CN104985007B - Prediction method for flaw length of Cu-Al sandwich rolling-bonded band head - Google Patents

Abstract

The invention provides a prediction method for the flaw length of a Cu-Al sandwich rolling-bonded band head. The prediction method comprises the following steps: obtaining the parameters of a prediction model for the flaw length of the Cu-Al sandwich rolling-bonded band head, and according to the parameters of the prediction model for the flaw length of the Cu-Al sandwich rolling-bonded band head, obtaining the thickness of a rolling-bonded initial band material, the half-thickness of the rolling-bonded initial band material, the thickness of an initial upper-layer band material, the half-thickness of an initial inner-layer band material and the half-thickness of a rolling-bonded final band material; obtaining a pass reduction rate according to the thicknesses of a rolling bonding outlet and a rolling bonding inlet; and obtaining the predicted flaw length of the band head through establishing the prediction model for the flaw length of the Cu-Al sandwich rolling-bonded band head and substituting the parameters of the prediction model for the flaw length of the Cu-Al sandwich rolling-bonded band head into the prediction model for the flaw length of the Cu-Al sandwich rolling-bonded band head. Therefore, the flaw length of the bonded band head can be predicted; as a result, the yield can be greatly increased, and unnecessary cutting losses are reduced.

Description

A kind of copper aluminium sandwich Rolling compund takes the lead the Forecasting Methodology of defect length

Technical field：

The present invention relates to copper aluminium sandwich Rolling compund takes the lead failure prediction field, more particularly to a kind of copper aluminium sandwich rolls The compound Forecasting Methodology for taking the lead defect length of system.

Background technology：

In industrial Solder for Al-Cu Joint Welding-aluminium sandwich Rolling compund, because aluminium strip is soft compared with copper strips matter, therefore aluminium strip can take the lead in becoming Shape, and along rolling direction produce it is certain extend, simultaneously as during rolling, the position of copper strips between two-layer aluminium strip, not with it is upper Lower two roll directly contacts, so copper strips had certain Relative sliding before compound, this is accomplished by lacking taking the lead of being combined Sunken length is predicted.

However, in actual production, the Forecasting Methodology that major part is used is the empirical equation without theoretical foundation, may Reduce the compound accuracy prediction yield taken the lead, or bring and unnecessary cut damage.

The content of the invention：

For the defect of prior art, the present invention provides the prediction that a kind of copper aluminium sandwich Rolling compund takes the lead defect length Method, can take the lead defect length and be predicted to compound, and then significantly improving yield and reduces and unnecessary cut damage.

The present invention provides the Forecasting Methodology that a kind of copper aluminium sandwich Rolling compund takes the lead defect length, including：

S1, acquisition copper aluminium sandwich Rolling compund take the lead the parameter of defect length forecast model, including：

Roll the upper strata metal thickness H of each band to be composite₁, middle layer metal thickness H₂With lower metal thickness H₃, rolling is again Close the thickness H of final band₀；

Outer layer metal initial tension σ_1iWith inner layer metal initial tension σ_2i；

The coefficient of friction of live roller radius R, roll surface and aluminum bronze, m₁And m₂；

S2, the parameter that defect length forecast model is taken the lead according to the copper aluminium sandwich Rolling compund, obtain Rolling compund The thickness H of initial band_i=H₁+H₂+H₃, the initial band of Rolling compund half thickness h_i=H_i/ 2, the thickness of initial upper layer band h_1i=H₁, initial internal layer band half thickness h_2i=H₂/ 2, the half thickness h of the final band of Rolling compund₀=H₀/2；

S3, according to the gateway thickness of Rolling compund, obtain percentage pass reduction r=(H_i-H₀)/H₀；

S4, set up copper aluminium sandwich Rolling compund and take the lead defect length forecast model, copper aluminium sandwich rolling is multiple The parameter of crossed belt head defect length forecast model is brought the copper aluminium sandwich Rolling compund into and takes the lead defect length forecast model, is obtained Defect length is taken the lead to prediction；

The copper aluminium sandwich Rolling compund takes the lead defect length forecast model, is calculated by following formula,

△ D=△ E- △ S

Wherein, △ D are the defect length of taking the lead of Rolling compund, and △ E are front outer layer metal extended distance, and △ S are internal layer gold Category skidding distance；

The front outer layer metal extended distance △ E, are calculated by following formula,

Wherein, x_AFor A in rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position of area's entrance, x_BFor B in rolling contact arc projection straight line₁、B₂And B₃Position at the corresponding common speed in compound beginning and inside and outside metal, h_1BBe x_BThe half thickness of place's outer layer band,

The inner layer metal skidding distance △ S, are calculated by following formula,

Wherein, β₀For outer layer after Rolling compund and the ratio of the thickness of internal layer.

Alternatively, A in the rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position of area's entrance x_A, calculated by following formula,

Alternatively, B in the rolling contact arc projection straight line₁、B₂And B₃Corresponding compound beginning and inside and outside metal Position x at common speed_B, calculated by following formula,

Wherein, k₂For internal layer band resistance of deformation, p_IIt is to work as x=x_BRolling compression in I regions causes outer layer metal to produce Raw surrender,For the integral constant of inner layer metal tension, τ_mFor the shear stress between metal and metal；

It is described to work as x=x_BRolling compression in I regions causes the surrender p that outer layer metal is produced_I, calculated by following formula,

Wherein,B_I=4k₁, D₁=2R (h_iβ_i+h₀-h_i), E_I=2R (- τ₁-τ_m), τ₁=k₁m₁,For product Divide constant,k₁It is anti-for outer layer deformation of strip Power, β_iFor outer layer before Rolling compund and the ratio of the thickness of internal layer；

The integral constant of the inner layer metal tensionCalculated by following formula,

Shear stress τ between the metal and metal_m, calculated by following formula,

τ_m=k₂m₂。

As shown from the above technical solution, a kind of copper aluminium sandwich Rolling compund of the invention takes the lead the prediction side of defect length Method, including：The parameter that copper aluminium sandwich Rolling compund takes the lead defect length forecast model is obtained, and according to the copper aluminium sandwich Rolling compund takes the lead the parameter of defect length forecast model, obtains thickness, the Rolling compund initial strip of the initial band of Rolling compund The half thickness of the half thickness of material, the thickness of initial upper layer band, the half thickness of initial internal layer band and the final band of Rolling compund, According to the gateway thickness of Rolling compund, percentage pass reduction is obtained, to take the lead defect long by setting up copper aluminium sandwich Rolling compund Degree forecast model, brings the parameter that the copper aluminium sandwich Rolling compund takes the lead defect length forecast model into described copper aluminium Sanming City Control Rolling compund and take the lead defect length forecast model, obtain predict take the lead defect length, thereby, it is possible to be combined take the lead lack Sunken length is predicted, and then significantly improving yield and reduces and unnecessary cut damage.

Description of the drawings：

Fig. 1 takes the lead the Forecasting Methodology flow process of defect length for the copper aluminium sandwich Rolling compund that one embodiment of the invention is provided Schematic diagram；

The Copper-Aluminum compound schematic diagram that Fig. 2 is provided for one embodiment of the invention；

Fig. 3 symmetrically models schematic diagram for the rolling 1/2 that one embodiment of the invention is provided；

The rolling subregion schematic diagram that Fig. 4 is provided for one embodiment of the invention；

The I areas force analysis schematic diagram that Fig. 5 is provided for one embodiment of the invention；

The defect length schematic diagram that Fig. 6 is provided for one embodiment of the invention；

The II areas force analysis schematic diagram that Fig. 7 is provided for one embodiment of the invention；

The III areas force analysis schematic diagram that Fig. 8 is provided for one embodiment of the invention.

Specific embodiment：

With reference to the accompanying drawings and examples, the specific embodiment of the present invention is described in further detail.Hereinafter implement Example is not limited to the scope of the present invention for illustrating the present invention.

Fig. 1 shows that the copper aluminium sandwich Rolling compund that one embodiment of the invention is provided takes the lead the Forecasting Methodology of defect length Schematic flow sheet, as shown in figure 1, the method for the present embodiment is as described below.

101st, the parameter that copper aluminium sandwich Rolling compund takes the lead defect length forecast model is obtained.

In this step, Fig. 2 shows the Copper-Aluminum compound schematic diagram that one embodiment of the invention is provided, as shown in Fig. 2 being up and down Two rolls, centre is respectively Solder for Al-Cu Joint Welding-aluminium three-layer metal, and above-mentioned copper aluminium sandwich Rolling compund takes the lead defect length prediction mould The parameter of type, specifically includes：

Roll the upper strata metal thickness H of each band to be composite₁, middle layer metal thickness H₂With lower metal thickness H₃, rolling is again Close the thickness H of final band₀；

Outer layer metal initial tension σ_1iWith inner layer metal initial tension σ_2i；

The coefficient of friction of live roller radius R, roll surface and aluminum bronze, m₁And m₂；

In actual applications, the thickness of each band that will be combined is obtained according to the calibrator measurement of each metallic coil of entrance Degree, upper strata metal thickness H₁, middle layer metal thickness H₂With lower metal thickness H₃, detected according to entrance tension force, measurement entrance Power, including outer layer metal initial tension σ_1iWith inner layer metal initial tension σ_2i, rolled according to the thickness gauge measurement of rolling outlet The compound final thickness of strip H of system₀, according to on-site actual situations roller radius R, and the friction system of roll surface and aluminum bronze are determined Number, m₁And m₂。

102nd, the parameter of defect length forecast model is taken the lead according to the copper aluminium sandwich Rolling compund, Rolling compund is obtained The thickness H of initial band_i=H₁+H₂+H₃, the initial band of Rolling compund half thickness h_i=H_i/ 2, the thickness of initial upper layer band h_1i=H₁, initial internal layer band half thickness h_2i=H₂/ 2, the half thickness h of the final band of Rolling compund₀=H₀/2。

In this step, it should be noted that because the operation of rolling is a full symmetric process, so desirable sandwich rolls Half side for research object in system, Fig. 3 shows rolling 1/2 that one embodiment of the invention provides symmetrically modeling schematic diagram, such as Fig. 3 institutes Show, x-axis is the rightabout of rolling, and y-axis is for straight up, initial outer layer metal thickness is h_1i, initial inner layer metal is partly Thickness is h_2i, roll is R, and the contact arc length projected length of rolling is l, and the outer layer metal thickness after rolling is h₁₀, terminate Inner layer metal half thickness is h₂₀, σ_1iAnd σ_2iThe tension of respectively initial outer layer and inner layer metal, σ₀For final composite strip Tension.

103rd, according to the gateway thickness of Rolling compund, percentage pass reduction r=(H are obtained_i-H₀)/H₀。

104th, set up copper aluminium sandwich Rolling compund and take the lead defect length forecast model, copper aluminium sandwich rolling is multiple The parameter of crossed belt head defect length forecast model is brought the copper aluminium sandwich Rolling compund into and takes the lead defect length forecast model, is obtained Defect length is taken the lead to prediction.

In this step, the copper aluminium sandwich Rolling compund takes the lead defect length forecast model, is calculated by following formula,

△ D=△ E- △ S

Wherein, △ D are the defect length of taking the lead of Rolling compund, and △ E are front outer layer metal extended distance, and △ S are internal layer gold Category skidding distance；

The front outer layer metal extended distance △ E, are calculated by following formula,

Wherein, x_AFor A in rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position of area's entrance, x_BFor B in rolling contact arc projection straight line₁、B₂And B₃Position at the corresponding common speed in compound beginning and inside and outside metal, h_1BBe x_BThe half thickness of place's outer layer band,

The inner layer metal skidding distance △ S, are calculated by following formula,

Wherein, β₀For outer layer after Rolling compund and the ratio of the thickness of internal layer.

Further, A in the rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position of area's entrance x_A, calculated by following formula,

Further, B in the rolling contact arc projection straight line₁、B₂And B₃Corresponding compound beginning and inside and outside gold Position x at the common speed of category_B, calculated by following formula,

Wherein, k₂For internal layer band resistance of deformation, p_IIt is to work as x=x_BRolling compression in I regions causes outer layer metal to produce Raw surrender,For the integral constant of inner layer metal tension, τ_mFor the shear stress between metal and metal；

It is described to work as x=x_BRolling compression in I regions causes the surrender p that outer layer metal is produced_I, calculated by following formula,

Wherein,B_I=4k₁, D₁=2R (h_iβ_i+h₀-h_i), E_I=2R (- τ₁-τ_m), τ₁=k₁m₁,For product Divide constantk₁It is anti-for outer layer deformation of strip Power；

The integral constant of the inner layer metal tensionCalculated by following formula,

Shear stress τ between the metal and metal_m, calculated by following formula,

τ_m=k₂m₂。

Specifically, Fig. 4 shows the rolling subregion schematic diagram that one embodiment of the invention is provided, as shown in figure 4, with reference to Fig. 5 Shown I areas force analysis schematic diagram, for I areas carry out force analysis, obtains the balance differential equation formula as exerted oneself, wherein on The region that layer deforms is：

Wherein,P=p₁+τ₁tanθ₁=p_m, p is in corresponding region Compression, σ is the tension in corresponding region, and τ is the shear stress in corresponding region；

Further, above formula can be reduced to：

Further, the compression in the region is expressed as after integration：

Wherein,B_I=4k₁,E_I=2R (- τ₁-τ_m),D_I=2R (h_iβ_i+h_o-h_i),τ₁=k₁m₁,τ_m=k₂m₂；

Work as x=x_ARolling compression in I areas can cause outer layer metal to produce surrender, be expressed as：

Wherein, integral constantIt is represented by：

It should be noted that metal of the metal yield intensity of internal layer more than outer layer, so there is p_I+σ_2i<2k₂, therefore, according to The balance differential equation that the situation of internal stress is obtained is expressed as：

Wherein, p=p₂=p_m,τ_m=m₂k₂。

Further, above formula is reduced to：

Therefore, the tension of inner layer metal is expressed as：

In x=x_A, the tension for obtaining inner layer metal according to boundary condition is initial tension,

Wherein, the integral constant in internal layer tension expression formulaFor：

It should be noted that in x=x_BPlace, the compression and tension of rolling can reach the yield strength of inner layer metal, p_I +σ_2i=2k₂；

Further, x_BCan be calculated by following formula,

Further, in x_BOuter layer internal memory thickness proportion be represented by：

Further, after double layer of metal is all surrendered, then two metals occur to be combined and its thickness ratio no longer occurs Change β_o=β_B, while it should be noted that the compound common speed of two metals generation of generation, is expressed as：

v_1B=v_2B

According to constancy of volume, have：

h_2iv_2i=h_2Bv_2B,h_2i=h_2B,v_2i=v_2B

Landing time of the inner layer metal in the middle of outer layer metal is expressed as：

Further, have：

Had according to metal mass flow equal principle：

The average speed of outer layer metal isIt is expressed as：

Therefore, skidding distance is represented by：

As shown in figure 4, metal is reached after B points, recombination process will start, and now relative displacement will not occur again, so Outer layer metal extended distance is before inner layer metal surrender：

Therefore, being combined the defect distance taken the lead is：

Fig. 6 shows the defect length schematic diagram that one embodiment of the invention is provided, as shown in fig. 6, due to extended spot outer layer Most of pressure have occurred and that and inner layer metal does not exist in outer layer metallic extensions, so, defect part can be near Like the difference for outer layer metal extended distance herein and inner layer metal skidding distance.

Fig. 7 shows the II areas force analysis schematic diagram that one embodiment of the invention is provided, and in II regions, three-layer metal is Generation recombination process, three-layer metal can be considered an entirety, therefore, the force analysis in II areas is represented by：

Wherein, p=p+ τ tan θ₁。

Further, above formula is reduced to：

Further, the compression in II areas is：

Wherein,B_II=4k_o,E_II=-2R τ, D_II=2Rh_o, τ=k_om₁。

Work as x=x_B,p_I=p_∏, it is continuous according to the compression of I areas and II areas at place, so the integral constant in II areas is：

Fig. 8 shows the III areas force analysis schematic diagram that one embodiment of the invention is provided, in III regions, last sandwich Composite strip moves into 3rd area, because now band linear velocity is faster than roll, so be zone of slippage on the delivery side domain, according to friction stree Change, reanalyse stress, there is following balance differential equation：

Wherein, p=p- τ tan θ₁；

Further, the compression in this region is represented by：

Wherein,B_III=4k_o,E_III=2R τ, D_III=2Rh_o, τ=k_om₁；

It should be noted that working as x=x_EThe relation of=0 compression and forward pull is p+ σ_o=2k_o, x_EFor the throwing of rolling contact arc E on shadow straight line₁、E₂And E₃Corresponding position, i.e. rolling nip area's outlet；

Therefore, integral constant is expressed as：

Finally it is noted that in neutral Angle Position x=x_DAt the interface in II areas and III areas, compression is simultaneously It is equal, p_II=p_III, then neutral Angle Position, is expressed as：

Wherein, x_DFor D in rolling contact arc projection straight line₁、D₂And D₃What corresponding position, i.e. rolling center face were located Position；

The copper aluminium sandwich Rolling compund of the present embodiment takes the lead the Forecasting Methodology of defect length, by rolling theory of mechanics Analysis can predict that sandwich is combined the analytic modell analytical model of the defect length taken the lead when rolling, and can take the lead defect length to what is be combined It is predicted, and then significantly improving yield and reduces and unnecessary cut damage.

Finally it should be noted that：Various embodiments above only to illustrate technical scheme, rather than a limitation；To the greatest extent Pipe has been described in detail with reference to foregoing embodiments to the present invention, it will be understood by those within the art that：Its according to So the technical scheme described in foregoing embodiments can be modified, either which part or all technical characteristic are entered Row equivalent；And these are changed or are replaced, the essence disengaging the claims in the present invention for not making appropriate technical solution are limited Fixed scope.

Claims (3)

1. a kind of copper aluminium sandwich Rolling compund takes the lead the Forecasting Methodology of defect length, the copper aluminium sandwich structure be Solder for Al-Cu Joint Welding- Aluminium three-layer metal, it is characterised in that include：

S1, acquisition copper aluminium sandwich Rolling compund take the lead the parameter of defect length forecast model, including：

The rolling upper strata metal thickness H for respectively taking the lead to be composite₁, middle layer metal thickness H₂With lower metal thickness H₃, Rolling compund is most The thickness H of whole band₀；

Outer layer metal initial tension σ_1iWith inner layer metal initial tension σ_2i；

The coefficient of friction of live roller radius R, roll surface and aluminum bronze, m₁And m₂；

S2, the parameter that defect length forecast model is taken the lead according to the copper aluminium sandwich Rolling compund, obtain Rolling compund initial The thickness H of band_i=H₁+H₂+H₃, the initial band of Rolling compund half thickness h_i=H_i/ 2, the thickness h of initial upper layer band_1i= H₁, initial internal layer band half thickness h_2i=H₂/ 2, the half thickness h of the final band of Rolling compund₀=H₀/2；

S3, according to the gateway thickness of Rolling compund, obtain percentage pass reduction r=(H_i-H₀)/H₀；

S4, set up copper aluminium sandwich Rolling compund and take the lead defect length forecast model, by the copper aluminium sandwich Rolling compund band The parameter of head defect length forecast model is brought the copper aluminium sandwich Rolling compund into and takes the lead defect length forecast model, obtains pre- That what is surveyed takes the lead defect length；

The copper aluminium sandwich Rolling compund takes the lead defect length forecast model, is calculated by following formula,

Δ D=Δ E- Δ S

Wherein, Δ D is the defect length of taking the lead of Rolling compund, and Δ E is front outer layer metal extended distance, and Δ S is inner layer metal cunning Move distance；

The front outer layer metal extended distance Δ E, is calculated by following formula,

$\mathrm{\&Delta;}E=\frac{(x_A-x_B)}{h_{1B}}-(x_A-x_B)$

Wherein, x_AFor A in rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position of area's entrance, x_BFor rolling B in contact arc projection straight line₁、B₂And B₃Position at the corresponding common speed in compound beginning and inside and outside metal, h_1BIt is in x_BPlace The half thickness of outer layer band,

The inner layer metal skidding distance Δ S, is calculated by following formula,

$\mathrm{\&Delta;}S=x_A-x_B-\frac{h_{2i}{\mathrm{\&beta;}}_0\sqrt{2R}}{(1-{\mathrm{\&beta;}}_0)\sqrt{h_0-h_{2i}}}(arctan\frac{x_A}{\sqrt{2R}(h_0-h_{2i})}-arctan\frac{x_B}{\sqrt{2R}(h_0-h_{2i})})$

Wherein, β₀For outer layer after Rolling compund and the ratio of the thickness of internal layer.

2. copper aluminium sandwich Rolling compund according to claim 1 takes the lead the Forecasting Methodology of defect length, it is characterised in that A in the rolling contact arc projection straight line₁、A₂And A₃Corresponding rolling nips the position x of area's entrance_A, calculated by following formula,

$x_A=\sqrt{R\&CenterDot;\mathrm{\&Delta;}h}=\sqrt{R\&CenterDot;(H_i-H_0)}.$

3. copper aluminium sandwich Rolling compund according to claim 1 takes the lead the Forecasting Methodology of defect length, it is characterised in that B in the rolling contact arc projection straight line₁、B₂And B₃Position x at the corresponding common speed in compound beginning and inside and outside metal_B, Calculated by following formula,

$x_B=\frac{2k_2-p_I{|}_{x=x_B}-C_{I2}^{*}}{\frac{-{\mathrm{\&tau;}}_m}{h_2}}$

Wherein, k₂For internal layer band resistance of deformation, p_IIt is to work as x=x_BRolling compression in I regions causes what outer layer metal was produced Surrender,For the integral constant of inner layer metal tension, τ_mFor the shear stress between metal and metal；

It is described to work as x=x_BRolling compression in I regions causes the surrender p that outer layer metal is produced_I, calculated by following formula,

$p_I=A_{I}x+\frac{B_I}{2}ln(x^2+D_1)+\frac{-A_I{D}_I+E_I}{\sqrt{D_I}}arctan\frac{x}{\sqrt{D_I}}+C_I^{*}$

Wherein,B_I=4k₁, D₁=2R (h_iβ_i+h₀-h_i), E_I=2R (- τ₁-τ_m), τ₁=k₁m₁,It is normal for integration Number,k₁For outer layer deformation of strip drag, β_i For outer layer before Rolling compund and the ratio of the thickness of internal layer；

The integral constant of the inner layer metal tensionCalculated by following formula,

$C_{I2}^{*}={\mathrm{\&sigma;}}_{2i}-\frac{{\mathrm{\&tau;}}_m}{h_{2i}}{x}_A$

Shear stress τ between the metal and metal_m, calculated by following formula,

τ_m=k₂m₂。