[6]
With this method, the boundary information between skull and melt were recorded and then the profile of the skull can be plotted. Based on the profile, the variation of skull size with inputting power, charge weight, and holding time were analyzed. 100 150 200 250 300.

[4]
[6] [8] [10] [12] [14] [16] [18] 3. 0Kg 3. 6Kg 4. 2Kg 4. 8Kg 5. 4Kg Rs /% Inputting power /kW 3. 0 3. 5 4. 0 4. 5 5. 0 5. 5.

[4]
[6] [8] [10] [12] [14] [16] [18] 100kW 150kW 200kW 250kW 300kW Rs /% Charge weight /Kg Fig. 2 Variation of Rs with charge weight Fig. 3 Variation of Rs with powers Results and discussion Fig. 1 shows the skull profile of ISM processing of 4. 2kg TiAl alloy when the energy equilibrium status is satisfied. In this figure, the data 1. 000' and '0. 5000' on the lines are referred to the liquid fraction in the corresponding area, respectively. Above the '1. 000' line, the liquid fraction is 1. 000, this region is filled with alloy melt. Below the '0. 5000, line, the liquid fraction is less than 0. 5000, this region is the solid skull. Obviously, in the axial direction, with the increase of the height, the liquid fraction increases. From Fig. 1, it is obvious that the skull bottom is thicker than skull wall because of the eddy effect of the externally applied electromagnetic field. With the increase of the inputting power, the thickness of skull bottom decreases. For example, comparing Fig. 1 (a) and (b), when the inputting power increases to 150kW from 100kW, the maximum thickness will decrease to 0. 8cm from 2. 0cm. At the same time, with the inputting power increasing, the magnetic pushing force increases, and as a result the height of skull wall is shortened. (a) (b) (c) Fig. 1 Final skull profile at difference inputting powers with the charge weight of 4. 2kg Fig. 2 gives the ratio Rs with different charge weight. It can be seen that with the increasing of the charge weight, Rs increases. When the inputting power is smaller, the variation of RS with the charge weight is rapider. This is attributed to the larger inputting power reducing the thickness and height of the skull, which can be seen in Fig. 1. Fig. 3 is the relationship between Rs and the inputting power with different charge weight. It can be seen that when the inputting power is less than 200kW, with the increasing of the inputting power, Rs sharply decreases. When the inputting power is large than 200kW, the variation of Rs with 0. 5000 1. 000.

DOI: https://doi.org/10.1093/rheumatology/kew068.002

[1]
[2] [3] [4] [5] [6] [7] [8] [9] power=150kW R adius direction /cm Axial direction /cm 0. 5000 1. 000.

[1]
[2] [3] [4] [5] [6] [7] [8] [9] power=100kW Radius direction /cm Axial direction /cm 0. 5000 1. 000.

[1] [2] [3] [4] [5] [6] [7] [8] [9] power=200kw R adius direction /cm Axial direction /cm Skull.

[1]
[4] [3] [2] [0] 2 4 6 8.

2000 4000 6000 8000 10000 12000 321 position 1 Al Ti Intensity Thickness /mm Fig. 4 Schematic of the thickness Fig. 5 Chemical composition variation measurement points in the skull along the samples' section the changing of the inputting power is not so markedly. The smooth lines in Fig. 3 are the regression results with an exponential decay fitting of first order based on the theoretical data. The correlation coefficients are above 0. 99. The regression results are written as following 3. 0kg: ( )0927. 51exp59606. 002874. 0 P Rs −⋅+= (2) 3. 6kg: ( )27723. 46exp83474. 003187. 0 P Rs −⋅+= (3) 4. 2kg: ( )11322. 44exp05396. 13424. 0 P Rs −⋅+= (4) 4. 8kg: ( )52573. 44exp20086. 13518. 0 P Rs −⋅+= (5) 5. 4kg: ( )82667. 45exp2729. 103567. 0 P Rs −⋅+= (6) It must be pointed out that in these functions the inputting powers should be in the range of 100kW to 300kW. In fact, in the melting practice, the inputting power is always in this range. Then, a general function can be written as: − ⋅+= C P BARs exp (7) From Eq. 2 through Eq. 6, we can know that A , B andC are dependent on charge weight. Using charge weight as an independent variable and corresponding constants in the equations as a dependent variable, A , B and C can be written as a polynomial form of second order. A =.

DOI: https://doi.org/10.1016/b9-78-044451-9/94850-0109

[2]
01331. 014045. 001405. 0 W W − +− (8).

[2]
08048. 096263. 057381. 1 W W B − +−= (9).

[2]
93836. 372949. 2628267. 104 W W C + − = (10) Here, W is the charge weight (kg). The correlation coefficient is never less than 0. 98. During ISM melting process, Rs can be reduced by increasing of inputting power. However, with the increasing of the inputting power, the melt temperature and the evaporation surface will increase, which enlarges the chemical composition deviation of the melt for the evaporation of elements in the melt with high equilibrium partial pressure [7]. Experiment and discussion The ISM furnace with a water-cold copper crucible of diameter 120mm and height 240mm was used to melt Ti-33Al (at%) alloy. The raw materials were composed of sponge titanium and high pure aluminum rod. The sponge titanium was pressed into a cylinder and then put into the crucible. The melting power increased from 20kW to 300kW step by step. After about 12 minutes, the sponge titanium was completely melted. Then the input power is decreased to 200kW and kept unchanged for about 5 minutes in order to guarantee the homogeneity of the temperature. Then the aluminum rod was inserted into the molten metal and completely melted with a short time. After about 5 minutes, the melt was cast into a mold and the solid skull was remained in the crucible. Then the skull weight and its thickness were measured. Fig. 4 indicates the 4 measurement points of the skull thickness. The skull thickness in the corresponding position is determined by measuring the Al content variation along the sample's section. As an example, the measurement results of position 1 are shown in Fig. 5. It can be seen that the section can be divided into three regions. Region 1 is the solid skull region and the Al content in this region is almost equal to zero. Region 3 is TiAl alloy region, which are formed by attached internal melt on the skull during pouring. Region 2 is the mushy region. During the melting processing, the liquid fractions in the region 1 and region 2 are below 1. 0. So, the whole skull thickness should be the sum of the thickness of the region 1 and region 2. The skull thickness and its weight based on Fig. 5 are given in table 1. In table 1, the skull thickness of numerical results is based in Fig. 2 (c). Table 1 shows that the numerical results are in good agreement with that of the experiment. Table 1 Comparison between the theoretical and experimental results Point.

DOI: https://doi.org/10.1055/s-2007-1091090

[4]
Skull wall height (mm) Rs (%) Numerical thickness (mm) 7. 896 3. 290 1. 316 1. 316 52. 346 4. 77 Experiment thickness (mm) 7. 680 4. 312 2. 314 1. 466 58. 445 5. 02 Conclusions 1. An exponent relationship between Rs and the input power during ISM process of TiAl alloy were set up. And the coefficients in the equation are depended on the charge weight. 2. An experiment is carried out to determine the thickness and the weight of the skull. The experimental results are in good agreement with the theoretical results. Acknowledgement The authors would like to thank projects NSFC (50395102) and G2000067202-2 and JC02-10 for their financial supports. References.

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