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

Abstract

The invention provides a method for predicting the defect length of a copper-aluminum sandwich rolling composite tape head, comprising: obtaining the parameters of a prediction model for the defect length of a copper-aluminum sandwich rolling composite tape head, and according to the copper-aluminum sandwich rolling composite tape head defect length prediction model The parameters of rolling and compounding the initial strip, the half-thickness of the rolling and compounding initial strip, the thickness of the initial upper layer strip, the half-thickness of the initial inner layer strip and the half-thickness of the rolling and compounding final strip, according to The thickness of the entrance and exit of the rolling compound is obtained, and the pass reduction rate is obtained. By establishing the defect length prediction model of the copper-aluminum sandwich rolling composite tape head, the parameters of the copper-aluminum sandwich rolling composite tape head defect length prediction model are brought into the copper-aluminum sandwich rolling. Sandwich rolling composite tape head defect length prediction model, the predicted length of the tape head defect is obtained, thus, the defect length of the composite tape head can be predicted, and then the output can be greatly improved and unnecessary cutting loss can be reduced.

Description

A Method for Predicting the Defect Length of Copper-Aluminum Sandwich Rolling Composite Strip Head

Technical field:

The invention relates to the field of defect prediction of copper-aluminum sandwich rolling composite tape head, in particular to a method for predicting defect length of copper-aluminum sandwich rolling composite tape head.

Background technique:

In industrial aluminum-copper-aluminum sandwich rolling and compounding, because the aluminum strip is softer than the copper strip, the aluminum strip will be deformed first and will extend along the rolling direction. At the same time, due to the position of the copper strip during rolling, It is between the two layers of aluminum strips and does not directly contact the upper and lower rollers, so the copper strips will have a certain relative slip before compounding, which requires prediction of the length of the compounded lead defects.

However, in actual production, most of the prediction methods used are empirical formulas without theoretical basis, which may reduce the accuracy of composite tape head prediction output, or cause unnecessary cutting loss.

Invention content:

Aiming at the defects of the prior art, the present invention provides a method for predicting the defect length of the composite tape head in copper-aluminum sandwich rolling, which can predict the defect length of the composite tape head, thereby greatly increasing the output and reducing unnecessary cutting loss.

The invention provides a method for predicting the defect length of a copper-aluminum sandwich rolling composite strip head, comprising:

S1. Obtain the parameters of the prediction model for the defect length of the copper-aluminum sandwich rolling composite strip head, including:

Rolling the upper layer metal thickness H ₁ , middle layer metal thickness H ₂ and lower layer metal thickness H ₃ of each strip to be compounded, rolling and compounding the thickness H ₀ of the final strip;

The initial tension of the outer metal σ _1i and the initial tension of the inner metal σ _2i ;

On-site roll radius R, friction coefficient between roll surface and aluminum copper, m ₁ and m ₂ ;

S2. According to the parameters of the prediction model for the head defect length of the copper-aluminum sandwich rolling composite strip, the thickness H _i =H ₁ +H ₂ +H ₃ of the initial rolling composite strip and the half-thickness h of the rolling composite initial strip are obtained _i = H _i /2, initial thickness h _1i = H ₁ of the upper strip, half thickness h _2i = H ₂ /2 of the initial inner strip, half thickness h ₀ = H ₀ / 2;

S3. According to the thickness of the entrance and exit of the rolling compound, the pass reduction ratio r=(H _i -H ₀ )/H ₀ is obtained;

S4. Establish a defect length prediction model for copper-aluminum sandwich rolling composite tape head, and bring the parameters of the copper-aluminum sandwich rolling composite tape head defect length prediction model into the copper-aluminum sandwich rolling composite tape head defect length prediction model to obtain the predicted lead defect length;

The copper-aluminum sandwich rolling compound strip head defect length prediction model is calculated by the following formula,

△D=△E-△S

Among them, △D is the length of the head defect of rolling composite, △E is the extension distance of the front outer metal, and △S is the slip distance of the inner metal;

The metal extension distance ΔE of the front outer layer is calculated by the following formula,

Among them, x _A is the position of the entrance of the rolling bite area corresponding to A ₁ , A ₂ and A ₃ on the rolling contact arc projection line, and x _B is B ₁ , B ₂ and B ₃ on the rolling contact arc projection line Corresponding to the starting point of recombination and the position of the inner and outer metal co-velocity, h _1B is the half thickness of the outer strip at x _B ,

The inner layer metal slip distance ΔS is calculated by the following formula,

Among them, _β0 is the ratio of the thickness of the outer layer to the inner layer after rolling cladding.

Optionally, the position x _A of the entrance of the rolling bite area corresponding to A ₁ , A ₂ and A ₃ on the rolling contact arc projection line is calculated by the following formula,

Optionally, the position x _B of the starting point of compounding corresponding to B ₁ , B ₂ and B ₃ on the projection line of the rolling contact arc and the co-velocity point of the inner and outer metals is calculated by the following formula,

Among them, k ₂ is the deformation resistance of the inner layer strip, p _I is the yield of the outer layer metal caused by the rolling compressive stress in the I region when x=x _B , is the integral constant of the tensile stress of the inner layer metal, and _τm is the shear stress between metal and metal;

The rolling compressive stress of _B in region I when x=x makes the yield p _I of the outer layer metal calculated by the following formula,

in, B _I =4k ₁ , D ₁ =2R(h _i β _i +h ₀ -h _i ), E _I =2R(-τ ₁ -τ _m ), τ ₁ =k ₁ m ₁ ,, is the integral constant, _{k 1} is the deformation resistance of the outer strip, and βi is the ratio of the thickness of the outer layer to the inner layer before rolling and compounding;

Integral constant of the inner layer metal tensile stress Calculated by the following formula,

The shear stress τ _m between the metal and the metal is calculated by the following formula,

τ _m =k ₂ m ₂ .

It can be known from the above technical solution that a method for predicting the defect length of a copper-aluminum sandwich rolling composite strip head according to the present invention includes: obtaining the parameters of the prediction model for the defect length of a copper-aluminum sandwich rolling composite strip head, and according to the copper-aluminum sandwich rolling composite strip head defect length prediction method, and The parameters of the composite strip head defect length prediction model are obtained to obtain the thickness of the rolling composite initial strip, the half thickness of the rolling composite initial strip, the thickness of the initial upper layer strip, the half thickness of the initial inner layer strip and the rolling composite final strip Half thickness of the material, according to the thickness of the entrance and exit of the rolling composite, the pass reduction rate is obtained, and the defect length prediction model of the copper-aluminum sandwich rolling composite tape is established, and the parameters of the copper-aluminum sandwich rolling composite tape head defect length prediction model Bringing into the copper-aluminum sandwich rolling composite tape head defect length prediction model, the predicted tape head defect length can be obtained, thus, the defect length of the composite tape head can be predicted, and then the output can be greatly improved and unnecessary cutting loss can be reduced.

Description of drawings:

Fig. 1 is a schematic flow chart of a method for predicting the defect length of a copper-aluminum sandwich rolling composite strip head provided by an embodiment of the present invention;

Fig. 2 is a schematic diagram of copper-aluminum composite provided by an embodiment of the present invention;

Fig. 3 is a schematic diagram of rolling 1/2 symmetrical modeling provided by an embodiment of the present invention;

Fig. 4 is a schematic diagram of rolling partitions provided by an embodiment of the present invention;

Fig. 5 is a schematic diagram of force analysis of zone I provided by an embodiment of the present invention;

Fig. 6 is a schematic diagram of defect length provided by an embodiment of the present invention;

Fig. 7 is a schematic diagram of force analysis of zone II provided by an embodiment of the present invention;

Fig. 8 is a schematic diagram of force analysis of zone III provided by an embodiment of the present invention.

detailed description:

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

Fig. 1 shows a schematic flowchart of a method for predicting defect length of copper-aluminum sandwich rolling composite strip head provided by an embodiment of the present invention. As shown in Fig. 1 , the method of this embodiment is as follows.

101. Obtain the parameters of the prediction model for the defect length of the copper-aluminum sandwich rolling compound strip head.

In this step, Figure 2 shows a schematic diagram of the copper-aluminum composite provided by an embodiment of the present invention. The parameters of the prediction model for the defect length of the composite lead are prepared, including:

Rolling the upper layer metal thickness H ₁ , middle layer metal thickness H ₂ and lower layer metal thickness H ₃ of each strip to be compounded, rolling and compounding the thickness H ₀ of the final strip;

The initial tension of the outer metal σ _1i and the initial tension of the inner metal σ _2i ;

On-site roll radius R, friction coefficient between roll surface and aluminum copper, m ₁ and m ₂ ;

In practical application, the thickness of each strip to be compounded is obtained by measuring the thickness of each metal coil at the entrance, the upper metal thickness H ₁ , the middle metal thickness H ₂ and the lower metal thickness H ₃ , and according to the entrance tension detection, measure the entrance Tension, including the initial tension σ _1i of the outer layer metal and σ _2i of the inner layer metal, the final strip thickness H ₀ of the rolling compound is obtained according to the thickness meter at the rolling exit, and the radius R of the roll is determined according to the actual situation on site, and the roll Surface and aluminum copper friction coefficient, m ₁ and m ₂ .

102. According to the parameters of the prediction model for the head defect length of the copper-aluminum sandwich rolling composite strip, obtain the thickness H _i =H ₁ +H ₂ +H ₃ of the initial rolling composite strip, and the half-thickness h of the rolling composite initial strip _i = H _i /2, initial thickness h _1i = H ₁ of the upper strip, half thickness h _2i = H ₂ /2 of the initial inner strip, half thickness h ₀ = H ₀ / 2.

In this step, it should be noted that since the rolling process is a completely symmetrical process, the upper half of the sandwich rolling can be taken as the research object. Figure 3 shows the rolling 1/2 symmetric Modeling diagram, as shown in Figure 3, the x-axis is the opposite direction of rolling, the y-axis is vertical upward, the initial outer metal thickness is h _1i , the initial inner metal half-thickness is h _2i , and the roll is R , the projected length of the rolling contact arc length is l, the thickness of the outer layer metal after rolling is h ₁₀ , the half-thickness of the terminated inner layer metal is h ₂₀ , σ _1i and σ _2i are the initial outer layer and inner layer metal respectively Tensile stress, σ ₀ is the final composite strip tensile stress.

103. According to the thickness of the entrance and exit of the rolling compound, the pass reduction rate r=(H _i -H ₀ )/H ₀ is obtained.

104. Establish a prediction model for the defect length of the copper-aluminum sandwich rolling composite tape head, bring the parameters of the copper-aluminum sandwich rolling composite tape head defect length prediction model into the copper-aluminum sandwich rolling composite tape head defect length prediction model, and obtain the predicted Take the lead defect length.

In this step, the defect length prediction model of the copper-aluminum sandwich rolling composite strip head is calculated by the following formula,

△D=△E-△S

Among them, △D is the length of the head defect of rolling composite, △E is the extension distance of the front outer metal, and △S is the slip distance of the inner metal;

The metal extension distance ΔE of the front outer layer is calculated by the following formula,

Among them, x _A is the position of the entrance of the rolling bite area corresponding to A ₁ , A ₂ and A ₃ on the rolling contact arc projection line, and x _B is B ₁ , B ₂ and B ₃ on the rolling contact arc projection line Corresponding to the starting point of recombination and the position of the inner and outer metal co-velocity, h _1B is the half thickness of the outer strip at x _B ,

The inner layer metal slip distance ΔS is calculated by the following formula,

Among them, _β0 is the ratio of the thickness of the outer layer to the inner layer after rolling cladding.

Further, the position x _A of the entrance of the rolling bite area corresponding to A ₁ , A ₂ and A ₃ on the rolling contact arc projection line is calculated by the following formula,

Further, the position x _B of the compositing starting point corresponding to B ₁ , B ₂ and B ₃ on the projection line of the rolling contact arc and the co-velocity point of the inner and outer metals is calculated by the following formula,

Among them, k ₂ is the deformation resistance of the inner layer strip, p _I is the yield of the outer layer metal caused by the rolling compressive stress in the I region when x=x _B , is the integral constant of the tensile stress of the inner layer metal, and _τm is the shear stress between metal and metal;

The rolling compressive stress of _B in region I when x=x makes the yield p _I of the outer layer metal calculated by the following formula,

in, B _I =4k ₁ , D ₁ =2R(h _i β _i +h ₀ -h _i ), E _I =2R(-τ ₁ -τ _m ), τ ₁ =k ₁ m ₁ , is the integral constant k ₁ is the deformation resistance of the outer strip;

Integral constant of the inner layer metal tensile stress Calculated by the following formula,

The shear stress τ _m between the metal and the metal is calculated by the following formula,

τ _m =k ₂ m ₂ .

Specifically, Fig. 4 shows a schematic diagram of rolling partitions provided by an embodiment of the present invention. As shown in Fig. 4, combined with the schematic diagram of force analysis of I zone shown in Fig. 5, the force analysis for I zone is carried out, and the following forces are obtained The equilibrium differential equation for , where the region where the upper layer deforms is:

in, p=p ₁ +τ ₁ tanθ ₁ =p _m , p is the compressive stress in the corresponding area, σ is the tensile stress in the corresponding area, and τ is the shear stress in the corresponding area;

Furthermore, the above formula can be simplified as:

Further, the compressive stress in this region after integration is expressed as:

in, B _I ＝4k ₁ , E _I ＝2R(-τ ₁ -τ _m ), D _I ＝2R(h _i β _i +h _o -h _i ), τ ₁ ＝k ₁ m ₁ , τ _m ＝k ₂ m ₂ ;

When x=x _A , the rolling compressive stress in zone I can make the outer metal yield, which is expressed as:

Among them, the integral constant Can be expressed as:

It should be noted that the yield strength of the metal in the inner layer is greater than that of the outer layer, so p _I +σ _2i <2k ₂ , therefore, the equilibrium differential equation obtained according to the internal stress is expressed as:

Wherein, p=p ₂ =p _m , τ _m =m ₂ k ₂ .

Further, the above formula can be simplified as:

Therefore, the tensile stress of the inner layer metal is expressed as:

At x=x _A , according to the boundary conditions, the tensile stress of the inner metal is the initial tensile stress,

Among them, the integral constant in the inner layer tensile stress expression for:

It should be noted that at x=x _B , the compressive stress and tensile stress of rolling can reach the yield strength of the inner layer metal, p _I +σ _2i =2k ₂ ;

Further, x _B can be calculated by the following formula,

Further, the thickness ratio of the outer memory at x _B can be expressed as:

Furthermore, after the yield of both layers of metals, the two metals recombine and their thickness ratio no longer changes β _o = β _B . At the same time, it should be noted that the recombined two metals have a common velocity, expressed as:

v _1B = v _2B

According to the constant volume, there are:

h _2i v _2i = h _2B v _2B , h _2i = h _2B , v _2i = v _2B

The sliding time of the inner metal in the middle of the outer metal is expressed as:

Further, there are:

According to the principle of equal metal second flow:

The average velocity of the outer metal is Expressed as:

Therefore, the slip distance can be expressed as:

As shown in Figure 4, after the metal reaches point B, the recombination process is about to start, and the relative displacement will not occur at this time, so the extension distance of the outer metal before the inner metal yields is:

Therefore, the defect distance of the composite lead is:

Figure 6 shows a schematic diagram of the defect length provided by an embodiment of the present invention. As shown in Figure 6, since most of the compression of the outer layer at the extension has occurred, and the inner metal does not exist in the extension of the outer metal, so, The defect part can be approximated as the difference between the extension distance of the outer metal and the slip distance of the inner metal.

Fig. 7 shows a schematic diagram of force analysis in zone II provided by an embodiment of the present invention. In zone II, the three-layer metal has undergone a composite process, and the three-layer metal can be regarded as a whole. Therefore, the force analysis in zone II can be Expressed as:

Wherein, p=p+τtanθ ₁ .

Further, the above formula can be simplified as:

Further, the compressive stress in Zone II is:

in, B _II = 4k _o , E _II = -2Rτ, D _II = 2Rh _o , τ = k _o m ₁ .

When x=x _B , p _I ＝p _∏ , according to the continuity of the compressive stress in the zone I and zone II, the integral constant in zone II is:

Fig. 8 shows a schematic diagram of force analysis in zone III provided by an embodiment of the present invention. In zone III, the last sandwich composite strip moves into zone three. Since the strip line speed is faster than that of the rollers at this time, it is a forward sliding zone. According to the change of the frictional stress, re-analyze the force, the following equilibrium differential equation:

Among them, p=p-τtanθ ₁ ;

Further, the compressive stress in this region can be expressed as:

in, B _III = 4k _o , E _III = 2Rτ, D _III = 2Rh _o , τ = k _o m ₁ ;

It should be noted that when x=x _E ＝0 the relationship between compressive stress and front tension is p+σ _o ＝2k _o , x _E is the position corresponding to E ₁ , E ₂ and E ₃ on the rolling contact arc projection line , that is, the outlet of the rolling nip area;

Therefore, the integral constant is expressed as:

Finally, it should be noted that at the neutral angle position x=x _D at the interface between Zone II and Zone III, the compressive stress is also equal at the same time, p _II =p _III , so the neutral angle position is expressed as:

Among them, x _D is the position corresponding to D ₁ , D ₂ and D ₃ on the rolling contact arc projection line, that is, the position of the rolling center plane;

The method for predicting the defect length of the composite tape head in copper-aluminum sandwich rolling of this embodiment can predict the analytical model of the defect length of the composite tape head during sandwich rolling through the analysis of rolling mechanics theory, and can predict the defect length of the composite tape head, and then Greatly increase output and reduce unnecessary cutting loss.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: It is still possible to modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope defined by the claims of the present invention .

Claims (3)

1. A method for predicting the defect length of a copper-aluminum sandwich rolled composite belt head is characterized in that the copper-aluminum sandwich structure is an aluminum-copper-aluminum three-layer metal, and the method comprises the following steps:

s1, obtaining parameters of the copper-aluminum sandwich rolling composite belt head defect length prediction model, including:

rolling the upper layer metal thickness H of each strip head to be compounded₁Thickness H of the middle layer metal₂And thickness H of the lower layer metal₃Thickness H of the rolled composite final strip₀；

Initial tension of outer metalσ_1iAnd initial tension of inner layer metal sigma_2i；

Radius R of the roll in situ, coefficient of friction between the roll surface and the aluminum copper, m₁And m₂；

S2, obtaining the thickness H of the rolled composite initial strip according to the parameters of the copper-aluminum sandwich rolled composite strip head defect length prediction model_i＝H₁+H₂+H₃Half thickness h of the rolled composite initial strip_i＝H_iInitial upper strip thickness h_1i＝H₁Half thickness h of the initial inner strip_2i＝H₂/2, half thickness h of the rolled composite final strip₀＝H₀/2；

S3, obtaining pass reduction r ═ H (H) according to the combined roll pass thickness_i-H₀)/H₀；

S4, establishing a copper-aluminum sandwich rolling composite belt head defect length prediction model, and substituting parameters of the copper-aluminum sandwich rolling composite belt head defect length prediction model into the copper-aluminum sandwich rolling composite belt head defect length prediction model to obtain the predicted belt head defect length;

the copper-aluminum sandwich rolling composite belt head defect length prediction model is calculated by the following formula,

ΔD＝ΔE-ΔS

wherein, Delta D is the length of the rolling composite belt head defect, Delta E is the extension distance of the front outer layer metal, and Delta S is the slippage distance of the inner layer metal;

the front outer layer metal extension distance deltae is calculated by the following formula,

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

wherein x is_AFor rolling A on the projection straight line of contact arc₁、A₂And A₃Corresponding position of roll bite entrance, x_BFor rolling contact arc projection straight line B₁、B₂And B₃The corresponding compound starting position and the position of the inner and outer metal at the same speed, h_1BIs at x_BThe half thickness of the outer layer of the strip,

the inner layer metal slip distance deltaS is calculated by the 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, β₀The thickness ratio of the outer layer to the inner layer after rolling and compounding.

2. The method for predicting the defect length of the copper-aluminum sandwich rolled composite strip head according to claim 1, wherein the projection line of the rolling contact arc is A₁、A₂And A₃Corresponding position x of the entrance of the rolling bite_AThe calculation is carried out by the following formula,

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

3. the method for predicting the defect length of the copper-aluminum sandwich rolled composite strip head according to claim 1, wherein the projection line of the rolling contact arc is B₁、B₂And B₃The corresponding position x of the composite starting position and the inner and outer metal common speed position_BThe calculation is carried out by the following formula,

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

wherein k is₂For resistance of the inner strip to deformation, p_IWhen x is equal to x_BThe rolling stress in region I causes the outer metal to yield,is the integral constant, tau, of the tensile stress of the metal of the inner layer_mIs the shear stress from metal to metal;

when x is equal to x_BThe rolling stress in the I region causes the yield p of the outer layer metal_IThe calculation is carried out by the 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，，in order to be an integration constant, the first,k₁resistance of the outer web to deformation, β_iThe thickness ratio of the outer layer to the inner layer before rolling and compounding;

integral constant of tensile stress of the inner layer metalBy the following calculation formula,

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

shear stress tau between said metals_mThe calculation is carried out by the following formula,

τ_m＝k₂m₂。