CN104308109B - A copper alloy strip pulse electromagnetic oscillation horizontal continuous casting method and device - Google Patents
A copper alloy strip pulse electromagnetic oscillation horizontal continuous casting method and device Download PDFInfo
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- 230000010355 oscillation Effects 0.000 title claims abstract description 131
- 229910000881 Cu alloy Inorganic materials 0.000 title claims abstract description 91
- 238000009749 continuous casting Methods 0.000 title claims abstract description 37
- 238000000034 method Methods 0.000 title claims abstract description 24
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 claims abstract description 53
- 229910002804 graphite Inorganic materials 0.000 claims abstract description 53
- 239000010439 graphite Substances 0.000 claims abstract description 53
- 238000005266 casting Methods 0.000 claims abstract description 32
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims abstract description 22
- 239000010949 copper Substances 0.000 claims abstract description 17
- 229910052802 copper Inorganic materials 0.000 claims abstract description 16
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 16
- 238000001816 cooling Methods 0.000 claims abstract description 14
- 229910000831 Steel Inorganic materials 0.000 claims abstract 4
- 239000010959 steel Substances 0.000 claims abstract 4
- 239000007788 liquid Substances 0.000 claims description 22
- 239000004568 cement Substances 0.000 claims description 4
- 230000004308 accommodation Effects 0.000 claims 2
- 210000003298 dental enamel Anatomy 0.000 claims 1
- 238000005204 segregation Methods 0.000 abstract description 16
- 229910045601 alloy Inorganic materials 0.000 abstract description 5
- 239000000956 alloy Substances 0.000 abstract description 5
- 208000037656 Respiratory Sounds Diseases 0.000 abstract 1
- 238000005555 metalworking Methods 0.000 abstract 1
- 238000007670 refining Methods 0.000 abstract 1
- 230000005284 excitation Effects 0.000 description 12
- 238000007711 solidification Methods 0.000 description 12
- 230000008023 solidification Effects 0.000 description 12
- 239000000155 melt Substances 0.000 description 11
- 230000007547 defect Effects 0.000 description 7
- 238000005516 engineering process Methods 0.000 description 7
- 239000010935 stainless steel Substances 0.000 description 7
- 229910001220 stainless steel Inorganic materials 0.000 description 7
- 229910000906 Bronze Inorganic materials 0.000 description 6
- 239000010974 bronze Substances 0.000 description 6
- KUNSUQLRTQLHQQ-UHFFFAOYSA-N copper tin Chemical compound [Cu].[Sn] KUNSUQLRTQLHQQ-UHFFFAOYSA-N 0.000 description 6
- 238000009826 distribution Methods 0.000 description 6
- 230000006911 nucleation Effects 0.000 description 6
- 238000010899 nucleation Methods 0.000 description 6
- 239000013078 crystal Substances 0.000 description 5
- 229910001369 Brass Inorganic materials 0.000 description 4
- 239000010951 brass Substances 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 229910052751 metal Inorganic materials 0.000 description 4
- 239000002184 metal Substances 0.000 description 4
- BSPSZRDIBCCYNN-UHFFFAOYSA-N phosphanylidynetin Chemical compound [Sn]#P BSPSZRDIBCCYNN-UHFFFAOYSA-N 0.000 description 4
- 229910000861 Mg alloy Inorganic materials 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 238000005265 energy consumption Methods 0.000 description 3
- 238000001125 extrusion Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000003756 stirring Methods 0.000 description 3
- 239000000498 cooling water Substances 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 230000002441 reversible effect Effects 0.000 description 2
- 238000010008 shearing Methods 0.000 description 2
- 229910000838 Al alloy Inorganic materials 0.000 description 1
- ATJFFYVFTNAWJD-UHFFFAOYSA-N Tin Chemical compound [Sn] ATJFFYVFTNAWJD-UHFFFAOYSA-N 0.000 description 1
- HCHKCACWOHOZIP-UHFFFAOYSA-N Zinc Chemical compound [Zn] HCHKCACWOHOZIP-UHFFFAOYSA-N 0.000 description 1
- 229910052782 aluminium Inorganic materials 0.000 description 1
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000000137 annealing Methods 0.000 description 1
- 238000003490 calendering Methods 0.000 description 1
- 239000011889 copper foil Substances 0.000 description 1
- 210000001787 dendrite Anatomy 0.000 description 1
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/14—Plants for continuous casting
- B22D11/142—Plants for continuous casting for curved casting
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/04—Continuous casting of metals, i.e. casting in indefinite lengths into open-ended moulds
- B22D11/045—Continuous casting of metals, i.e. casting in indefinite lengths into open-ended moulds for horizontal casting
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/10—Supplying or treating molten metal
- B22D11/11—Treating the molten metal
- B22D11/114—Treating the molten metal by using agitating or vibrating means
- B22D11/115—Treating the molten metal by using agitating or vibrating means by using magnetic fields
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Continuous Casting (AREA)
Abstract
Description
技术领域technical field
本发明涉及金属加工技术领域，尤其涉及一种铜合金板带脉冲电磁振荡水平连续铸造方法及装置。The invention relates to the technical field of metal processing, in particular to a pulse electromagnetic oscillation horizontal continuous casting method and device for a copper alloy strip.
背景技术Background technique
目前，铜及铜合金已成为第二大有色金属，是全球经济各行业中广泛需求的基础材料。铜及铜合金板带材占世界铜加工材总量的35％左右。近10年来，世界经济蓬勃发展，特别是以中国为代表的新兴发展中国家的国民经济高速发展，带动了铜及铜合金板带材需求量及产量的迅速攀升。在现代工业技术中，对高精铜及铜合金板带材的需求量更是不断增加，如高品质电连接器铜合金带材(接插元件带材)、集成电路引线框架带材、变压器带、汽车水箱带、高档压延柔性铜箔等。制备优质的铜及铜合金板带材坯锭是获得高精铜及铜合金板带材产品的前提条件。At present, copper and copper alloys have become the second largest non-ferrous metals and are the basic materials widely demanded in various industries of the global economy. Copper and copper alloy plates and strips account for about 35% of the world's total copper processed materials. In the past 10 years, the vigorous development of the world economy, especially the rapid development of the national economy of emerging developing countries represented by China, has led to a rapid increase in the demand and output of copper and copper alloy plates and strips. In modern industrial technology, the demand for high-precision copper and copper alloy strips is increasing, such as high-quality electrical connector copper alloy strips (strips for plug-in components), integrated circuit lead frame strips, and transformers. Belts, automotive water tank belts, high-grade calendered flexible copper foil, etc. The preparation of high-quality copper and copper alloy plate and strip ingots is a prerequisite for obtaining high-precision copper and copper alloy plate and strip products.
但是，目前的水平连铸机生产的铜合金板带存在组织粗大、表面存在裂纹、缩松、偏析及反偏析等铸造缺陷。例如，锡黄铜、铝青铜、锡磷青铜等合金，溶质元素含量较高时，凝固组织粗大、溶质元素偏析比较严重，铸造过程中极易形成裂纹，板带产品废品率较高。因此针对板带水平连续铸造技术存在的不足，在改善铜合金板带坯锭质量方面，许多人在设备及工艺改进方面做了大量工作。However, the copper alloy strip produced by the current horizontal continuous casting machine has casting defects such as coarse structure, surface cracks, shrinkage porosity, segregation and reverse segregation. For example, tin brass, aluminum bronze, tin phosphor bronze and other alloys, when the content of solute elements is high, the solidification structure is coarse, the segregation of solute elements is serious, cracks are easily formed during the casting process, and the scrap rate of strip products is high. Therefore, many people have done a lot of work in improving the equipment and process in order to improve the quality of the copper alloy strip billet in view of the shortcomings of the strip horizontal continuous casting technology.
专利200510047193.7通过在石墨结晶器上下两侧安装行波磁场，在熔体内产生强制搅拌，获得组织均匀、晶粒细化、无裂纹、无偏析的铜合金板带。Patent 200510047193.7 installs a traveling wave magnetic field on the upper and lower sides of the graphite crystallizer to generate forced stirring in the melt to obtain copper alloy strips with uniform structure, fine grain, no cracks, and no segregation.
专利200810155756.8通过在结晶器部位安装磁场装置，同时在石墨结晶器横向侧的两侧壁之间横向施加电流，在拉坯方向上产生强迫搅拌，从而有助于形成等轴晶，抑制偏析和反偏析，获得较高质量的青铜板坯。Patent 200810155756.8 installs a magnetic field device at the crystallizer, and applies a current laterally between the two side walls of the graphite crystallizer to generate forced stirring in the casting direction, thereby helping to form equiaxed crystals and inhibit segregation and reflection. Segregation to obtain higher quality bronze slabs.
专利200910182373.4通过在保温炉侧面，结晶器上方设置线性磁场发生器，其产生的磁场垂直拉坯方向。磁场作用结晶器内的熔体，细化铸坯微观组织、降低熔体含气量、提高铸坯致密度、使合金元素均匀分布。In patent 200910182373.4, a linear magnetic field generator is installed on the side of the holding furnace and above the crystallizer, and the magnetic field generated by it is perpendicular to the casting direction. The magnetic field acts on the melt in the crystallizer to refine the microstructure of the slab, reduce the gas content of the melt, increase the density of the slab, and make the alloy elements evenly distributed.
脉冲磁场是最近几年发展起来的新型磁场装置，会在金属熔体中产生电磁搅拌和电磁振荡等多重作用，具有输出峰值高、设备负荷小、能耗低等优点。可以显著细化金属凝固组织，提高其力学性能。The pulsed magnetic field is a new type of magnetic field device developed in recent years. It will produce multiple effects such as electromagnetic stirring and electromagnetic oscillation in the metal melt. It has the advantages of high output peak value, small equipment load, and low energy consumption. It can significantly refine the metal solidification structure and improve its mechanical properties.
专利201110236278.5通过在垂直半连续铸造结晶器内部设置脉冲磁场励磁线圈，从而在结晶器内的镁合金熔体中产生强制对流，打碎粗大的树枝晶，增加形核率，从而获得晶粒细化的镁合金棒材。但是，这种脉冲磁场只在具有低密度的镁合金、铝合金细化方面取得了较好的效果，对于高密度和粘度的铜合金而言，则需要更强的脉冲磁场。目前，尚未有关脉冲电磁振荡技术在大宽厚比的铜合金板带水平连续铸造中的应用。In patent 201110236278.5, a pulsed magnetic field excitation coil is set inside the vertical semi-continuous casting mold to generate forced convection in the magnesium alloy melt in the mold, break up the thick dendrites, increase the nucleation rate, and obtain grain refinement magnesium alloy rods. However, this pulsed magnetic field only achieves good results in the refinement of low-density magnesium alloys and aluminum alloys. For high-density and viscous copper alloys, a stronger pulsed magnetic field is required. At present, there is no application of pulse electromagnetic oscillation technology in horizontal continuous casting of copper alloy strips with large aspect ratios.
发明内容Contents of the invention
针对现有技术中的水平连铸设备和方法生产的铜合金板带存在组织粗大、表面存在裂纹、缩松、偏析及反偏析等铸造缺陷的问题，本发明提出了一种铜合金板带脉冲电磁振荡水平连续铸造的方法及装置，能够改善铜合金板带的凝固组织，而且能减少偏析和裂纹等铸造缺陷，从而提高铜合金板带坯的成品率。Aiming at the problems of casting defects such as coarse structure, surface cracks, shrinkage porosity, segregation and reverse segregation in the copper alloy strip produced by the horizontal continuous casting equipment and method in the prior art, the present invention proposes a copper alloy strip pulse The electromagnetic oscillation horizontal continuous casting method and device can improve the solidification structure of copper alloy strips and reduce casting defects such as segregation and cracks, thereby increasing the yield of copper alloy strip blanks.
本发明提供了一种铜合金板带脉冲电磁振荡水平连续铸造装置，所述装置包括：The invention provides a pulse electromagnetic oscillation horizontal continuous casting device for copper alloy strips, said device comprising:
保温炉、结晶器底板、脉冲电磁振荡发生器、不锈钢水冷套、冷却铜套和石墨结晶器，所述保温炉与所述石墨结晶器连通，所述脉冲电磁振荡发生器为环形，并套设在所述石墨结晶器上靠近所述保温炉的一端；所述脉冲电磁振荡发生器未与所述保温炉和所述石墨结晶器接触的面被所述结晶器底板所包覆，并通过所述结晶器底板固定在所述保温炉上；所述石墨结晶器未被所述结晶器底板和所述脉冲电磁振荡发生器所包覆的部分由内向外依次套设所述冷却铜套和所述不锈钢水冷套。Holding furnace, crystallizer bottom plate, pulse electromagnetic oscillation generator, stainless steel water cooling jacket, cooling copper jacket and graphite crystallizer, the holding furnace is connected with the graphite crystallizer, the pulse electromagnetic oscillation generator is ring-shaped, and is set On the graphite crystallizer near the end of the holding furnace; the surface of the pulse electromagnetic oscillation generator that is not in contact with the holding furnace and the graphite crystallizer is covered by the bottom plate of the crystallizer, and passes through the The base plate of the crystallizer is fixed on the holding furnace; the part of the graphite crystallizer that is not covered by the base plate of the crystallizer and the pulse electromagnetic oscillation generator is sequentially covered with the cooling copper sleeve and the The stainless steel water cooling jacket.
进一步的，所述脉冲电磁振荡发生器与所述石墨结晶器、所述保温炉、所述结晶器底板之间的间隙填充有耐火水泥。Further, the gap between the pulse electromagnetic oscillation generator and the graphite crystallizer, the holding furnace, and the bottom plate of the crystallizer is filled with refractory cement.
进一步的，所述脉冲电磁振荡发生器的励磁线圈的夹角是圆心角为180至270度的圆弧。Further, the included angle of the excitation coil of the pulse electromagnetic oscillation generator is a circular arc with a central angle of 180 to 270 degrees.
进一步的，所述脉冲电磁振荡发生器的励磁线圈是由直径为1至2mm的漆包铜线缠绕而成。Further, the excitation coil of the pulse electromagnetic oscillation generator is wound by enamelled copper wire with a diameter of 1 to 2 mm.
对应地，本发明还提供了一种铜合金板带脉冲电磁振荡水平连续铸造方法，所述方法包括：Correspondingly, the present invention also provides a copper alloy strip pulse electromagnetic oscillation horizontal continuous casting method, the method comprising:
在铜合金板带脉冲电磁振荡水平连续铸造装置的保温炉内铜合金液温度达到1000至1200℃时，开动牵引机，带动铜合金板带坯运动，同时启动脉冲电磁振荡发生器，所述脉冲电磁振荡发生器对石墨结晶器中的铜合金液产生电磁力，进而对石墨结晶器中的铜合金液的径向进行电磁振荡。When the temperature of the copper alloy liquid in the holding furnace of the copper alloy strip pulse electromagnetic oscillation horizontal continuous casting device reaches 1000 to 1200 °C, the tractor is started to drive the movement of the copper alloy strip billet, and the pulse electromagnetic oscillation generator is started at the same time. The electromagnetic oscillation generator generates electromagnetic force on the copper alloy liquid in the graphite crystallizer, and then conducts electromagnetic oscillation on the radial direction of the copper alloy liquid in the graphite crystallizer.
进一步的，所述脉冲电磁振荡发生器连接到充电电压可调的脉冲电源上，电压的调节范围为100至800V。Further, the pulse electromagnetic oscillation generator is connected to a pulse power supply with adjustable charging voltage, and the voltage adjustment range is 100 to 800V.
进一步的，所述脉冲电磁振荡发生器通入脉冲电流的脉冲宽度在铸造过程中为1ms的整数倍连续调节，以及脉冲频率为1Hz的整数倍连续调节。Further, the pulse width of the pulse current supplied by the pulse electromagnetic oscillation generator is continuously adjusted to an integer multiple of 1 ms during the casting process, and the pulse frequency is continuously adjusted to an integer multiple of 1 Hz.
进一步的，脉冲宽度调节范围为1至10ms，脉冲频率调节范围为50至150Hz。Further, the pulse width can be adjusted in a range of 1 to 10 ms, and the pulse frequency can be adjusted in a range of 50 to 150 Hz.
本发明提供的一种铜合金板带脉冲电磁振荡水平连续铸造的方法及装置，利用结晶器底板包覆脉冲电磁振荡发生器，并通过所述结晶器底板将脉冲电磁振荡发生器固定在所述保温炉上，能够减少结晶器底板对脉冲电磁振荡发生器的挤压，延长其使用寿命，选用环形的脉冲电磁振荡发生器，并利用脉冲信号作为电磁振荡信号作用于石墨结晶器内的铜合金液，产生的磁场力能够在石墨结晶器中的铜合金液中引起强烈振荡和强迫对流，不仅能将石墨结晶器壁上先形成的大量晶核冲刷下来并带入石墨结晶器中的铜合金液中，从而增加形核率，而且使板带边部和中心部位的温度场趋于均匀。并且将所述脉冲电磁振荡发生器的励磁线圈的夹角设置成圆心角为180至270的圆弧，能够获得较为均匀的磁场分布。本发明提供的脉冲磁场发生器能耗低，设备简单、操作方便易行，安全可靠，将脉冲电磁振荡技术应用到较大宽厚比的铜合金板带水平连续铸造中，不仅能改善铜合金板带的凝固组织，而且能减少偏析和裂纹等铸造缺陷，细化合金组织，从而提高铜合金板带坯的成品率。通过本发明提供的方法能制备出凝固组织均匀、晶粒细化、无裂纹及无溶质元素偏析的铜合金板带铸坯，适用于大宽厚比的铜合金板带铸造领域。The invention provides a method and device for horizontal continuous casting of copper alloy strips with pulsed electromagnetic oscillation. The pulsed electromagnetic oscillation generator is covered by the crystallizer bottom plate, and the pulsed electromagnetic oscillation generator is fixed on the said crystallizer bottom plate. On the holding furnace, it can reduce the extrusion of the crystallizer bottom plate on the pulse electromagnetic oscillation generator and prolong its service life. The annular pulse electromagnetic oscillation generator is selected, and the pulse signal is used as the electromagnetic oscillation signal to act on the copper alloy in the graphite crystallizer. Liquid, the magnetic force generated can cause strong oscillation and forced convection in the copper alloy liquid in the graphite crystallizer, which can not only wash down a large number of crystal nuclei formed on the graphite crystallizer wall and bring them into the copper alloy in the graphite crystallizer In the liquid, the nucleation rate is increased, and the temperature field at the edge and center of the strip tends to be uniform. In addition, the included angle of the exciting coil of the pulse electromagnetic oscillation generator is set as a circular arc with a central angle of 180 to 270°, so that a relatively uniform magnetic field distribution can be obtained. The pulsed magnetic field generator provided by the present invention has low energy consumption, simple equipment, convenient and easy operation, and is safe and reliable. Applying the pulsed electromagnetic oscillation technology to the horizontal continuous casting of copper alloy strips with a large width-thickness ratio can not only improve the copper alloy plate The solidification structure of the strip can be reduced, casting defects such as segregation and cracks can be reduced, and the alloy structure can be refined, thereby improving the yield of copper alloy strip blanks. The method provided by the invention can prepare a copper alloy strip casting slab with uniform solidification structure, fine grains, no cracks and no solute element segregation, and is suitable for the field of copper alloy strip casting with a large width-thickness ratio.
附图说明Description of drawings
图1为本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造装置的结构示意图；Fig. 1 is a schematic structural view of a pulsed electromagnetic oscillation horizontal continuous casting device for copper alloy strips provided by an embodiment of the present invention;
图2为图1中A-A线的剖视图；Fig. 2 is the sectional view of A-A line among Fig. 1;
图3为脉冲电磁振荡发生器的主视图；Fig. 3 is the front view of pulse electromagnetic oscillation generator;
图4为脉冲电磁振荡发生器的俯视图；Fig. 4 is the top view of pulse electromagnetic oscillation generator;
图5为不同频率下脉冲电磁振荡发生器未设计凸起圆角的熔体内磁场的分布示意图；Fig. 5 is a schematic diagram of the distribution of the magnetic field in the melt in which the pulse electromagnetic oscillation generator is not designed with raised rounded corners at different frequencies;
图6为本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造方法的实现流程图；Fig. 6 is a flow chart of realizing the pulse electromagnetic oscillation horizontal continuous casting method of copper alloy strip provided by the embodiment of the present invention;
图中的附图标记指代的技术特征为：The technical characteristics indicated by the reference numerals in the figure are:
1、保温炉；2、结晶器底板；3、脉冲电磁振荡发生器；4、不锈钢水冷套；5、冷却铜套；6、石墨结晶器；7、铜合金板；8、脉冲电磁振荡发生器进水口；9、脉冲电磁振荡发生器出水口。1. Holding furnace; 2. Crystallizer bottom plate; 3. Pulse electromagnetic oscillation generator; 4. Stainless steel water cooling sleeve; 5. Cooling copper sleeve; 6. Graphite crystallizer; 7. Copper alloy plate; 8. Pulse electromagnetic oscillation generator Water inlet; 9. Water outlet of pulse electromagnetic oscillation generator.
具体实施方式detailed description
为使本发明解决的技术问题、采用的技术方案和达到的技术效果更加清楚，下面结合附图和实施例对本发明作进一步的详细说明。可以理解的是，此处所描述的具体实施例仅仅用于解释本发明，而非对本发明的限定。另外还需要说明的是，为了便于描述，附图中仅示出了与本发明相关的部分而非全部内容。In order to make the technical problems solved by the present invention, the technical solutions adopted and the technical effects achieved clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, but not to limit the present invention. In addition, it should be noted that, for the convenience of description, only parts related to the present invention are shown in the drawings but not all content.
实施例一Embodiment one
图1为本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造装置的结构示意图。如图1所示，本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造装置包括：保温炉1、结晶器底板2、脉冲电磁振荡发生器3、不锈钢水冷套4、冷却铜套5和石墨结晶器6，其中，所述保温炉1与所述石墨结晶器6连通，所述脉冲电磁振荡发生器3为环形，并套设在所述石墨结晶器6上靠近所述保温炉1的一端；所述脉冲电磁振荡发生器3未与所述保温炉1和所述石墨结晶器6接触的面被所述结晶器底板2所包覆，并通过所述结晶器底板2固定在所述保温炉1上；所述石墨结晶器6未被所述结晶器底板2和所述脉冲电磁振荡发生器3所包覆的部分由内向外依次套设所述冷却铜套5和所述不锈钢水冷套4。Fig. 1 is a schematic structural diagram of a pulsed electromagnetic oscillation horizontal continuous casting device for copper alloy strips provided by an embodiment of the present invention. As shown in Figure 1, the copper alloy strip pulse electromagnetic oscillation horizontal continuous casting device provided by the embodiment of the present invention includes: a holding furnace 1, a crystallizer bottom plate 2, a pulse electromagnetic oscillation generator 3, a stainless steel water cooling jacket 4, and a cooling copper jacket 5 And graphite crystallizer 6, wherein, described holding furnace 1 is communicated with described graphite crystallizer 6, and described pulse electromagnetic oscillation generator 3 is annular, and is sleeved on described graphite crystallizer 6 and is close to described holding furnace 1 One end of the pulse electromagnetic oscillation generator 3 that is not in contact with the holding furnace 1 and the graphite crystallizer 6 is covered by the crystallizer bottom plate 2, and is fixed on the crystallizer bottom plate 2 by the crystallizer bottom plate 2 above the holding furnace 1; the part of the graphite crystallizer 6 that is not covered by the crystallizer bottom plate 2 and the pulse electromagnetic oscillation generator 3 is sequentially sleeved with the cooling copper sleeve 5 and the stainless steel Water cooling jacket4.
其中，本发明首次将脉冲电磁振荡技术应用到较大宽厚比的铜合金板带水平连续铸造中。例如，对厚度为8mm，宽度为450mm的黄铜(H70)的铸造，对厚度为12mm,宽度为600mm的锡磷青铜(QSn6.5-0.1)的铸造。通过所述脉冲电磁振荡发生器3未与所述保温炉1和所述石墨结晶器6接触的面被所述结晶器底板2所包覆，并通过结晶器底板2固定在所述保温炉1上，能够减少结晶器底板2对脉冲电磁振荡发生器3的挤压，延长其使用寿命。例如，通过将脉冲电磁振荡发生器3设置在结晶器底板2的凹槽中，进而在通过结晶器底板2将脉冲电磁振荡发生器3固定在所述保温炉1上。另外，脉冲电磁振荡发生器3与石墨结晶器6、保温炉1、结晶器底板2之间的间隙填充有耐火水泥，间隙填充有耐火水泥能够使脉冲电磁振荡发生器进行充分的定位，同时能很好地缓解结晶器地板对脉冲脉冲发生器的挤压。Among them, the present invention applies the pulse electromagnetic oscillation technology to the horizontal continuous casting of copper alloy strips with a large aspect ratio for the first time. For example, the casting of brass (H70) with a thickness of 8mm and a width of 450mm, and the casting of tin phosphor bronze (QSn6.5-0.1) with a thickness of 12mm and a width of 600mm. The surface that is not in contact with the holding furnace 1 and the graphite crystallizer 6 by the pulse electromagnetic oscillation generator 3 is covered by the crystallizer bottom plate 2, and is fixed on the holding furnace 1 by the crystallizer bottom plate 2 On the other hand, the extrusion of the pulse electromagnetic oscillation generator 3 by the base plate 2 of the crystallizer can be reduced, and its service life can be prolonged. For example, by arranging the pulse electromagnetic oscillation generator 3 in the groove of the crystallizer bottom plate 2 , the pulse electromagnetic oscillation generator 3 is fixed on the holding furnace 1 through the crystallizer bottom plate 2 . In addition, the gap between the pulse electromagnetic oscillation generator 3 and the graphite crystallizer 6, the holding furnace 1, and the crystallizer bottom plate 2 is filled with refractory cement, and the gap is filled with refractory cement to enable the pulse electromagnetic oscillation generator to be fully positioned and at the same time Great relief from pinching of the crystallizer floor against the pulse generator.
图2为图1中A-A线的剖视图。图3为脉冲电磁振荡发生器的主视图。图4为脉冲电磁振荡发生器的俯视图。从图3和图4可以看出本发明提供的脉冲电磁振荡发生器3为环形，脉冲电磁振荡发生器3的环形，“环”为环绕的意思，是与所述石墨结晶器6相配合的环形，也可以为矩形的环。另外，本发明将电磁振荡发生器3的信号选择为脉冲信号是由于：不仅节省能源，同时脉冲电流能在较短的时间里达到最大值，即脉冲电磁振荡发生器能在较短的时间产生较大的磁场。这样使得脉冲电磁振荡发生器所用励磁线圈所用铜线截面积较小，因此和行波磁场相较而言，脉冲电磁振荡发生器设备简单、体积较小，更适合实际生产的使用。脉冲电磁振荡发生器产生脉冲磁场，作用于石墨结晶器内的铜合金液，产生的磁场力在石墨结晶器中的铜合金液中引起强烈振荡和强迫对流，不仅能将石墨结晶器壁上先形成的大量晶核冲刷下来并带入铜合金液，进而增加形核率，而且使板带边部和中心部位的温度场趋于均匀。Fig. 2 is a sectional view of line A-A in Fig. 1 . Fig. 3 is a front view of the pulsed electromagnetic oscillation generator. Fig. 4 is a top view of the pulsed electromagnetic oscillation generator. As can be seen from Fig. 3 and Fig. 4, the pulsed electromagnetic oscillation generator 3 provided by the present invention is annular, and the annular shape of the pulsed electromagnetic oscillation generator 3, "ring" means surrounding, and is matched with the graphite crystallizer 6 A ring can also be a rectangular ring. In addition, the present invention selects the signal of the electromagnetic oscillation generator 3 as a pulse signal because: not only energy is saved, but the pulse current can reach the maximum value in a shorter time, that is, the pulse electromagnetic oscillation generator can generate Larger magnetic field. This makes the cross-sectional area of the copper wire used in the excitation coil used in the pulse electromagnetic oscillation generator smaller. Therefore, compared with the traveling wave magnetic field, the pulse electromagnetic oscillation generator has simple equipment and a small volume, and is more suitable for actual production. The pulse electromagnetic oscillation generator generates a pulsed magnetic field, which acts on the copper alloy liquid in the graphite crystallizer, and the generated magnetic field force causes strong oscillation and forced convection in the copper alloy liquid in the graphite crystallizer, not only can the graphite crystallizer wall be first A large number of crystal nuclei formed are washed down and brought into the copper alloy liquid, thereby increasing the nucleation rate, and making the temperature field at the edge and center of the strip tend to be uniform.
在上述方案中，所述脉冲电磁振荡发生器3的励磁线圈的夹角是圆心角为180至270的圆弧。从图2可以看出脉冲电磁振荡发生器3的励磁线圈的夹角是圆心角为钝角的圆弧，以获得较为均匀的磁场分布。其中，励磁线圈的夹角处设计成圆心角为钝角的圆弧是由于：根据表征磁场特性的场函数即毕奥-沙瓦-拉普拉斯定律可知，矩形磁场具有尖角效应，即磁场总是在尖角处最大。为了验证尖角效应，因此对环形的脉冲电磁振荡发生器产生的磁场用ANSYS软件数值模拟，从模拟结果看出，磁场在边角处最大。为了获得较为均匀的磁场分布，对脉冲电磁振荡发生器做了相应的修改，即把环形的脉冲电磁振荡发生器的边角处设计成圆心角为钝角的圆弧，这样使得铸锭的边角离脉冲电磁振荡发生器的边角处的距离增加，从而减弱边角处的磁场强度，进而使的得到的铜合金板7带边角处所受磁场力趋于均匀，从而能很好的避免因磁场力分布的不均匀造成铜合金板带角部出现表面裂纹等铸造缺陷。其中，所述脉冲电磁振荡发生器3的励磁线圈可以由直径为1至2mm的漆包铜线缠绕而成。In the above solution, the included angle of the excitation coil of the pulse electromagnetic oscillation generator 3 is a circular arc with a central angle of 180° to 270°. It can be seen from FIG. 2 that the included angle of the excitation coil of the pulse electromagnetic oscillation generator 3 is a circular arc with an obtuse central angle, so as to obtain a relatively uniform magnetic field distribution. Among them, the included angle of the excitation coil is designed as a circular arc whose central angle is an obtuse angle because: According to the field function that characterizes the magnetic field characteristics, that is, the Biot-Shavat-Laplace law, it can be known that the rectangular magnetic field has a sharp-angle effect, that is, the magnetic field Always largest at sharp corners. In order to verify the sharp corner effect, the magnetic field generated by the annular pulse electromagnetic oscillator generator is numerically simulated by ANSYS software. From the simulation results, it can be seen that the magnetic field is the largest at the corner. In order to obtain a relatively uniform magnetic field distribution, the pulse electromagnetic oscillation generator has been modified accordingly, that is, the corners of the ring-shaped pulse electromagnetic oscillation generator are designed as arcs with an obtuse angle at the center of the circle, so that the corners of the ingot The distance from the corners of the pulse electromagnetic oscillation generator increases, thereby weakening the magnetic field strength at the corners, and then making the magnetic field force on the corners of the obtained copper alloy plate 7 tend to be uniform, so that it can well avoid Casting defects such as surface cracks appear at the corners of the copper alloy strip due to the uneven distribution of the magnetic field force. Wherein, the excitation coil of the pulse electromagnetic oscillation generator 3 can be wound by enamelled copper wire with a diameter of 1 to 2 mm.
图5为不同频率下脉冲电磁振荡发生器未设计凸起圆角的熔体内磁场的分布示意图。从图5可以表征出励磁线圈的棱角处未设计成凸起圆角时，磁场在边缘分布较大，因此本发明的脉冲电磁振荡发生器的励磁线圈设计成了夹角是圆心角为钝角的圆弧形状。Fig. 5 is a schematic diagram of the distribution of the magnetic field in the melt in which the pulsed electromagnetic oscillation generator is not designed with raised rounded corners at different frequencies. From Fig. 5, it can be shown that when the edges and corners of the excitation coil are not designed as raised rounded corners, the magnetic field is distributed relatively large at the edge, so the excitation coil of the pulse electromagnetic oscillation generator of the present invention is designed so that the included angle is that the central angle is an obtuse angle arc shape.
在上述方案中，优选的，所述脉冲磁场发生器的励磁线圈是由直径为1至2mm的漆包铜线缠绕而成。可选的，脉冲电磁振荡发生器外部由不锈钢封闭，内部通冷却水。从图4中可知在脉冲电磁振荡发生器工作时，从脉冲电磁振荡发生器进水口8进水，从脉冲电磁振荡发生器出水口9出水。外部选用壁厚为1至3mm厚的不锈钢可以减少发生器外壳对磁场的屏蔽，同时内部的冷却水能够很好的冷却励磁线圈，使得脉冲电磁振荡发生器能够安全的运行。In the above solution, preferably, the excitation coil of the pulsed magnetic field generator is wound with an enameled copper wire with a diameter of 1 to 2 mm. Optionally, the outside of the pulse electromagnetic oscillation generator is closed by stainless steel, and the inside passes through cooling water. It can be seen from Fig. 4 that when the pulse electromagnetic oscillation generator is working, water is taken in from the water inlet 8 of the pulse electromagnetic oscillation generator, and water is discharged from the water outlet 9 of the pulse electromagnetic oscillation generator. The external selection of stainless steel with a wall thickness of 1 to 3mm can reduce the shielding of the generator shell to the magnetic field, and the internal cooling water can well cool the excitation coil, so that the pulse electromagnetic oscillation generator can run safely.
本发明提供的铜合金板带脉冲电磁振荡水平连续铸造装置，利用结晶器底板包覆脉冲电磁振荡发生器，并通过所述结晶器底板将脉冲电磁振荡发生器固定在所述保温炉上，能够减少结晶器底板对脉冲电磁振荡发生器的挤压，延长其使用寿命，选用环形的脉冲电磁振荡发生器，并利用脉冲信号作为电磁振荡信号作用于石墨结晶器内的铜合金液，产生的磁场力能够在石墨结晶器中的铜合金液中引起强烈振荡和强迫对流，不仅能将石墨结晶器壁上先形成的大量晶核冲刷下来并带入石墨结晶器中的铜合金液中，从而增加形核率，而且使板带边部和中心部位的温度场趋于均匀。本发明提供的脉冲磁场发生器能耗低，设备简单、操作方便易行，安全可靠，将脉冲电磁振荡技术应用到较大宽厚比的铜合金板带水平连续铸造中，不仅能改善铜合金板带的凝固组织，而且能减少偏析和裂纹等铸造缺陷，从而提高铜合金板带坯的成品率。The pulse electromagnetic oscillation horizontal continuous casting device for copper alloy strips provided by the present invention uses the crystallizer bottom plate to cover the pulse electromagnetic oscillation generator, and fixes the pulse electromagnetic oscillation generator on the holding furnace through the crystallizer bottom plate, which can To reduce the extrusion of the pulse electromagnetic oscillation generator from the bottom plate of the crystallizer and prolong its service life, a ring-shaped pulse electromagnetic oscillation generator is selected, and the pulse signal is used as an electromagnetic oscillation signal to act on the copper alloy liquid in the graphite crystallizer to generate a magnetic field The force can cause strong oscillation and forced convection in the copper alloy liquid in the graphite crystallizer, which can not only wash down a large number of crystal nuclei formed on the graphite crystallizer wall and bring them into the copper alloy liquid in the graphite crystallizer, thereby increasing Nucleation rate, and the temperature field at the edge and center of the strip tends to be uniform. The pulsed magnetic field generator provided by the present invention has low energy consumption, simple equipment, convenient and easy operation, and is safe and reliable. Applying the pulsed electromagnetic oscillation technology to the horizontal continuous casting of copper alloy strips with a large width-thickness ratio can not only improve the copper alloy plate The solidification structure of the strip can be reduced, and casting defects such as segregation and cracks can be reduced, thereby improving the yield of copper alloy strip blanks.
实施例二Embodiment two
本实施例可以采用实施例一提供的铜合金板带脉冲电磁振荡水平连续铸造装置。In this embodiment, the copper alloy strip pulse electromagnetic oscillation horizontal continuous casting device provided in Embodiment 1 can be used.
图6为本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造方法的实现流程图。如图6所示，本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造方法包括：Fig. 6 is a flow chart of the implementation of the pulse electromagnetic oscillation horizontal continuous casting method for copper alloy strips provided by the embodiment of the present invention. As shown in Figure 6, the pulse electromagnetic oscillation horizontal continuous casting method for copper alloy strips provided by the embodiment of the present invention includes:
在铜合金板带脉冲电磁振荡水平连续铸造装置的保温炉内铜合金液温度达到1000至1200℃时，开动牵引机，带动铜合金板带坯运动，同时启动环形的脉冲电磁振荡发生器，所述脉冲电磁振荡发生器对石墨结晶器中的铜合金液产生电磁力，进而对石墨结晶器中的铜合金液的径向进行电磁振荡。When the temperature of the copper alloy liquid in the holding furnace of the copper alloy strip pulse electromagnetic oscillation horizontal continuous casting device reaches 1000 to 1200 °C, the tractor is started to drive the movement of the copper alloy strip billet, and the annular pulse electromagnetic oscillation generator is started at the same time. The pulse electromagnetic oscillation generator generates electromagnetic force on the copper alloy liquid in the graphite crystallizer, and then performs electromagnetic oscillation on the radial direction of the copper alloy liquid in the graphite crystallizer.
在上述方案中，优选的，所述环形的脉冲电磁振荡发生器连接到充电电压可调的脉冲电源上，电压的调节范围为100至800V。In the above solution, preferably, the ring-shaped pulse electromagnetic oscillation generator is connected to a pulse power supply with adjustable charging voltage, and the voltage adjustment range is 100 to 800V.
在上述方案中，优选的，所述环形的脉冲电磁振荡发生器通入脉冲电流的脉冲宽度在铸造过程中为1ms的整数倍连续调节，以及脉冲频率为1Hz的整数倍连续调节。脉冲宽度调节范围为1至10ms，脉冲频率调节范围为50至150Hz。In the above solution, preferably, the pulse width of the pulse current supplied by the ring-shaped pulse electromagnetic oscillation generator is continuously adjusted to an integer multiple of 1 ms, and the pulse frequency is continuously adjusted to an integer multiple of 1 Hz during the casting process. The pulse width adjustment range is 1 to 10ms, and the pulse frequency adjustment range is 50 to 150Hz.
在铸造过程中，脉冲电磁振荡发生器产生的电磁力在液体中引起强烈振荡，磁感应强度可以达到100至10000Gs。During the casting process, the electromagnetic force generated by the pulse electromagnetic oscillation generator causes strong oscillation in the liquid, and the magnetic induction intensity can reach 100 to 10000Gs.
本发明在铜合金板带的铸造过程中，脉冲电磁振荡发生器对石墨结晶器中的铜合金液产生的磁场力能够在熔体中引起强烈振荡和强迫对流，能够将石墨结晶器壁上先形成的大量晶核冲刷下来并带入熔体，从而增加形核率。In the casting process of copper alloy strips in the present invention, the magnetic field force generated by the pulse electromagnetic oscillation generator on the copper alloy liquid in the graphite crystallizer can cause strong oscillation and forced convection in the melt, and the graphite crystallizer wall can be first A large number of nuclei formed are washed down and carried into the melt, thereby increasing the nucleation rate.
下面以实例的形式对本发明实施例提供的铜合金板带脉冲电磁振荡水平连续铸造方法进行说明：The pulse electromagnetic oscillation horizontal continuous casting method of the copper alloy strip provided by the embodiment of the present invention is described below in the form of an example:
例如，对厚度为8mm，宽度为450mm的黄铜(H70)的铸造：将环形的脉冲电磁振荡发生器套在石墨结晶器上，固定在保温炉与结晶器底板之间，接线端子与充电电压为100～800V的脉冲电源相连接。当保温炉内的黄铜铜液H70达到1070～1100℃时，开动牵引机，开始连续铸造。同时开启电源开关，调节脉冲电源，使得通入脉冲电磁振荡发生器的脉冲电流的脉冲宽度为1ms、频率为120Hz，熔体通过贯穿石墨结晶器的磁场时，受到洛伦兹力的作用，洛伦兹力使石墨结晶器内的熔体产生强烈振荡。通过观察板带坯的表面状况，调整通入脉冲磁场发生器的脉冲电压，直到表面颜色为灰白相间、凝固痕平直为止，保持此稳定状态，进行生产。进一步的，利用剪板机截取板带试样，观察其凝固组织及宏观形貌，板带坯上未发现裂纹，成分分析结果表明铸造组织中锌元素无偏析。For example, for the casting of brass (H70) with a thickness of 8mm and a width of 450mm: put the ring-shaped pulse electromagnetic oscillation generator on the graphite crystallizer, fix it between the holding furnace and the bottom plate of the crystallizer, and connect the terminals to the charging voltage It is connected to a pulse power supply of 100-800V. When the brass copper liquid H70 in the holding furnace reaches 1070-1100°C, start the tractor and start continuous casting. At the same time, turn on the power switch and adjust the pulse power supply so that the pulse width of the pulse current fed into the pulse electromagnetic oscillation generator is 1ms and the frequency is 120Hz. When the melt passes through the magnetic field penetrating the graphite crystallizer, it is affected by the Lorentz force. The Renz force causes the melt in the graphite crystallizer to vibrate strongly. By observing the surface condition of the slab, adjust the pulse voltage fed into the pulse magnetic field generator until the surface color is gray and white, and the solidification mark is straight, and the stable state is maintained for production. Further, the strip sample was cut with a shearing machine, and its solidification structure and macroscopic appearance were observed. No cracks were found on the strip billet, and the composition analysis results showed that there was no segregation of zinc in the cast structure.
或者例如，对厚度为12mm,宽度为600mm的锡磷青铜(QSn6.5-0.1)的铸造：将环形的脉冲磁场发生器套在石墨结晶器上，固定在保温炉与结晶器底板之间，接线端子与充电电压为100～800V的脉冲电源相连接。当保温炉内的锡磷青铜液QSn6.5-0.1达到1140～1170℃时，开动牵引机，开始连续铸造。同时开启电源开关，调节脉冲电源参数。使得通入脉冲电磁振荡场发生器的脉冲电流宽度为5ms、频率为140Hz，熔体通过贯穿石墨结晶器的磁场时，受到洛伦兹力的作用，洛伦兹力使石墨结晶器内的熔体产生强烈振荡。通过观察板带坯的表面的颜色和凝固痕，调整通入脉冲磁场发生器的脉冲电压，直到表面颜色为灰白相间、凝固痕平直为止，保持此稳定状态，进行生产。进一步的，利用剪板机截取板带试样，观察其凝固组织，测试其力学性能。铸态试样屈服强度降为180～200MPa，伸长率50～55％，均匀化退火时间由原来的8～12小时降为4小时以下，铸造温度降低30℃。Or, for example, for the casting of tin phosphor bronze (QSn6.5-0.1) with a thickness of 12mm and a width of 600mm: put the annular pulsed magnetic field generator on the graphite crystallizer, and fix it between the holding furnace and the bottom plate of the crystallizer, The connecting terminal is connected with a pulse power supply with a charging voltage of 100-800V. When the tin phosphor bronze liquid QSn6.5-0.1 in the holding furnace reaches 1140-1170°C, start the tractor and start continuous casting. At the same time, turn on the power switch to adjust the parameters of the pulse power supply. Make the pulse current width of 5 ms and frequency 140 Hz passed into the pulse electromagnetic oscillation field generator. The body vibrates strongly. By observing the color and solidification marks on the surface of the slab, adjust the pulse voltage fed into the pulse magnetic field generator until the surface color is gray and white, and the solidification marks are straight, and then maintain this stable state for production. Further, the strip sample was cut with a shearing machine, its solidified structure was observed, and its mechanical properties were tested. The yield strength of the as-cast sample is reduced to 180-200MPa, the elongation is 50-55%, the homogenization annealing time is reduced from the original 8-12 hours to less than 4 hours, and the casting temperature is reduced by 30°C.
本发明提供的铜合金板带脉冲电磁振荡水平连续铸造方法，与现有的行波磁场辅助水平连续铸造的方法相比，在铜合金板带的铸造过程中，利用脉冲信号作为电磁振荡信号作用于石墨结晶器内的铜合金熔体，产生的磁场力能够在熔体中引起强烈振荡和强迫对流，不仅能将石墨结晶器壁上先形成的大量晶核冲刷下来并带入熔体，从而增加形核率，而且使板带边部和中心部位的温度场趋于均匀。通过上述方法能制备出凝固组织均匀、晶粒细化、无裂纹及无溶质元素偏析的铜合金板带铸坯，适用于大宽厚比的铜合金板带铸造领域。本发明提供的铜合金板带脉冲电磁振荡水平连续铸造方法将脉冲电磁振荡技术应用到较大宽厚比的铜合金板带水平连续铸造中，不仅能改善铜合金板带的凝固组织，而且能减少偏析和裂纹等铸造缺陷，细化合金组织，从而提高铜合金板带坯的成品率。The pulse electromagnetic oscillation horizontal continuous casting method for copper alloy strips provided by the present invention, compared with the existing traveling wave magnetic field assisted horizontal continuous casting method, uses pulse signals as electromagnetic oscillation signals in the casting process of copper alloy strips For the copper alloy melt in the graphite crystallizer, the magnetic field force generated can cause strong oscillation and forced convection in the melt, which can not only wash down a large number of crystal nuclei formed on the graphite crystallizer wall and bring them into the melt, thus Increase the nucleation rate, and make the temperature field at the edge and center of the strip tend to be uniform. Copper alloy strip casting slabs with uniform solidification structure, fine grain, no cracks and no solute element segregation can be prepared by the above method, which is suitable for the field of copper alloy strip casting with large width-thickness ratio. The pulse electromagnetic oscillation horizontal continuous casting method for copper alloy strips provided by the invention applies the pulse electromagnetic oscillation technology to the horizontal continuous casting of copper alloy strips with a large aspect ratio, which can not only improve the solidification structure of copper alloy strips, but also reduce Casting defects such as segregation and cracks are eliminated, and the alloy structure is refined, thereby improving the yield of copper alloy strip blanks.
最后应说明的是：以上各实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述各实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其对前述各实施例所记载的技术方案进行修改，或者对其中部分或者全部技术特征进行等同替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的范围。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: Modifications to the technical solutions described in the foregoing embodiments, or equivalent replacement of some or all of the technical features thereof, do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the various embodiments of the present invention.
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