CN114074118B - Rolling stability prediction method of six-roller cold rolling mill - Google Patents

Abstract

The invention discloses a method for predicting rolling stability of a six-roller cold rolling mill, and relates to the technical field of automatic production in a rolling process. The method considers the entrance oil film extrusion effect, introduces the vertical vibration speed of the roller into an oil film thickness calculation formula to obtain the dynamic entrance oil film thickness, and calculates the change condition of the friction stress distribution of a deformation region along with time by combining the roughness distribution hypothesis; the Kalman differential equation derivation of the vertical vibration speed of the roller is considered, and the Kalman differential equation derivation is brought into the distribution of the friction stress in a deformation area, and the dynamic rolling force and the rolling force fluctuation amount caused by the vertical vibration of the roller are calculated; establishing a vertical vibration dynamic equation of a rolling mill system according to the stress relation among the roller, the rolled piece and the memorial archways, solving by adopting a Newmark-Beta method, and taking the vertical displacement of the roller as a basis for judging the stability of the rolling mill, wherein if the displacement curve of the roller is converged, the rolling mill is stable, and if the displacement curve of the roller is diverged, the rolling mill is unstable. The method can be used for more accurately predicting the stability of the rolling mill in the rolling process.

Description

A rolling stability prediction method for a six-high cold rolling mill

technical field

The invention relates to the technical field of automatic production of rolling process, in particular to a rolling stability prediction method of a six-high cold rolling mill.

Background technique

Rolling mill vibration is a common and urgent problem to be solved in plate and strip production. During high-speed rolling of thin-gauge high-strength steel, due to the strong coupling and nonlinearity of process parameters, equipment status and control system, various abnormal vibrations that are difficult to eliminate by adjusting process parameters often occur in the rolling mill, such as the self-excited vibration in the vertical direction of the rolling mill. The self-excited vibration in the vertical direction of the rolling mill will cause periodic vibration lines on the surface of the strip and the roll, which seriously affects the quality of the product; and the self-excited vibration in the vertical direction of the rolling mill will also aggravate the wear of the roll and bearing, and even cause the roll and strip to break. Threats to the lives of workers. The reason for the self-excited vibration in the vertical direction of the rolling mill is that in the interaction between the dynamic change of the rolling mill structure and the rolling process, the change of process parameters causes the equivalent damping and stiffness of the rolling interface to change, resulting in a decrease in the equivalent damping of the interface. If the total damping of the rolling stock-rolling mill system is negative, the system will continuously absorb energy from the transmission device, so that the amplitude of the rolls will continue to increase, which will lead to instability in the rolling process.

Aiming at the problem of self-excited vibration in the vertical direction of the rolling mill that constantly occurs during high-speed rolling, researchers have done a lot of related research. However, these studies mainly have two deficiencies: (1) It is assumed that the friction state of the rolling interface remains unchanged during the vibration process. However, in fact, the self-excited vibration in the vertical direction of the rolling mill will cause periodic changes in the interface lubrication state. This change will become more obvious as the vibration intensifies. If this change is not considered, the accuracy of the self-excited vibration determination will be reduced. . (2) Using the Kalman differential equation to calculate the rolling force when the vibration occurs, the result is not accurate enough because the influence of the vertical vibration velocity of the roll is not considered.

SUMMARY OF THE INVENTION

Aiming at the above-mentioned deficiencies of the prior art, the present invention provides a rolling stability prediction method of a six-high cold rolling mill, which can predict the change of the lubrication state of the rolling interface and the dynamic rolling according to the existing rolling regulations and rolling mill structure parameters. force calculation, and can more accurately predict the stability of the rolling mill during the rolling process, so as to avoid the self-excited vibration of the rolling mill in the vertical direction caused by the high rolling speed or the unreasonable formulation of the rolling schedule, so as to improve the surface of the strip. quality and the purpose of stable operation of the rolling process.

For achieving the above object, the technical scheme provided by the invention is:

A method for predicting rolling stability of a six-high cold rolling mill, the method comprising the following steps:

Step 1: Collect relevant parameters, including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structure parameters;

Step 2: Calculate the dynamic contact arc length of the deformation zone according to the steel strip parameters, the roll diameter and the vertical vibration speed of the roll, discretize the deformation zone along the rolling direction, and calculate the micro-elements obtained after the discretization process. the average deformation resistance of the body;

Step 3: Calculate the dynamic inlet oil film thickness using the one-dimensional Reynolds equation;

Step 4: Combine the dynamic inlet oil film thickness and Christensen roughness distribution assumptions obtained in step 3 to calculate the friction stress distribution in the deformation zone;

Step 5: The Kalman differential equation is improved, and the friction stress distribution obtained in step 4 is substituted into the improved Kalman differential equation to solve the rolling force fluctuation ΔP ₁ caused by the vertical vibration of the roll;

Step 6: Calculate the amount of back tension change caused by vibration and the rolling force fluctuation ΔP ₂ caused by the back tension change according to the tension relationship between the stands;

Step 7: According to the force relationship between the components of each rolling mill and the total amount of rolling force fluctuation ΔP=ΔP ₁ +ΔP ₂ , establish the vertical vibration dynamics equation of the rolling mill system and solve it to obtain the roll displacement and velocity response, so as to predict the stability of the rolling process.

Further, according to the method for predicting the rolling stability of the six-high cold rolling mill, the strip parameters include: strip grade, strip width, and thickness of incoming material for hot rolling; the lubricating oil parameters include lubricating oil viscosity and viscosity coefficient; the rolling process parameters include: front and rear tension between stands, rolling speed of each pass, strip inlet speed of each pass, and thickness of strip entrance and exit of each pass; the rolling mill structural parameters include: roll Quality, roll material, roll diameter, roll length, rolling mill stiffness coefficient, damping coefficient of each part of the rolling mill, arch quality; the rolling mill stiffness coefficient includes the roll stiffness coefficient and the arch stiffness coefficient.

According to the rolling stability prediction method of the six-high cold rolling mill, the step 2 further includes the following steps:

Step 2.1: Calculate the dynamic contact arc length in the deformation zone according to the thickness of the strip entrance and exit, the diameter of the roll and the vertical vibration velocity of the roll;

Step 2.2: Discretize the deformation zone along the rolling direction to obtain several micro-elements;

Step 2.3: Calculate the average deformation resistance of each micro-element by using the deformation resistance model according to the material of the strip and the thickness of the micro-element.

Further, according to the rolling stability prediction method of the six-high cold rolling mill, the calculation formula of the dynamic contact arc length l is as follows:

In the above formula, l is the dynamic contact arc length; R is the roll flattening radius; _{y in} and y _out are the thickness of the strip inlet and outlet; θ is the change of the bite angle; is positive; v _out is the strip outlet speed.

Further, according to the rolling stability prediction method of the six-high cold rolling mill, the method for calculating the dynamic inlet oil film thickness using the one-dimensional Reynolds equation in the step 3 is:

The one-dimensional Reynolds equation considering the squeezing effect is as follows:

In the above formula, h ₁ is the oil film thickness in the inlet area; x _f is the distance from the inlet and outlet; p is the rolling pressure distribution in the deformation area; η is the viscosity of lubricating oil under different pressures; v is the average speed of the strip and roll; t for time;

Since the oil film pressure in the inlet area is small, the formula for the viscosity of the lubricating oil adopts the Barus formula, as shown below:

η=η ₀ e ^γp (12)

The dimensionless parameter φ is introduced:

In the above formula, γ is the viscous pressure coefficient of the Barus formula; p is the rolling pressure distribution in the deformation zone; η ₀ is the viscosity of the lubricating oil under atmospheric pressure;

Integrating the one-dimensional Reynolds equation and replacing the integration constant with the steady-state result for v _y = 0 gives:

为咬入角变化速率；σ_b为带钢后张力；当x_f趋于无穷大时，润滑油油膜压力趋于0，因此可得到如下边界条件1：In the above formula, α is the bite angle;

is the rate of change of the bite angle; σ _b is the back tension of the strip; when x _f tends to infinity, the lubricating oil film pressure tends to 0, so the following boundary condition 1 can be obtained:

x _f = ∞, h ₁ = ∞, φ = 1 (15)

的表达式并整理可得：Substitute boundary condition 1 into

expression and tidy up to get:

According to the calculation of the lubricating oil film pressure at the junction of the inlet area and the deformation area according to the Tresca yield criterion p=σ _s -σ _b , the following boundary condition 2 can be obtained:

Substitute boundary condition 2 into the expression of φ and arrange it to get:

为入口油膜厚度变化速率；h_0,d为动态入口油膜厚度；Δt为时间步长；h₀为稳态时的入口油膜厚度，可由下式确定：in,

is the change rate of the inlet oil film thickness; h _0,d is the dynamic inlet oil film thickness; Δt is the time step; h ₀ is the inlet oil film thickness at steady state, which can be determined by the following formula:

Among them, v _in is the strip inlet speed; v _r is the rolling speed; l ₀ is the length of the deformation zone in the steady state.

Further, according to the rolling stability prediction method of the six-high cold rolling mill, the method for calculating the friction stress distribution in the deformation zone described in the step 4 is:

According to the dynamic inlet oil film thickness obtained in step 3 and the principle of constant volume, the oil film thickness distribution h(x) in the deformation zone can be expressed as follows:

In the above formula, h(x) is the oil film thickness distribution in the deformation zone; v _r is the rolling speed; v _in is the strip inlet velocity; v _s is the strip velocity distribution along the rolling direction; h _0,d is the dynamic inlet oil film thickness;

According to the Christensen roughness distribution assumption, the actual contact area ratio _Ac and the average oil film thickness h _t can be expressed as:

In the above formula, δ is the roughness distribution; Z=h/3R _q is a dimensionless parameter; f(δ) is the probability density function, which can be expressed as:

In the above formula, R _q is the comprehensive surface roughness of the strip and roll;

Finally, the friction stress distribution τ in the deformation zone can be expressed as:

In the above formula, τ is the total friction stress distribution in the deformation zone; τ _a is the friction stress generated by rough contact; τ _f is the friction stress generated by fluid lubrication; k is the shear strength of the material.

Further, according to the rolling stability prediction method of the six-high cold rolling mill, the step 5 further includes the following steps:

Step 5.1: After analyzing the force of the micro-elements in the deformation zone, formulate the static equilibrium relation equation for the micro-elements in the deformation zone along the rolling direction, and obtain the improved Kalman differential equation from the static equilibrium relation equation;

Step 5.2: Substitute the frictional stress distribution obtained in step 4 into the improved Kalman differential equation, and obtain the rolling force fluctuation ΔP ₁ caused by the vertical vibration of the roll after integration.

8. The method for predicting rolling stability of a six-high cold rolling mill according to claim 1, wherein the step 7 comprises the following steps:

Step 7.1: According to the simplified model of one-half of the six-high cold rolling mill and the force relationship between the rolls, the rolling stock and the arch, combined with the mechanical vibration theory, establish the vertical vibration dynamic equation of the rolling mill system;

Step 7.2: Use the Newmark-Beta method to solve the vertical vibration dynamics equation of the rolling mill system, and use the vertical speed of the roll as the input of the calculation process at the next moment, and use the vertical displacement of the roll as the basis for judging the stability of the rolling mill. If the roll displacement curve converges, the rolling mill is stable, and if the roll displacement curve diverges, the rolling mill is unstable.

In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art: First, the method of the present invention considers the change of the rolling interface lubrication state and the change of the rolling force caused by the vibration of the roll, and the calculation result of the rolling force more accurate; secondly, the method of the present invention can predict the rolling process stability of most of the six-high cold rolling mills on the basis of the existing rolling regulations or real-time collected data, combined with the pressing experiment, and has wide applicability; Thirdly, the method of the present invention can avoid the self-excited vibration in the vertical direction of the rolling mill caused by the high rolling speed or the unreasonable formulation of the rolling schedule, so as to improve the surface quality of the strip steel and improve the enterprise benefit; finally, the method of the present invention is based on the rolling process. Simulation and simulation of control theory and mechanical dynamics can effectively avoid equipment loss and damage caused by experiments and reduce enterprise costs.

Description of drawings

1 is a schematic flowchart of a rolling stability prediction method for a six-high cold rolling mill of the present embodiment;

Fig. 2 is a schematic diagram of the oil film thickness distribution between the roll and the strip;

Fig. 3 is a schematic diagram of the force analysis of the micro-element body according to the present embodiment, wherein Fig. (a) is the force analysis diagram of the micro-element body when the vertical vibration speed of the roller is _vy 00; Fig. (b) is the vertical vibration speed of the _roller . The force analysis diagram of the micro-element body when <0;

In Fig. 4, (a) is a schematic structural diagram of a UCM six-high cold rolling mill; (b) is a schematic diagram of a simplified model of half of the six-high cold rolling mill shown in (a);

Figure 5 is the predicted curve of the displacement response of the work rolls under different process parameters, in which Figure (a) is the predicted curve of the displacement response of the work rolls under different reduction ratios; Figure (b) is the displacement response of the work rolls under different post tensions. Prediction curve; Figure (c) is the prediction curve of the displacement response of the work roll under different roughness; Figure (d) is the prediction curve of the displacement response of the work roll under different viscosities; Figure (e) is the work roll under different rolling speeds. Prediction plot of roll displacement response.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are only used to explain the present invention, and are not intended to limit the present invention.

The core ideas of the method of the invention include: 1. Considering the extrusion effect of the inlet oil film, the vertical vibration velocity of the roll is introduced into the oil film thickness calculation formula to obtain the dynamic inlet oil film thickness, and combined with the roughness distribution assumption, calculate the deformation zone friction stress distribution with time 2. Derive the Kalman differential equation considering the vertical vibration velocity of the roll, and bring it into the friction stress distribution in the deformation zone to calculate the dynamic rolling force and the rolling force fluctuation caused by the vertical vibration of the roll; 3. According to The force relationship between the roll, the rolling stock and the arch, establishes the vertical vibration dynamic equation of the rolling mill system, and then uses the Newmark-Beta method to solve it, and uses the vertical displacement of the roll as the basis for judging the stability of the rolling mill. If the roll displacement curve converges , the rolling mill is stable, and if the roll displacement curve diverges, the rolling mill is unstable.

In this embodiment, the 1450mm UCM six-high tandem cold rolling mill of a factory is taken as an example, and its rolling stability is predicted. The structure of the UCM six-high cold rolling mill is shown in (a) in Figure 4. for flat rolls. FIG. 1 is a schematic flowchart of the rolling stability prediction method of the six-high cold rolling mill in the present embodiment. As shown in FIG. 1 , the rolling stability prediction method of the six-high cold rolling mill includes the following steps:

Step 1: Collect relevant parameters, including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structure parameters;

The strip steel parameters include: strip steel grade, strip width and thickness of incoming material for hot rolling; the lubricating oil parameters include lubricating oil viscosity and viscosity pressure coefficient; the rolling process parameters include: Pass rolling speed, strip inlet speed of each pass, strip thickness of each pass; the rolling mill structural parameters include: roll quality, roll material, roll diameter, roll length, rolling mill stiffness coefficient, and the damping of each part of the rolling mill coefficient, archway quality;

In this embodiment, all strip steel parameters, all rolling process parameters, and roll quality, roll material, roll diameter in the structural parameters of the rolling mill are obtained from the primary control system and secondary control system on the cold rolling production line. , Roll length, archway quality.

The rolling mill stiffness coefficient includes the roll stiffness coefficient and the arch stiffness coefficient. The rolling mill stiffness coefficient is obtained through the on-site pressing experiment, and then the roll stiffness coefficient is obtained by calculating the Hertz contact theory, and finally the arch stiffness coefficient is calculated according to Hooke's law.

In the present embodiment, firstly, by performing a pressing test on a 1450mm UCM six-high tandem cold rolling mill on site, the stiffness coefficient of the rolling mill is obtained as K=4.4×10 ⁹ N/m. Then according to the Hertz contact theory, the roll stiffness coefficient K _i when the two rolls are compressed can be expressed by equation (1):

In the above formula, K _i is the stiffness coefficient of the roll, in N/m; P is the rolling force, in kN; E is the elastic modulus of the roll,

The empirical value is 2.1×1011Pa; v is the Poisson’s ratio of the roll, and the empirical value is 0.3; D ₁ and D ₂ are the diameters of the two rolls, in mm.

After the stiffness coefficient of the roll is determined, the stiffness coefficient K _s of the upper half of the archway in the simplified model of half of the rolling mill can be calculated according to Hooke's law shown in formula (2):

In the above formula, K is the stiffness coefficient of the rolling mill; K _w is the stiffness coefficient of the work roll, K _im is the stiffness coefficient of the intermediate roll, K _b is the stiffness coefficient of the backup roll, and K _s is the stiffness coefficient of the upper half of the arch, in N/m.

The damping coefficient of each part of the rolling mill is obtained according to the Rayleigh damping formula and the stiffness coefficient of the roll and the stiffness coefficient of the arch. Rayleigh damping is a common structural damping construction method, which assumes that the damping matrix C of the structure is a linear combination of the mass matrix M and the stiffness matrix K, namely:

C=β ₁ M+β ₂ K (3)

In the above formula, C is the damping matrix, in N s/m; M is the mass matrix, in kg; K is the stiffness matrix, in N/m; β ₁ and β ₂ are proportional coefficients; ω ₁ and ω ₂ are inherent frequency, the empirical values are 100Hz and 500Hz respectively; ξ ₁ and ξ ₂ are the damping ratios, and the empirical value is 0.03.

In this embodiment, the parameters of the strip steel and the lubricating oil are shown in Table 1, the parameters of the rolling process are shown in Table 2, and the structural parameters of the rolling mill are shown in Table 3.

Table 1 Strip steel parameters and lubricating oil parameters

Table 2 Rolling process parameters

Table 3 Mill structure parameters

Step 2: Calculate the dynamic contact arc length of the deformation zone according to the steel strip parameters, the roll diameter and the vertical vibration speed of the roll, discretize the deformation zone along the rolling direction, and calculate the micro-elements obtained after the discretization process. the average deformation resistance of the body;

Step 2.1: Calculate the dynamic contact arc length in the deformation zone according to the thickness of the strip entrance and exit, the diameter of the roll and the vertical vibration velocity of the roll;

Since the vertical vibration of the roll will cause the change of the deformation zone, it is corrected on the basis of the traditional rolling theory, and the calculation formula of the dynamic contact arc length l is obtained as follows:

In the above formula, l is the dynamic contact arc length, in mm; R is the roll flattening radius, in mm; y _in and y _out are the thickness of the strip inlet and outlet, in mm; θ is the change in the bite angle, in rad ; v _y is the vertical vibration speed of the roll, the speed is positive upward, the unit is m/s; v _out is the strip outlet speed, the unit is m/s.

The roll flattening radius is calculated according to the Hitchcock formula shown in formula (7):

In the above formula, R ₀ is the initial radius of the roll, in mm; E _w is the elastic modulus of the work roll, which is 2.1×10 ¹¹ Pa; _pi is the rolling force N/m per unit length.

Step 2.2: In order to improve the calculation accuracy, the deformation area is discretized into 1000 parts along the rolling direction. Since each part is very small, it is called a micro-element;

Step 2.3: Calculate the average deformation resistance of each micro-element by using the deformation resistance model according to the material of the strip steel and the thickness of the micro-element;

In this embodiment, the grade of strip steel is Q195, and the average deformation resistance σ _s is calculated by the following formulas (8) to (9):

为道次平均厚度。Among them, σ _s is the average deformation resistance, in MPa; the empirical values of each coefficient are A = 498 MPa, B = 136 MPa, C = 0.2, D = 5; ε _Σ is the accumulated deformation; y ₀ is the incoming hot rolling thickness;

is the average thickness of the pass.

Step 3: Calculate the dynamic inlet oil film thickness using the one-dimensional Reynolds equation;

The oil film thickness distribution between the roll and the strip is shown in Figure 2, where y _in and y _out are the thickness of the strip inlet and outlet, respectively, in mm; R ₀ and R are the initial radius and flattening radius of the roll, in mm; h ₀ and h ₁ are the thickness of the oil film at the inlet and the inlet area, respectively, in mm; α is the bite angle, in rad; x _f is the distance from the inlet and outlet, in mm. Using the one-dimensional Reynolds equation to calculate the dynamic inlet oil film thickness is carried out as follows;

The one-dimensional Reynolds equation considering the squeezing effect is as follows:

Since the oil film pressure in the inlet area is small, the formula for the viscosity of the lubricating oil adopts the Barus formula, as shown below:

η=η ₀ e ^γp (12)

The dimensionless parameter φ is introduced:

In the above formula, t is the time, the unit is s; v is the average speed of the strip and the roll, the unit is m/s; γ is the viscosity coefficient of the Barus formula, the unit is MPa ^-1 ; MPa; η ₀ is the viscosity of lubricating oil under atmospheric pressure, in Pa·s; η is the viscosity of lubricating oil under different pressures, in Pa·s.

Integrating the one-dimensional Reynolds equation and replacing the integration constant with the steady-state result for v _y = 0 gives:

为咬入角变化速率，单位rad/s；σ_b为带钢后张力，单位MPa。当x_f趋于无穷大时，润滑油油膜压力趋于0，因此可得到如下边界条件1：in,

is the rate of change of the bite angle, in rad/s; σ _b is the back tension of the strip, in MPa. When x _f tends to infinity, the lubricating oil film pressure tends to 0, so the following boundary condition 1 can be obtained:

x _f = ∞, h ₁ = ∞, φ = 1 (15)

的表达式并整理可得：Substitute boundary condition 1 into

expression and tidy up to get:

And because at the junction of the inlet area and the deformation area, the oil film pressure of the lubricating oil can be calculated according to the Tresca yield criterion p=σ _s -σ _b , so the following boundary condition 2 can be obtained:

Substitute boundary condition 2 into the expression of φ and arrange it to get:

为入口油膜厚度变化速率，单位mm/s；h_0,d为动态入口油膜厚度，单位mm；Δt为时间步长，单位s；h₀为稳态时的入口油膜厚度，单位mm，可由下式确定：in,

is the change rate of the inlet oil film thickness, in mm/s; h _0,d is the dynamic inlet oil film thickness, in mm; Δt is the time step, in s; h ₀ is the inlet oil film thickness at steady state, in mm, which can be calculated from the following The formula is determined:

Among them, v _in is the strip inlet speed, in m/s; v _r is the rolling speed, in m/s; l ₀ is the length of the deformation zone at steady state, in mm.

Step 4: Calculate the friction stress distribution in the deformation zone based on the dynamic inlet oil film thickness and roughness distribution assumptions obtained in step 3;

According to the dynamic inlet oil film thickness obtained in step 3 and the principle of constant volume, the oil film thickness distribution h(x) in the deformation zone can be expressed by equation (22):

In the above formula, h(x) is the oil film thickness distribution in the deformation zone, in mm; v _s is the velocity distribution of the strip along the rolling direction, in m/s.

According to the Christensen roughness distribution assumption, the actual contact area ratio _Ac and the average oil film thickness h _t can be expressed as:

In the above formula, A _c is the actual contact area ratio; h _t is the average oil film thickness, in mm; Z=h/3R _q is a dimensionless parameter; f(δ) is the probability density function, which can be expressed as:

In the above formula, δ is the roughness distribution, in μm; R _q is the comprehensive surface roughness of the strip and roll, in μm.

Finally, the friction stress distribution τ in the deformation zone can be expressed as:

In the above formula, τ is the total friction stress distribution in the deformation zone, unit MPa; τ _a is the friction stress generated by rough contact, unit MPa; τ _f is the friction stress generated by fluid lubrication, unit MPa; k is the shear strength of the material, The unit is MPa.

Step 5: Substitute the frictional stress distribution obtained in Step 4 into the modified Kalman differential equation to solve the rolling force fluctuation caused by the vertical vibration of the roll;

Step 5.1: List the static equilibrium relation equation for the micro-element body in the deformation zone along the rolling direction;

The force analysis of the micro-element in the deformation zone is shown in Figure 3, in which Figure (a) is the force analysis diagram of the micro-element when the vertical vibration speed of the roll is v _y 00; Figure (b) is the vertical vibration speed of the roll v. The force analysis diagram of the micro-element body when _y < 0. In the figure, dx is the width of the microelement, in mm; y, dy and δy are the thickness of the microelement, the thickness increment and the thickness change caused _by the vertical vibration of the roller, in mm; σx and _dσx are the microelement Stress and Stress Increment. Taking Figure (a) as an example, the force on each edge of the micro-element is projected in the rolling direction to obtain:

f _ABx = (σ _x +dσ _x )(y+dy) (27)

f _EFx = -σ _x (y+2δy) (28)

After finishing, you can get:

According to the geometric relationship:

After finishing, the improved Kalman differential equation is as follows:

Among them, K _p =1.155σ _s is the plane deformation resistance of the material, in MPa; "+" is the rear sliding area, and "-" is the front sliding area.

Step 5.2: Substitute the frictional stress distribution obtained in step 4 into the improved Kalman differential equation, and obtain the rolling force fluctuation ΔP ₁ caused by the vertical vibration of the roll after integration;

Substitute the frictional stress distribution obtained in step 4 into the improved Kalman differential equation obtained in step 5.1, and integrate it along the deformation zone to obtain the dynamic rolling force P _d caused by the vertical vibration of the roll, then the vertical rolling force P d caused by the vertical vibration of the roll can be obtained. The rolling force fluctuation ΔP ₁ caused by vibration can be expressed as:

ΔP ₁ =P _d −P _s (32)

Among them, P _s is the steady-state rolling force when _vy = 0, and the unit is kN.

Step 6: Calculate the amount of back tension change caused by vibration and the rolling force fluctuation ΔP ₂ caused by the change of back tension according to the tension relationship between the stands. The specific steps are as follows:

Step 6.1: Calculate the amount of back tension change caused by vibration according to the tension relationship between the frames;

The vibration of the roll will lead to the change of the strip inlet speed, and then the back tension will change through the tension relationship between the stands. The expression of the back tension change Δσ _b is as follows:

Among them, E _s is the elastic modulus of the strip steel, the value is 2.1×10 ¹¹ Pa; L is the distance between the racks, the value is 5m; v _in,i is the current rack inlet speed, in m/s; v _{out , i-1} is the exit speed of the previous rack, in m/s.

Step 6.2: Calculate the rolling force fluctuation ΔP ₂ caused by the change of the back tension;

The rolling force fluctuation ΔP ₂ caused by the post tension change is:

Among them, Q _p is the stress state coefficient, w is the width of the rolling stock, and the value is 1000mm.

Step 7: According to the force relationship between the components of each rolling mill and the total amount of rolling force fluctuation ΔP=ΔP ₁ +ΔP ₂ , establish the vertical vibration dynamics equation of the rolling mill system and solve it to obtain the roll displacement and velocity response, so as to predict the stability of the rolling process.

Step 7.1: According to the simplified model of one half of the six-high cold rolling mill shown in (b) in Figure 4, the force relationship between the rolls, the rolling stock and the arch, and combined with the mechanical vibration theory, establish the vertical vertical of the rolling mill system. The dynamic equation of the vibration is as follows:

和

分别为轧机上半部分牌坊速度、支撑辊速度、中间辊速度和工作辊速度，单位m/s；

和

分别为轧机上半部分牌坊加速度、支撑辊加速度、中间辊加速度和工作辊加速度，单位m/s²；ΔP为轧制力波动总量，单位kN。In the above formula, M _s , M _b , M _im and M _w are the mass of the upper half of the mill, the mass of the backup roll, the mass of the intermediate roll and the mass of the work roll, respectively, in kg; C _b , C _im and C _w are the support, respectively Roll damping, intermediate roll damping and work roll damping, unit N·s/m; K _s , K _b , _Kim and K _w are the arch stiffness, backup roll stiffness, intermediate roll stiffness and work roll stiffness of the upper half of the rolling mill, respectively, The unit is N/m; x _s , x _b , x _im and x _w are the arch displacement, backup roll displacement, intermediate roll displacement and work roll displacement of the upper half of the rolling mill, respectively, in m;

and

are the speed of the upper part of the mill, the speed of the backup roll, the speed of the intermediate roll and the speed of the work roll, in m/s;

and

are the arch acceleration, backup roll acceleration, intermediate roll acceleration and work roll acceleration in the upper half of the rolling mill, respectively, in m/s ² ; ΔP is the total amount of rolling force fluctuation, in kN.

Step 7.2: Use the Newmark-Beta method to solve the vertical vibration dynamics equation of the rolling mill system; the vertical speed of the roll is used as the input of the calculation process at the next moment; the vertical displacement of the roll is used as the basis for judging the stability of the rolling mill. If the curve converges, the rolling mill is stable, and if the roll displacement curve diverges, the rolling mill is unstable.

The prediction effect of rolling mill stability under different process parameters is shown in Figure 5. In Fig. 5(a), the increase of reduction ratio causes the roll displacement curve to change from convergence to divergence, the rolling mill is unstable and self-excited vibration occurs; in Fig. 5(b), the increase of post tension makes the roll displacement curve becomes convergent and improves the stability of the rolling mill, but the effect is not significant; in Fig. 5(c) and (d), the reduction of roughness and the increase of viscosity both improve the lubrication performance of the rolling interface, which in turn reduces the interface The friction energy dissipation capacity of , causes the instability of the rolling mill; in Fig. 5(e), with the continuous increase of the rolling speed, the roll displacement curve changes from convergence to constant amplitude and then to divergence, indicating that the increase of rolling speed will Destabilize the rolling mill. It can be seen that the method of the present invention can judge whether the established rolling schedule is reasonable through the simulation calculation before production, so as to avoid problems such as production accident and equipment damage.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit 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; The technical solutions described in the foregoing embodiments are modified, or some or all of the technical features thereof are equivalently replaced; therefore, 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 (8)

1. a rolling stability prediction method of a six-high cold rolling mill, is characterized in that, the method comprises the steps: Step 1: Collect relevant parameters, including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structure parameters; Step 2: Calculate the dynamic contact arc length of the deformation zone according to the steel strip parameters, the roll diameter and the vertical vibration speed of the roll, discretize the deformation zone along the rolling direction, and calculate the micro-elements obtained after the discretization process. the average deformation resistance of the body; Step 3: Calculate the dynamic inlet oil film thickness using the one-dimensional Reynolds equation; Step 4: Combine the dynamic inlet oil film thickness and Christensen roughness distribution assumptions obtained in step 3 to calculate the friction stress distribution in the deformation zone; Step 5: The Kalman differential equation is improved, and the friction stress distribution in the deformation zone obtained in step 4 is substituted into the improved Kalman differential equation to solve the rolling force fluctuation ΔP ₁ caused by the vertical vibration of the roll; Step 6: Calculate the amount of back tension change caused by vibration and the rolling force fluctuation ΔP ₂ caused by the back tension change according to the tension relationship between the stands; Step 7: According to the force relationship between the components of each rolling mill and the total rolling force fluctuation ΔP=ΔP ₁ +ΔP ₂ , establish the vertical vibration dynamics equation of the rolling mill system and solve it to obtain the vertical displacement and velocity response of the roll, Thereby predicting the stability of the rolling process. 2. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, wherein the strip parameters include: strip grade, strip width and thickness of incoming material for hot rolling; the lubricating Oil parameters include lubricating oil viscosity and viscosity pressure coefficient; the rolling process parameters include: front and rear tension between stands, rolling speed of each pass, strip inlet speed of each pass, and thickness of strip steel entrance and exit of each pass; the The structural parameters of the rolling mill include: roll quality, roll material, roll diameter, roll length, rolling mill stiffness coefficient, damping coefficient of each part of the rolling mill, and archway quality; the rolling mill stiffness coefficient includes the roll stiffness coefficient and the archway stiffness coefficient. 3. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, wherein the step 2 further comprises the following steps: Step 2.1: Calculate the dynamic contact arc length in the deformation zone according to the thickness of the strip entrance and exit, the diameter of the roll and the vertical vibration velocity of the roll; Step 2.2: Discretize the deformation zone along the rolling direction to obtain several micro-elements; Step 2.3: Calculate the average deformation resistance of each micro-element by using the deformation resistance model according to the material of the strip and the thickness of the micro-element. 4. The rolling stability prediction method of a six-high cold rolling mill according to claim 3, wherein the calculation formula of the dynamic contact arc length l is as follows:

In the above formula, l is the dynamic contact arc length, in mm; R is the roll flattening radius, in mm; y _in and y _out are the thickness of the strip inlet and outlet, in mm; θ is the change in the bite angle, in rad ; v _y is the vertical vibration speed of the roll, the speed is positive upward, the unit is m/s; v _out is the strip outlet speed, the unit is m/s. 5. the rolling stability prediction method of the six-high cold rolling mill according to claim 1, is characterized in that, described in the described step 3, utilizes the one-dimensional Reynolds equation to calculate the method for dynamic inlet oil film thickness: The one-dimensional Reynolds equation considering the squeezing effect is as follows:

In the above formula, h ₁ is the oil film thickness in the inlet area, in mm; x _f is the distance from any position in the inlet area to the junction of the inlet area and the deformation area, in mm; p is the rolling pressure distribution in the deformation area, in MPa; η is the viscosity of lubricating oil under different pressures, in Pa s;

is the average speed of strip and roll, in m/s; t is time, in s; Since the oil film pressure in the inlet area is small, the formula for the viscosity of the lubricating oil adopts the Barus formula, as shown below: η=η ₀ e ^γp (12) The dimensionless parameter φ is introduced:

In the above formula, γ is the viscosity-pressure coefficient of the Barus formula, in MPa ^-1 ; p is the rolling pressure distribution in the deformation zone, in MPa; η ₀ is the viscosity of lubricating oil under atmospheric pressure, in Pa·s; Integrating the one-dimensional Reynolds equation and replacing the integral constant with the steady-state result when the vertical vibration velocity of the roll _vy = 0 gives:

In the above formula, α is the bite angle, in rad;

is the rate of change of the bite angle, in rad/s; σ _b is the back tension of the strip, in MPa; σ _s is the average deformation resistance, in MPa;

is the change rate of the inlet oil film thickness, in mm/s; h ₀ is the inlet oil film thickness in a steady state, in mm; When x _f tends to infinity, the lubricating oil film pressure tends to 0, so the following boundary condition 1 can be obtained: x _f = ∞, h ₁ = ∞, φ = 1 (15) Substitute boundary condition 1 into

expression and tidy up to get:

Among them, σ _s is the average deformation resistance, in MPa; R is the flattening radius of the roll, in mm; According to the calculation of the lubricating oil film pressure at the junction of the inlet area and the deformation area according to the Tresca yield criterion p=σ _s -σ _b , the following boundary condition 2 can be obtained:

Substitute boundary condition 2 into the expression of φ and arrange it to get:

in,

is the change rate of the inlet oil film thickness, in mm/s; h _0,d is the dynamic inlet oil film thickness, in mm; Δt is the time step, in s; h ₀ is the inlet oil film thickness at steady state, in mm, which can be calculated from the following The formula is determined:

Among them, v _in is the strip inlet speed, in m/s; v _r is the rolling speed, in m/s; l ₀ is the length of the deformation zone at steady state, in mm; σ _s is the average deformation resistance, in MPa ; R is the roll flattening radius, in mm. 6. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, wherein the method for calculating the friction stress distribution in the deformation zone described in the step 4 is: According to the dynamic inlet oil film thickness obtained in step 3 and the principle of constant volume, the oil film thickness distribution h(x) in the deformation zone can be expressed as follows:

In the above formula, h(x) is the oil film thickness distribution in the deformation zone, in mm; x is the distance from any position in the deformation zone to the junction of the inlet zone and the deformation zone, in mm; v _r is the rolling speed, in m/s ; v _in is the strip inlet velocity, in m/s; v _s is the strip velocity distribution along the rolling direction, in m/s; h _{0, d} is the dynamic inlet oil film thickness, in mm; According to the Christensen roughness distribution assumption, the actual contact area ratio _Ac and the average oil film thickness h _t can be expressed as:

In the above formula, δ is the roughness distribution, in μm; Z=h(x)/3R _q is a dimensionless parameter; R _q is the comprehensive surface roughness of the strip and roll, in μm; f(δ) is the probability density function, which can be expressed as:

In the above formula, R _q is the comprehensive surface roughness of the strip and roll, in μm; Finally, the friction stress distribution τ in the deformation zone can be expressed as:

In the above formula, τ is the total friction stress distribution in the deformation zone, in MPa; τ _a is the friction stress generated by rough contact, in MPa; τ _f is the friction stress generated by fluid lubrication, in MPa; k is the shear strength of the material, The unit is MPa; η is the viscosity of the lubricating oil under different pressures, in Pa·s. 7. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, wherein the step 5 further comprises the following steps: Step 5.1: After analyzing the force of the micro-elements in the deformation zone, formulate the static equilibrium relation equation of the micro-elements in the deformation zone along the rolling direction, and obtain the improved Kalman differential equation from the static equilibrium relation equation; Step 5.2: Substitute the friction stress distribution obtained in step 4 into the improved Kalman differential equation, and obtain the rolling force fluctuation ΔP ₁ caused by the vertical vibration of the roll after integration. 8. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, wherein the step 7 comprises the following steps: Step 7.1: According to the simplified model of one-half of the six-high cold rolling mill and the force relationship between the rolls, the rolling stock and the arch, combined with the mechanical vibration theory, establish the vertical vibration dynamic equation of the rolling mill system; Step 7.2: Use the Newmark-Beta method to solve the vertical vibration dynamics equation of the rolling mill system, and use the vertical speed of the roll as the input of the calculation process at the next moment, and use the vertical displacement of the roll as the basis for judging the stability of the rolling mill. If the vertical displacement curve of the rolls converges, the rolling mill is stable, and if the vertical displacement curve of the rolls diverges, the rolling mill is unstable.

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