上海交通大学博士后研究工作报告
Development of Online Accelerated-Cooling Process for Seamless Tube
Guanghong Yin
Abstract：The effect of chemical composition, and as well as of production process parameters, on the microstructure and mechanical properties is investigated under accelerated cooling conditions. The results show that accelerated cooling after mandrel milling using the spray cooling method can produce ideal N80 oil casing, and the quenching-tempering treatment is no longer necessary.
1 Background
The purpose of thermal deformation applied to steels is not only to obtain the expected grain size, but also to improve the mechanical properties of steels. Thermal mechanical treatments (TMT) are just such a process by using both the thermal and the deformation effect produced during manufacturing. Among them, thermal mechanical controlled process（TMCP）falls into this category. TMCP is a complex technique that includes controlled rolling（CR） and accelerated cooling（ACC）[1].Nowadays, TMCP has been successfully applied to the production of structural steels, for example, steel plates, strips, etc., however, as to seamless steel tube, TMCP has always been far away from industrial production owing to its complexity and particularity of shape, of thermo mechanical process and of manufacturing equipment [2].
Ever since 1980, researchers have endeavored to the investigation on the TMCP of seamless steel tube. It is clear now that on-line normalization （OLN）and on-line accelerated cooling （OALC）are the two main methods to realize TMCP.
On-line normalization （OLN）is described as follows, firstly, the tube is cooled to below the transformation temperature Ac1, through the phase transformation of austenite to ferrite after mandrel milling and before reheating, then phase transforms again after austenitization at the reheating furnace, thus the austenite grain size is refined through the paths of phase transformation. [2,4-6]。
On-line accelerated cooling （OALC） [2,3,5-7] is a process that the deformed austenite obtained at the non-recrystallization temperature （Tnr）goes through the transformation temperature region of 750～500℃ with a heating rate of 10～50℃/s, resulting in the refined microstructure and improved strength and ductility.
Because TMCP could realize the on-line heat treatment, including OLN and OALC, replace for the expensive quenching-tempering treatment [8], and boost production efficiency while lower product expense, hereafter, the application prospect is promising. The research aims to the feasibility of realizing OLN and OALC on the product line of Baosteel Φ140 rolling mill unit, together with the development of N80 casing steel suitable for TMCP.
2 Steel developments
The steel composition should be designed and the steel species should be developed before the study of the feasibility of TMCP in Baosteel.
The key point of steel development is that the microstructure of the steel should keep dynamic recrystallizaiton when rolling at 1000℃, guaranteeing against the phenomenon of mixing gain size. Such elements as C 、V、Ti、N assures much precipitation of the carbide or nitride of V and Ti to pin the grain boundary and to refine the grain size at high temperatures, and thus TMCP could be conveniently realized on the production line at the absent of OLN.
Another key point is that the deformed grains recrystallize neither statically nor dynamically within 10 s after the final rolling at about 850℃, and then, fine bainite microstructure could be obtained after rapid cooling to the temperature region of 400～600℃, as a result, the requirement for strength of N80 grade casing could be reached.
Composition design
As for N80 casing according to the API standard, (s ≥552MPa, (b≥689MPa. To satisfy such mechanical properties from the point of composition, the carbon content should not be too low, otherwise the strength should be too low. It is considered that the carbon content falls into ％, Mn ％, and the microalloying elements V, Ti, Nb, Mo, a certain amount as seen in Table 1.
Tabel 1 Composition of the tested steel
C
Si
Mn
V
Ti
Nb
Mo
N
Al
≤
≤
≤
Dynamic recrystallization
According to the hot-rolling parameters of (( tube, the equivalent strains calculated are shown in Table 2.
The tube temperature is measured by using an infrared temperature recorder, and the results are listed in Table 3.
Table 2 equivalent strains calculated for different processes of hot-rolling
Before deformation, mm
After deformation,
mm
Longitudinal
(1
Radial
(2
Circumferential
(3
Equivalent
(H
OD D0，
thicknessS0
OD, Dz，
thicknessSz
Piercing*
/
/
/
/
/
/
/
Reducing of hollow billet
0
Mandrel milling
Stretch Reducing
*According to literatures.
Table 3 Tube temperatures for different processes of hot rolling ℃
Rotary hearth furnace
Before piercing
Before Reducing of hollow billet
Before Mandrel milling
Reheating furnace
Before stretch reducing
1260
1230
1162
1044
970
903
Figure 1 shows the dynamic recrystallization under a strain rate of -1（T-(H）. It can be seen that complete dynamic recrystallization occurs after piercing（1230℃，(H =）, and during mandrel milling only occurs incomplete dynamic recrystallization（1040℃， (H =）; dynamic recrystallization does not take place both after reducing of hollow billet (1160℃，(H =) and after stretch reducing （900℃, (H =）, thus the work-hardened microstructure is kept.
Fig. 1 dynamic recrystallization of hot-deformed austenite (T-(H)
Microstructure and properties
Table 4 and 5 show the hot-rolling parameters and the corresponding mechanical properties, respectively. The microstructure is shown in Fig. 2
Table 4 Hot-rolling parameters
Rotary hearth furnace
Piercing
Reducing of hollow billet
Phase transformation
Reheating
Stretch Reducing
Cooling
1220℃
～1320℃
～1200℃
～1000℃
Not necessary
950℃
～980℃
850℃
～900℃
Cooling to 400～650℃at 20～200℃/S
Table 5 mechanical properties
Steel species
Air cooling after rolling
Accelerated cooling after rolling
σ
σb
σ
σb
Tested steel
483
655
653
749
Microstructure observation indicated that a mixture of ferrite and pearlite exists in the air-cooling specimens; while in the accelerated cooling specimens bainite exists, moreover, no obvious difference is found near the outer and the inner surface of the tube, and ideal bainite microstructure is attained under such cooling parameters.
Fig. 2 Hot-rolling microstructure under (a) air cooling, (b) accelerated cooling
3 Accelerated cooling
Cooling methods
The effects of water-cooling and spray cooling were conducted at the lab. Only the outer surface of the tube could be cooled after rolling, and the experiment set consists of a water ring and an air ring, on which there are many nozzles. Spray cooling acts if water and air were sent to the nozzles simultaneously while water-cooling acts if only water were let out. The water quantity W2 of such set ranges 0(50m3/h with an effective covering space of S2=. Right cooling methods together with proper cooling parameters can be determined by adjusting water quantity, air quantity, and the step rate of the tube according to the temperature of both the outer and inner tube surface measured by thermocouples.
Fig. 2 and Fig. 3 show the temperature dependence of time curves of water-cooling and of spray cooling, respectively. It can be seen the effect of spray cooling is much better than that of water-cooling. Both the inner and the outer temperatures of the tube can reach the 500～600℃ temperature region, with much less water quantity, much higher step rate, and much less difference between the outer and inner temperatures of the tube. Therefore, spray cooling is selected as the ideal cooling method in this paper.
Fig. 2 Inner and outer temperatures dependence of time under water cooling（water quantity 20m3/h, tube step rate
Inner and outer temperatures dependence of time under spray cooling（water quantity 18m3/h, air quantity5 m3/h, tube step rate
Simulation set for accelerated cooling experiment on the production line
The guided pass of the tensile reducer was reconstructed to realize the function of water and spray cooling, based on the requirements of accelerated cooling and of the production line. Five guided passes are needed whenΦ139× tube is produced on the 28-pass tensile reducer unit. One set of air ring is equipped on each side of guided pass, and a set of spray ring in the middle of the pass, and then there are total ten sets of spray ring and five sets of water ring that work on the tube outer surface under the conditions of accelerated cooling. The final accelerated cooling set is reconstructed after many experiments as shown in Fig. 4.
Fig. 4 Accelerated cooling set
guided pass ring ring spray nozzle to water sleeve sleeve 9. spray entrance entrance 12. water sleeve entrance
Tube quality after accelerated cooling
Tube straightness
That how about the straightness of tube after accelerated cooling concerns the whole production process going on wheels. At the initial state of industrial experiment, tube might bend severely so that cutting and straightening cannot proceed any more after accelerated cooling.
Generally, this phenomenon should involve with the circumferential cooling non-uniformity, and it is the stress introduced by asymmetrically cooling that cause tube bend. After improvement of the cooling methods, the straightness of tube is fairly well, as seen in Fig. 5.
Fig. 5 Tube morphology after accelerated cooling
longitudinal uniformity
The yield strength and tensile strength along the longitudinal direction were determined after accelerated cooling using two steels 25MnVN(G1) and 25MnMoVN(G4), as shown in .
Fig. 6 Yield and tensile strength dependence of distance
It can be seen that a good uniformity of mechanical properties can be reached to satisfy the requirement of N80 casing.
circumferential uniformity
The circumferential uniformity of strength and hardness was investigated along the 30-meter tube after accelerated cooling.
Table 6 shows the strength distribution dependence of circumferential direction in the middle length of 25Mn2VN tube. The fluctuation of strength is within 50MPa, and the uniformity is very good.
Table 6 Circumferential strength of 25Mn2Vn tube after accelerated cooling
1
2
3
4
5
6
7
8
9
MPa
694
700
738
714
685
692
712
686
719
Rm MPa
852
847
884
860
845
846
856
832
864
Table 7 lists the changes of circumferential hardness measured in the head, middle, and end length of tube after rolling under the same cooling conditions.
Table 7 Circumferential hardness HV30
Position
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Head
254
246
235
254
249
258
275
260
263
262
261
256
256
253
258
258
262
262
Middle
265
263
268
277
250
256
260
262
262
264
264
268
258
247
258
248
258
263
End
217
221
219
242
228
247
239
252
252
245
246
227
250
238
246
242
235
228
The hardness fluctuation is within 20HV between different sections, and also the uniformity is very good.
Radial uniformity
Because only outer surface cooling is adopted, the difference of microstructure and mechanical properties between near the inner and near the outer surface may exist, thereafter affecting the tube quality. Many researches have been carried out on the investigation of steel species and of cooling parameters, and finds that there is little difference in the outer and inner microstructures at wall thickness of less than 10mm. Detailed analyses have also made on the radial uniformity during the industrial experiment. Table 8 shows the hardness along the radial direction from outer to inner wall surface.
Table 8 Hardness along radial direction
Cooling parameter
From outer to inner wall, HV30
1
245
247
230
240
237
2
257
264
266
266
263
Fig. 7 shows the microstructure of inner and outer walls after accelerated cooling. The same kind of mixture of ferrite and pearlite and a small amount of sorbite is observed，and the grain size is also comparable. The microstructure observed corresponds well to the hardness measured. The difference from the bainite microstructure realized in lab is mainly attributed to the influence of the chemical composition, and also of the final rolling temperature.
(a) Outer surface (b) Inner surface
Fig. 7 Microstructure after accelerated cooling
4 Conclusions
The steel developed exhibits a complete dynamic recrystallization microstructure after piercing or mandrel milling while the work-hardened austenite microstructure both after stretch reducing. Therefore, OLN is not necessary after mandrel milling, and the accelerated cooling is very effective to elevate the material strength.
Spray cooling is much better than water cooling, accompanied by a reduction of water quantity and an improvement of the tube uniformity.
with the spray cooling method, the uniformity of strength and hardness can be reached to satisfy the product requirements on all the longitudinal, radial, and circumferential directions.
Using such 25MnVN9 or 25MnMoVN microalloyed steels，N80 grade casing can be produced after rolling under accelerated cooling conditions.
References
1. F.布赖恩，皮克林. 材料科学与技术丛书(第7卷)—钢的组织与性能. 刘嘉禾等译. 科学出版社, 1999:165-192, 316-362
2. , , . Metallurgical Design of Accelerated-Cooling Process for Seamless Pipe Production. Proceedings from Materials Solutions ’97 on Accelerated Cooling /Direct Quenching Steels. 15-18 September 1997, Indiana 3 3
3. , , . Effect of Intermediate Cooling on Grain Refinement and Precipitation During Rolling of Seamless Tubes. Materials Science and Technology. 1991, 7(2): 129-136
4. 陈绍林. 在线常化工艺对J55钢管性能的影响. 钢管. 1999，28（4）: 9-11
5. , , . New Proess for On-Line Normalizing of Seamless Pipes. 38th Mechanical Working and Steel Processing Conference Proceedings. Vol. XXXIV, Cleveland, Ohio, USA, 13-16 Oct. 1996
6. , , . Microalloyed Steels for On-Line Treated Seamless Tubes. 36th Mechanical Working and Steel Processing Conference, Baltimore, Maryland, USA, 16-19 Oct. 1994
7. , , , . Seamless Steel Pipe of Large Diameter by the Hot Rotary Expansion Process. In Proceedings of the 2th Int. Pipeline Technological Conference, Ostend, Belgium, Spt. 1995, 377-387
8. , , . Laboratory Simulation of Seamless Tube Piercing and Rolling Using Dynamic Recrystallization Schedules. Metallurgical Transactions A. 1990, 21A(1): 153-164
� EMBED ���
Temperature, ℃
Equivalent strain ((H)
a)
(b)
Temperature , ℃
Time ,s
� EMBED ���
� EMBED ���
Temperature , ℃
Time , s
� EMBED ���
PAGE
12
轴向拉伸
712 898 755 914
640 861 750 885
672 873 719 879
668 848 723 883
730 875 714 860
676 820 706 867
666 843 699 869
728 858 750 906
702 860 717 860
730 862 624 834
703 853 688 890
736 866 688 872
665 844 749 917
674 841 741 869
704 867 697 868
G1
G1 Rm
G4
G4 Rm
距离，m
强度，MPa
延伸率
23 23 16 26 26
22 25 16
25 24 25 16
26 25 16 28
24 26 16 29 28
25 16
26 27 16 28 25
16 28
24 16 28
23 16 29
24 16 26 27
26 23 16 27 29
22 16
25 24 16
23 23 16
G1
G2
G3
G4
G6
N80 下限
F2
F3
F4
F5
F6
F7
距离， m
, %
控轧控冷第六次和第七次工业试验的延伸率
冲击韧性
18 23 20
24 16
19 17
22
G1 Akv
G4 Akv
G6 Akv
距离，m
Akv, J
Sheet1
1号 G1(B8含Mo) 4号 G4(B9不含Mo)
长度，m Rm Akv 长度，m Rm Akv ≥689 N80 下限 2号 G2(B9不含Mo) 3号 G3(B8含Mo) 5号 G5(B8含Mo) 6号 G6(B9不含Mo)
0 712 898 18 0 755 914 23 552 758 689 16 长度，m Rm Akv 长度，m Rm Akv 长度，m Rm Akv 长度，m Rm Akv
2 640 861 2 750 885 552 758 689 16 0 668 876 0 755 882 23 0 669 880 25 21 0 711 861
4 672 873 25 4 719 879 24 552 758 689 16 15 652 875 15 736 884 22 736 864 25 4 705 852 25
6 668 848 26 6 723 883 552 758 689 16 28 730 869 7 733 884 20 8 730 872 25 20
8 730 875 8 714 860 24 552 758 689 16 735 877 25 12 658 826 25
10 676 820 10 706 867 552 758 689 16 759 897 25 14 654 826 26 16
12 666 843 26 12 699 869 27 552 758 689 16 686 889 719 874 25 17
15 728 858 24 15 750 906 552 758 689 16 756 868 23
17 702 860 19 19 717 860 24 552 758 689 16
19 730 862 21 624 834 23 552 758 689 16
21 703 853 23 688 890 24 552 758 689 16
23 736 866 26 22 25 688 872 23 552 758 689 16 Akv Akv 1号 G1(B8含Mo)
25 665 844 27 749 917 22 552 758 689 16 6号 G6(B9不含Mo) 4号 G6(B9不含Mo) 长度，m Akv
27 674 841 25 29 741 869 24 23 552 758 689 16 长度，m Akv 长度，m Akv 0 18
29 704 867 23 31 697 868 23 552 758 689 16 8 20 29 23 15 24
14 16 17 19
17 23 22
F1 37Mn5 F2 F3
长度，m Rm Rm Rm
0 501 708 599 844 26 651 854
2 493 699 583 827 647 861
4 498 700 34 604 847 663 867
6 487 698 600 839 657 869
8 501 710 613 845 29 661 866
10 496 706 34 619 847 650 861
12 501 706 33 631 846 28 653 866
14 477 691 629 842 28 563 811
16 478 702 651 856 559 808
18 492 698 34 657 859 565 805
20 488 708 645 853 26 581 818
22 495 709 659 848 577 823
24 482 711 620 835 581 819
26 489 719 548 803 566 815
28 479 712 32 556 795 573 818
F4 F5 F6
长度，m Rm Rm Rm
0 678 854 621 818 26 697 864
2 678 849 657 855 699 869
4 680 852 639 844 689 858
6 677 850 662 853 703 867
8 691 854 666 863 691 857 28
10 703 862 635 839 682 857
12 695 859 658 863 25 693 861
14 594 805 596 818 628 805
16 621 827 574 810 626 811
18 586 791 29 579 814 634 816
20 615 848 577 808 27 645 830
22 618 818 572 806 27 646 831
24 622 821 600 821 685 853
26 627 835 614 828 658 859
28 626 828 583 814 689 888
F7
长度，m Rm
0 706 868
2 719 874
4 684 846
6 695 856 28
8 682 841
10 708 860
12 709 854
14 611 808
16 595 792 28
18 608 814
20 587 793
22 582 786 29
24 589 773
26 598 791
28 598 775
Sheet2
Sheet3
图表1
900 900 950 950 1000 1000 1050 1050 1050 1100 1100 1100 1150 1150 1150 1200 1200 1200 1215 1238
900 900 950 950 1000 1000 1050 1050 1100 1100 1100 1150 1150 1150 1200 1200 1200 1150 1171
900 900 950 950 1000 1000 1050 1050 1100 1100 1150 1150 1200 1200 1070 1116
900 950 950 1000 1000 1050 1050 1100 1150 1200 1004 1003
900 950 1000 936
900 861
Sheet1
当量变形 压下量
900
14 900
17 900
25 900
34 900
43 900
53 -- 900
65 -- 900
76 -- 900
950 --
14 950 --
17 950 --
25 950 --
34 950 --
43 -- 950
53 -- 950
65 -- 950
76 -- 950
1000 --
14 1000 --
17 1000 --
25 1000 --
34 -- 1000
43 -- 1000
53 -- 1000
65 -- 1000
76 -- 1000 --
1050 -- --
14 1050 -- --
17 1050 -- --
25 1050 -- --
34 -- 1050 --
43 -- 1050 --
53 -- 1050 --
65 -- 1050 --
76 -- -- 1050
1100 -- --
14 1100 -- --
17 1100 -- --
25 -- 1100 --
34 -- 1100 --
43 -- 1100 --
53 -- 1100 --
65 -- -- 1100
76 -- -- 1100
1150 -- --
14 1150 -- --
17 1150 -- --
25 -- 1150 --
34 -- 1150 --
43 -- 1150 --
53 -- 1150 --
65 -- -- 1150
76 -- -- 1150
1200 -- --
14 1200 -- --
17 -- 1200 --
25 -- 1200 --
34 -- 1200 --
43 -- 1200 --
53 -- -- 1200
65 -- -- 1200
76 -- -- 1200
14 -- -- -- 1215 --
18 -- -- -- 1150 --
25 -- -- -- 1070 --
-- -- -- 1004 --
42 -- -- -- 936 --
53 -- -- -- 861 --
47 -- -- -- -- 1238
50 -- -- -- -- 1171
-- -- -- -- 1116
82 -- 1003
Sheet2
Sheet3
w(50cm bian)
791 793 803 813 823 847 791 631
783 750 759 793 759 842 786 621
776 764 756 762 774 840 735 546
762 702 781 678 775 786 735 491
738 610 800 662 743 747 678 470
654 572 825 588 716 704 654 478
621 572 786 471 681 690 654 527
621 554 704 513 659 664 666 553
591 537 631 480 654 645 666 569
574 537 630 480 657 624 654
591 560 627 466 673 600 654
607 584 752 419 598 664
788 455 593 676
795 395 588 678
738 466 588
692 466 600
678 525 617
661 562
654 584
654 595
640 808
762 786
762 762
793 652
762 584
700 560
692 499
633 513
582 471
471
490
518
480
466
489
502
534
568
676
630
572
466
428
v=,w=40%,inner
v=,w=40%,outer
v=,w=60%,inner
v=,w=60%,outer
v=,w=40%,g=40%,inner
v=,w=40%,g=40%,outer
v=,w=18%,g=%,inner
v=,w=18%,g=%,outer
时间
温度
热电偶接触设定喷射范围时为时间轴的零点
xiaoguan w(50cmbian,kou)
828 828
820 820
818 818
798 798
793 793
695 695
685 685
643 643
584 584
537 537
534 534
539 539
584 584
619 619
,60%,*14,50cm bian
,60%,*14,kou
g(50,20cmbian)
823 847 791 631
759 842 786 621
774 840 735 546
775 786 735 491
743 747 678 470
716 704 654 478
681 690 654 527
659 664 666 553
654 645 666 569
657 624 654
673 600 654
598 664
593 676
588 678
588
600
617
v=,w=40%,g=40%,inner
v=,w=40%,g=40%,outer
v=,w=18%,g=,inner
v=,w=18%,g=%,outer
时间
温度
热电偶接触设定水气喷射范围时为时间轴的零点
图表1
791 793
783 750
776 764
762 702
738 610
654 572
621 572
621 554
591 537
574 537
591 560
607 584
852
853
852
750
704
680
897
874
847
855
842
796
725
682
654
607
水气双偶
860 678 752 803 791 631 823 847
837 631 706 659 786 621 759 842
773 583 697 619 735 546 774 840
721 511 697 576 735 491 775 786
702 468 690 557 678 470 743 747
680 459 678 557 654 478 716 704
678 459 673 588 654 527 681 690
673 476 607 666 553 659 664
656 476 666 569 654 645
485 654 657 624
558 654 673 600
595 664 598
607 676 593
678 588
588
600
617
inner(前)
outer(前)
inner(后)
outer(后)
inner'
outer'
;
水气单环双偶原始
884 872 862 857 200 200
852 847 855 847 1000 1000
842 803 810 830
832 659 803 793
822 619 803 786
752 576 823 728
706 557 823 688
697 557 798 652
697 588 791 645
690 607 786 631
678 735 621
673 735 546
678 491
654 470
654 478
666 527
666 553
654 569
654
664
676
678
inner(后)
outer(后)
inner(后)'
outer(后)'
水气单环双偶(v=,w=18%,g=%)
水气双环原始
872 867 200 200
868 847 1000 1000
847 842
823 840
759 786
774 747
775 704
743 690
716 664
681 645
659 624
654 600
657 598
673 593
588
588
600
617
inner
outer
水气双环(v=,w=40%,g=40%)
水(60%)原始
847 823 872 835 818 818 200 200
842 813 872 827 823 818 1000 1000
803 793 764 808 776 676
759 762 752 786 762 630
756 678 788 762 762 572
781 662 795 652 793 466
800 588 738 584 762 428
825 471 692 560 700
786 513 678 499 692
704 480 661 513 633
631 480 654 471 582
630 466 654 471
627 419 640 490
455 518
395 480
466 466
466 489
525 502
562 534
584 568
595
inner
outer
inner'
outer'
inner''
outer''
水(v=,w=60%)
水(40%)原始
840 823 200 200
833 820 1000 1000
800 793
791 750
783 764
776 702
762 610
738 572
654 572
621 554
621 537
591 537
574 560
591 584
607
inner
outer
水(v=,w=40%)
水气单环双偶(前)原始
884 867 200
877 852 1000
845 845
860 818
860 818
860 678
837 631
773 583
721 511
702 468
680 459
678 459
673 476
656 476
485
558
595
607
inner(前)
outer(前)
水气单环双偶原始(后)
887 872 200
887 842 1000
855 823
803 707
823 619
828 506
823 490
786 508
786 468
750 443
631 478
569 513
553 525
579
584
605
inner(后)
outer(后)
水气单环(v=,w=20%,g=21%)
897 877 200
884 862 1000
793 852
774 847
771 798
702 555
631 492
631 362
631 362
612 348
626 350
367
508
529
480
537
inner(前)
outer(前)
水气单环双偶(前)(v=,w=20%,g=21%)
890 872 200 200
884 857 1000 1000
836 786
822 750
812 671
466 560
436 510
466 484
490 486
inner
outer
w=36%,g=45%,v=
910 872 200 200
880 855 1000 1000
835 742
855 673
847 583
707 532
683 436
683 386
419
513
542
inner
outer
w18%,%,
w60%,
870 200 200
852 1000 1000
803
565
560
470
510
513
584
outer
w60%,
w60,
822 200 200
820 1000 1000
797
607
525
478
466
508
525
548
outer
w=60%,
w40%,
877 200 200
872 1000 1000
852
852
823
697
666
567
564
530
525
527
530
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w40%,
901 884 200 200
897 877 1000 1000
865 860
852 850
860 702
862 704
773 652
766 668
755 596
683 605
675 610
668 623
661 628
654 607
inner
outer
w40,
40,
892 867 200 200
882 840 1000 1000
827 830
827 678
840 673
837 640
773 638
761 640
725 638
680 630
668 638
656
654
inner
outer
w40%,
897 873 200 200
880 860 1000 1000
822 852
845 842
847 835
750 800
725 798
721 645
714 562
685 588
680 583
678 602
678 607
612
630
inner
outer
W=40%,V=
w40,
904 880 200 200
900 864 1000 1000
877 850
847 822
840 670
828 560
750 537
678 541
645 546
619 550
607 555
598 558
590 560
583
inner
outer
W=40%,V=
w20,
907 880 200 200
904 874 1000 1000
897 872
882 867
878 862
857 852
845 837
793 828
707 750
687 685
675 635
671 612
664 607
657 588
654 583
600
605
600
inner
outer
W=20%,V=
w20,
897 874 200 200
894 872 1000 1000
890 870
884 860
882 835
872 773
852 685
793 630
745 588
723 544
709 560
695 583
685 607
685 623
678 628
675 630
678 635
inner
outer
W=20%,V=
补丁
850 862 857 867 837 862
825 795 828 850 813 837
621 813 783 793 752 752
457 776 778 800 574 783
386 534 482 560 492 750
334 548 364 405 400 409
334 314 457 362 480
409 338 459 409 513
421 386 433
391
433
o3
i3
o2
i2
o1
i1
补丁试验
.
798 774 897 857
774 725 872 842
713 607 842 822
713 532 852 593
728 562 803 562
725 508 803 548
725 471 752 616
654 496 752 661
567 544 783 678
584 572 761
607 607
631
i
o
I
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877 892
872 850
845 852
788 860
683 825
612 683
560 654
537 654
541 648
560 650
583 654
o
i
872
867
823
823
786
650
646
630
i
,
872 904
852 892
825 835
619 847
501 798
485 607
466 513
485 520
527
o
i
Sheet1
t=s/v=21cm/
iner outer iner outer 前 后 前 后 2002,5,23
T t bian kou T t true t bian kou iner outer iner outer iner outer T t bian kou T t true t bian kou
840 0 823 0 T t bian kou T t true t bian kou iner outer T t bian kou T t true t bian kou T t bian kou T t true t bian kou 847 0 828 0 T t bian T t bian T t bian T t true t bian kou T t bian T t bian T t bian T t true t bian kou iner outer iner outer outer
833 820 4 847 0 823 0 T t bian kou T t true t bian kou iner outer 872 0 867 0 862 0 857 0 847 820 884 0 867 0 884 0 872 0 897 0 877 0 887 2 0 872 0 T t bian T t bian T t bian T t bian T t iner outer
800 4 793 7 842 813 872 0 835 0 T t bian kou T t true t bian kou 868 847 855 2 847 822 818 877 852 -3 852 847 8 884 862 6 887 6 4 842 10 890 0 872 0 910 0 872 0 870 0 T t T t
791 750 803 793 6 872 827 6 818 0 818 0 847 842 810 3 830 810 798 845 845 -2 842 803 793 852 855 823 13 884 4 857 880 855 852 outer 897 0 874 0 iner outer iner outer
783 764 759 762 764 808 823 818 823 840 8 803 -8 793 793 860 818 832 12 659 774 847 803 707 18 2 836 7 786 835 742 7 803 T t 894 1 872 1 T t T t T t T t outer inner outer inner outer inner outer
776 702 756 678 752 786 776 676 759 786 803 4 786 695 860 818 -1 822 619 771 5 798 823 619 17 822 9 750 11 855 673 9 565 9 822 0 890 2 870 3 798 0 774 7 897 0 857 1 T t T t T t T t T t T t T t
762 610 781 662 788 762 762 630 774 747 9 823 5 728 685 11 860 678 0 752 576 702 8 555 828 506 18 812 17 671 13 847 17 583 560 820 iner iner outer iner outer iner outer iner outer 884 860 5 774 7 725 16 872 8 842 850 0 862 2 1 857 0 867 1 0 837 0 862 1 0 847 0
738 572 800 588 795 652 762 5 572 775 9 704 823 -5 688 12 643 9 837 631 1 706 557 631 11 492 823 490 20 466 22 560 19 707 532 13 470 15 797 6 T t T t T t T t T t T t T t T t T t 882 3 835 713 9 607 18 842 822 825 5 795 6 5 828 850 4 3 813 837 9 8 813
654 572 825 471 9 738 584 9 793 466 743 690 9 798 -2 652 11 584 773 583 2 697 17 557 631 15 362 18 786 508 22 436 25 510 23 683 26 436 510 20 607 8 877 0 892 0 867 0 897 0 873 0 904 0 880 0 907 0 880 0 872 5 773 713 532 19 852 13 593 17 621 10 813 9 8 783 9 793 752 14 752 605
621 10 554 786 8 513 692 560 762 428 14 716 664 791 0 645 537 721 511 4 697 19 588 631 21 362 786 468 25 466 30 484 30 683 386 513 525 10 872 3 iner outer 882 2 840 880 860 4 900 864 7 904 1 874 1 852 6 685 8 728 562 803 562 19 457 776 13 12 778 800 574 783 16 15 421
621 537 704 480 14 678 499 700 681 645 11 786 12 631 13 534 702 468 6 690 607 612 31 348 750 443 490 35 486 35 419 584 478 852 T t T t 827 830 822 4 852 877 3 850 897 3 872 3 793 8 630 725 13 508 803 548 386 534 19 18 482 560 492 750 19 18 329
591 537 15 631 480 661 513 692 8 659 624 735 3 621 539 16 680 459 8 678 626 43 350 631 478 31 513 466 14 852 901 0 884 0 827 5 678 11 845 5 842 5 847 822 882 867 5 745 10 588 10 725 471 752 616 25 334 19 548 36 35 364 405 400 409 266
574 560 630 466 13 654 471 633 654 600 735 546 200 584 678 459 9 673 367 569 513 40 542 508 17 823 897 2 877 2 840 673 12 847 835 840 7 670 12 878 7 862 7 723 11 544 11 654 496 25 752 20 661 31 334 22 314 20 457 362 480 219 20
591 584 627 419 654 16 471 12 582 11 657 598 678 4 491 1000 619 673 476 10 508 553 525 49 525 21 697 8 865 860 6 837 8 640 14 750 9 800 828 11 560 14 857 9 852 9 709 12 560 12 567 22 544 783 23 678 37 409 26 338 459 409 513 246 30
607 752 455 640 490 673 593 654 16 470 656 476 11 529 579 548 31 666 852 5 850 5 773 9 638 15 725 798 750 14 537 845 12 837 10 695 14 583 13 584 23 572 761 35 421 35 386 26 433 290 40
852 810 788 395 518 588 654 5 478 485 480 584 200 567 12 860 6 702 761 12 640 17 721 12 645 9 678 17 541 18 793 828 685 17 607 15 607 607 39 391 409
853 9 774 14 795 466 480 588 23 666 17 527 558 13 537 605 1000 564 15 862 8 704 8 725 14 638 19 714 14 562 11 645 19 546 20 707 18 750 13 685 19 623 19 631 37 433 15 433
852 580 738 466 466 200 600 666 7 553 200 595 18 200 6 530 18 773 11 652 680 17 630 21 685 17 588 13 619 21 550 23 687 685 14 678 22 628 22
750 605 23 692 525 20 489 1000 617 26 654 8 569 1000 607 31 1000 6 200 13 200 200 525 20 766 668 668 20 638 26 680 20 583 607 23 555 26 675 635 16 675 630 27 18
704 678 562 200 502 654 21 1000 13 1000 1000 527 25 755 596 14 656 23 678 23 602 17 598 26 558 29 671 24 612 678 32 635 32
680 661 584 1000 534 664 12 530 30 683 15 605 15 654 26 678 26 607 20 590 29 560 32 664 27 607
897 5 200 654 595 568 676 14 200 675 16 610 18 612 23 583 32 657 588
874 1000 3 654 16 808 678 18 1000 668 20 623 21 630 26 654 34 583 24 200 4 water=36%,gas=45%,v= * water=36%,gas=45%,v= *
847 640 786 661 24 628 25 600 27 1000 4 water=36%,gas=45%,v= *
855 762 762 200 654 30 607 34 200 200 5 200 605
842 762 5 652 1000 1000 1000 5 1000 600 34 outer inner inner
796 793 584 9 T t T t T t outer inner
725 762 560 200 5 200 877 0 897 0 872 0 T t ture T t
682 15 700 499 1000 5 1000 872 2 892 867 2 912 0 904 0
654 692 8 513 845 4 850 823 872 6 892 6
607 633 471 788 852 823 852 835 9
582 11 471 12 683 8 860 6 786 825 847 13
490 612 825 8 650 619 17 798
518 560 683 646 501 21 607 21
480 537 654 630 485 24 513 24
466 541 654 466 29 520 30
489 560 648 485 35 527 35
502 583 650
534 654
568
676 5
630
572
466
428 14
Sheet2
图表1
877 892
872 853
845 861
788 855
678 797
594 628
518 584
500 589
524 599
562
outer
inner
W=36%,G=45%,V=
Sheet1
water=36%,gas=45%,v= *
outer inner
T t T t
877 0 897 0
872 2 892
845 4 853
788 861 6
678 8 855 8
594 797
518 628
500 584
524 589
562 599
5
Sheet2
Sheet3
