A method for quantitative calculation of warpage in tension-free composite rolling of double-layer metal sheet and strip

Abstract

This invention relates to a method for quantifying warpage during tension-free composite rolling of double-layer metal strip, comprising: acquiring relevant parameters of the metal strip and rolling mill equipment; calculating the length of the plastic deformation zone based on the relevant parameters of the metal strip and rolling mill equipment; calculating the lengths of the inlet elastic deformation zone and the outlet elastic deformation zone based on the relevant parameters of the metal strip and the length of the plastic deformation zone; calculating the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip based on the lengths of the plastic deformation zone, the inlet elastic deformation zone, and the outlet elastic deformation zone; establishing a rolling pressure calculation model based on the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip; dividing the rolling deformation zone of the double-layer metal strip; and calculating the warpage of the double-layer metal strip based on the divided deformation zones and the rolling pressure calculation model. This invention closely addresses the characteristics of the double-layer metal composite rolling process, effectively avoiding the blindness and repetitiveness of experiments.

Description

Technical Field

[0001] This invention relates to the field of composite rolling technology for metal sheet and strip, and in particular to a method for quantifying warpage in tension-free composite rolling of double-layer metal sheet and strip. Background Technology

[0002] In recent years, against the backdrop of the rapid development of high-end industries such as aerospace, electronic communications, and rail transportation, micro-manufacturing and microelectronics have become important pathways to improve the intelligence level of equipment and ensure system stability, playing an irreplaceable role. Simultaneously, to meet the raw material demands of advanced manufacturing, the market and enterprises have placed increasingly stringent requirements on the preparation processes and product quality of metallic materials. Metal composite materials, by overcoming the inherent limitations of single-metal functions and exhibiting the comprehensive advantages of each component, have become an indispensable material foundation for high-end manufacturing industries.

[0003] Because the two metals exhibit different deformation capabilities during rolling, warping deformation occurs after rolling of metal composite strips. Warping defects are a common problem in the rolling process of metal composite materials, but the occurrence of post-rolling warping defects not only affects the rolling process settings and dimensional accuracy, but also makes it difficult to meet the high-quality production requirements of downstream precision manufacturing processes. Currently, there is no specific mechanistic model to calculate the warping of double-layer metal strips. If the warping deformation could be quantified, the amount of warping after rolling could be predicted in advance, reducing some unnecessary material losses in the production process. Moreover, quantitative calculation is the theoretical basis for finding the optimal process standard to solve the warping problem. Therefore, a method for quantitatively calculating the warping of tension-free composite rolling of double-layer metal strips is needed to solve the above problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for quantitatively calculating warpage in tension-free composite rolling of double-layer metal strips, which closely relates to the characteristics of the double-layer metal composite rolling process and effectively avoids the blindness and repetitiveness of experiments.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for quantifying warpage during tension-free composite rolling of double-layer metal strip includes:

[0007] Obtain relevant parameters for metal sheet and strip, as well as relevant parameters for rolling mill equipment;

[0008] Calculate the length of the plastic deformation zone based on the relevant parameters of the metal sheet and strip and the relevant parameters of the rolling mill equipment;

[0009] Based on the relevant parameters of the metal strip and the length of the plastic deformation zone, calculate the length of the inlet elastic deformation zone and the length of the outlet elastic deformation zone;

[0010] Based on the length of the plastic deformation zone, the length of the inlet elastic deformation zone, and the length of the outlet elastic deformation zone, calculate the contact arc length of the upper and lower rolling deformation zones of the double-layer metal strip;

[0011] A rolling pressure calculation model is established based on the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip.

[0012] The deformation zone of the double-layer metal strip rolling process is divided, and the warpage of the double-layer metal strip is calculated based on the divided deformation zone and the rolling pressure calculation model.

[0013] Preferably, the relevant parameters of the metal strip include: base metal inlet thickness, base metal outlet thickness, cladding metal inlet thickness, and cladding metal outlet thickness;

[0014] The relevant parameters of the rolling mill equipment include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0015] Preferably, calculating the length of the plastic deformation zone includes:

[0016] Calculate the material property influence coefficient of the double-layer metal strip based on the relevant parameters of the metal strip;

[0017] Calculate the maximum value of rolling pressure distribution in the deformation zone of the double-layer metal strip;

[0018] The length of the plastic deformation zone is calculated based on the material property influence coefficient, the maximum value of the rolling pressure distribution in the deformation zone, the relevant parameters of the metal strip, and the relevant parameters of the rolling mill equipment.

[0019] Preferably, the material property influence coefficient includes the material property influence coefficient of the base metal sheet and the material property influence coefficient of the cladding metal sheet;

[0020] The material property influence coefficient of the base metal strip is:

[0021]

[0022] The material property influence coefficient of the clad metal strip is:

[0023]

[0024] Where, ξ 1J ξ is the influence coefficient of the properties of the base metal material. 1F σ is the influence coefficient of the properties of the coating metal material. s1J For the deformation resistance of the base metal outlet, v J For the base metal Poisson's ratio, h 1J E represents the measured thickness of the base metal outlet. JFor the Young's modulus of the base metal, h 0J σ represents the measured thickness of the base metal inlet. s1F For the deformation resistance of the clad metal outlet, v F E represents the Poisson's ratio of the coated metal. F h represents the Young's modulus of the cladding metal. 0F h is the measured value of the inlet thickness of the cladding metal. 1F This is the measured value of the coating metal outlet thickness;

[0025] The maximum value of the rolling pressure distribution in the deformation zone of the double-layer metal strip includes the maximum value of the rolling pressure distribution in the deformation zone of the base metal strip and the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal strip.

[0026] The maximum value of the rolling pressure distribution in the deformation zone of the base metal strip is:

[0027]

[0028] The maximum value of the rolling pressure distribution in the deformation zone of the clad metal strip is:

[0029]

[0030] Where, p Jmax The maximum value of rolling pressure distribution in the deformation zone of the base metal is given by α, which is the specific gravity coefficient of the elliptical model. J l is the unit rolling force between the roll and the base metal. JZ p is the contact arc length of the deformation zone of the base metal rolling process. Fmax p represents the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal. F l is the unit rolling force between the roll and the cladding metal. FZ The contact arc length of the deformation zone during the rolling of the cladding metal;

[0031] The length of the plastic deformation zone includes the length of the plastic deformation zone of the base metal strip and the length of the plastic deformation zone of the cladding metal strip.

[0032] The length of the plastic deformation zone of the base metal strip is:

[0033]

[0034] The length of the plastic deformation zone of the clad metal strip is:

[0035]

[0036] Among them, l J R is the length of the plastic deformation zone of the base metal strip, R is the radius of the work roll, and E is the length of the plastic deformation zone of the base metal strip. r v is the Young's modulus of the work roll. r For the Poisson's ratio of the working roll, lF This represents the length of the plastic deformation zone of the clad metal sheet / strip.

[0037] Preferably, the lengths of the inlet elastic deformation zone and the outlet elastic deformation zone are calculated as follows:

[0038] The length of the elastic deformation zone at the entrance of the base metal strip is:

[0039]

[0040] The length of the exit elastic deformation zone of the base metal strip is:

[0041]

[0042] Where, Δx 0J σ is the length of the elastic deformation zone at the entrance of the base metal strip. s0J For the deformation resistance of the base metal inlet, Δx 1J The length of the elastic deformation zone at the exit of the base metal strip, μ rz The coefficient of friction;

[0043] The length of the elastic deformation zone at the entrance of the clad metal strip is:

[0044]

[0045] The length of the exit elastic deformation zone of the clad metal strip is:

[0046]

[0047] Where, Δx 0F σ is the length of the elastic deformation zone at the entrance of the clad metal strip. s0F For the deformation resistance of the cladding metal inlet, Δx 1F This refers to the length of the exit elastic deformation zone of the clad metal strip.

[0048] Preferably, the rolling pressure calculation model is as follows:

[0049] P J (x)=ψ J (x)+α J (x);

[0050] P F (x)=ψ F (x)+α F (x);

[0051]

[0052] Where x is the position coordinate of the double-layer metal sheet and strip composite rolling process, a 1J , a2JLet a be the x-coordinate of the two intersection points where the rolling pressure of the base metal sheet / strip is 0. 1F a 2F Let P be the x-coordinate of the two intersection points where the rolling pressure function of the base metal sheet / strip is 0, and α be the rolling force. J (x), α F (x) represents the empirical error term for rolling pressure, P J (x) is the rolling pressure function of the base metal sheet / strip, ψ J (x) is the initial rolling pressure function of the base metal sheet / strip, P F (x) is the rolling pressure function of the clad metal sheet / strip, ψ F (x) is the initial rolling pressure function of the clad metal sheet / strip.

[0053] Preferably, the division of the deformation zone during the rolling of double-layer metal strip includes:

[0054] Based on the stress and composite state of the double-layer metal strip, the rolling deformation zone of the double-layer metal strip is divided into the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone.

[0055] Preferably, calculating the warpage of the double-layer metal strip includes:

[0056] The warpage of the divided entry semi-rolling zone, relative sliding zone, rolling composite zone, and exit semi-rolling zone is quantified in sequence to construct a warpage model and calculate the warpage of the double-layer metal strip. The warpage of the entry semi-rolling zone is zero, the warpage of the sliding zone is obtained based on the radius of the lower roll in the flattened state, the warpage of the rolling composite zone is obtained based on geometric relationships, and the warpage of the exit semi-rolling zone is obtained based on the diameter of the lower work roll.

[0057] The warping model is as follows:

[0058] δ=M1δ 相对滑动区 +M2δ 轧制复合区 +M3δ 出口半轧区 ;

[0059] Where M1, M2, and M3 are process parameters, and δ is the warpage of the double-layer metal strip. 相对滑动区 δ 轧制复合区 δ 出口半轧区 These are the warpage amounts in the relative sliding zone, the warpage amounts in the rolling composite zone, and the warpage amounts in the exit semi-rolling zone, respectively.

[0060] Preferably, quantifying the warpage of the rolling composite zone includes:

[0061] Determine the critical rolling pressure value of the double-layer metal strip and input it into the rolling pressure calculation model to obtain the abscissa of the critical point of the rolling composite zone;

[0062] Substitute the abscissa of the critical point of the rolling composite zone and the abscissa of the intersection of the rolling pressure calculation model and the x-axis into the geometric relationship model of the upper and lower rolls to obtain the theoretical value of the inlet thickness, the theoretical value of the outlet thickness, and the thickness variation of the rolling composite zone;

[0063] The length variation of the rolling composite zone in the rolling direction is obtained based on the Poisson's ratio of the base layer and the cladding metal and the thickness variation of the rolling composite zone.

[0064] Based on the theoretical values ​​of the inlet and outlet thicknesses of the rolling composite zone, the thickness variation, and the length variation along the rolling direction, the equivalent circular arc is obtained.

[0065] Based on the equivalent circular arc, the warpage of the rolling composite zone is obtained.

[0066] Preferably, the warpage amount of the rolled composite zone is:

[0067]

[0068] Where, r 等效 L is the equivalent radius of the circular arc. J L F Δh represents the initial length of the base metal and the cladding metal. fhF For the variation in coating metal thickness, Δh fhJ h represents the variation in the thickness of the base metal. 1J 'V' represents the theoretical value of the thickness of the base metal outlet. F v is the Poisson's ratio of the cladding metal. J For the base metal Poisson's ratio, h 1F 'This is the theoretical value for the thickness of the cladding metal at the outlet.'

[0069] The beneficial effects of this invention are as follows: By combining relevant parameters of double-layer metal strip and rolling mill equipment with the rolling mechanism of double-layer metal, this invention sequentially calculates the elastic deformation zones at the exit, inlet, and plastic deformation zones of the base and cladding materials, and obtains the contact arc length formulas for the base and cladding metals. Combining the contact arc length with the rolling force, a rolling pressure function for the base and cladding metals is established, describing the rolling pressure variation law of the double-layer metal during rolling, and obtaining the rolling composite critical point. Utilizing the stress characteristics of the base layer and cladding materials, as well as the composite state of the base layer and cladding materials, the process is divided into the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone. Since the formation of warpage defects can be understood as a comprehensive manifestation of the influence of each zone, the influence of each zone on warpage is studied separately based on the characteristics of each zone, and the zone is quantitatively described using a formula. By combining the descriptions of the above zones and the process parameters, a quantitative method for warpage is obtained, realizing the quantitative characterization of the degree of warpage in tensionless double-layer metal strip composite rolling. This effectively avoids the blindness and repetition of experiments in exploring tensionless double-layer metal strip composite rolling processes. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 This is a schematic diagram of the warpage quantification calculation device for the double-layer metal composite rolling process according to an embodiment of the present invention;

[0072] Figure 2 This is a flowchart illustrating the overall process of calculating warpage quantification in tension-free composite rolling of double-layer metal strip according to an embodiment of the present invention.

[0073] Figure 3 This is a schematic diagram of the contact arc length in the deformation zone during the double-layer metal composite rolling process according to an embodiment of the present invention.

[0074] Figure 4 This is a schematic diagram of the rolling mechanism of the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone in an embodiment of the present invention;

[0075] Figure 5 This is a flowchart illustrating the quantitative calculation of the rolling composite zone in an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] like Figure 2 As shown, this embodiment provides a method for quantifying warpage in tension-free composite rolling of double-layer metal strip, including:

[0079] Obtain relevant parameters for metal sheet and strip, as well as relevant parameters for rolling mill equipment;

[0080] Calculate the length of the plastic deformation zone based on relevant parameters of the metal sheet and strip and the rolling mill equipment;

[0081] Based on the relevant parameters of the metal strip and the length of the plastic deformation zone, the lengths of the inlet elastic deformation zone and the outlet elastic deformation zone are calculated.

[0082] Based on the lengths of the plastic deformation zone, the inlet elastic deformation zone, and the outlet elastic deformation zone, calculate the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip.

[0083] Based on the contact arc length of the upper and lower rolling deformation zones of the double-layer metal strip, a rolling pressure calculation model is established; the rolling deformation zone of the double-layer metal strip is divided, and the warpage of the double-layer metal strip is calculated based on the divided deformation zone and the rolling pressure calculation model.

[0084] Specifically, this embodiment combines the relationship between contact arc length and rolling force, rolls, and strip parameters to sequentially calculate the contact arc length of the elastic deformation zone at the exit of the base material and cladding material, the elastic deformation zone at the entrance of the base material and cladding material, the plastic deformation zone of the base material and cladding material, and the entire deformation zone of the base material and cladding material. Then, utilizing the stress characteristics of the base material and cladding material and the composite state of the base material and cladding material, it is sequentially divided into the entrance semi-rolling zone, the relative sliding zone, the rolling composite zone, and the exit semi-rolling zone, and each is quantitatively described to obtain a quantification method for warpage.

[0085] Furthermore, the relevant parameters of the metal strip include: base metal inlet thickness, base metal outlet thickness, cladding metal inlet thickness, and cladding metal outlet thickness;

[0086] The relevant parameters of rolling mill equipment include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0087] Furthermore, calculating the length of the plastic deformation zone includes:

[0088] Calculate the material property influence coefficient of the double-layer metal strip based on the relevant parameters of the metal strip;

[0089] Calculate the maximum value of rolling pressure distribution in the deformation zone of the double-layer metal strip;

[0090] The length of the plastic deformation zone is calculated based on the material property influence coefficient, the maximum value of the rolling pressure distribution in the deformation zone, relevant parameters of the metal sheet and strip, and relevant parameters of the rolling mill equipment.

[0091] Furthermore, the length l of the plastic deformation zone of the double-layer metal strip is calculated. J l F ,like Figure 3 As shown, it includes the following steps:

[0092] (a1) Calculate the material property influence coefficient of the double-layer metal strip, including the material property influence coefficient of the base metal strip and the material property influence coefficient of the cladding metal strip;

[0093] The influence coefficient of material properties of the base metal sheet / strip is:

[0094]

[0095] The material property influence coefficient of the clad metal sheet / strip is:

[0096]

[0097] Where, ξ 1J ξ is the influence coefficient of the properties of the base metal material. 1F σ is the influence coefficient of the properties of the coating metal material. s1J For the deformation resistance of the base metal outlet, v J For the base metal Poisson's ratio, h 1J E represents the measured thickness of the base metal outlet. J For the Young's modulus of the base metal, h 0J σ represents the measured thickness of the base metal inlet. s1F For the deformation resistance of the clad metal outlet, v F E represents the Poisson's ratio of the coated metal. F h represents the Young's modulus of the cladding metal. 0F h is the measured value of the inlet thickness of the cladding metal. 1F This is the measured value of the coating metal outlet thickness;

[0098] (a2) Calculate the maximum value of the rolling pressure distribution in the deformation zone of the double-layer metal strip, including the maximum value of the rolling pressure distribution in the deformation zone of the base metal strip and the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal strip.

[0099] The maximum value of the rolling pressure distribution in the deformation zone of the base metal strip is:

[0100]

[0101] The maximum value of the rolling pressure distribution in the deformation zone of the clad metal sheet / strip is:

[0102]

[0103] Where, p Jmax The maximum value of rolling pressure distribution in the deformation zone of the base metal is given by α, which is the specific gravity coefficient of the elliptical model. J l is the unit rolling force between the roll and the base metal. JZ p is the contact arc length of the deformation zone of the base metal rolling process. Fmax p represents the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal. F l is the unit rolling force between the roll and the cladding metal. FZ The contact arc length of the deformation zone during the rolling of the cladding metal;

[0104] (a3) Calculate the length of the plastic deformation zone of the double-layer metal strip, including the length of the plastic deformation zone of the base metal strip and the length of the plastic deformation zone of the cladding metal strip.

[0105] The length of the plastic deformation zone of the base metal strip is:

[0106]

[0107] The length of the plastic deformation zone of the clad metal strip is:

[0108]

[0109] Where lJ is the length of the plastic deformation zone of the base metal strip, R is the radius of the work roll, and E r v is the Young's modulus of the work roll. r For the Poisson's ratio of the working roll, l F This represents the length of the plastic deformation zone of the clad metal sheet / strip.

[0110] Furthermore, the lengths of the inlet and outlet elastic deformation zones of the double-layer metal strip are calculated, including the inlet elastic deformation zone length of the base metal strip, the outlet elastic deformation zone length of the base metal strip, the inlet elastic deformation zone length of the cladding metal strip, and the outlet elastic deformation zone length of the cladding metal strip.

[0111] The length of the elastic deformation zone at the entrance of the base metal strip is:

[0112]

[0113] The length of the exit elastic deformation zone of the base metal strip is:

[0114]

[0115] Where, Δx 0J σ is the length of the elastic deformation zone at the entrance of the base metal strip. s0J For the deformation resistance of the base metal inlet, Δx1J The length of the elastic deformation zone at the exit of the base metal strip, μ rz The coefficient of friction;

[0116] The length of the elastic deformation zone at the entrance of the clad metal strip is:

[0117]

[0118] The length of the exit elastic deformation zone of the clad metal strip is:

[0119]

[0120] Where, Δx 0F σ is the length of the elastic deformation zone at the entrance of the clad metal strip. s0F For the deformation resistance of the cladding metal inlet, Δx 1F This refers to the length of the exit elastic deformation zone of the clad metal strip.

[0121] Furthermore, the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip are calculated, including the contact arc length l of the base metal strip. JZ Contact arc length l of the clad metal strip FZ The contact arc length of the rolling deformation zone is related to the length of the inlet elastic deformation zone, the length of the plastic deformation zone, and the length of the outlet elastic deformation zone. The contact arc length of the rolling deformation zone is also the range of action of the rolling pressure function, and the specific expression is as follows:

[0122] l JZ =Δx 0J +l J +Δx 1J ;

[0123] l FZ =Δx 0F +l F +Δx 1F ;

[0124] The contact arc length of the rolling deformation zone is obtained by combining the formulas for the length of the plastic deformation zone of the base layer and the cladding metal strip, the length of the elastic deformation zone at the entrance of the base layer and the cladding metal strip, and the contact arc length of the rolling deformation zone.

[0125] Furthermore, the rolling pressure function of the base layer and cladding metal is calculated, including the following steps:

[0126] (b1) Set the x-coordinates of the two intersection points where the rolling pressure of the base metal sheet / strip is 0 from left to right as a 1J a 2J The x-coordinates of the two intersection points where the rolling pressure function of the clad metal sheet / strip is 0, from left to right, are a. 1F a 2F ;

[0127] (b2) When the rolling force is P, based on the characteristics of the rolling pressure function of the base layer and the cladding metal strip, the following relationship exists:

[0128] a 2J -a 1J =l JZ ;

[0129] a 2F -a 1F =l FZ ;

[0130] Among them, a 1J a 2J Let P be the x-coordinate of the intersection of the base rolling pressure function and the x-axis, P be the rolling force, μ be the mean of the function, σ be the variance of the function, and a be the x-coordinate of the intersection of the base rolling pressure function and the x-axis. 1F a 2F The x-coordinate of the intersection of the cladding rolling pressure function and the x-axis;

[0131] (b3) Calculate the rolling pressure function of the double-layer metal strip, i.e., the rolling pressure calculation model, including the initial rolling pressure function of the base metal strip. Initial rolling pressure function of clad metal sheet and strip

[0132] Where x represents the position coordinates during the double-layer metal sheet and strip composite rolling process;

[0133] (b4) The empirical error term α of rolling pressure was determined based on experiments. J (x), calculate the specific rolling pressure function, i.e., P J (x)=ψ J (x)+α J (x), P F (x)=ψ F (x)+α F (x).

[0134] Furthermore, the division of the deformation zone in the rolling of double-layer metal strip includes:

[0135] Based on the stress and composite state of the double-layer metal strip, the rolling deformation zone of the double-layer metal strip is divided into the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone.

[0136] Specifically, such as Figure 4 As shown in Figure (c1), the inlet semi-rolling zone is divided into two sections. The easily deformable side contacts the upper roll first, but the less deformable side does not contact the lower roll. The two are not combined and both tend to lean towards the lower work roll surface, forming a semi-rolled state. (c2) The relative sliding zone is divided into two sections. It is slightly different from the outlet and inlet semi-rolling zones. There is rolling force on both sides in this zone, but the rolling pressure is not enough to make them combine. Since the force of the upper roll per unit arc length is different from that of the lower roll, and the double-layer metal strip has been squeezed between the upper and lower rolls at this time, there is no gap between it and the rolls. (c3) The rolling composite zone is divided into two sections. It is an important area that determines whether the double-layer metal strip can be combined. When the rolling force is higher than the composite critical value, the double-layer metal strip is in a composite state. (c4) The outlet semi-rolling zone is divided into two sections. Since the lower surface of the less deformable side is unloaded, the double-layer metal strip is pressed against the lower work roll surface, forming a semi-rolled state.

[0137] Furthermore, calculating the warpage of the double-layer metal strip includes:

[0138] The warpage of the divided entry semi-rolling zone, relative sliding zone, rolling composite zone, and exit semi-rolling zone is quantified in sequence, a warpage model is constructed, and the warpage of the double-layer metal strip is calculated. Among them, the warpage of the entry semi-rolling zone is zero, the warpage of the sliding zone is obtained based on the radius of the lower roll in the flattened state, the warpage of the rolling composite zone is obtained based on geometric relationships, and the warpage of the exit semi-rolling zone is obtained based on the diameter of the lower work roll.

[0139] The warping model is as follows:

[0140] δ=M1δ 相对滑动区 +M2δ 轧制复合区 +M3δ 出口半轧区

[0141] Where M1, M2, and M3 are process parameters, and δ is the warpage of the double-layer metal strip. 相对滑动区 δ 轧制复合区 δ 出口半轧区 These are the warpage amounts in the relative sliding zone, the warpage amounts in the rolling composite zone, and the warpage amounts in the exit semi-rolling zone, respectively.

[0142] Specifically, the quantitative description of warpage in each region of rolling deformation includes the following steps:

[0143] (d1) In the semi-rolled zone at the inlet, based on the characteristics of the region, the two do not combine; they only reflect the flow direction of the double-layer metal, i.e., δ. 入口半轧区 ≈0;

[0144] (d2) Quantify the relative sliding zone. Based on the characteristics of the region, the warpage of the relative sliding zone is equal to the radius curvature of the lower roll in the flattened state, where R′ is the radius of the lower roll in the flattened state.

[0145] (d3) Quantitative rolling composite zone, based on the characteristics of the zone, such as Figure 5 As shown, the following relationship exists:

[0146] (d3-1) Set the critical rolling pressure β for steel / aluminum strip composite. 轧制 The x-coordinate of the rolling composite critical point is determined based on the rolling pressure function of the base layer and the cladding layer. 轧制 The specific relationship is as follows:

[0147] β 轧制 =ψ J (x 轧制 )+α J (x 轧制 )

[0148] β 轧制 =ψ F (x 轧制 )+α F (x 轧制 )

[0149] Two x values ​​are obtained from the rolling pressure functions of the base layer and the cladding layer. 轧制 The minimum value is taken as x calculated in steps d3-3 and d3-4. 轧制 ;

[0150] (d3-2) The coordinate system of the roll geometric equation coincides with that of the rolling pressure function, and the established upper roll geometric equation (geometric relationship model) is as follows: The geometric equation (geometric relationship model) of the lower roll is as follows: Where λ1, λ2, λ3, and λ4 are geometric influence parameters determined based on actual working conditions;

[0151] (d3-3) The x-coordinate of the critical point of rolling composite 轧制 The x-coordinate of the intersection point of the rolling pressure function and the x-axis is a. 2J Substituting the values ​​into the geometric equation of the upper roll in contact with the base metal, we obtain the value of y, and thus the theoretical value of the base metal inlet thickness h. fhJ Theoretical value of outlet thickness h 1J The thickness variation Δh of the base metal was obtained. fhJ ;

[0152] (d3-4) The x-coordinate of the critical point of rolling composite 轧制 The x-coordinate of the intersection point of the rolling pressure function and the x-axis is a. 2FSubstituting this into the geometric equation of the lower roll in contact with the cladding metal, we obtain the theoretical value h of the cladding metal inlet thickness. fhF Theoretical value of outlet thickness h 1F The change in coating metal thickness Δh was obtained. fhF ;

[0153] (d3-5) Given that the initial lengths of the base layer and cladding metal are L J L F Δh obtained from (d3-3) and (d3-4) fhJ Δh fhF The Poisson's ratio is defined by the base layer and the cladding metal. The length variation Δl of the base layer and cladding metal in the rolling direction can be obtained. zJ Δl zF ;

[0154] (d3-6) Based on the changes in the rolling length and thickness of the base layer and cladding layer, their geometric relationship is equivalent to a circular arc, where the radius is R. 等效 The included angle is θ 等效 The calculation process is as follows:

[0155]

[0156] We can obtain:

[0157] (d3-7) yields the quantization expression for the rolling composite zone, as follows:

[0158]

[0159] (d4) In the semi-rolled zone at the quantified exit, based on the characteristics of this area, the double-layer metal strip is pressed against the surface of the lower work roll. At this point, the warpage is related to the diameter of the lower work roll; that is, the warpage in this area is approximately equal to the curvature of the lower roll.

[0160] (d5) Based on the experimental results, the process parameters M1, M2, and M3 under given operating conditions are obtained, and a warpage quantification expression is established, namely δ = M1δ 相对滑动区 +M2δ 轧制复合区 +M3δ 出口半轧区 .

[0161] like Figure 1 As shown, this embodiment also provides a warpage quantification calculation device suitable for double-layer metal composite strips, comprising:

[0162] Step D1: Collection module, used to collect relevant parameters of metal sheet and strip and relevant parameters of rolling mill equipment;

[0163] The relevant parameters for metal strips include: base metal inlet thickness, base metal outlet thickness, cladding metal inlet thickness, and cladding metal outlet thickness;

[0164] The relevant parameters of rolling mill equipment include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

[0165] Step D2: Define the module, which is used to define the calculation parameters for the double-layer metal strip rolling process;

[0166] The calculation parameters include: the length of the elastic deformation zone at the base metal inlet, the length of the plastic deformation zone at the base metal outlet, the maximum value of the rolling pressure distribution in the deformation zone of the base metal, the Poisson's ratio of the base metal, the influence coefficient of the material properties of the base metal, the length of the elastic deformation zone at the cladding metal inlet, the length of the plastic deformation zone at the cladding metal outlet, the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal, the Poisson's ratio of the cladding metal, and the influence coefficient of the material properties of the cladding metal.

[0167] Step D3, Calculation module, is used to calculate the contact arc length of the upper and lower rolling deformation zones of the double-layer metal strip;

[0168] The length of the plastic deformation zone is calculated based on the relevant parameters of the metal sheet and strip and the relevant parameters of the rolling mill equipment;

[0169] Based on the relevant parameters of the metal strip and the length of the plastic deformation zone, the lengths of the inlet elastic deformation zone and the outlet elastic deformation zone are calculated.

[0170] Based on the lengths of the plastic deformation zone, the inlet elastic deformation zone, and the outlet elastic deformation zone, calculate the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip.

[0171] Step D4: Establish a module to create a rolling pressure quantification function for the base layer and cladding metal;

[0172] Based on the contact arc length of the upper and lower rolling deformation zones of the double-layer metal strip, a rolling pressure quantification function, i.e., a rolling pressure calculation model, is established.

[0173] Step D5: Divide the module to divide the area with the characteristics of double-layer metal strip rolling deformation zone;

[0174] The division of the deformation zone in the rolling of double-layer metal strip includes:

[0175] Based on the stress and composite state of the double-layer metal strip, the rolling deformation zone of the double-layer metal strip is divided into the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone.

[0176] Step D6, Quantization module, is used to quantify the warpage of each region of rolling deformation and establish a warpage model.

[0177] Calculating the warpage of a double-layer metal strip includes:

[0178] The warpage of the divided entry semi-rolling zone, relative sliding zone, rolling composite zone, and exit semi-rolling zone is quantified in sequence, a warpage model is constructed, and the warpage of the double-layer metal strip is calculated. Among them, the warpage of the entry semi-rolling zone is zero, the warpage of the sliding zone is obtained based on the radius of the lower roll in the flattened state, the warpage of the rolling composite zone is obtained based on geometric relationships, and the warpage of the exit semi-rolling zone is obtained based on the diameter of the lower work roll.

[0179] The warping model is as follows:

[0180] δ=M1δ 相对滑动区 +M2δ 轧制复合区 +M3δ 出口半轧区

[0181] Where M1, M2, and M3 are process parameters, and δ is the warpage of the double-layer metal strip. 相对滑动区 δ 轧制复合区 δ 出口半轧区 These are the warpage amounts in the relative sliding zone, the warpage amounts in the rolling composite zone, and the warpage amounts in the exit semi-rolling zone, respectively.

[0182] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for quantitatively calculating warpage in tension-free composite rolling of double-layer metal sheet and strip, characterized in that, include: Obtain relevant parameters for metal sheet and strip, as well as relevant parameters for rolling mill equipment; Calculate the length of the plastic deformation zone based on the relevant parameters of the metal sheet and strip and the relevant parameters of the rolling mill equipment; Based on the relevant parameters of the metal strip and the length of the plastic deformation zone, calculate the length of the inlet elastic deformation zone and the length of the outlet elastic deformation zone; Based on the length of the plastic deformation zone, the length of the inlet elastic deformation zone, and the length of the outlet elastic deformation zone, calculate the contact arc length of the upper and lower rolling deformation zones of the double-layer metal strip; A rolling pressure calculation model is established based on the contact arc lengths of the upper and lower rolling deformation zones of the double-layer metal strip. The deformation zone of the double-layer metal strip rolling process is divided, and the warpage of the double-layer metal strip is calculated based on the divided deformation zone and the rolling pressure calculation model. The division of the deformation zone in the rolling of double-layer metal strip includes: Based on the stress and composite state of the double-layer metal strip, the rolling deformation zone of the double-layer metal strip is divided into the inlet semi-rolling zone, the relative sliding zone, the rolling composite zone, and the outlet semi-rolling zone. Calculating the warpage of a double-layer metal strip includes: The warpage of the divided entry semi-rolling zone, relative sliding zone, rolling composite zone, and exit semi-rolling zone is quantified sequentially to construct a warpage model and calculate the warpage of the double-layer metal strip. The warpage of the entry semi-rolling zone is zero, the warpage of the relative sliding zone is obtained based on the radius of the lower roll in the flattened state, the warpage of the rolling composite zone is obtained based on geometric relationships, and the warpage of the exit semi-rolling zone is obtained based on the diameter of the lower work roll. The warping model is as follows: δ=M1δ 相对滑动区 +M2δ 轧制复合区 +M3d 出口半轧区 ; Where M1, M2, and M3 are process parameters, and δ is the warpage of the double-layer metal strip. 相对滑动区 δ 轧制复合区 δ 出口半轧区 These are the warpage amounts in the relative sliding zone, the warpage amounts in the rolling composite zone, and the warpage amounts in the exit semi-rolling zone, respectively. Quantifying the warpage of the rolling composite zone includes: Determine the critical rolling pressure value of the double-layer metal strip and input it into the rolling pressure calculation model to obtain the abscissa of the critical point of the rolling composite zone; Substitute the abscissa of the critical point of the rolling composite zone and the abscissa of the intersection of the rolling pressure calculation model and the x-axis into the geometric relationship model of the upper and lower rolls to obtain the theoretical value of the inlet thickness, the theoretical value of the outlet thickness, and the thickness variation of the rolling composite zone; The length variation of the rolling composite zone in the rolling direction is obtained based on the Poisson's ratio of the base layer and the cladding metal and the thickness variation of the rolling composite zone. Based on the theoretical values ​​of the inlet and outlet thicknesses of the rolling composite zone, the thickness variation, and the length variation along the rolling direction, the equivalent circular arc is obtained. Based on the equivalent circular arc, the warpage of the rolling composite zone is obtained.

2. The method for quantifying warpage in tension-free composite rolling of double-layer metal strips according to claim 1, characterized in that, The relevant parameters of the metal strip include: base metal inlet thickness, base metal outlet thickness, cladding metal inlet thickness, and cladding metal outlet thickness; The relevant parameters of the rolling mill equipment include: work roll radius, work roll Young's modulus, and work roll Poisson's ratio.

3. The method for quantifying warpage in tension-free composite rolling of double-layer metal sheet and strip according to claim 1, characterized in that, Calculating the length of the plastic deformation zone includes: Calculate the material property influence coefficient of the double-layer metal strip based on the relevant parameters of the metal strip; Calculate the maximum value of rolling pressure distribution in the deformation zone of the double-layer metal strip; The length of the plastic deformation zone is calculated based on the material property influence coefficient, the maximum value of the rolling pressure distribution in the deformation zone, the relevant parameters of the metal strip, and the relevant parameters of the rolling mill equipment.

4. The method for quantifying warpage in tension-free composite rolling of double-layer metal strips according to claim 3, characterized in that, The material property influence coefficient includes the material property influence coefficient of the base metal sheet and the material property influence coefficient of the cladding metal sheet; The material property influence coefficient of the base metal strip is: The material property influence coefficient of the clad metal strip is: Where, ξ 1J ξ is the influence coefficient of the properties of the base metal material. 1F σ is the influence coefficient of the properties of the coating metal material. s1J For the deformation resistance of the base metal outlet, v J For the base metal Poisson's ratio, h 1J E represents the measured thickness of the base metal outlet. J For the Young's modulus of the base metal, h 0J σ represents the measured thickness of the base metal inlet. s1F For the deformation resistance of the clad metal outlet, v F E represents the Poisson's ratio of the coated metal. F h represents the Young's modulus of the cladding metal. 0F h is the measured value of the inlet thickness of the cladding metal. 1F This is the measured value of the coating metal outlet thickness; The maximum value of the rolling pressure distribution in the deformation zone of the double-layer metal strip includes the maximum value of the rolling pressure distribution in the deformation zone of the base metal strip and the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal strip. The maximum value of the rolling pressure distribution in the deformation zone of the base metal strip is: The maximum value of the rolling pressure distribution in the deformation zone of the clad metal strip is: Where, p Jmax The maximum value of rolling pressure distribution in the deformation zone of the base metal is given by α, which is the specific gravity coefficient of the elliptical model. J l is the unit rolling force between the roll and the base metal. JZ p is the contact arc length of the deformation zone of the base metal rolling process. Fmax p represents the maximum value of the rolling pressure distribution in the deformation zone of the cladding metal. F l is the unit rolling force between the roll and the cladding metal. FZ The contact arc length of the deformation zone during the rolling of the cladding metal; The length of the plastic deformation zone includes the length of the plastic deformation zone of the base metal strip and the length of the plastic deformation zone of the cladding metal strip. The length of the plastic deformation zone of the base metal strip is: The length of the plastic deformation zone of the clad metal strip is: Among them, l J R is the length of the plastic deformation zone of the base metal strip, R is the radius of the work roll, and E is the length of the plastic deformation zone of the base metal strip. r v is the Young's modulus of the work roll. r For the Poisson's ratio of the working roll, l F This represents the length of the plastic deformation zone of the clad metal sheet / strip.

5. The method for quantifying warpage in tension-free composite rolling of double-layer metal strips according to claim 4, characterized in that, The lengths of the inlet elastic deformation zone and the outlet elastic deformation zone are calculated as follows: The length of the elastic deformation zone at the entrance of the base metal strip is: The length of the exit elastic deformation zone of the base metal strip is: Where, Δx 0J σ is the length of the elastic deformation zone at the entrance of the base metal strip. s0J For the deformation resistance of the base metal inlet, Δx 1J The length of the elastic deformation zone at the exit of the base metal strip, μ rz The coefficient of friction; The length of the elastic deformation zone at the entrance of the clad metal strip is: The length of the exit elastic deformation zone of the clad metal strip is: Where, Δx 0F σ is the length of the elastic deformation zone at the entrance of the clad metal strip. s0F For the deformation resistance of the cladding metal inlet, Δx 1F This refers to the length of the exit elastic deformation zone of the clad metal strip.

6. The method for quantifying warpage in tension-free composite rolling of double-layer metal sheet and strip according to claim 1, characterized in that, The rolling pressure calculation model is as follows: P J (x)=ψ J (x)+a J (x); P F (x)=ψ F (x)+a F (x); Among them, a 2J -a 1J =l JZ a 2F -a 1F =l FZ x represents the position coordinates during the double-layer metal sheet and strip composite rolling process, a 1J a 2J Let a be the x-coordinate of the two intersection points where the rolling pressure of the base metal sheet / strip is 0. 1F a 2F Let P be the x-coordinate of the two intersection points where the rolling pressure of the clad metal sheet / strip is 0, and α be the rolling force. J (x), α F (x) represents the empirical error term for rolling pressure, P J (x) is the rolling pressure function of the base metal sheet / strip, ψ J (x) is the initial rolling pressure function of the base metal sheet / strip, P F (x) is the rolling pressure function of the clad metal sheet / strip, ψ F (x) is the initial rolling pressure function of the clad metal sheet / strip, l JZ For the contact arc length of the deformation zone of the base metal rolling, l FZ It is the contact arc length of the deformation zone during the rolling of the cladding metal.

7. The method for quantifying warpage in tension-free composite rolling of double-layer metal sheet and strip according to claim 1, characterized in that, The warpage amount of the rolled composite zone is: Where, r 等效 L is the equivalent radius of the circular arc. J L is the initial length of the base metal. F Initial length of cladding metal, Δh fhF For the variation in coating metal thickness, Δh fhJ h represents the variation in the thickness of the base metal. 1J 'V' represents the theoretical value of the thickness of the base metal outlet. F v is the Poisson's ratio of the cladding metal. J For the base metal Poisson's ratio, h 1F ' is the theoretical value of the coating metal outlet thickness, h fhJ h is the theoretical value of the thickness of the base metal inlet. fhF This is the theoretical value for the inlet thickness of the cladding metal.

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