INVESTIGATION OF THE POSSIBILITY OF USING A DEFLECTING SYSTEM FOR MAGNETIC FIELDS IMPACT COMPENSATION DURING ELECTRON-BEAM WELDING

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Introduction. High demands on quality of welded joints in aerospace branch, shipbuilding, automotive d Bn (z) = B0 d 2 . (2) industry, nuclear power engineering assume precise align- ment of an electron beam with an interfacing surface at the electron beam welding (EBW). The magnetic fields occuring during dissimilar materials welding and products with a residual magnetization cause a deflection of an electron beam from an optical axis of the electron beam 2 + (l - z) Thus, distribution of a longitudinal component mag- netic induction of the interference field on the way of an electron beam will be as follows ì gun in an interval from the gun to the welded product and on the depth of weld penetration channel as well. If these ïB0 B (z) = ï , 0 £ z £ l; (3) deflections exceed 0.3 mm, then they lead to incomplete root penetration, especially at welding of thicker parts n í ïB æ1- 2z + 2l ö , l < z £ l + d. ï 0 ç d d ÷ [1-7]. A more perspective way of electron beam protection against magnetic fields interference is their compensation in a welding zone. For this purpose a longitudinal in rela- tion to a welded joint component of a magnetic field î è ø The slope angle of an electron beam trajectory and amount of deflection of the beam from an axis of the elec- tron beam gun can be estimated according to approximate formulas [8]: 0 is measured in area the electron beam gun - the welded e z product, and carry out its compensations [8; 9]. The compensation of a longitudinal component of y = mV ò B(z)dz; (4) a magnetic field impact on an electron beam when welding dissimilar materials can be carried out by applying the welded parts of the local compensating magnetic field, z z mV e x = òò B(z)dz, 0 0 parallel to the interfacing surface which is generated by electromagnetic coils [10], or introduction of compen- sating currents to the welded product which are counter- directed to thermoEMF currents [11; 12]. When welding products from ferromagnetic materials compensation of a longitudinal component of a residual magnetization magnetic field can be carried out by means of the elec- tromagnet creating a compensating magnetic field in the welded product, counter an interference field [12; 13]. These methods of magnetic fields compensation assume a possibility of a contact supply of the compensating field where e = 1,602·10-19 - electron charge, Kl; V (m/s) - electron speed which can be calculated on the known accelerating voltage, U (В) [16]: 5, 93×105 U (1+ 0, 983×10-6U ) V = , 1+1, 967 ×10-6U m - electron mass determined by a formula m = m0 , V 2 1c2 in the welded product that in some cases complicates their technical realization. Therefore consideration of a possiwhere m0 = 9,109·10-31 - rest mass of electron, kg; 8 bility of an interference magnetic field compensation by means of the deflection system located in an interval between the electron beam gun and the welded product is relevant. Magnetic field of interference. It is known that weldc = 2,977·10 - light velocity, m/s; B(z) - the distribution law of a longitudinal component of a magnetic field in- duction in the space between a gun and a welded product. Substituting (3) in formulas (4) and (5) and integrating ranging from 0 to (l + δ/2), we will get ing of products from dissimilar materials is followed by e z e d d + 2l e d the magnetic fields caused by action of thermoelectric currents. In the absence of external magnetic fields distribution of an induction of a longitudinal component of the field in the channel of weld penetration has almost linear characyn = mV ò Bn (z)dz = mV B0 2 ln d 0 e z z mV xn = òò Bn (z)dz = 0 0 + mV B0 4 ; (6) ter [14; 15]. The size of an induction of a magnetic field has the maximal values B0 on a product surface, decreases to the center of the channel of weld penetration and is defined from the ratio: = e d æ d2 d ö e d2 B0 ç l + ln ÷ + B0 . mV 2 è 2 d+ 2l ø mV 12 Formulas (6) and (7) allow to define the slope angle and amount of deflection of an electron beam from an B (z) = æ 2z 2l ö (1) optical axis of the gun caused by action of magnetic inter- è ø n B0 ç1 - d + d ÷ , where B0 - the size of a magnetic induction on a surface of the welded product near a joint; δ - thickness of the welded product; l - distance from the electron beam gun to a surface of the welded product. Over the surface of welded parts in the space between a product and an electron beam gun a magnetic induction of a longitudinal component of the interference field decreases on dependence which is defined by expression [13]: ferences in the center of the channel of weld penetration. The size of the circulating thermoelectric currents can reach 100 A [17] and the deflection of an electron beam caused by these currents from an optical axis of the gun on a surface of a product can make 1 mm and more. Substituting expression (2) in formula (5), integrating in the range from 0 to l, it is possible to receive a formula for the definition of an induction of a magnetic field on the surface of the welded product near a joint on the known deflection of an electron beam from an optical axis of the gun B0 = 2xmV . æ d2 d ö (8) + e × Bmax × L ´ mV 2 × 0.715 e ×dç l + 2 ln d+ 2l ÷ é ù è ø ê L L ú ê The values of magnetic induction calculated by forz - a - ´ 2 + 2 + a ú mula (8) at various deflections of x beam from an optical ê 2 2 ú , (11) axis of the gun for products of various thickness δ are presented in tab. 1. ê L2 + æ L - z + a ö L2 + æ L + a ö ú ê ç ÷ ç ÷ ú 2 2 ë è ø è ø û Thus, distribution of a longitudinal component mag- netic induction of a residual magnetization field on the way of an electron beam will appear as: x = e × Bmax × L ´ c mV 2 × 0.715 ì n í B (z) = ïB0 d 2 + (l - z) , 0 £ z £ l; (9) ´ é L2 + æ L ç 2 ê è ê ë + z - a + ï B , l < z £ l + d. + e × Bmax × L ´ îï 0 mV 2 × 0.715 The compensating system. Compensation of the magnetic field rejecting an electron beam can be carried out in an interval between an electron beam gun and ´ é L2 + æ L ç 2 ê ê è - z + a + a welded product by means of compensating system repre- ë û senting electromagnetic coils placed in the metal cylinder made of a permalloy. The axis of the cylinder coincides + e × Bmax × L ´ mV 2 × 0.715 with an optical axis of the electron beam gun (fig. 1). é æ L ö æ L ö ù In the vicinity of the compensating system center there is a zone of the homogeneous magnetic field. The size of an induction of a compensating system magnetic field ê + a z ´ 2 - ê è ø ç ÷ ê 2 L ç - a ÷ z ú 2 ú è ø . L 2 ú (12) in the arbitrary point with z coordinate on an axis of ê L2 + æ + a ö L2 + æ - a ö ú ê ç 2 ÷ ç 2 ÷ ú system can be described by the equation ë è ø è ø û max B L3 Bc (z) = 2 × 0.715 ´ Operation of the compensating system has to be di- rected to elimination of a deflection of an electron beam from an optical axis of the gun and decrease of a tangent æ 2 é ´ê L2 + æ L + z ö 3 - 2 ö 2 + æ L2 + æ L - z ö - 3 ù ö 2 ú , (10) slope angle to a beam trajectory. The system of equations êçç ç 2 ÷ ÷÷ çç ç 2 ÷ ÷÷ ú êè è ø ø è è ø ø ú ìyn - yc = 0, ë û íx - x = 0, (13) where Bmax - the size of a magnetic induction in the center of the compensating system; L - the height of the com- pensating system (diameter of electromagnetic coils). The normalized distribution of an induction of a mag- netic field (Bс(z)/Bmax) of the compensating system on axis Z at L = 25 mm is presented in fig. 2. Substituting (10) in formulas (4) and (5), considering that an origin of coordinates is ЭЛП (Electron Beam Gun), integrating ranging from 0 to z, we will get î n c allows to determine the size of a magnetic induction Bmax necessary for elimination of a deflection of an electron beam from a gun axis, and distance of a where the com- pensating system concerning the gun has to be installed so that the beam trajectory slope angle was equal to zero in the center of the channel of weld penetration. In fig. 3-5 schedules of dependence ψ(a) = ψn - ψc a tangent slope angle to an electron beam trajectory from e yc = mV × Bmax × L ´ 2 × 0.715 height of installation of the compensating system for the welded parts of various thickness made of dissimilar é ù materials are submitted. ê z - a + L L - a ú ê ú ´ ê 2 - 2 ú + ê ú ê ú ë û At a product thickness δ = 25 mm the center of the compensating system has to be at the height of 43.05 mm from a product surface, at δ = 50 mm - at the height of 36.98 mm, at δ = 100 mm - at the height of 16.95 mm. Table 1 Values of a magnetic induction of the field caused by a current of thermoEMF δ, mm 25 50 100 x, mm B0, мТл 1 0.321 0.179 0.106 2.5 0.802 0.447 0.265 5 1,6 0.894 0.53 The analysis of the presented dependences shows: the size of a magnetic induction field caused by action of ìxn - xc = 0, íx - x = 0.0003, (14) thermoelectric currents does not exert an impact on height of installation of the compensating system; if the distance from the gun to the welded product remains constant, then with the increase in thickness of a product up to some critical value the coordinate of the application of the com- pensating magnetic field approaches a product surface. In tab. 2 the values of deflections of an electron beam are given in a root of penetration at compensation of the magnetic fields caused by thermoEMF currents for details of various thickness. In fig. 6 schedules of dependence ψ(a) = ψn - ψc a tangent slope angle to an electron beam trajectory from height of installation of the compensating system for the welded parts with a residual magnetization of various thickness are given. At a product thickness δ = 25 mm the center of the compensating system has to be at the height of 34.56 mm from a product surface, at δ = 50 mm - at the height of 26.16 mm, at δ = 75 mm - at the height of 15.2 mm; at a product thickness δ = 100 mm technical realization of system of compensation of the considered design is impossible. It is necessary to apply a design of the compensating system with the magnetic tips used for con- centration of a magnetic field. To use the considered compensating system it is necessary to limit acceptable magnetic fields of interference. Let the center of the compensating system be located at the height of 17.5 mm from a product surface the thickness of which is equal to 100 mm. The solution of a system of equations î rn rc where 0.0003 - the maximum permissible deflection in a root of penetration, m; xrn - the deflection in a root of penetra- tion caused by action of the field of a residual magnetiza- tion; xrс - the deflect in a root of penetration caused by action of a magnetic field of the compensating system; allows to determine the most admissible size of an induc- tion of a magnetic field of a hindrance B0 = 0.1257 мТл that corresponds to a magnetic intensity of 100 A/m. In tab. 3 values of deflections of an electron beam are given in a root of penetration at compensation of fields of a residual magnetization of parts of various thickness. Thus, for most cases happening in practice it is possi- ble to define the distance from a product surface to the center of the compensating system providing acceptable values of a beam deflection in the root of penetration. During thicker products welding when this distance is very small and does not allow to realize compensation of a residual magnetization fields technically, it is necessary to introduce restrictions on the size of a magnetic field of interference induction. Conclusion: 1. With the use of the deflection system installed at a particular height over the welded product, it is possible to eliminate an impact on the quality of welded joints of magnetic fields caused by thermoelectric currents and a residual magnetization. 2. At electron beam welding of products of larger thickness with a residual magnetization it is necessary to limit acceptable magnetization for the purpose of ex- ception of incomplete penetration. Fig. 1. The scheme of ЭЛС (Electron Beam Welding) installation with the compensating system (a) and distribution of an induction of a magnetic field of the compensating system (b): ЭЛП - the electron beam gun; КС - the compensating system; ОИ - a workpiece Рис. 1. Схема установки ЭЛС с компенсирующей системой (а) и распределение индукции магнитного поля компенсирующей системы (б): ЭЛП - электронно-лучевая пушка; КС - компенси- рующая система; ОИ - обрабатываемое изделие Fig. 2. Distribution of magnetic induction on axis Z Подпись: Beam slope angle, rad.Рис. 2. Распределение магнитной индукции по оси Z Fig. 3. Dependency ψ(a) at δ = 25 mm, l = 250 mm, L = 25 mm Подпись: Beam slope angle, rad.Рис. 3. Зависимость ψ(a) при δ = 25 мм, l = 250 мм, L = 25 мм Fig. 4. Dependency ψ(a) at δ = 50 mm, l = 250 mm, L = 25 mm 638 Рис. 4. Зависимость ψ(a) при δ = 50 мм, l = 250 мм, L = 25 мм Подпись: Beam slope angle, rad.Fig. 5. Dependency ψ(a) at δ = 100 mm, l = 250 mm, L = 25 mm Рис. 5. Зависимость ψ(a) при δ = 100 мм, l = 250 мм, L = 25 мм Table 2 Deflections in a root of penetration at compensation of the magnetic fields caused by thermoelectric currents δ, mm 25 50 100 B0, мТл Beam deflection in a root of penetration, mm 0.94 0.0576 0.2306 0.9222 0.5 0.0307 0.1226 0.4905 0.4 0.0245 0.0981 0.3924 0.3 0.0184 0.0736 0.2943 Подпись: The angle of deflection of the beam, rad.Fig. 6. Dependancy ψ(a) at B0 = 0,94 мТл, l = 250 mm, L = 25 mm Рис. 6. Зависимость ψ(a) при B0 = 0,94 мТл, l = 250 мм, L = 25 мм Deflections in a root penetration at compensation of fields of a residual magnetization Table 3 639 δ, mm 25 50 75 100 B0, мТл Beam deflection in a root of penetration, mm 0.94 0.0865 0.3458 0.7781 2.3 0.5 0.046 0.184 0.4139 1.2 0.4 0.0368 0.1472 0.3311 0.9593 0.2 0.0184 0.0736 0.1656 0.4797 0.125 0.0115 0.046 0.1035 0.2998

About the authors

A. A. Druzhinina

Siberian Federal University

Email: druzhininasasha@rambler.ru
79, Svobodny Av., Krasnoyarsk, 660041, Russian Federation

V. D. Laptenok

Reshetnev Siberian State University of Science and Technology

31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation

P. V. Laptenok

Reshetnev Siberian State University of Science and Technology

31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation

A. V. Murygin

Reshetnev Siberian State University of Science and Technology

31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation

References

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