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

Method for predicting defect length of copper-aluminum sandwich rolled composite belt head

the technical field is as follows:

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

Background art:

when the industrial aluminum-copper-aluminum sandwich is rolled and compounded, the aluminum strip is softer than the copper strip, so that the aluminum strip deforms first and extends to a certain extent along the rolling direction, and meanwhile, the position of the copper strip is between two layers of aluminum strips and does not directly contact with an upper roller and a lower roller during rolling, so that the copper strip has certain relative slippage before compounding, and the defect length of the compounded strip head needs to be predicted.

However, in actual production, most of the prediction methods used are empirical formulas without theoretical basis, which may reduce the yield of accurate prediction of the composite tape head or bring unnecessary cut loss.

The invention content is as follows:

aiming at the defects of the prior art, the invention provides a method for predicting the defect length of a copper-aluminum sandwich rolled composite strip head, which can predict the defect length of the composite strip head, thereby greatly improving the yield and reducing unnecessary cutting loss.

The invention provides a method for predicting the defect length of a copper-aluminum sandwich rolled composite belt head, which comprises the following steps:

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

thickness H of upper layer metal of each strip to be compounded₁Thickness H of the middle layer metal₂And underlying layer goldThickness of₃Thickness H of the rolled composite final strip₀；

Initial tension of outer layer metal sigma_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,

△D＝△E-△S

wherein, Delta D is the defect length of the rolled and compounded belt head, 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 extension distance Delta E of the front outer layer metal is calculated by the following formula,

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 sliding distance Delta S is calculated by the following formula,

wherein, β₀The thickness ratio of the outer layer to the inner layer after rolling and compounding.

Optionally, A on the projection straight line of the rolling contact arc₁、A₂And A₃Corresponding position x of the entrance of the rolling bite_AThe calculation is carried out by the following formula,

optionally, the rolling contact arc projection straight line 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,

wherein k is₂For resistance of the inner strip to deformation, p_IWhen x is equal to x_BRolling stress in the I regionSo that the yield of the metal of the outer layer is generated,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,

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,

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

τ_m＝k₂m₂。

according to the technical scheme, the method for predicting the defect length of the copper-aluminum sandwich rolling composite belt head comprises the following steps: obtaining parameters of a defect length prediction model of the copper-aluminum sandwich rolling composite belt head, obtaining the thickness of a rolling composite initial belt material, the half thickness of the rolling composite initial belt material, the thickness of an initial upper layer belt material, the half thickness of an initial inner layer belt material and the half thickness of a rolling composite final belt material according to the parameters of the defect length prediction model of the copper-aluminum sandwich rolling composite belt head, obtaining pass reduction according to the thickness of an inlet and an outlet of rolling compounding, building a copper-aluminum sandwich rolling compound belt head defect length prediction model, substituting the parameters of the copper-aluminum sandwich rolling compound belt head defect length prediction model into the copper-aluminum sandwich rolling compound belt head defect length prediction model to obtain the predicted belt head defect length, therefore, the defect length of the composite tape head can be predicted, and further the yield is greatly improved and unnecessary cutting loss is reduced.

Description of the drawings:

fig. 1 is a schematic flow chart of a method for predicting the defect length of a copper-aluminum sandwich rolled composite tape head according to an embodiment of the present invention;

fig. 2 is a schematic diagram of copper-aluminum compounding according to an embodiment of the present invention;

FIG. 3 is a schematic diagram illustrating a symmetric modeling of rolling 1/2 according to an embodiment of the present invention;

FIG. 4 is a schematic view of a rolling mill section according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of a force analysis of zone I according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of a defect length according to an embodiment of the present invention;

FIG. 7 is a schematic view of a stress analysis of zone II provided in accordance with an embodiment of the present invention;

fig. 8 is a schematic view of a stress analysis of a region III according to an embodiment of the present invention.

The specific implementation mode is as follows:

the following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

Fig. 1 shows a schematic flow chart of a method for predicting a defect length of a copper-aluminum sandwich rolled composite tape head according to an embodiment of the present invention, and as shown in fig. 1, the method of the embodiment is as follows.

101. And obtaining parameters of a copper-aluminum sandwich rolling composite belt head defect length prediction model.

In this step, fig. 2 shows a schematic diagram of copper-aluminum compounding according to an embodiment of the present invention, as shown in fig. 2, two rollers are provided at the top and bottom, and the middle is an aluminum-copper-aluminum three-layer metal respectively, and the parameters of the model for predicting the defect length of the copper-aluminum sandwich rolled composite tape head specifically include:

thickness H of upper layer metal of each strip 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 layer metal sigma_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；

In practical application, the thickness of each strip to be compounded is obtained according to the measurement of a thickness meter of each metal coil at the inlet, and the thickness H of the upper layer metal₁Thickness H of the middle layer metal₂And thickness H of the lower layer metal₃Measuring the inlet based on inlet tension detectionTension, including outer layer metal initial tension σ_1iAnd initial tension of inner layer metal sigma_2iThe final strip thickness H of the rolling compound is measured according to a thickness meter at the rolling outlet₀Determining the radius R of the roller and the friction coefficient between the roller surface and the aluminum copper according to the actual conditions on site, and m₁And m₂。

102. 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。

In this step, it should be noted that, since the rolling process is a completely symmetrical process, the top half side of the sandwich rolling can be taken as a research object, fig. 3 shows a symmetrical modeling schematic diagram of rolling 1/2 according to an embodiment of the present invention, as shown in fig. 3, the x-axis is the opposite direction of the rolling, the y-axis is vertical upward, and the initial outer layer metal thickness is h_1iInitial half thickness of the inner layer metal is h_2iThe roller is R, the projection length of the rolled contact arc length is l, and the thickness of the rolled outer layer metal is h₁₀The half thickness of the metal of the inner layer is h₂₀，σ_1iAnd σ_2iTensile stress, σ, of the initial outer and inner layer metals, respectively₀The final composite strip tensile stress.

103. According to the thickness of the inlet and outlet of the rolling compound, the pass reduction rate r is (H)_i-H₀)/H₀。

104. Establishing a copper-aluminum sandwich rolling composite belt head defect length prediction model, and substituting the 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.

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

△D＝△E-△S

wherein, Delta D is the defect length of the rolled and compounded belt head, 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 extension distance Delta E of the front outer layer metal is calculated by the following formula,

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 sliding distance Delta S is calculated by the following formula,

wherein, β₀The thickness ratio of the outer layer to the inner layer after rolling and compounding.

Further, A on the projection straight line of the rolling contact arc₁、A₂And A₃Corresponding position x of the entrance of the rolling bite_AThe calculation is carried out by the following formula,

further, B on the projection straight line of the rolling contact arc₁、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,

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,

wherein,B_I＝4k₁，D₁＝2R(h_iβ_i+h₀-h_i)，E_I＝2R(-τ₁-τ_m)，τ₁＝k₁m₁，is an integration constantk₁Is an outer layerResistance to strip deformation;

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

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

τ_m＝k₂m₂。

specifically, fig. 4 shows a schematic view of a rolling sub-area provided by an embodiment of the present invention, as shown in fig. 4, and a schematic view of a stress analysis of an I-area shown in fig. 5 is combined to perform stress analysis on the I-area, so as to obtain the following equilibrium differential equation of forces, where an area where an upper layer deforms is:

wherein,p＝p₁+τ₁tanθ₁＝p_mp is the compressive stress in the corresponding region, σ is the tensile stress in the corresponding region, and τ is the shear stress in the corresponding region;

further, the above equation can be simplified as:

further, the compressive stress of the region after integration is expressed as:

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；

when x is equal to x_AThe rolling stress in zone I may cause the outer layer metal to yield, expressed as:

wherein the integral constantCan be expressed as:

it should be noted that the metal yield strength of the inner layer is greater than the metal of the outer layer, so that there is p_I+σ_2i<2k₂Therefore, the equilibrium differential equation obtained from the case of the internal stress is expressed as:

wherein p ═ p₂＝p_m,τ_m＝m₂k₂。

Further, the above formula is simplified as:

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

where x is x_AObtaining the tensile stress of the inner layer metal as the initial tensile stress according to the boundary condition,

wherein, the integral constant in the expression of the tensile stress of the inner layerComprises the following steps:

it should be noted that x is x_BThe rolling compressive stress and the rolling tensile stress can reach the yield strength p of the inner layer metal_I+σ_2i＝2k₂；

Further, x_BCan be calculated by the following formula,

further, in x_BThe outer memory thickness ratio of (a) may be expressed as:

further, after both metals yield, the metals are combined and their thickness ratio no longer changes β_o＝β_BIt should also be noted that the two metals undergoing recombination produce a common velocity, expressed as:

v_1B＝v_2B

according to the volume, the following are:

h_2iv_2i＝h_2Bv_2B,h_2i＝h_2B,v_2i＝v_2B

the slip 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 method comprises the following steps:

the average velocity of the outer metal isExpressed as:

thus, the glide distance can be expressed as:

as shown in fig. 4, after the metal reaches point B, the recombination process is about to start, and at this time, the relative displacement does not occur any more, so the extension distance of the outer layer metal before the inner layer metal yields is:

thus, the defect distance of the composite tape head is:

fig. 6 shows a defect length diagram provided by an embodiment of the present invention, as shown in fig. 6, since most of the pressing down of the outer layer at the extension has already occurred and the inner layer metal is not present in the extension of the outer layer metal, the defect portion can be approximated as the difference between the outer layer metal extension distance and the inner layer metal slip distance at this point.

Fig. 7 is a schematic diagram of stress analysis of region II provided in an embodiment of the present invention, in region II, a three-layer metal has undergone a composite process, and the three-layer metal can be regarded as a whole, so that the stress analysis of region II can be represented as:

wherein,p＝p+τtanθ₁。

further, the above formula is simplified as:

further, the compressive stress in zone II is:

wherein,B_II＝4k_o,E_II＝-2Rτ,D_II＝2Rh_o,τ＝k_om₁。

when x is equal to x_B,p_I＝p_∏The compressive stress at region I and region II continues, so the integration constant in region II is:

FIG. 8 is a schematic diagram illustrating a stress analysis of area III, where the final sandwich composite strip moves into three areas, where the strip is in a forward slip region because the linear velocity is faster than the roll, and the stress is reanalyzed according to the change of frictional stress, and the equilibrium differential equation is as follows:

wherein p ═ p- τ tan θ₁；

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

wherein,B_III＝4k_o,E_III＝2Rτ,D_III＝2Rh_o,τ＝k_om₁；

it should be noted that when x ═ x_EThe relationship between compressive stress and pre-tension is p + sigma_o＝2k_o，x_EFor rolling contact arc projection straight line E₁、E₂And E₃The corresponding position is the outlet of the rolling bite area;

thus, the integration constant is expressed as:

finally, it should be noted that in the neutral angular position x, x_DAt the interface between zone II and zone III, the compressive stresses are also equal, p_II＝p_IIIThe neutral angular position, then, is expressed as:

wherein x is_DFor rolling contact arc projection on straight line D₁、D₂And D₃The corresponding position, namely the position of the rolling central plane;

according to the method for predicting the defect length of the copper-aluminum sandwich rolling composite strip head, the analysis model of the defect length of the composite strip head during the sandwich rolling can be predicted through the analysis of the rolling mechanics theory, the composite strip head defect length can be predicted, and therefore the yield is greatly improved, and unnecessary cutting loss is reduced.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

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。