CN103439195B - Method for predicting two-dimensional variable camber bending recovery of small-diameter thick-wall pipe - Google Patents

Abstract

The invention discloses a method for predicting two-dimensional variable camber bending recovery of a small-diameter thick-wall pipe, which is used for solving the technical problem of incapability of two-dimensional variable camber bending recovery of an existing small-diameter thick-wall pipe. According to the technical scheme, the method includes the steps of building a small-diameter thick-wall pipe bending recovery analytical model, performing discretization on the two-dimensional variable camber bent pipe along the axis, establishing a bending recovery radius relation expression by use of approximately pure bending recovery experiment, predicting the discrete bent pipe recovery, simply splicing the recovery predicted discrete bent pipe, and correcting the discrete bent pipe recovery splicing. The method can be used for predicting two-dimensional variable camber bending recovery of the small-diameter thick-wall pipe.

Description

Small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology

Technical field

The present invention relates to a kind of tubing two dimension variable curvature bending springback Forecasting Methodology, particularly relate to a kind of small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology.

Background technology

Small-diameter thick-wall pipe refers to that tube outer diameter is less than 10mm, the tubing that external diameter and wall ratio are less than 20.This pipe structure has intensity, rigidity is high, and saves the feature of material, good looking appearance, has good formed machining performance simultaneously.So based on the hollow structure of various metal pipe material, be widely used in the fields such as Aero-Space, boats and ships, vehicle, petrochemical complex, building and pressure vessel.To inevitably produce certain resilience after bending pipes unloading, have a strong impact on precision and the efficiency of bend pipe production, especially for tubing variable curvature bending forming, resilience problem is more complicated, and the Accurate Prediction of resilience is the prerequisite effectively controlling Spring-back of Pipe Bending defect.

Due to requirements such as design performance, installing space and lightweights, the design shape of pipe fitting also becomes increasingly sophisticated, as at compact airframe and engine interior, category of piping materials and quantity various, the strange complexity of shape (comprising two-dimentional variable curvature configuration), acts on very important again.Because the curved shape of this two-dimentional variable-curvature bent pipe is irregular, there is unevenness feature with tradition compared with determining curvature bending, thus enhance its geometrical non-linearity and boundary nonlinear degree, resilience problem is complicated, seriously adds the difficulty to its research.

At present for variable curvature bending pipes, a kind of bending device for changeable curvature pipe [publication number CN202061958U; Publication date 20111207], realize the bending device and method [CN102489564A of tubing space three-dimensional variable curvature; Publication date 20120613] adopt roller or roller engagement flex mode, can bending forming two dimension variable-curvature bent pipe, but the rebound phenomenon occurred in BENDING PROCESS is furtherd investigate, for Accurate Prediction and control resilience defect and do not do related description.

Category of piping materials is various, and performance requirement is different, and wherein small-diameter thick-wall pipe (tube outer diameter is less than 10mm, and external diameter is less than 20 with wall ratio) bending forming has the advantages that resilience is main forming defects compared with wrinkling, the cross section distortion of breaking.

Summary of the invention

In order to overcome the insurmountable deficiency of existing small-diameter thick-wall pipe two dimension variable curvature rotary draw bending resilience problem, the invention provides a kind of small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology.The method is by setting up the analytic model of small-diameter thick-wall pipe bending springback, by discrete for two-dimentional variable-curvature bent pipe axis, approximate pure bending resilience experiment is utilized to set up bending springback radius relationship formula, discrete Spring-back of Pipe Bending prediction, the discrete bend pipe simple concatenation of springback Prediction, discrete Spring-back of Pipe Bending splicing is revised.Can predict small-diameter thick-wall pipe two dimension variable curvature bending springback.

The technical solution adopted for the present invention to solve the technical problems is: a kind of small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology, is characterized in comprising the following steps:

Step one, carry out Bi_arc fitting and approach, namely press the given a series of orderly shape value point m of bending axis _i, by two tangent circle segmental arc C between every adjacent node _j, C _j+1composition, two arc sections are respectively by given two node m _i, m _i+1, and equal at the slope of this Nodes with variable curvature axis at the tangent slope of Nodes.G1 continuous print multi-section circular arc C is separated into according to bending axis curvature variation _jif, C _j, C _j+1all the time do not meet approximate error, then encrypt shape value point m _i, repeat step one.

Step 2, arc radius according to discrete bending axis, utilize approximate pure bending resilience experimental provision, fixed one end of tubing, the other end rotates an angle around stiff end, make angle of bend reach required numerical value, unload the power acted on bend pipe, the angular dimension after record Spring-back of Pipe Bending.The angle value of experimentation pointer indication is the angle of bend of this bend pipe, and the bend pipe length at the position that bends between two clamps is this section of arc length, therefore pointer indication angle value substitution following formula can be obtained radius value.

$\mathrm{\ρ}=\frac{180L}{\∂\·\mathrm{\π}}$

In formula, L is arc length, unit mm; ρ is arc radius, unit mm; angle of bend, unit °.

Utilize bending radius experimental data before and after cubic polynomial matching Spring-back of Pipe Bending, set up bending radius functional relation before and after resilience

y=a·x ³+b·x ²+c·x+d （1）

In formula, y is the arc radius value after resilience; X is the arc radius value before resilience; A, b, c, d are undetermined coefficients.

Step 3, the arc section radius value x that discrete for step one bending axis is obtained _j, substitute in the formula (1) that obtains of step 2, obtain arc radius y after the discrete arc section resilience of bending axis _j, to guarantee before and after resilience under each arc section end points place G1 continuous print prerequisite, obtaining arc section C before resilience _jcorresponding springback Prediction arc section C ^* _j.

Step 4, guaranteeing before and after initial end resilience under arc section end points place G1 continuous print prerequisite, according to splice point place G1 continuous print principle, completing multistage resilience arc section C ^* _jsplicing, obtain G1 continuous print circular arc spline C ^* _j-C ^* _j+1.

Step 5, theoretical bending axis is separated into limited unit, make this die face center line be Q, form initial sets Q by n unit, it is S that discrete resilience G1 splices the bending axis set obtained continuously, then

Q＝{q _i|q _i∈R ³,1≤i≤n}

S＝{s _i|s _i∈R ³,1≤i≤n}

For node i, by q after the discrete resilience G1 of tubing splices continuously _ibecome s _i, the overall resilience goal set of actual tubing is P, then

P＝{p _i|p _i∈R ³,1≤i≤n}

P＝f(g(A),h(B))＝f(Q,S,h(B)) （2）

In formula, g (A) is the function relevant to tubing physical parameter and Form springback boundary condition, and with Q, S-phase is closed; H (B) is the function relevant to discrete resilience bending axis complexity.

Make w=h (B), then postulation formula (2) becomes

$P=Q+w(S-Q)\⇔p_i=q_i+w_i(s_i-q_i),\∀i---\left(3\right)$

In formula, w is correction function.

Correction function is relevant to axis complexity, is namely characterized by by Curvature varying

$w=\frac{1}{\max \left[{\mathrm{\ρ}}_i\right]}\·\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{l}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{l}_i},i=\mathrm{1,2},...,n---\left(4\right)$

In formula, ρ _iit is arc section bending radius; l _iit is arc section arc length.

Through type (3), formula (4) carry out correction-compensation to bending axis, complete the splicing of discrete Spring-back of Pipe Bending and revise; Ensureing, under the prerequisite that P and Q origin endpoint tangent slope is equal, by getting a method for matching SPL, finally to obtain the fairing bending axis revised.

The invention has the beneficial effects as follows: the method is by setting up the analytic model of small-diameter thick-wall pipe bending springback, by discrete for two-dimentional variable-curvature bent pipe axis, approximate pure bending resilience experiment is utilized to set up bending springback radius relationship formula, discrete Spring-back of Pipe Bending prediction, the discrete bend pipe simple concatenation of springback Prediction, discrete Spring-back of Pipe Bending splicing is revised.Small-diameter thick-wall pipe two dimension variable curvature bending springback is predicted.

Below in conjunction with drawings and Examples, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the inventive method Bi_arc fitting approximating curve.

Fig. 2 is the photo that the inventive method is similar to pure bending resilience experimental provision.

Fig. 3 is the inventive method discrete bending axis springback Prediction and the continuous spliced map of G1.

Fig. 4 is the inventive method discrete bending axis resilience splicing fair curve.

Fig. 5 is the inventive method embodiment alloy steel two dimension variable-curvature bent pipe axis.

Fig. 6 is the inventive method embodiment alloy steel two dimension variable-curvature bent pipe axis discrete curve.

Fig. 7 is that the inventive method embodiment alloy steel two dimension variable-curvature bent pipe axis discrete segments springback Prediction and G1 splice curve continuously.

Fig. 8 is the inventive method embodiment alloy steel two dimension variable-curvature bent pipe bending springback prediction axis.

Embodiment

With reference to Fig. 1-8.The concrete steps of small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology of the present invention are as follows:

For certain alloy steel two dimension variable-curvature bent pipe axis shown in Fig. 5, this bend pipe external diameter 3mm, internal diameter 1mm, the long 120mm of axis.

Specific implementation process is as follows:

1. 3 of this bending axis given orderly shape value point (node) m ₁, m ₂, m ₃, adjacent node m ₁, m ₂between by two tangent circle segmental arc C ₁, C ₂composition, two arc section C ₁, C ₂respectively by given two node m ₁, m ₂, and at node m ₁, m ₂the tangent slope at place is equal at the slope of this Nodes with axis.In like manner, two other tangent circle segmental arc C is obtained ₃, C ₄.This bending axis is separated into G1 continuous print 4 sections of circular arc C ₁-C ₂-C ₃-C ₄, and C ₁, C ₂, C ₃, C ₄being 0.38mm with the maximum approximate error of theoretical axis, meeting error requirements, without the need to encrypting shape value point (node) number, as shown in Figure 6.

2. utilize approximate pure bending resilience experimental provision shown in Fig. 2, choose some sections of straight tubes, one end of tubing is fixed, the other end rotates to an angle around stiff end, make angle of bend reach required numerical value, unload the power acted on bend pipe, the angular dimension after record Spring-back of Pipe Bending, the bend pipe length at position of bending between two clamps in experimentation gets definite value 20mm, substitutes into following formula

$\mathrm{\ρ}=\frac{180L}{\∂\·\mathrm{\π}}$

In formula: L-arc length, get definite value 20mm;

ρ-arc radius (mm);

-angle of bend (°).

Series of arc radius value can be obtained.

Utilize bending radius experimental data before and after cubic polynomial matching Spring-back of Pipe Bending, thus set up bending radius functional relation before and after resilience

y=0.000189x ³+0.006209x ²+1.319866x-2.487030 （1）

In formula: the arc radius value after y-resilience;

Arc radius value before x-resilience.

3. the arc section C discrete bending axis obtained ₁, C ₂, C ₃, C ₄radius value x ₁=61.26mm, x ₂=33.40mm, x ₃=24.40mm, x ₄=19.07mm substitutes in formula (5), and after calculating resilience, arc radius value is respectively y ₁=145.12mm, y ₂=55.57mm, y ₃=36.16mm, y ₄=26.25mm, to guarantee before and after resilience under each arc section end points place G1 continuous print prerequisite, obtains arc section C before resilience ₁, C ₂, C ₃, C ₄corresponding springback Prediction arc section C ^* ₁, C ^* ₂, C ^* ₃, C ^* ₄.

4. arc section C before and after resilience ₁with C ^* ₁initial end m ₁under place G1 continuous print prerequisite, according to each splice point place G1 continuous print principle, complete the splicing of multistage resilience arc section, thus obtain G1 continuous print circular arc spline C ^* ₁-C ^* ₂-C ^* ₃-C ^* ₄, as shown in Figure 7.

5. theoretical bending axis is separated into 56 sections, namely on this die face center line Q, chooses 57 ordered nodes, chooses circular arc spline C simultaneously ^* ₁-C ^* ₂-C ^* ₃-C ^* ₄57 nodes corresponding in S set, then

Q＝{q _i|q _i∈R ³,1≤i≤57}

S＝{s _i|s _i∈R ³,1≤i≤57}

For node i, by q after the discrete resilience G1 of tubing splices continuously _ibecome s _i, and the overall resilience goal set of actual tubing is P, then

P＝{p _i|p _i∈R ³,1≤i≤57}

Correction function w is relevant to axis complexity, is namely characterized by by Curvature varying

$w=\frac{1}{\max \left[{\mathrm{\ρ}}_i\right]}\·\frac{\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{l}_i}{\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{l}_i}=0.59$

In formula, ρ _i-arc section bending radius, ρ ₁=61.26mm, ρ ₂=33.40mm, ρ ₃=24.40mm, ρ ₄=19.07mm;

L _i-arc section arc length, l ₁=35.75mm, l ₂=31.40mm, l ₃=23.09mm, l ₄=29.97mm.

Substitute into

$P=Q+w(S-Q)\⇔p_i=q_i+w_i(s_i-q_i),\∀i$

Calculate P={p _i| p _i∈ R ³, 1≤i≤57}, under the prerequisite ensureing P and Q origin endpoint tangent slope equal (G1 is continuous), by getting a method for matching SPL, finally obtains the fairing bending axis P revised, as shown in Figure 8.Thus complete this alloy steel small-diameter thick-wall pipe two dimension variable curvature bending springback prediction, namely when the theoretical shape of this two-dimentional variable-curvature bent pipe axis is Q, after unloading spring-back, its axis shape is actual is P.

Claims (1)

1. a small-diameter thick-wall pipe two dimension variable curvature bending springback Forecasting Methodology, is characterized in that comprising the following steps:

Step one, carry out Bi_arc fitting and approach, namely press the given a series of orderly shape value point m of bending axis _i, by two tangent circle segmental arc C between every adjacent node _j, C _j+1composition, two arc sections are respectively by given two node m _i, m _i+1, and equal at the slope of this Nodes with variable curvature axis at the tangent slope of Nodes; G1 continuous print multi-section circular arc C is separated into according to bending axis curvature variation _jif, C _j, C _j+1all the time do not meet approximate error, then encrypt shape value point m _i, repeat step one;

Step 2, arc radius according to discrete bending axis, utilize approximate pure bending resilience experimental provision, fixed one end of tubing, the other end rotates an angle around stiff end, make angle of bend reach required numerical value, unload the power acted on bend pipe, the angular dimension after record Spring-back of Pipe Bending; The angle value of experimentation pointer indication is the angle of bend of this bend pipe, and the bend pipe length at the position that bends between two clamps is this section of arc length, therefore pointer indication angle value substitution following formula can be obtained radius value;

$\mathrm{\ρ}=\frac{180L}{\∂\·\mathrm{\π}}$

In formula, L is arc length, unit mm; ρ is arc radius, unit mm; angle of bend, unit °;

Utilize bending radius experimental data before and after cubic polynomial matching Spring-back of Pipe Bending, set up bending radius functional relation before and after resilience

y＝a·x ³+b·x ²+c·x+d (1)

In formula, y is the arc radius value after resilience; X is the arc radius value before resilience; A, b, c, d are undetermined coefficients;

Step 3, the arc section radius value x that discrete for step one bending axis is obtained _j, substitute in the formula (1) that obtains of step 2, obtain arc radius y after the discrete arc section resilience of bending axis _j, to guarantee before and after resilience under each arc section end points place G1 continuous print prerequisite, obtaining arc section C before resilience _jcorresponding springback Prediction arc section

Step 4, guaranteeing before and after initial end resilience under arc section end points place G1 continuous print prerequisite, according to splice point place G1 continuous print principle, completing multistage resilience arc section splicing, obtain G1 continuous print circular arc spline

Step 5, theoretical bending axis is separated into limited unit, makes this die face center line be Q, form initial sets Q by n unit, discrete resilience G1 splices continuously and obtains bending axis S set, then

Q＝{q _i|q _i∈R ³,1≤i≤n}

S＝{s _i|s _i∈R ³,1≤i≤n}

For node i, by q after the discrete resilience G1 of tubing splices continuously _ibecome s _i, the overall resilience goal set of actual tubing is P, then

P＝{p _i|p _i∈R ³,1≤i≤n}

P＝f(g(A),h(B))＝f(Q,S,h(B)) (2)

In formula, g (A) is the function relevant to tubing physical parameter and Form springback boundary condition, and with Q, S-phase is closed; H (B) is the function relevant to discrete resilience bending axis complexity;

Make w=h (B), then postulation formula (2) becomes

$P=Q+w(S-Q)\⇔p_i=q_i+w_i(s_i-q_i),\∀i---\left(3\right)$

In formula, w is correction function;

Correction function is relevant to axis complexity, is namely characterized by by Curvature varying

$w=\frac{1}{\max \left[{\mathrm{\ρ}}_i\right]}\·\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{l}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{l}_i},i=\mathrm{1,2},...,n---\left(4\right)$

In formula, ρ _iit is arc section bending radius; l _iit is arc section arc length;

Through type (3), formula (4) carry out correction-compensation to bending axis, complete the splicing of discrete Spring-back of Pipe Bending and revise; Ensureing, under the prerequisite that P and Q origin endpoint tangent slope is equal, by getting a method for matching SPL, finally to obtain the fairing bending axis revised.