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• CALCULATION OF UPSETTING FORCEIN FLASH BUTT WELDING

OF CLOSED-SHAPE PRODUCTS

P.N. CHVERTKO, A.V. MOLTASOV and S.M. SAMOTRYASOVE.O. Paton Electric Welding Institute, NASU

11 Bozhenko Str., 03680, Kiev, Ukraine. E-mail: office@paton.kiev.ua

In structure elements of flying vehicles the ring-type parts of high-alloy steel and alloys are widely applied.To manufacture such structure elements different methods of fusion welding are applied including flashbutt welding (FBW). Technology of FBW of such parts requires high upsetting speeds 50mm/s with aspecific force of not less than 120200 MPa. In FBW of parts of a closed shape it is important to determinethe value of necessary upsetting force. At unlimited or insufficient upsetting force the necessary conditionsfor joint formation in a solid phase will not be provided, and during overheating the part shortening willbe rather large. Both conditions will lead to violation of shape of ring-type parts, in particular, in perimeter.In the process of welding the elastic forces appear in product being welded, hindering the joint formation,which should be determined in the development of technology and equipment for welding. Besides, inwelding of ring-type billets of a large section, which are characterized by a significant elasticity, it isnecessary to take into account the possibility of a welded butt rupture due to elasticity of billet at insufficienttime of upsetting without passing of electric current. Calculation of the above-mentioned forces was carriedout according to the theory of thin rods under the conditions, when stress-strain state was considered tobe linear. Also the calculation of given forces using the methods of elasticity theory was carried out, andas a result the plain problem of elasticity theory was solved. The comparison of results of calculation ofeight rings with different characteristic sizes showed that maximum difference of values of upsetting force,calculated by the theory of thin rods and formulae of plane problem, was about 2 %, and the values offorces, rupturing a butt after welding, was less than 1 %. Moreover, in decrease of ratio of external radiusof the ring to its internal radius the accuracy of calculation according to the theory of thin rods is increased.7 Ref., 1 Table, 4 Figures.

Keywo r d s : flash butt welding, rings, high-alloyedsteels, stress-strain state, upsetting force, theory of thinrods, plain problem

In industry, to manufacture the parts and struc-tures of a closed shape of different purpose (ele-ments of engines, different bandages, turntables,bearings, flanges, etc.), different methods ofwelding are applied (arc, electron beam, flash

butt, etc.) on which the service characteristicsof welded joint greatly depend.

One of the most saving and technically simpleprocesses of manufacture of ring-type billets isFBW [1]. This method provides high stable qual-ity of welded joints, unites welding and assemblyoperations in one cycle and does not require ap-plication of auxiliary consumables (electrodes,fluxes, welding wires, shielding gases, etc.).

At the E.O. Paton Electric Welding Institutethe technology and equipment [2] for FBW ofring-type parts under the industrial conditionswere developed (Figure 1). The technology wasbased on the method of FBW with pulsatingflashing [3], which provides the highly-concen-trated heating, due to which the HAZ is de-creased.

The calculation diagram of loading the ring,on which the upsetting force P and reactive mo-ment M from the movable clamping device of themachine, corresponding to Figure 1, are affected,is given in Figure 2.

It can be assumed as the first approximationthat the sizes of the cross section of the ring are

Figure 1. Ring-type billet in the clamping devices of buttwelding machine K607

P.N. CHVERTKO, A.V. MOLTASOV and S.M. SAMOTRYASOV, 2014

46 1/2014

• small as compared to its average radius, then theproblem can be solved using the thin rods theory.

To determine forces P it is rationally to relateit with the value of elastic movement el fromthe initial gap up to the final position consideringthe shortening of part due to flashing and upset-ting. The value of elastic movement in a curvi-linear contour should be determined using Moreintegral:

el = S

M___

MpdsEIz

, (1)

where M___

is the expression for moment from singleforce applied in the direction of force P; Mp isthe expression for the moment from active andreactive forces; Iz is the moment of section inertia;E is the elasticity modulus of the first kind.

Using canonic equations of method of forces[4], the value of reactive moment M = P(a ++ b)/2 was found. Considering that the expres-sion for bending moment in ring sections has aform

Mp = 12 P(a + b) cos . (2)

Expression for determination of moment fromaction of single force P = 1 will be written in aform

M___

= 12 (a + b)(1 cos ). (3)

Substituting expressions (2) and (3) into (1),the value of elastic movement was determined:

el = 1

EIz

2

0

12 P (a + b) cos

12 (a + b) (1 cos )

12 (a + b)d

=

= P(a + b)3

8EIz,

from which it is possible to obtain the upsettingforce

P = 8EIz

(a + b)3 el. (4)

We obtain the more precise solution of thisproblem by solution of plane problem of theoryof elasticity. This solution belongs to Kh.S.Golovin and is described in work [5]. Therefore,we give only expressions for stresses:

r =

rr +

2

r22 =

2Ar

2B

r3 +

Dr cos ,

+ 2

r2 =

6Ar +

2B

r3 +

Dr cos ,

r =

r

r =

2Ar

2B

r3 +

Dr sin ,

(5)

where A, B and D are the constants determinedby the boundary conditions. In our case they areequal:

A = P2R

; B = Pa2b2

2R; D =

PR

(a2 + b2). (6)

Moreover

R = a2 b2 + (a2 + b2) ln ba.

Unlike work [5] where during study of move-ments the functions of complex variable wereused, we used the method, which was applied in[6] for solution of problem about the action oftangent force applied at the end of a curvilinearrod.

The components of deformation in the polarcoordinates has the following form:

r = u

r; =

ur +

v

r; r =

u

r +

v

r

vr. (7)

Through the components of stress (5) the com-ponents of deformation in plain-stressed state areexpressed in the following way:

r = 1E

(r ); = 1E

( r); r = rG

, (8)

where

1/2014 47

• G = E

2(1 + ).

Having compared the expressions for r from(7) and (8) considering (5), we obtained afterintegration

u = cos

E

Ar2(1 3) +

B

r2 (1 + ) + D(1 ) ln r

+ f(),

(9)

where f() is the function depending only on theargument , which will be determined below. Bysubstitution of obtained expression (9) into ex-pression for from (7) considering (8) we shallobtain after integration

v = sin

E

Ar2(5 + ) +

B

r2 (1 + ) + D(1 )(1 ln r)

f()d + F(r),

(10)

where F(r) is the function depending only on theargument r, which also will be determined below.Substituting obtained expression (10) togetherwith expression (9) into expression for r from(7) considering (8) we shall obtain

4D sin E

= r dFdr

+ f()d F(r) + df()d ,

which should comply with functions f() andF(r). These functions were determined by theauthors in the following form:

f() = 2DE

sin + K sin + L cos ; F(r) = Hr, (11)

where K, L, H are the arbitrary constants deter-mined from the conditions of clamping.

Considering (11) the expressions for compo-nents of movement have a form

u = 2DE

sin + cos

E

Ar2(1 3) +

B

r2 (1 + ) +

+ D(1 ) ln r] + K sin + L cos ;

v = 2DE

cos + sin

E

A r2(5 + ) +

B

r2 (1 + ) +

+ D[(1 )(1 ln r) 2]] + K cos L sin + Hr.

(12)

Tangential movement of a free end can be ob-tained by substituting value = 0 into expressionfor v, then

v( = 0) = K + Hr. (13)

Constants K, H are determined from the con-ditions on stationary fixed end = 2, where v == 0, v/r = 0. Substituting that into expressionfor v from (12) the unknown constants were de-termined:

K = 4DE

; H = 0. (14)

Thus, using formulae (6) we will find at = 0

v = el = 4P(a2 + b2)

E a2 b2 + (a2 + b2) ln

ba

. (15)

From formula (15) we shall determine the up-setting force:

P = Eelt

4(a2 + b2) a2 b2 + (a2 + b2) ln

ba. (16)

The character evidences that direction ofmovement v does not coincide with the directionof growth . It should be noted that thickness twas introduced to formula (16) as for the solutionof plane problem we would obtain the force pera unit of thickness. Rejects and defects in weldingare mainly detected after operation of calibrationor in the process of subsequent mechanical treat-ment. Those rings can be considered defective,in which during removal of upsetting force thecracks are formed in a butt or fracture along thewelded butt is occurred.

During determination of force tending to rup-ture the butt joint after welding, it is necessaryto consider that during removal of the upsettingforce the reactive moment stops acting as far asclamping device creating this reaction is open.Thus, when a weldement is trying to obtain theprevious geometric shape, the stressed state ispredetermined only by the effect of the force P,directed to the opposite direction to the upsettingforce (Figure 3).