EP0461006A1 - Method and apparatus for bending tubes - Google Patents

Abstract

The technical field of the present invention is that of devices intended for bending pipes. <??>The invention relates to a pipe-bending shoe, of cylindrical shape, from the lateral surface of which a groove is hollowed out whose cross-section is a semi-circle of diameter equal to the diameter of a pipe to be bent, characterised in that the base of the cylinder is delimited, on the one hand, by a logarithmic spiral portion defined in polar coordinates by the formula equation (1) P = Poe<-k> theta , portion delimited by the points theta  = 0 and theta  = 2 pi , and in which P0 and k are positive constants and, on the other hand, by a straight segment joining the points of the spiral for which theta  = 0 and theta  = 2 pi . <??>Application to the accurate bending of pipework. <IMAGE>

Description

The present invention relates to a device for bending pipes. More specifically, the invention relates to shoes for bending pipes and to the method of using the shoe according to the invention.

Il en résulte que si l'on veut cintrer une tuyauterie avec précision d'un angle β, le rayon de courbure étant R, il faut utiliser un sabot de cintrage plus petit que R. Il se trouve que le surcintrage β est lui-même une fonction croissante de l'angle β de telle sorte que plus on veut cintrer d'un angle important, plus, pour conserver le même rayon de courbure, le rayon du sabot à utiliser doit être petit. Ce phénomène étant connu on utilise jusqu'à présent pour chaque rayon de cintrage des jeux de sabots et par exemple on peut, pour obtenir un rayon R donné pour des cintrages compris entre 0 et 30°, utiliser un sabot circulaire de rayon R1 tel que R1 < R, puis pour cintrer entre 30° et 60° un sabot de rayon R2 , R2 < R1 et ainsi de suite jusqu'à obtenir la gamme complète des cintrages que l'on souhaite réaliser. Les rayons R1, R2 des sabots que l'on utilise pour les différentes sous-gammes sont déterminés par expérimentation sur des échantillons représentatifs des tuyaux que l'on veut cintrer.To bend a pipe with a bending angle β, a bending shoe mounted on a bender is used. Such shoes have the shape of cylinders, the base surface of which is a circle and the lateral surface of which has a groove, the cross section of which is a semicircle with a diameter equal to the outside diameter of the pipe to be bent. We apply the pipe against the shoe at the level of the groove of the lateral surface and we turn the pipe by an angle, greater than β, equal to (β + α) because we know that after relaxation it will undergo a elastic deformation tending to reduce bending. In the remainder of the text, the permanent bending which it is desired to obtain will be denoted β and the over-bending, that is to say the additional angle whose pipe must be turned around the shoe to obtain the permanent bending β, will be denoted α . For all practical purposes, it is recalled that the bending of a pipe is the angle formed by the neutral fibers of two consecutive straight parts of a pipe, the neutral fiber itself being the geometric location of the centers of the straight sections of the pipe. . The bending radius is the radius of the arc of circumference of the neutral fiber between two consecutive straight parts. The curve described by the neutral fiber between two straight parts may not be a circumference, in this case the mean radius R of bending will be defined by the ratio S / β in which S is the length of the curve between two straight parts, and β the bending. When bending a pipe on a circular shoe of radius R, it is wound as explained above by an angle greater than the angle β, the winding angle then being β + α. In this way the radius of curvature after the elastic deformation is larger it becomes: $$\text{R + Δ R =}\frac{\text{β + α}}{\text{β}}\text{. R = R (1 +}\frac{\text{α}}{\text{β}}\text{)}$$

It follows that if one wants to bend a pipe with precision by an angle β, the radius of curvature being R, it is necessary to use a bending shoe smaller than R. It turns out that the overbending β is itself an increasing function of the angle β so that the more you want to bend a large angle, the more, to keep the same radius of curvature, the radius of the shoe to be used must be small. As this phenomenon is known, hoof sets have been used up to now for each bending radius, and for example it is possible, to obtain a given radius R for bending between 0 and 30 °, using a circular shoe of radius R1 such that R1 <R, then to bend a shoe of radius R2, R2 <R1 between 30 ° and 60 ° and so on until obtaining the full range of bends that one wishes to achieve. The radii R1, R2 of the shoes that are used for the different sub-ranges are determined by experimentation on representative samples of the pipes that we want to bend.

The state of the art as just described is illustrated in FIGS. 1 and 2.

In Figure 1 we see a circular shoe 1 on which by means of a jaw 2 is applied the pipe 3. The latter is wound by means of the jaw 2 of an angle (β + α) 4 equal to the angle 5 that the neutral fiber segments 6 located on either side of the hanger do between them.

FIG. 1 illustrates the first phase of pipe forming, the second phase will consist in advancing the pipe by a length Δ L, possibly turning it on itself, to achieve a bend and then to perform the following bending with possible change of shoe if the desired bending angle for the next hanger requires a shoe of different radius.

Figure 2 illustrates the new position of the pipe at the end of phase 2 we essentially see the pipe 3 and its neutral fiber 6 comprising two segments on either side of the hanger, due to the elastic deformation these two segments form between them an angle 7 in principle equal to β if the overcut α has been well chosen.

This state of the art has two drawbacks: on the one hand, it requires changing the shoe each time one passes from one bending range to another, on the other hand it leaves an error on the radius of curvature and / or on the bending due to the fact that the changes in shoe radius (R1, R2 ...) are discontinuous. This error can be significant and unacceptable in the case of piping intended to be housed in large numbers in cramped locations such as submarine hulls. Part of the error comes from the bending tool, the circular shoe, whose radius varies only by jumps, another part comes from the lack of knowledge that we have, of the overcuts α to apply.

The object of the invention is to remedy the aforementioned drawbacks on the one hand by a bending shoe whose mean bending radius is continuously variable and, on the other hand, by a method of using said shoe making it possible to produce bends for which the necessary overbends are better appreciated.

To this end, the subject of the invention is a shoe for bending pipes, in the form of a cylinder from the lateral surface of which a groove is hollowed out, the cross section of which is a semicircle of diameter equal to the diameter of the pipe to be bent, characterized in that the base of the cylinder is delimited, on the one hand, by a portion of logarithmic spiral defined in polar coordinates by the equation P = P₀ e ^-kϑ (1), portion delimited by the points ϑ = 0 and ϑ = 2 π, and in which P₀ and k are positive constants and, on the other hand, by a line segment joining the points of the spiral for which ϑ = 0 and ϑ = 2 π.

lorsque ϑ = 0 à la valeur $\text{R2 = P₀}\sqrt{\text{1 + k²}}{\text{e}}^{\text{-k2π}}$

lorsque ϑ = 2π. Un sabot ayant ce pourtour offre donc la possibilité d'obtenir des rayons de courbure moyens pour le cintrage des tuyaux, variables de façon continue entre deux limites comprises dans l'intervalle entre R1 et R2.The equation curve (1) is a logarithmic spiral. This curve has the property that the radius of curvature decreases steadily in a continuous manner $\text{R1 = P₀}\sqrt{\text{1 + <figure-callout id="2" label="k" filenames="imgf0001.png" state="{{state}}">k</figure-callout> ²}}$

when ϑ = 0 to the value $\text{R2 = P₀}\sqrt{\text{1 + k²}}{\text{e}}^{\text{-k2π}}$

when ϑ = 2π. A shoe having this periphery therefore offers the possibility of obtaining average radii of curvature for bending the pipes, which are continuously variable between two limits included in the interval between R1 and R2.

de telle sorte qu'après relaxation d'un angle α le rayon de courbure soit justement égal à R.If the limits R1 and R2 are well chosen it will always be possible to find a portion on the spiral between two vector radii forming between them the angle β + α and such that the mean radius of curvature of this portion is equal to $$\text{R - ΔR =}\frac{\text{β}}{\text{β + α}}\text{R}$$

so that after relaxation of an angle α the radius of curvature is precisely equal to R.

• la figure 3 représente une spirale logarithmique et est destinée à illustrer le principe, les avantages de l'invention et le mode de détermination des dimensions du sabot en fonction des caractéristiques des tuyaux à cintrer,
• la figure 4 est une vue de dessus d'un exemple particulier de sabot réalisé selon l'invention,
• la figure 5 est une vue latérale du même exemple particulier.

Other characteristics and advantages of the invention will emerge from the following description made with reference to the appended drawings in which:

• FIG. 3 represents a logarithmic spiral and is intended to illustrate the principle, the advantages of the invention and the method of determining the dimensions of the shoe as a function of the characteristics of the pipes to be bent,
• FIG. 4 is a top view of a particular example of a shoe produced according to the invention,
• Figure 5 is a side view of the same particular example.

Figure 3 represents a portion of logarithmic spiral (8) according to the equation: $${\text{P = P₀ e}}^{\text{-kϑ}}$$

It goes from point B to point A when the angle ϑ varies from 0 to 2π.

$$\text{P₁ est égal à OA}$$

The center of the polar coordinates is shown by point 0. $$\text{P₀ is equal to OB}$$

$$\text{P₁ is equal to OA}$$

P₀ being fixed P₁ is a function of the coefficient k.

• tout d'abord on détermine sur une gamme d'échantillons représentative des tuyaux de diamètre D à cintrer sur le sabot, les surcintrages α correspondant aux cintrages β souhaités. Pour des rayons de courbure compris entre 2,5D et 3D (cas le plus courant). On peut retenir que le surcintrage peut être déterminé par l'équation linéaire : $$\text{β = a+bβ}$$
  
  où a et b sont des constantes. Par exemple pour un tuyau de diamètre 30 mm, "a" peut être compris entre 1 et 6° et "b" peut varier entre 0,02 et 0,05. Il est utile de noter pour la suite de l'exposé que a et b sont des valeurs moyennes pour une même catégorie de tuyaux réalisés dans la même matière. Ces valeurs sont comprises entre deux valeurs butées a1, a2 et b1, b2. Ces valeurs butées peuvent être assez éloignées l'une de l'autre et l'on ne connaît pas a priori la valeur à retenir pour effectuer un cintrage particulier.
  Ces valeurs sont différentes le long d'un même tuyau ceci en raison du manque d'homogénéité de la matière et surtout en raison de l'ovalisation variable du tuyau. Le fait que le sabot permet une variation en continu du rayon de courbure et donc une meilleure précision au niveau du rayon de courbure rend possible et avantageux un procédé de cintrage qui sera décrit plus loin où l'on tient compte des résultats obtenus sur les cintrages précédents pour effectuer le cintrage suivant.
  Les plages a1, a2 - b1, b2 et les valeurs moyennes a et b étant connues P₀ et k sont déterminés par le calcul de la façon suivante :
• soit R le rayon de courbure que l'on souhaite obtenir. On sait que : $$\text{R = S/β}$$
  
  Dans cette équation S est la longueur de l'arc de spirale MoM1 (fig. 3) compris entre les rayons vecteurs déterminés par les angles ϑ₀ et (ϑ₀ + β + α).

The periphery of the hoof will be entirely determined when P₀ and k have been fixed. How to proceed will be examined below:

• firstly, over a range of samples representative of pipes of diameter D to be bent on the shoe, the overcuts α corresponding to the desired bends β are determined. For radii of curvature between 2.5D and 3D (the most common case). It can be remembered that the overcrowding can be determined by the linear equation: $$\text{β = a + bβ}$$
  
  where a and b are constants. For example, for a 30 mm diameter pipe, "a" can be between 1 and 6 ° and "b" can vary between 0.02 and 0.05. It is useful to note for the remainder of the description that a and b are average values for the same category of pipes made of the same material. These values are between two stop values a1, a2 and b1, b2. These stop values can be quite far from each other and we do not know a priori the value to be used to perform a particular bending.
  These values are different along the same pipe this because of the lack of homogeneity of the material and especially because of the variable ovalization of the pipe. The fact that the shoe allows a continuous variation of the radius of curvature and therefore a better precision at the level of the radius of curvature makes possible and advantageous a bending process which will be described below where account is taken of the results obtained on bending previous steps to perform the next bend.
  The ranges a1, a2 - b1, b2 and the average values a and b being known P₀ and k are determined by the calculation as follows:
• let R be the radius of curvature that we wish to obtain. We know that : $$\text{R = S / β}$$
  
  In this equation S is the length of the spiral arc MoM1 (fig. 3) between the vector radii determined by the angles ϑ₀ and (ϑ₀ + β + α).

The length of MoM1 is for an angle β given a function of Po, k, and also of ϑo which determines the point of the spiral from which one begins to bend. When Po and k are fixed, that is to say when using a determined shoe, the length of MoM1 is only a function of ϑ₀. It is therefore advisable to ensure during the fixing of P₀ and k that equation (2) will always have a solution in ϑ₀ such that the corresponding point Mo is indeed on a point of the curve 8 that is to say that we need a solution 0 <ϑ₀ <2π.

This simple condition is not enough it is still necessary that from the point Mo defined by the angle ϑ₀, it is possible to bend by an angle (β + α) while remaining along the curve (8). This condition will always be fulfilled for large bending angles for which it is always advantageous to choose angles for the start of small bending, that is to say close to ϑ = 0.

On the other hand, for low bending angles it will be necessary for ϑ₀ to meet the condition: ϑ₀ <2π - (β _m + α _m + γ) in which γ is defined by the fact that the angle 2π - γ corresponds to point M6 of curve 8, point for which the tangent to curve 8 passes through point B. (For the convenience of the drawing this point has been represented in FIG. 4). The introduction of the angle γ is necessary so as not to be hampered by the drop in the curve 8 in the vicinity of ϑ = 0.

$$\text{R =}\frac{\text{1}}{{\text{β}}_{\text{M}}}\frac{\sqrt{\text{1 + k²}}}{\text{k}}{\text{P₀ e}}^{\text{-kϑM}}{\text{( e}}^{\text{-k(βM+αM)}}\text{- 1 )}$$

We therefore proceed as follows: we know the minimum bending β _m that we want to achieve, this bending corresponds to an over-bending α _m and a bend start angle ϑ _m . The points of the spiral 8 corresponding to ϑ _m and (ϑ _m + β _m + α _m ) are represented by M2 and M3. We also know the maximum bending that we want to achieve is β _m which corresponds to an overbending α _M and a bending start angle ϑ _M. The points of the spiral 8 corresponding to the angles ϑ _M and (ϑ _M + α _M + β _M ) are represented by M4 and M5. For the two values of β, equation (2) above becomes by calculating M2M3 and M4M5 according to conventional methods, $$\text{R =}\frac{\text{1}}{{\text{β}}_{\text{m}}}\frac{\sqrt{\text{1 + k²}}}{\text{k}}{\text{P₀ e}}^{\text{-kϑm}}{\text{(e}}^{\text{-k (βm + αm)}}\text{- 1)}$$

$$\text{R =}\frac{\text{1}}{{\text{<figure-callout id="1" label="β M" filenames="imgf0001.png,imgf0003.png" state="{{state}}">β </figure-callout>}}_{\text{M}}}\frac{\sqrt{\text{1 + k²}}}{\text{k}}{\text{P₀ e}}^{\text{-kϑM}}{\text{(e}}^{\text{-k (βM + αM)}}\text{- 1)}$$

The division of these 2 member-to-member equations leads to an equation (6) where only k is: $$\text{(6) 1 =}\frac{{\text{β}}_{\text{m}}}{{\text{β}}_{\text{M}}}{\text{e}}^{\text{-k (ϑM-ϑm)}}\frac{{\text{e}}^{\text{-k (βM + αM)}}\text{- 1}}{{\text{e}}^{\text{-k (βm + αm)}}\text{- 1}}$$

The coefficient k is small because the necessary spiral taking into account the usual values of the over-bending is close to a circle. Under these conditions we can use the first degree of the limited development of the expression e ^x , e ^x ≈ 1 + x.

With this approximation we get: $$\text{(7) k =}\frac{\text{1}}{{\text{ϑ}}_{\text{M}}{\text{-ϑ}}_{\text{m}}}\text{(1 -}\frac{{\text{β}}_{\text{m}}{\text{+ α}}_{\text{m}}}{{\text{β}}_{\text{M}}{\text{= α}}_{\text{M}}}\text{·}\frac{{\text{β}}_{\text{M}}}{{\text{β}}_{\text{m}}}\text{)}$$

ϑ _M is the bending start angle for the maximum bending β _M. For large angles ΔR is small, we are therefore close to the large vector rays of the spiral, therefore close to the angles close to O, ϑ _M must be small, the only criterion to be taken into account is not to be hampered by the setback of curve 8 for ϑ = O.

ϑ _m is the bending start angle for minimum bending, therefore corresponding to radii of curvature of the small shoe. ϑ _m must therefore be as large as possible but nevertheless less than (2π - (β _m + α _m + γ)) so that it is still possible to bend the angle (β _m + α _m ) without being hindered by the drop in curve 8 in the vicinity of ϑ = O

Taking for example

We obtain the following values of k as a function of a and b

on trouve $$\text{P₀ = 0,97 R et}$$

$$\text{P₁ = 0,82 P₀}$$

The value of P₀ is obtained by carrying over the value of k in one of equations (4) or (5)

we find $$\text{P₀ = 0.97 R and}$$

$$\text{P₁ = 0.82 P₀}$$

We see that P₀ is little different from R, so we can also set P₀ = R and determine k by setting the minimum value of the bending angle that we will achieve on the shoe by replacing P₀ by R in the equation (4) above.

The particular embodiment shown in top view in FIG. 4 and in side view in FIG. 5 was carried out according to this latter mode.

It is a shoe intended to bend pipes of diameter D = 30 mm with a bending radius R = 2.9 D or 87 mm. It is therefore the value chosen for P₀ of the spiral 8. This shoe makes it possible to bend pipes for which a is between 1 ° and 2 °, b being variable from 0.01 to 0.05. The coefficient k being in this case equal to 0.008. The groove 9 hollowed out from the lateral surface also has a spiral shape.

The bore 10 is conventionally intended for adaptation on a bender. The opposite faces 11 and 12 have angular graduations which are not shown.

The values in cm of the vector radius of the spiral 8 are indicated below for values of ϑ from 0 to 350 ° in steps of 10 °. The values of the vector radius corresponding to the bottom of the groove are deduced from the first by subtraction of 1.5 cm.

The procedure for using this shoe is as follows:

• l'angle α₁ + β₁
• l'angle de début de cintrage ϑ₁
• l'angle de fin de cintrage ϑ₁ + α₁ + β₁
• les plages de variation de chacun de ces trois angles.

Having determined by sampling the coefficients a and b relative to the pipes to be bent as well as their ranges of variation a1 a2, b1 b2 we create a table giving for each value of B

• the angle α₁ + β₁
• the bend start angle ϑ₁
• the end of bending angle ϑ₁ + α₁ + β₁
• the ranges of variation of each of these three angles.

The shoe being graduated in the same unit as the table, the hose is wound on the shoe from the angle ϑ₁, to the angle ϑ₁ + β₁ + α₁. In this way the neutral fiber of the pipe has turned well from the angle β₁ + α₁, since the spiral has the property that the tangent at a point of the spiral makes with the corresponding vector radius a constant angle.

After relaxation, the error Δβ₁ is measured, this error is used when it is negative to correct by adding Δβ₁, the bending which has just been carried out and in all cases to refine the value of the overbending according to β₂ by taking $$\text{Δβ₂ = Δβ₁}\frac{\text{β₂}}{\text{β₁}}$$

For the following bending, the correction made on β₃ will be deduced by linear extrapolation of the errors noted during the two previous bends.

Claims (6)

1 - Pipe bending shoe, in the form of a cylinder from the lateral surface from which a groove is hollowed out, the cross section of which is a semicircle of diameter equal to the diameter of the pipe to be bent, characterized in that the base of the cylinder is delimited, on the one hand, by a portion of logarithmic spiral defined in polar coordinates by the equation of formula (1) P = Poe-kϑ, portion delimited by the points ϑ = 0 and ϑ = 2π, and in which Po and k are positive constants and, on the other hand, by a line segment joining the points of the spiral for which ϑ = 0 and ϑ = 2π. 2 - Shoe according to claim 1 characterized in that the value of the coefficient k is determined as a function of the minimum angles β _m and maximum β _M that it is desired to obtain, of the corresponding angles of overcut α _m and α _M and of start of bending ϑ _m and ϑ _M by the formula: $$\text{k =}\frac{\text{1}}{{\text{ϑ}}_{\text{M}}{\text{-ϑ}}_{\text{m}}}\text{(1 -}\frac{{\text{β}}_{\text{m}}{\text{+ α}}_{\text{m}}}{{\text{β}}_{\text{M}}{\text{+ α}}_{\text{M}}}\text{·}\frac{{\text{β}}_{\text{M}}}{{\text{β}}_{\text{m}}}\text{)}$$

3 - Shoe according to claim 2 characterized in that the value of Po is determined by equation 4

in which R represents the desired radius of curvature. 4 - Shoe according to claim 1 characterized in that the module P₀ is equal to the radius of curvature R that one wishes to obtain. 5 - Shoe according to claim 4 characterized in that the coefficient k is determined by the formula $$\text{1 =}\frac{\text{1}}{{\text{β}}_{\text{m}}}\frac{\sqrt{\text{1 + k²}}}{\text{k}}{\text{e}}^{\text{-kϑm}}{\text{(e}}^{\text{-k (βm + αm}}\text{) - 1)}$$

6 - Bending process using the device according to claim 1 characterized in that one uses the errors found on the previous bends to correct the next bending by linear extrapolation of these errors.

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