array to study the effects of three composition variables and seven process variables simultaneously on the core loss and hardness of continuous annealed low carbon elec-
trical steels. First, we obtain an orthogonal statistical design in ten controllable variables by using modifications of an existing orthogonal array. This design gives 32 different tests. Then, after the collection of the data from the tests, the effects of variables are analysed and quantitative relationships of core loss and hardness with their dondnant factors were also established by the regression method. Moreover, the effects of composition and process variables on grain size and texture were analysed to account for core loss of low carbon electrical steels.
Table 1 Chemical composition and process variables of each test Test no.
C (wt%)
P (wt%)
Si (wt%)
Norm. temp.
Cold red.
(°c)
Anneal temp.
Anneal time
Primary cooling
Aging temp.
(%)
(o C)
(s)
rate
(o C)
time (s)
550 500 450 400 500 550 400 450 500 550 400 450 550 500 450 400 450 400 550 500 400 450 500 550 400 450 500 550 450 400 550 500
360 180 360 180 180 360 180 360 180 360 180 360 360 180 360 180 180 360 180 360 360 180 360 180 360 180 360 180 180 360 180 360
Aging
(°C/s) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
0.02 0.02 0.02 0.02 0.02 002 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005
0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650
75 58 58 75 58 75 75 58 58 75 75 58 75 58 58 75 75 58 58 75 58 75 75 5R 58 75 75 58 75 58 58 75
850 800 750 700 850 80C 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700
100 50 50 100 100 50 50 100 50 100 100 50 50 10O 100 50 50 100 100 50 50 100 100 50 100 50 50 100 100 50 50 100
50 35 20 5 20 5 50 35 50 35 20 5 20 5 50 35 35 50 5 20 5 20 35 50 35 50 5 20 5 20 35 50
C.K. Hou, P.C. War7e / Core loss and hardness of low carbon electrical steels
2. Experimental procedures
111
rs -.,R'Clsec
Ten variables in three categories are considered in our experiment for the study on four characteristics of low carbon electrical steels, the core loss, the hardness, the grain size and texture. Carbon, phosphorus and silicon contents in the chemical composition are factors in one catego~', while the process variables are factors in the other two categories. The latter two categories are the general processing variables (normalizing temperature of hot rolled bands, and cold rolled reduction ratio) and the continuous annealing variables (annealing temperature, annealing time, p r m a r y cooling rate, aging temperature and aging time). Due to the cost consideration, at most 32 experimental tests could be carried out and thus some of interaction effects, such as C x P, have to be sacrificed. Also, 4 levels are considered in some variables for the achievement of the optimum. To meet these limitations, a modified L32 orthogonal array was taken for the design of our experiment. A usual L32 orthogonal array in Taguchi [14] has 31 columns for assignments for 2-level factors. Here we have three 4-level factors and thus the techniq~ e of replacement in Dey [15] are applied to three different sets of three columns in the usual array to gain a modified one. After an appropriate assignment of all these factors, the conditions of all 32 tests, which are shown in table t. were obtained. In order to meet the test conditions designed in table 1, four heats of low carbon electrical steels were prepared from a 500 pound vacuum induction furnace. Table 2 lists the chemical composition of steels. The steel ingots of 100 m m in thickness were hot rolled at 1200°C in two steps by a two-high pilot hot-rolling mill with an intermediate annealing at 1200°C for half an hour. The thickness of hot roiled plates after these two
/
I
Fig. 1. Schematic illustration of continuous annealing of low carbon electrical steels.
steps were reduced to 20 and 3.2 ram, respectively, and their finishing temperature was 830 o C. After being air cooled to room temperature, the hot rolled plates were normalized at 720 and 650 o C, for one hour and then furnace cooled. They were uniformly ground to 2.0 and 1 2 m m in thickness to remove any scale. Finally, c~,ld-rolling was conducted by a four-high pilot cold-rolling mill and the thickness of the cold-rolled sheet was 0.5 mm. The cold-rolled reduction ratios are 58 and 75%, respectively. The continuous annealing treatment was simulated with a Duffers Gleeble 1500 Dynamic Thermal and Mechanical Simulator. The specimen size is 0.5 × 30 × 280 mm 3 and the temperature uniformity of the specimen in lengthwise direction is 100 mm. Fig. 1 shows the histogram of the continuous annealing process. T~, t,, R, T~ and t a represent annealing temperature, annealing time, primary cooling rate, aging temperature and aging time, respectively. Annealing temperatures are 700, 750, 800 and 850 o C. Annealing times are 50 and 100 s. Primary cooling rates are 5, 20, 35 and 50 ° C / s . Aging temperatures are 400, 450, 500 and 550°C. Aging times are 180 and 360 s. The testing coupons of 3 × 28 cm 2 aligned either longitudinal or transverse with respect to cold-rolling direction were cut from the cold-rolled steel sheets. The microstructure of hot-rolled plates and cold
Table 2 Chemical composition of low carbon electrical steels (wt%) Steel
C
Si
Mn
P
S
AI
N
O
B1 B2 B3 B4
0.02 0.02 0.005 0.005
0.5 0.2 0.2 0.5
0.23 0.27 0.26 0.26
0.067 0.005 0.067 0.005
0.006 0.005 0.004 0.005
0.002 0.002 0.002 0.002
0.0022 0.0016 0.0017 0.0016
0.0083 0.0085 0.0090 0.0093
112
C K. Hot~ P.C. Wang / Core loss and hardness of low carbon electrical steels
rolled sheets after continuous annealing were examined by optical means. The grain size was measured with the intercept method based cn ASTM E-112. Specimens for texture examination were ground to midplane and etched by hydrogen peroxide solution mixed with several drops of hydrogen fluoride. The texture measurement was conducted through the inverse pole intensity of a specific plane with a Siemens D500 X-ray diffractometer and a texture attachment, the Mo target operating at 40 kV and 25 mA. A slow scanning speed 0 . 5 ° / m i n was employed. A pressed and sintered iron powder specimen was taken as a random sample. Core loss was measured by a Soken DACBHW-2T single-strip electrical steel sheet tester operating at 1.5 T and 50 Hz. Both longitudinal and transverse specimens were measured, and their values were averaged. Vicker hardness of coldrolled specimens after continuous annealing was measured by a hardness tester operating at a 5 kg load. An analysis of the valance table [16] was employed to study the effects of the factors on grain size, texture, core loss and hardness. To determine which factors are predominaiat, we used the values of F-statistics corresponding to all the factors. The higher a F-statistic value of a factor is, the more significant its effect is. Comparing these values with F-values from F-table [17], we identified the important factors at the 90% confidence levels. When the predominant factors were determined from the analysis of variance, further analyses were carried out using the statistical package MINITAB for regression. Finally, two equations that represent the relationships between the performance characteristics, core loss and hardness, of low carbon electrical steels and the corresponding predominant factors are obtained. The terms in the two equations are all significant at least at the 90% confidence level.
3. Results and discussion
We present our analyses and results for each response in a different subsection.
3.1. Grain size
The analysis of the variance table fer the grain size is given in table 3. The range of the grain size is from 10.23 to 49.4 ~tm. It was found that the phosphorus contents, cold-rolled reduction ratio, normalizing temperature, annealing temperature and carbon contents are the predominant factors influencing final grain size. Annealing time also influences the final grain size, but its effect is weaker. Other factors, such as silicon contents, primary cooling rate, aging temperature and aging time, have negligible effect on the grain size. Moreover, the grain size increases with normalizing temperature, annealing temperature and annealing time, and decreases with increasing carbon contents, phosphorus contents and cold reduction ratio. 3.2. Texture
The analysis of the variance table for the relative intensity of the (200) plane is given in table 4. The range of (I/IR)20o is from 0.7 to 1.69. It was found that the carbon content and normalizing temperature have significant effects on the relative intensity of the (200) plane. The silicon content has less influence on the relative intensity of the
Table 3 Analysis of variance and effect on grain size Factors
Degree of freedom
Mean square of varlance
Fstatistic
Effect
carbon phosphorus silicon normalizing temperature cold reduction
1 1 1
71.40 518.40 21.45
3.26 23.74 0.98
refining refining negligible
1 1
108.80 160.20
4.98 7.33
coarsening refining
temperature annealing time primary cooling rate aging temperature aging time error
3 1
91.83 48.02
4.20 2.19
coarsening coarsening
3 3 1 15
10.66 16.17 14.05 21.83
0.48 0.74 0.64
negligible negligible negligible
C.K. Hou, P.C Wang / Core loss and hardness of low carbon electrical steels
Table 4 Analysis of variance and effect on relative intensity of the (200) plane, (I/IR)20 o Factors
Degree Mean of free- square dom of vat-
Fstatis-
carbon phosphorus silicon
normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Table 6 Analysis of variance and effect on core loss, W~5/5o Factors
Degree Mean of free- square dora of vatiance
Effect
tic
iance
1 1 1
2.247 0.00045 0.0435
109.0 enhance 0.021 negligible 2.11 enhance
1 1
0.1741 0.0136
8.43 0.66
enhance negligible
3 1
0.0222 0.0078
1.07 0.37
negligible negligible
3 3 1 15
0.0166 0.0165 0.0136 0.0206
0.80 0.80 0,66
negligible negligible negligible
(200) plane. Other factors h a v e negligible effects on the relative intensity of the (200) plane. M o r e over, ( I / I R ) 2 O o increases with carbon content, normalizing temperature a n d silicon content. Analysis of the variance table for the relative intensity of the (222) plane is given in table 5. T h e range of ( I / I R ) 2 2 2 is f r o m 0.66 to 2.39. It was
113
carbon phosphorus silicon
normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Fstatictic
Effect
1 1 1
11.56 17.45 3.387
2 6 . 4 8 increase 3 9 . 9 7 increase 7.75 decrease
1 1
6.799 1.867
15.57 decrease 4.27 increase
3 1
4.467 0.200
10.23 decrease 0.45 negligible
3 3 1 15
0.537 0.420 0.091 0.436
1.23 0.96 0.20
negligible negligible negligible
found that the cold-rolled r e d u c t i o n ratio, phosphorus contents and silicon contents have significant effect on the relative intensity of the (222) plane. O t h e r factors have negligible influences on the relative intensity of the (222) plane. Moreover, ( I / I R ) 2 2 2 increases with p h o s p h o r u s contents and cold-rolled reduction ratio, and decreases with silicon contents. 3.3. Core loss
Table 5 Analysis of variance and effect on relative intensity of the (222) plane, (I//IR)222 Factors
Degree
Mean square of variance
FEffect statistic
1 1 1
0.0116 0.8288 0.3938
0.16 negligible 11.41 enhance 5.42 suppress
1 1
0.0830 4.256
1.14 negligible 58.57 enhance
3 1
0.0393 0.0569
0.54 0.78
negligible negligible
3 3 1 15
0.0323 0.0209 0.0871 0.0726
0.44 0.28 1.19
negligible negligible negligible
of free-
dora carbon phosphorus silicon normalizing temperature cold reduction ap~e~ing temperature annealing timc primary cooling rate aging temperature aging time error
The analysis of the variance table for core loss is given in table 6. The range of core loss is from 5.66 to 11.02 W / k g . It was f o u n d that carbon content, p h o s p h o r u s content, silicon content, norrealizing temperature, cold-rolled reduction ratio an6 annealing temperature are the p r e d o m i n a n t fa~:tors influencing the core loss of low carbon electrical steels. The effects of other factors, such as annealing time, primary cooling rate, aging temperature a n d aging time on core loss are negligible. T h e regressior~ e q u a t i o n for those pred o m i n a n t factors and core loss can be represented as below, W15/5 o = 22.9 + 83.2 × C (%) + 17.3 × P (%)
- 3.67 × Si (%) - 0.0132T~ ( ° C )
+ 0.0285 × CR ( ~ ) - e.0109K,
(1)
114
CK. Hou, P.C. Wang / Core loss and hardness of low carbon electrical steels
where Wls/5o: core loss, in W/kg, T~: normalizing temperature, in °C, CR: cold-rolled reduction ratio, in %, ~: annealing temperature, in ° C. The adjusted squared multiple correlation of above equation is 78.3% and the standard error is 0.67. The standard deviations of each coefficient corresponding to the constant, C, P, Si, T~, CR and ~ are 3.0z, 15.98, 3.99, 1.19, 0.0033, 0.013 and 0.0021, respectively. It is known that factors, such as grain size, texture, resistivity, impurity and precipitate, influ-~nce core loss of electrical steels [2-4,18-20]. Since a grain boundary is a barrier to domain movement and a precipitate pins a domain during magnetization, both of them increase the hysteresis loss of low carbon electrical steels. There exist easy magnetizaron directions, [001] axes, in the (100) plane. Therefore, a higher relative intensity of the (200) plane parallel to the rolling plane is a good texture to reduce the core loss. On the other hand, easy magnetization axes do not lie down on the (111) plane. Higher relative intensity of the (222) plane parallel to rolling plane is a poor texture and increases the core loss. From table 3, it was found that carbon is a predominant factor refining the grain size and detrimental to core loss. It is evident that the amount of cementite in steel sheets increases with carbon content. It is also harmful to core loss. Although carbon improves the ( I / I R)2oo texture, as shown in table 4, it is still detrimental to core loss, as shown in eq. (1). From tables 3 and 5, phosphorus refines the grain size and enhances the (1/I R)222 plane intensity. Both effects are negative to the core loss. On the other hand, phosphorus increases the electrical resistivity and decreases the eddy current loss of e!ectrical steels [5]. Since its negative effects dominate, phosphorus increases the core loss, as shown in eq. (1). From tables 4 and 5, silicon enhances the (l/IR)2oo texture and suppresses the ( I / I R)222 texture. Silicon also increases the resistivity and decreases the eddy current loss [2]. All effects are beneficial to the core loss, as shown in eq. (1). From tables 3 and 4, normalizing temperature increases the grain size and enhances the ( I / I R )200 texture. Both effects are positive to the core loss, as shown in eq. (1). From tables 3 and 5, the cold-rolled reduction ratio refines the grain size
and enhances the (1/IR)222 texture. Both effects are harmful to the core loss, as shown in eq. (1). From table 3, annealing temperature enlarges the grain size and reduces the core loss, as shown in eq. (1).
3.4. Hardness Analysis of the variance table for the hardness is given in table 7. The range of the Vicker hardness is from 90 to 154. It was found that carbon content, phosphorus content, silicon content and annealing temperature are the predominant factors influencing the hardness. Normalizing temperature and aging time also affect the hardness but not so significantly. Other factors have negligible effects on the hardness. The regression equation between hardneas and predominant factors is represented as, H v = 116 + 809 x C (%) + 392 x P (%) + 50.3 × Si (%) - 0.0546 T~,
(2)
where Hv: Vicker hardness. The adjusted squared multipTe correlation of above equation is 89.3% and the standard error is 5.69. The standard deviations of each coefficient corresponding to the constant, C, P, Si and Ts are 14.45, 135, 33, 1t3 and 0.018, respectively. Table 7 Analysis of variance and effect on vicker hardness, Hv Factors
carbon phosphorus silicon normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Degree of freedom 1 1 1
Mean square of varlance
Fstatistic
Effect
1263 5968 935.3
39.49 186.61 29.24
increase increase increase
1 1
87.78 34.03
2.74 1.06
decrease negligible
3 1
121.02 5.28
3.78 0.16
decrease negligible
3 3 1 15
0.11 39.11 87.78 31.98
0.0035 1.22 2.74
negligible negligible increase
C.K. Hou, P. C Wang / Core loss and hardness of low carbon electrical steels
It is known that carbon, phosphorus and silicon are strengthening elements in steels [21]. Therefore, they all increase the hardness of low carbon electrical steels, as shown in eq. (2). On the other hand, as discussed previously, annealing temperature increases the grain size. According to the Hall-Petch [22] relationship, the strength inversely decreases with the square root of the grain size. Therefore, the annealing temperature decreases the hardness.
4. Summary and conclusion The effects of chemical composition and process variables on core loss and hardness of continuous annealed low carbon electrical steels have been studied in a statistically designed experiment. It was found that carbon, phosphorus, silicon content, normalizing temperature, cold-rolled reduction ratio and annealing temperature are the predominant factors influencing the core loss. Carbon increases the core loss through refinement of grain size and the amount of cementite. Phosphorus increases the core loss through both refinement of the gl'ain size and development of a poor texture. Silicon improves the core loss through the development of a good texture and increasing resistivity. Normalizing temperature decreases the core loss through combining effects of coarsening grain size and development of good texture. Cold-rolled reduction ratio is detrimental to the core loss through the combined effects of refinement of the grain size and development of poor texture. Annealing temperature reduces the core loss through the effect of coarsening the grain size. It was also found that carbon content, phosphorus content, sqicon content and annealing temperature are the predominant factors influencing the hardness of continuous annealed low carbon electrical steels. Additionally, two useful regression equations are established to represent quantitative relationships between those predominant factors and two characteristics, the core loss and hardness of electrical steels.
115
Acknowledgement The authors wish to thank the China Steel Corporation i'or permission to publish this paper.
References [1] C.K. Hou, C.T. Hu and Sanboh Lee, J. Mater. Sci. Eng. A125 (1990) 241. [2] M.F. Littman, IEEE Trans. Magn. MAG-'~ (1971) 48. [3] P. Brissonneau, J. Magn. Magn. Mat. 19 (1980) 52. [4] H. Shimanaka, Y. Ito, K. Matsumura and B. Fukuda, J. Magn. Magn. Mat. 26 (1982) 57. [5] P. Arato, I. Boc and T. Grof, J. Magn. Magn. Mat. 41 (1984) 53. [6] J.M. Shapiro, in: Energy Efficient Electrical Steels, eds. A.R. Marder and E.T. Stephenson (TMS-AIME, Warrendale, PA, 1981) p. 33. [7] E.T. Stephenson and M.R. Amman, in: Energy Efficient Electrical Steels, eds. A.R. Marder and E.T. Stephenson (TMS-AIME, Warrendale, PA, 1981) p. 43. [8] P.L. Charpentier and J.H. Bucher, Mechanical Working and Steel Processing X, AIME (1972) p. 61. [9] S. Szymura, C. Adamczyk, H. Majchrzak, J. Mehlis and A. Zawada, J. Mater. oct. Lett. 6 (1987) 1259. [10] G. Lyudkovsky and J.M. Shapiro. J. Appl. Phys. 57 (1985) 4235. [il] K.C. Liao, Metall. Trans. 17A (1986) 1259. [12] G. Taguchi, Introduction to Quality Engineering (Asian Productivity Organization, Tokyo, Japan, 1986) p. 103 [13] American Supplier Institute, Proc. Symp. on Taguchi Methods (American Supplier Institute, Dearborn, MI, 1983-1988). [14] G. Taguchi, System of Experimental Design, vols. I and 2, (UNIPUB, Kraus International Publications, New York, 1987) p. 1132. [151 A. Dey, Orthogonal Fractional Factorial Designs (Wiley, New Delhi, 1985) p. 82. I161 D.C. Montgomery, Design & Analysis of Experiments, 2nd ed. (John Wiley, New York, 1984) p. 46. 1171 D.C. Montgomery, Design & Analysis of Experiments, 2nd ed. (John Wiley, New York, 1984) p. 511. 1181 E.T. Stephenson and A.R. Marder, IEEE Trans. Magn. MAG-22 (1986) 101. [191 I.F. Hughes and J.M. Shapiro, Metall. Trans. 2 (1971) 3347. '"'~ [201 B.D. Cuiiity, introduction to Magnetic .[ V. l.d.i g. l. . l a 1'-3 [~'~*Ot" dison Wesley, Reading, MA. 1971) p. 287. [211 F.B. Picketing, Physical Metallurgy and The Design of Steels (Applied Science Publishers, London, 1978) p. 10. [22] N.J. Petch, J. Iron Steel Inst. 174 (1953) 25.
109
Effects of composition and process variables on core loss and hardness of low carbon electrical steels C.K. Hou Steel and Aluminum Research and Development Department, China Steel Corporation, Hsiao Kang, Kaohsiung 81233, Taiwan
and P.C. Wang Graduate Institute of Statistics, National Central University, Chung-Li 32054, Taiwan Received 2 March 1990; in revised form 29 May 1990
The effects of chemical composition and process variables on core loss and hardness of continuous annealed low carbon electrical steels have been studied i~ an experiment of statistical design. After data were collected from the experiment, statistical analyses were carded out for finding the dominant factors. Factors that influence the core loss, hardness, grain size and texture of low carbon electrical steels are found. Additionally, two regression equations are established to represent quantitative relationships between those dominant factors and two characteristics, the core loss and hardness, of the electrical steels.
1. Introduction Low c a r b o n electrical steels are commonly used to m a k e lamination cores of fractional horsepower m o t o r s for economic reasons. Their chemical compositions contain smaller a m o u n t s of alloy elements, such as silicon and a l u m i n u m , than nonoriented electrical steels. However, one must keep the c a r b o n content and other impurities as low as possible to enhance magnetic properties, and increase the phosphorus to increase the hardness. Moreover, in order to avoid the detrimental effects of a l u m i n u m nitride on grain growth and magnetic properties, low c a r b o n electrical steel is often killed with silicon instead of aluminum during steelmaking. M o d e r n steelmaking technology has reduced carbon content to less than 50 p p m through vacuum-degasser treatment. Recently, continuous annealing lines have been widely installed all over the world for the obvious ad-
vantages of shortening annealing time, improving sheet flatness a n d saving energy. W i t h these advances, it becomes possible for the steel mill to produce low c a r b o n electrical steels. T h e effects of factors, such as chemical composition, thickness, texture and microstructure, on the magnetic properties of low c a r b o n electrical steels and nonoriented electrical steels have been studied by many researchers [1-11]. Some of them adopted factorial design m e t h o d s to conduct their experiments [10,11]. S o m e of them a d o p t e d nonfactor/al desi~,.l m e t h o d s to conduct the~l" experiments [5,6,8]. Some of them designed their experiments with factorial m e t h o d s in certain variables but not in others [7,9]. However, there are no papers using the orthogonal statistical design m e t h o d to investigate the effects of composition and process variables on the core loss of low c a r b o n electrical steels. The orthogonal statistical design that can be established by the method of orthogonal array
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
1 iO
C.K. Hou, P.C. Wang / Core loss and hardness of low carbon electrical steels
has the advantage to study the effects of many factors and some of their interactions with a few tests in an experiment. In fact, the methods of orthogonal array have been widely used in Japanese industry for quality improvements, and recently in the industry of the United States [12,13]. In this work, we set up an experiment using the method of orthogonal array to study the effects of three composition variables and seven process variables simultaneously on the core loss and hardness of continuous annealed low carbon elec-
trical steels. First, we obtain an orthogonal statistical design in ten controllable variables by using modifications of an existing orthogonal array. This design gives 32 different tests. Then, after the collection of the data from the tests, the effects of variables are analysed and quantitative relationships of core loss and hardness with their dondnant factors were also established by the regression method. Moreover, the effects of composition and process variables on grain size and texture were analysed to account for core loss of low carbon electrical steels.
Table 1 Chemical composition and process variables of each test Test no.
C (wt%)
P (wt%)
Si (wt%)
Norm. temp.
Cold red.
(°c)
Anneal temp.
Anneal time
Primary cooling
Aging temp.
(%)
(o C)
(s)
rate
(o C)
time (s)
550 500 450 400 500 550 400 450 500 550 400 450 550 500 450 400 450 400 550 500 400 450 500 550 400 450 500 550 450 400 550 500
360 180 360 180 180 360 180 360 180 360 180 360 360 180 360 180 180 360 180 360 360 180 360 180 360 180 360 180 180 360 180 360
Aging
(°C/s) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
0.02 0.02 0.02 0.02 0.02 002 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005
0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650 720 720 720 720 650 650 650 650
75 58 58 75 58 75 75 58 58 75 75 58 75 58 58 75 75 58 58 75 58 75 75 5R 58 75 75 58 75 58 58 75
850 800 750 700 850 80C 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700 850 800 750 700
100 50 50 100 100 50 50 100 50 100 100 50 50 10O 100 50 50 100 100 50 50 100 100 50 100 50 50 100 100 50 50 100
50 35 20 5 20 5 50 35 50 35 20 5 20 5 50 35 35 50 5 20 5 20 35 50 35 50 5 20 5 20 35 50
C.K. Hou, P.C. War7e / Core loss and hardness of low carbon electrical steels
2. Experimental procedures
111
rs -.,R'Clsec
Ten variables in three categories are considered in our experiment for the study on four characteristics of low carbon electrical steels, the core loss, the hardness, the grain size and texture. Carbon, phosphorus and silicon contents in the chemical composition are factors in one catego~', while the process variables are factors in the other two categories. The latter two categories are the general processing variables (normalizing temperature of hot rolled bands, and cold rolled reduction ratio) and the continuous annealing variables (annealing temperature, annealing time, p r m a r y cooling rate, aging temperature and aging time). Due to the cost consideration, at most 32 experimental tests could be carried out and thus some of interaction effects, such as C x P, have to be sacrificed. Also, 4 levels are considered in some variables for the achievement of the optimum. To meet these limitations, a modified L32 orthogonal array was taken for the design of our experiment. A usual L32 orthogonal array in Taguchi [14] has 31 columns for assignments for 2-level factors. Here we have three 4-level factors and thus the techniq~ e of replacement in Dey [15] are applied to three different sets of three columns in the usual array to gain a modified one. After an appropriate assignment of all these factors, the conditions of all 32 tests, which are shown in table t. were obtained. In order to meet the test conditions designed in table 1, four heats of low carbon electrical steels were prepared from a 500 pound vacuum induction furnace. Table 2 lists the chemical composition of steels. The steel ingots of 100 m m in thickness were hot rolled at 1200°C in two steps by a two-high pilot hot-rolling mill with an intermediate annealing at 1200°C for half an hour. The thickness of hot roiled plates after these two
/
I
Fig. 1. Schematic illustration of continuous annealing of low carbon electrical steels.
steps were reduced to 20 and 3.2 ram, respectively, and their finishing temperature was 830 o C. After being air cooled to room temperature, the hot rolled plates were normalized at 720 and 650 o C, for one hour and then furnace cooled. They were uniformly ground to 2.0 and 1 2 m m in thickness to remove any scale. Finally, c~,ld-rolling was conducted by a four-high pilot cold-rolling mill and the thickness of the cold-rolled sheet was 0.5 mm. The cold-rolled reduction ratios are 58 and 75%, respectively. The continuous annealing treatment was simulated with a Duffers Gleeble 1500 Dynamic Thermal and Mechanical Simulator. The specimen size is 0.5 × 30 × 280 mm 3 and the temperature uniformity of the specimen in lengthwise direction is 100 mm. Fig. 1 shows the histogram of the continuous annealing process. T~, t,, R, T~ and t a represent annealing temperature, annealing time, primary cooling rate, aging temperature and aging time, respectively. Annealing temperatures are 700, 750, 800 and 850 o C. Annealing times are 50 and 100 s. Primary cooling rates are 5, 20, 35 and 50 ° C / s . Aging temperatures are 400, 450, 500 and 550°C. Aging times are 180 and 360 s. The testing coupons of 3 × 28 cm 2 aligned either longitudinal or transverse with respect to cold-rolling direction were cut from the cold-rolled steel sheets. The microstructure of hot-rolled plates and cold
Table 2 Chemical composition of low carbon electrical steels (wt%) Steel
C
Si
Mn
P
S
AI
N
O
B1 B2 B3 B4
0.02 0.02 0.005 0.005
0.5 0.2 0.2 0.5
0.23 0.27 0.26 0.26
0.067 0.005 0.067 0.005
0.006 0.005 0.004 0.005
0.002 0.002 0.002 0.002
0.0022 0.0016 0.0017 0.0016
0.0083 0.0085 0.0090 0.0093
112
C K. Hot~ P.C. Wang / Core loss and hardness of low carbon electrical steels
rolled sheets after continuous annealing were examined by optical means. The grain size was measured with the intercept method based cn ASTM E-112. Specimens for texture examination were ground to midplane and etched by hydrogen peroxide solution mixed with several drops of hydrogen fluoride. The texture measurement was conducted through the inverse pole intensity of a specific plane with a Siemens D500 X-ray diffractometer and a texture attachment, the Mo target operating at 40 kV and 25 mA. A slow scanning speed 0 . 5 ° / m i n was employed. A pressed and sintered iron powder specimen was taken as a random sample. Core loss was measured by a Soken DACBHW-2T single-strip electrical steel sheet tester operating at 1.5 T and 50 Hz. Both longitudinal and transverse specimens were measured, and their values were averaged. Vicker hardness of coldrolled specimens after continuous annealing was measured by a hardness tester operating at a 5 kg load. An analysis of the valance table [16] was employed to study the effects of the factors on grain size, texture, core loss and hardness. To determine which factors are predominaiat, we used the values of F-statistics corresponding to all the factors. The higher a F-statistic value of a factor is, the more significant its effect is. Comparing these values with F-values from F-table [17], we identified the important factors at the 90% confidence levels. When the predominant factors were determined from the analysis of variance, further analyses were carried out using the statistical package MINITAB for regression. Finally, two equations that represent the relationships between the performance characteristics, core loss and hardness, of low carbon electrical steels and the corresponding predominant factors are obtained. The terms in the two equations are all significant at least at the 90% confidence level.
3. Results and discussion
We present our analyses and results for each response in a different subsection.
3.1. Grain size
The analysis of the variance table fer the grain size is given in table 3. The range of the grain size is from 10.23 to 49.4 ~tm. It was found that the phosphorus contents, cold-rolled reduction ratio, normalizing temperature, annealing temperature and carbon contents are the predominant factors influencing final grain size. Annealing time also influences the final grain size, but its effect is weaker. Other factors, such as silicon contents, primary cooling rate, aging temperature and aging time, have negligible effect on the grain size. Moreover, the grain size increases with normalizing temperature, annealing temperature and annealing time, and decreases with increasing carbon contents, phosphorus contents and cold reduction ratio. 3.2. Texture
The analysis of the variance table for the relative intensity of the (200) plane is given in table 4. The range of (I/IR)20o is from 0.7 to 1.69. It was found that the carbon content and normalizing temperature have significant effects on the relative intensity of the (200) plane. The silicon content has less influence on the relative intensity of the
Table 3 Analysis of variance and effect on grain size Factors
Degree of freedom
Mean square of varlance
Fstatistic
Effect
carbon phosphorus silicon normalizing temperature cold reduction
1 1 1
71.40 518.40 21.45
3.26 23.74 0.98
refining refining negligible
1 1
108.80 160.20
4.98 7.33
coarsening refining
temperature annealing time primary cooling rate aging temperature aging time error
3 1
91.83 48.02
4.20 2.19
coarsening coarsening
3 3 1 15
10.66 16.17 14.05 21.83
0.48 0.74 0.64
negligible negligible negligible
C.K. Hou, P.C Wang / Core loss and hardness of low carbon electrical steels
Table 4 Analysis of variance and effect on relative intensity of the (200) plane, (I/IR)20 o Factors
Degree Mean of free- square dom of vat-
Fstatis-
carbon phosphorus silicon
normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Table 6 Analysis of variance and effect on core loss, W~5/5o Factors
Degree Mean of free- square dora of vatiance
Effect
tic
iance
1 1 1
2.247 0.00045 0.0435
109.0 enhance 0.021 negligible 2.11 enhance
1 1
0.1741 0.0136
8.43 0.66
enhance negligible
3 1
0.0222 0.0078
1.07 0.37
negligible negligible
3 3 1 15
0.0166 0.0165 0.0136 0.0206
0.80 0.80 0,66
negligible negligible negligible
(200) plane. Other factors h a v e negligible effects on the relative intensity of the (200) plane. M o r e over, ( I / I R ) 2 O o increases with carbon content, normalizing temperature a n d silicon content. Analysis of the variance table for the relative intensity of the (222) plane is given in table 5. T h e range of ( I / I R ) 2 2 2 is f r o m 0.66 to 2.39. It was
113
carbon phosphorus silicon
normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Fstatictic
Effect
1 1 1
11.56 17.45 3.387
2 6 . 4 8 increase 3 9 . 9 7 increase 7.75 decrease
1 1
6.799 1.867
15.57 decrease 4.27 increase
3 1
4.467 0.200
10.23 decrease 0.45 negligible
3 3 1 15
0.537 0.420 0.091 0.436
1.23 0.96 0.20
negligible negligible negligible
found that the cold-rolled r e d u c t i o n ratio, phosphorus contents and silicon contents have significant effect on the relative intensity of the (222) plane. O t h e r factors have negligible influences on the relative intensity of the (222) plane. Moreover, ( I / I R ) 2 2 2 increases with p h o s p h o r u s contents and cold-rolled reduction ratio, and decreases with silicon contents. 3.3. Core loss
Table 5 Analysis of variance and effect on relative intensity of the (222) plane, (I//IR)222 Factors
Degree
Mean square of variance
FEffect statistic
1 1 1
0.0116 0.8288 0.3938
0.16 negligible 11.41 enhance 5.42 suppress
1 1
0.0830 4.256
1.14 negligible 58.57 enhance
3 1
0.0393 0.0569
0.54 0.78
negligible negligible
3 3 1 15
0.0323 0.0209 0.0871 0.0726
0.44 0.28 1.19
negligible negligible negligible
of free-
dora carbon phosphorus silicon normalizing temperature cold reduction ap~e~ing temperature annealing timc primary cooling rate aging temperature aging time error
The analysis of the variance table for core loss is given in table 6. The range of core loss is from 5.66 to 11.02 W / k g . It was f o u n d that carbon content, p h o s p h o r u s content, silicon content, norrealizing temperature, cold-rolled reduction ratio an6 annealing temperature are the p r e d o m i n a n t fa~:tors influencing the core loss of low carbon electrical steels. The effects of other factors, such as annealing time, primary cooling rate, aging temperature a n d aging time on core loss are negligible. T h e regressior~ e q u a t i o n for those pred o m i n a n t factors and core loss can be represented as below, W15/5 o = 22.9 + 83.2 × C (%) + 17.3 × P (%)
- 3.67 × Si (%) - 0.0132T~ ( ° C )
+ 0.0285 × CR ( ~ ) - e.0109K,
(1)
114
CK. Hou, P.C. Wang / Core loss and hardness of low carbon electrical steels
where Wls/5o: core loss, in W/kg, T~: normalizing temperature, in °C, CR: cold-rolled reduction ratio, in %, ~: annealing temperature, in ° C. The adjusted squared multiple correlation of above equation is 78.3% and the standard error is 0.67. The standard deviations of each coefficient corresponding to the constant, C, P, Si, T~, CR and ~ are 3.0z, 15.98, 3.99, 1.19, 0.0033, 0.013 and 0.0021, respectively. It is known that factors, such as grain size, texture, resistivity, impurity and precipitate, influ-~nce core loss of electrical steels [2-4,18-20]. Since a grain boundary is a barrier to domain movement and a precipitate pins a domain during magnetization, both of them increase the hysteresis loss of low carbon electrical steels. There exist easy magnetizaron directions, [001] axes, in the (100) plane. Therefore, a higher relative intensity of the (200) plane parallel to the rolling plane is a good texture to reduce the core loss. On the other hand, easy magnetization axes do not lie down on the (111) plane. Higher relative intensity of the (222) plane parallel to rolling plane is a poor texture and increases the core loss. From table 3, it was found that carbon is a predominant factor refining the grain size and detrimental to core loss. It is evident that the amount of cementite in steel sheets increases with carbon content. It is also harmful to core loss. Although carbon improves the ( I / I R)2oo texture, as shown in table 4, it is still detrimental to core loss, as shown in eq. (1). From tables 3 and 5, phosphorus refines the grain size and enhances the (1/I R)222 plane intensity. Both effects are negative to the core loss. On the other hand, phosphorus increases the electrical resistivity and decreases the eddy current loss of e!ectrical steels [5]. Since its negative effects dominate, phosphorus increases the core loss, as shown in eq. (1). From tables 4 and 5, silicon enhances the (l/IR)2oo texture and suppresses the ( I / I R)222 texture. Silicon also increases the resistivity and decreases the eddy current loss [2]. All effects are beneficial to the core loss, as shown in eq. (1). From tables 3 and 4, normalizing temperature increases the grain size and enhances the ( I / I R )200 texture. Both effects are positive to the core loss, as shown in eq. (1). From tables 3 and 5, the cold-rolled reduction ratio refines the grain size
and enhances the (1/IR)222 texture. Both effects are harmful to the core loss, as shown in eq. (1). From table 3, annealing temperature enlarges the grain size and reduces the core loss, as shown in eq. (1).
3.4. Hardness Analysis of the variance table for the hardness is given in table 7. The range of the Vicker hardness is from 90 to 154. It was found that carbon content, phosphorus content, silicon content and annealing temperature are the predominant factors influencing the hardness. Normalizing temperature and aging time also affect the hardness but not so significantly. Other factors have negligible effects on the hardness. The regression equation between hardneas and predominant factors is represented as, H v = 116 + 809 x C (%) + 392 x P (%) + 50.3 × Si (%) - 0.0546 T~,
(2)
where Hv: Vicker hardness. The adjusted squared multipTe correlation of above equation is 89.3% and the standard error is 5.69. The standard deviations of each coefficient corresponding to the constant, C, P, Si and Ts are 14.45, 135, 33, 1t3 and 0.018, respectively. Table 7 Analysis of variance and effect on vicker hardness, Hv Factors
carbon phosphorus silicon normalizing temperature cold reduction annealing temperature annealing time primary cooling rate aging temperature aging time error
Degree of freedom 1 1 1
Mean square of varlance
Fstatistic
Effect
1263 5968 935.3
39.49 186.61 29.24
increase increase increase
1 1
87.78 34.03
2.74 1.06
decrease negligible
3 1
121.02 5.28
3.78 0.16
decrease negligible
3 3 1 15
0.11 39.11 87.78 31.98
0.0035 1.22 2.74
negligible negligible increase
C.K. Hou, P. C Wang / Core loss and hardness of low carbon electrical steels
It is known that carbon, phosphorus and silicon are strengthening elements in steels [21]. Therefore, they all increase the hardness of low carbon electrical steels, as shown in eq. (2). On the other hand, as discussed previously, annealing temperature increases the grain size. According to the Hall-Petch [22] relationship, the strength inversely decreases with the square root of the grain size. Therefore, the annealing temperature decreases the hardness.
4. Summary and conclusion The effects of chemical composition and process variables on core loss and hardness of continuous annealed low carbon electrical steels have been studied in a statistically designed experiment. It was found that carbon, phosphorus, silicon content, normalizing temperature, cold-rolled reduction ratio and annealing temperature are the predominant factors influencing the core loss. Carbon increases the core loss through refinement of grain size and the amount of cementite. Phosphorus increases the core loss through both refinement of the gl'ain size and development of a poor texture. Silicon improves the core loss through the development of a good texture and increasing resistivity. Normalizing temperature decreases the core loss through combining effects of coarsening grain size and development of good texture. Cold-rolled reduction ratio is detrimental to the core loss through the combined effects of refinement of the grain size and development of poor texture. Annealing temperature reduces the core loss through the effect of coarsening the grain size. It was also found that carbon content, phosphorus content, sqicon content and annealing temperature are the predominant factors influencing the hardness of continuous annealed low carbon electrical steels. Additionally, two useful regression equations are established to represent quantitative relationships between those predominant factors and two characteristics, the core loss and hardness of electrical steels.
115
Acknowledgement The authors wish to thank the China Steel Corporation i'or permission to publish this paper.
References [1] C.K. Hou, C.T. Hu and Sanboh Lee, J. Mater. Sci. Eng. A125 (1990) 241. [2] M.F. Littman, IEEE Trans. Magn. MAG-'~ (1971) 48. [3] P. Brissonneau, J. Magn. Magn. Mat. 19 (1980) 52. [4] H. Shimanaka, Y. Ito, K. Matsumura and B. Fukuda, J. Magn. Magn. Mat. 26 (1982) 57. [5] P. Arato, I. Boc and T. Grof, J. Magn. Magn. Mat. 41 (1984) 53. [6] J.M. Shapiro, in: Energy Efficient Electrical Steels, eds. A.R. Marder and E.T. Stephenson (TMS-AIME, Warrendale, PA, 1981) p. 33. [7] E.T. Stephenson and M.R. Amman, in: Energy Efficient Electrical Steels, eds. A.R. Marder and E.T. Stephenson (TMS-AIME, Warrendale, PA, 1981) p. 43. [8] P.L. Charpentier and J.H. Bucher, Mechanical Working and Steel Processing X, AIME (1972) p. 61. [9] S. Szymura, C. Adamczyk, H. Majchrzak, J. Mehlis and A. Zawada, J. Mater. oct. Lett. 6 (1987) 1259. [10] G. Lyudkovsky and J.M. Shapiro. J. Appl. Phys. 57 (1985) 4235. [il] K.C. Liao, Metall. Trans. 17A (1986) 1259. [12] G. Taguchi, Introduction to Quality Engineering (Asian Productivity Organization, Tokyo, Japan, 1986) p. 103 [13] American Supplier Institute, Proc. Symp. on Taguchi Methods (American Supplier Institute, Dearborn, MI, 1983-1988). [14] G. Taguchi, System of Experimental Design, vols. I and 2, (UNIPUB, Kraus International Publications, New York, 1987) p. 1132. [151 A. Dey, Orthogonal Fractional Factorial Designs (Wiley, New Delhi, 1985) p. 82. I161 D.C. Montgomery, Design & Analysis of Experiments, 2nd ed. (John Wiley, New York, 1984) p. 46. 1171 D.C. Montgomery, Design & Analysis of Experiments, 2nd ed. (John Wiley, New York, 1984) p. 511. 1181 E.T. Stephenson and A.R. Marder, IEEE Trans. Magn. MAG-22 (1986) 101. [191 I.F. Hughes and J.M. Shapiro, Metall. Trans. 2 (1971) 3347. '"'~ [201 B.D. Cuiiity, introduction to Magnetic .[ V. l.d.i g. l. . l a 1'-3 [~'~*Ot" dison Wesley, Reading, MA. 1971) p. 287. [211 F.B. Picketing, Physical Metallurgy and The Design of Steels (Applied Science Publishers, London, 1978) p. 10. [22] N.J. Petch, J. Iron Steel Inst. 174 (1953) 25.