CN114074118B - Rolling stability prediction method of six-roller cold rolling mill - Google Patents
Rolling stability prediction method of six-roller cold rolling mill Download PDFInfo
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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
Technical Field
The invention relates to the technical field of automatic production of rolling processes, in particular to a method for predicting rolling stability of a six-roller cold rolling mill.
Background
The vibration of a rolling mill is a problem which generally exists in the production of plate strips and needs to be solved urgently. When thin high-strength steel is rolled at high speed, various abnormal vibrations which are difficult to eliminate by adjusting process parameters, such as self-excited vibration in the vertical direction of the rolling mill, often appear in the rolling mill due to strong coupling and nonlinearity of the process parameters, equipment states and a control system. The self-excited vibration of the rolling mill in the vertical direction can cause periodic vibration lines on the surfaces of strip steel and a roller, and the product quality is seriously influenced; and the self-excited vibration of the rolling mill in the vertical direction can also aggravate the abrasion of the roller and the bearing, even cause the roller and the belt to be broken, and threaten the life safety of workers. The reason for generating the self-excited vibration in the vertical direction of the rolling mill is that in the interaction of the dynamic change of the rolling mill structure and the rolling process, the process parameters are changed to cause the equivalent damping and the rigidity of a rolling interface to be changed, so that the equivalent damping of the interface is reduced. If the total damping of the rolled piece-rolling mill system is negative, the system continuously absorbs energy from the transmission device, so that the amplitude of the roller is continuously increased, and the rolling process is unstable.
Researchers have made many related studies to solve the problem of self-excited vibration in the vertical direction of a rolling mill which constantly occurs in the high-speed rolling process. However, these studies have two major disadvantages: (1) The friction state of the rolling interface is assumed to be unchanged during the vibration. However, in practice, the self-excited vibration in the vertical direction of the rolling mill causes periodic changes of the interface lubrication state, the changes are more obvious as the vibration is intensified, and the accuracy of judging the self-excited vibration is reduced if the changes are not considered. (2) And calculating the rolling force when the vibration occurs by using a Kalman differential equation, wherein the obtained result is not accurate because the influence of the vertical vibration speed of the roller is not considered.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a rolling stability prediction method of a six-roller cold rolling mill, which can calculate the lubricating state change and the dynamic rolling force of a rolling interface according to the existing rolling regulation and the structural parameters of the rolling mill, can more accurately predict the stability of the rolling mill in the rolling process, further avoid the self-excited vibration of the rolling mill in the vertical direction caused by overhigh rolling speed or unreasonable setting of the rolling regulation, and achieve the purposes of improving the surface quality of strip steel and stably operating the rolling process.
In order to realize the purpose, the technical scheme provided by the invention is as follows:
a rolling stability prediction method of a six-roller cold rolling mill comprises the following steps:
step 1: collecting related parameters including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structure parameters;
step 2: calculating the dynamic contact arc length of a deformation area according to the parameters of the strip steel, the roll diameter of the roll and the vertical vibration speed of the roll, carrying out discretization treatment on the deformation area along the rolling direction, and calculating the average deformation resistance of each infinitesimal body obtained after the discretization treatment;
and step 3: calculating the thickness of the dynamic inlet oil film by using a one-dimensional Reynolds equation;
and 4, step 4: calculating the distribution of the friction stress of the deformation region by combining the dynamic inlet oil film thickness obtained in the step 3 and the Christensen roughness distribution hypothesis;
and 5: improving the Kalman differential equation, substituting the friction stress distribution obtained in the step 4 into the improved Kalman differential equation to solve the rolling force fluctuation quantity delta P caused by the vertical vibration of the roller 1 ；
And 6: calculating the variation of post tension caused by vibration and the fluctuation delta P of rolling force caused by the variation of post tension according to the tension relation between frames 2 ；
And 7: according to the stress relation among all parts of each rolling mill and the total fluctuation quantity delta P = delta P of the rolling force 1 +ΔP 2 And establishing a vertical vibration dynamic equation of the rolling mill system and solving to obtain the displacement and speed response of the roller, thereby predicting the stability of the rolling process.
Further, according to the method for predicting the rolling stability of the six-roller cold rolling mill, the strip steel parameters comprise: the grade of the strip steel, the width of the strip steel and the thickness of hot rolling incoming materials; the lubricating oil parameters comprise lubricating oil viscosity and viscosity-pressure coefficient; the rolling process parameters comprise: front and back tension between the racks, rolling speed of each pass, strip steel inlet speed of each pass and strip steel outlet and inlet thickness of each pass; the structural parameters of the rolling mill comprise: the mass of the roller, the material of the roller, the diameter of the roller, the length of the roller, the rigidity coefficient of the rolling mill, the damping coefficient of each part of the rolling mill and the mass of the housing; the rigidity coefficient of the rolling mill comprises a rigidity coefficient of a roller and a rigidity coefficient of a housing.
According to the rolling stability prediction method of the six-roller cold rolling mill, the step 2 further comprises the following steps:
step 2.1: solving the dynamic contact arc length of a deformation area according to the thickness of the strip steel inlet and outlet, the roll diameter of the roll and the vertical vibration speed of the roll;
step 2.2: discretizing the deformation area along the rolling direction to obtain a plurality of microelements;
step 2.3: and calculating the average deformation resistance of each infinitesimal body by using a deformation resistance model according to the material quality of the strip steel and the thickness of the infinitesimal body.
Further, according to the rolling stability prediction method of the six-roller 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 flattening radius of the roller; y is in And y out The thickness of the strip steel inlet and outlet; theta is the variation of the biting angle; v. of y The vertical vibration speed of the roller is positive; v. of out The strip steel outlet speed.
Further, according to the method for predicting the rolling stability of the six-roll cold rolling mill, the method for calculating the dynamic inlet oil film thickness by using the one-dimensional Reynolds equation in the step 3 includes:
the one-dimensional Reynolds equation, which takes the squeezing effect into account, is given by:
in the above formula, h 1 The thickness of the oil film in the inlet area; x is the number of f Is the distance from the inlet; p is the rolling pressure distribution of the deformation zone; eta is the viscosity of the lubricating oil under different pressures; v is the average speed of the strip steel and the roller; t is time;
because the oil film pressure in the inlet area is small, the lubricating oil viscosity formula adopts a Barus formula as follows:
η＝η 0 e γp (12)
introducing a dimensionless parameter phi:
in the above formula, γ is the viscosity-pressure coefficient of Barus formula; p is the rolling pressure distribution of the deformation zone; eta 0 The lubricating oil viscosity at atmospheric pressure;
integrate the one-dimensional Reynolds equation and use v y The steady state result when =0 replaces the integration constant, one can get:
in the above formula, α is a bite angle;
is the bite angle rate of change; sigma b The strip steel back tension; when x is f When the pressure tends to infinity, the lubricating oil film pressure tends to 0, and therefore the following boundary condition 1 can be obtained:
x f ＝∞,h 1 ＝∞，φ＝1 (15)
substituting boundary condition 1 into
And the expression of (A) and the arrangement can obtain:
according to the Tresca yielding criterion p = σ available at the intersection of the entry zone and the deformation zone s -σ b Calculating moistenThe following boundary conditions 2 can be obtained for the lubricating oil film pressure:
substituting the boundary condition 2 into the expression of phi and arranging to obtain:
wherein the content of the first and second substances,
is the inlet oil film thickness change rate; h is 0,d Is the dynamic inlet oil film thickness; Δ t is the time step; h is 0 The inlet oil film thickness at steady state can be determined by:
wherein v is in The strip steel inlet speed; v. of r The rolling speed is used; l. the 0 The length of the deformation zone at steady state.
Further, according to the method for predicting rolling stability of the six-roll cold rolling mill, the method for calculating the friction stress distribution of the deformation region in the step 4 is as follows:
according to the principle of the dynamic inlet oil film thickness and the volume invariance obtained in the step 3, the oil film thickness distribution h (x) in the deformation region can be represented by the following formula:
in the above formula, h (x) is the oil film thickness distribution in the deformation region; v. of r The rolling speed is used; v. of in The strip steel inlet speed; v. of s The speed of the strip steel is distributed along the rolling direction; h is a total of 0,d Is the dynamic inlet oil film thickness;
from the Christensen roughness distribution assumption, the actual contact area ratio A c And average oil film thickness h t Can be represented as:
in the above formula, δ is the roughness distribution; z = h/3R q Is a dimensionless parameter; f (δ) is a probability density function, which can be expressed as:
in the above formula, R q The comprehensive surface roughness of the strip steel and the roller;
finally, the deformation zone frictional stress distribution τ can be expressed as:
in the above formula, τ is the total friction stress distribution in the deformation zone; tau. a Frictional stress generated for rough contact; tau is f Frictional stress for fluid lubrication; k is the shear strength of the material.
Further, according to the method for predicting rolling stability of the six-roll cold rolling mill, the step 5 further includes the steps of:
step 5.1: analyzing the stress of the deformation area infinitesimal body, and then aligning a static equilibrium relation equation of the deformation area infinitesimal body along the rolling direction, and obtaining an improved Kalman differential equation by the static equilibrium relation equation;
step 5.2: substituting the friction stress distribution obtained in the step 4 into an improved Kalman differential equation, and integrating to obtain the rolling force fluctuation quantity delta P caused by the vertical vibration of the roller 1 。
8. The rolling stability prediction method of a six-high cold-rolling mill according to claim 1, characterized in that the step 7 comprises the steps of:
step 7.1: according to a half simplified model of a six-roller cold rolling mill and the stress relation among a roller, a rolled piece and a housing, and by combining a mechanical vibration theory, establishing a vertical vibration kinetic equation of a rolling mill system;
and 7.2: solving a vertical vibration dynamic equation of a rolling mill system by adopting a Newmark-Beta method, taking the vertical speed of the roller as the input quantity of the calculation process at the next moment, taking the vertical displacement of the roller as the 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.
Generally, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art: firstly, the method considers the change of the lubrication state of the rolling interface and the change of the rolling force caused by the vibration of the roller, and the calculation result of the rolling force is more accurate; secondly, the method can predict the stability of the rolling process of most of the six-roller cold rolling mills by combining the pressing experiment on the basis of the existing rolling schedule or real-time data acquisition, and has wide applicability; thirdly, the method can avoid self-excited vibration in the vertical direction of the rolling mill caused by overhigh rolling speed or unreasonable establishment of rolling regulations, thereby achieving the purposes of improving the surface quality of the strip steel and improving enterprise benefits; finally, the method is based on the rolling theory and the simulation of mechanical dynamics, so that equipment loss and damage caused by experiments can be effectively avoided, and the enterprise cost is reduced.
Drawings
Fig. 1 is a schematic flow chart of a rolling stability prediction method of a six-roll cold rolling mill according to the present embodiment;
FIG. 2 is a schematic view showing the thickness distribution of an oil film between a roll and a strip steel;
FIG. 3 is a schematic view showing the force analysis of the infinitesimal body according to the present embodiment, wherein (a) is the vertical vibration velocity v of the roller y A force analysis chart of the micro-element body at 00 hours; FIG. b shows the vertical vibration velocity v of the roll y <Force analysis diagram of the micro-element body at 0;
FIG. 4 (a) is a schematic view of a six roll UCM cold mill; (b) The drawing is a schematic diagram of a simplified model of one-half of the six-roll cold-rolling mill shown in figure (a);
FIG. 5 is a graph showing the predicted response of displacement of a work roll under different process parameters, wherein (a) is a graph showing the predicted response of displacement of a work roll under different reduction ratios; FIG. b is a graph of predicted work roll displacement response under different post tensions; FIG. c is a graph of predicted work roll displacement response at different roughness; FIG. d is a graph showing predicted displacement responses of the work rolls at different viscosities; and (e) is a prediction graph of the displacement response of the working roll at different rolling speeds.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
The core thought of the method comprises the following steps: 1. the method comprises the steps of considering an entrance oil film extrusion effect, introducing the vertical vibration speed of a roller into an oil film thickness calculation formula to obtain the dynamic entrance oil film thickness, and calculating the change condition of the friction stress distribution of a deformation region along with time by combining the roughness distribution hypothesis; 2. considering Kalman differential equation derivation of the vertical vibration speed of the roller, and introducing the Kalman differential equation derivation into the friction stress distribution of a deformation area to calculate dynamic rolling force and rolling force fluctuation caused by the vertical vibration of the roller; 3. 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.
In the present embodiment, the rolling stability of a 1450mm UCM six-roll cold continuous rolling mill set of a certain plant is predicted, and the structure of the UCM six-roll cold rolling mill is shown in fig. 4 (a), in which the rolls of the mill are flat rolls. Fig. 1 is a schematic flow chart of a rolling stability prediction method of a six-roll cold rolling mill according to the present embodiment, and as shown in fig. 1, the rolling stability prediction method of the six-roll cold rolling mill includes the steps of:
step 1: collecting relevant parameters including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structural parameters;
the strip steel parameters comprise: the grade of the strip steel, the width of the strip steel and the thickness of hot rolling incoming materials; the lubricating oil parameters comprise lubricating oil viscosity and viscosity-pressure coefficient; the rolling process parameters comprise: front and back tension between the racks, rolling speed of each pass, strip steel inlet speed of each pass and strip steel outlet and inlet thickness of each pass; the structural parameters of the rolling mill comprise: the mass of the roller, the material of the roller, the diameter of the roller, the length of the roller, the rigidity coefficient of the rolling mill, the damping coefficient of each part of the rolling mill and the mass of the housing;
in this embodiment, the first-level control system and the second-level control system on the cold rolling production line are used to obtain all strip steel parameters, all rolling process parameters, and the roll quality, the roll material, the roll diameter, the roll length, and the housing quality in the rolling mill structural parameters.
The rigidity coefficient of the rolling mill comprises a rigidity coefficient of the rolling mill and a rigidity coefficient of the memorial archway, the rigidity coefficient of the rolling mill is obtained through a field pressing experiment, then the rigidity coefficient of the rolling mill is obtained through calculation by using a Hertz contact theory, and finally the rigidity coefficient of the memorial archway is obtained through calculation according to a Hooke law.
In this example, a rolling mill stiffness coefficient of K =4.4 × 10 was obtained by performing a pressing test on a 1450mm UCM six-roll cold continuous rolling mill in the field 9 N/m. Then according to Hertz contact theory, the rigidity coefficient K of the two rollers during compression i Can be represented by the formula (1):
in the above formula, K i The rigidity coefficient of the roller is N/m; p is rolling force in kN; e is the modulus of elasticity of the roller,
the empirical value is 2.1 × 1011Pa; v is the roll poisson ratio, and the experience value is 0.3; d 1 And D 2 The diameter of the two rollers is in mm.
After the rigidity coefficient of the roller is determined, the rigidity coefficient K of the upper half of the housing in a one-half simplified model of the rolling mill s It can be calculated according to the Hooke's law shown in formula (2):
in the above formula, K is the rigidity coefficient of the rolling mill; k w Is the work roll stiffness coefficient, K im Is the intermediate roll stiffness coefficient, K b Is the stiffness coefficient of the support roll, K s The rigidity coefficient of the memorial archway in the upper half is the unit of N/m.
The damping coefficients of all parts of the rolling mill are obtained according to a Rayleigh damping formula, a roller rigidity coefficient and a memorial archway rigidity coefficient. Rayleigh damping is a common structural damping construction method, which assumes that the damping matrix C of the structure is a linear combination of a mass matrix M and a stiffness matrix K, i.e.:
C＝β 1 M+β 2 K (3)
in the above formula, C is a damping matrix with the unit of N.s/m; m is a mass matrix, unit kg; k is a rigidity matrix with the unit of N/m; beta is a 1 And beta 2 Is a proportionality coefficient; omega 1 And omega 2 The natural frequency is obtained by respectively taking the empirical values of 100Hz and 500Hz; xi shape 1 And xi 2 The empirical value is 0.03 for the damping ratio.
In this example, the strip parameters and the lubricating oil parameters are shown in table 1, the rolling process parameters are shown in table 2, and the rolling mill structural parameters are shown in table 3.
TABLE 1 strip parameters and lube parameters
TABLE 2 Rolling Process parameters
TABLE 3 Rolling mill structural parameters
Step 2: calculating the dynamic contact arc length of a deformation area according to the parameters of the strip steel, the roll diameter of the roll and the vertical vibration speed of the roll, carrying out discretization treatment on the deformation area along the rolling direction, and calculating the average deformation resistance of each infinitesimal body obtained after the discretization treatment;
step 2.1: solving the dynamic contact arc length of a deformation area according to the thickness of the strip steel inlet and outlet, the roll diameter of the roll and the vertical vibration speed of the roll;
because the vertical vibration of the roller can cause the change of a deformation zone, the change 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 flattening radius of the roller and is in mm; y is in And y out The thickness of the strip steel inlet and outlet is in mm; theta is the bite angle variation, unit rad; v. of y The vertical vibration speed of the roller is positive in the upward direction and is in the unit of m/s; v. of out Is the strip steel outlet speed in m/s.
The roll flattening radius is calculated according to the Hitchcock formula shown in equation (7):
in the above formula, R 0 Is the initial radius of the roller in mm; e w The elastic modulus of the working roll is 2.1 multiplied by 10 11 Pa；p i Is the rolling force per unit length N/m.
Step 2.2: in order to improve the calculation precision, the deformation area is dispersed into 1000 parts along the rolling direction, and each part is very small, so the deformation area is called a infinitesimal body;
step 2.3: calculating the average deformation resistance of each infinitesimal body by using a deformation resistance model according to the material quality of the strip steel and the thickness of the infinitesimal body;
in this example, the strip steel has a designation Q195 and an average deformation resistance σ s Calculated using the following formulas (8) to (9):
wherein σ s Is the average deformation resistance in MPa; the empirical values of the coefficients are a =498MPa, B =136MPa, C =0.2, D =5, respectively; epsilon Σ To accumulate the deformation; y is 0 The thickness of hot rolling incoming material;
is the pass average thickness.
And 3, step 3: calculating the thickness of the dynamic inlet oil film by using a one-dimensional Reynolds equation;
the oil film thickness distribution between the rolls and the strip is shown in FIG. 2, where y in And y out The thickness of the strip steel inlet and outlet is respectively mm; r is 0 And R is the initial radius and the flattening radius of the roller, and the unit is mm; h is a total of 0 And h 1 The oil film thickness at the inlet and the inlet area respectively is in mm; α is the bite angle, unit rad; x is a radical of a fluorine atom f Is the distance from the inlet in mm. Calculating the thickness of the dynamic inlet oil film by utilizing a one-dimensional Reynolds equation specifically according to the following method;
the one-dimensional Reynolds equation, which takes into account the squeezing effect, is shown below:
because the oil film pressure in the inlet area is small, the lubricating oil viscosity formula adopts a Barus formula as follows:
η＝η 0 e γp (12)
introducing a dimensionless parameter phi:
in the above formula, t is time in units of s; v is the average speed of the strip steel and the roller, and the unit is m/s; gamma is the viscosity-pressure coefficient of Barus formula, unit MPa -1 (ii) a p is rolling pressure distribution in a deformation area and has a unit of MPa; eta 0 Is the lubricating oil viscosity at atmospheric pressure, in Pa · s units; eta is the viscosity of the lubricating oil under different pressures, unit Pa · s.
Integrate the one-dimensional Reynolds equation and use v y The steady state result when =0 replaces the integration constant, one can get:
wherein the content of the first and second substances,
the change rate of the biting angle is in unit rad/s; sigma b Is the back tension of the strip steel in MPa. When x is f When the pressure tends to infinity, the lubricating oil film pressure tends to 0, and therefore the following boundary condition 1 can be obtained:
x f ＝∞,h 1 ＝∞，φ＝1 (15)
substituting boundary condition 1 into
The expression of (c) and arrangement can obtain:
and the lubricating oil film pressure at the interface of the inlet zone and the deformation zone can be according to the Tresca yield criterion p = sigma s -σ b The following boundary conditions 2 can thus be obtained:
substituting the boundary condition 2 into the expression of phi and arranging to obtain:
wherein the content of the first and second substances,
the change rate of the thickness of the oil film at the inlet is in mm/s; h is 0,d Is the dynamic inlet oil film thickness in mm; Δ t is the time step, unit s; h is 0 The inlet oil film thickness at steady state, in mm, can be determined by:
wherein v is in The strip steel inlet speed is in the unit of m/s; v. of r Is the rolling speed, unit m/s; l 0 The length of the deformation zone in the steady state is in mm.
And 4, step 4: calculating the friction stress distribution of the deformation region by combining the dynamic inlet oil film thickness and roughness distribution hypothesis obtained in the step 3;
according to the dynamic inlet oil film thickness and volume invariance principle obtained in the step 3, the oil film thickness distribution h (x) in the deformation region can be represented by the formula (22):
in the above formula, h (x) is the oil film thickness distribution in the deformation region, and the unit is mm; v. of s The unit is m/s for the speed distribution of the strip steel along the rolling direction.
From the Christensen roughness profile assumption, the actual contact area ratio A c And average oil film thickness h t Can be respectively expressed as:
in the above formula, A c Is the actual contact area ratio; h is t Is the average oil film thickness in mm; z = h/3R q Is a dimensionless parameter; f (δ) is a probability density function, which can be expressed as:
in the above formula, δ is the roughness distribution in μm; r is q Is the comprehensive surface roughness of the strip steel and the roller, and has unit of mu m.
Finally, the deformation zone frictional stress distribution τ can be expressed as:
in the above formula, τ is the total friction stress distribution in the deformation region, in MPa; tau is a Friction stress generated by rough contact, unit MPa; tau is f Friction stress generated by fluid lubrication, unit MPa; k is the shear strength of the material in MPa.
And 5: substituting the friction stress distribution obtained in the step 4 into a modified Kalman differential equation to solve the rolling force fluctuation amount caused by the vertical vibration of the roller;
step 5.1: a static equilibrium relation equation of the deformation area infinitesimal body along the rolling direction is calculated;
the force analysis of the deformation zone infinitesimal body is shown in figure 3, wherein the figure (a) is the vertical vibration speed v of the roller y A force analysis chart of the infinitesimal body at 00 hours; FIG. b shows the vertical vibration velocity v of the roll y <Force analysis chart of the micro element body at 0. In the figure, dx is the width of the infinitesimal body in mm; y, dy and deltay are the thickness of the infinitesimal body, the thickness increment and the thickness variation caused by the vertical vibration of the roller, and the unit is mm; sigma x And d σ x The stress and the stress increment which are applied to the micro-element body. Taking the diagram (a) as an example, the projection of the force on each side of the micro-element body in the rolling direction can be obtained:
f ABx ＝(σ x +dσ x )(y+dy) (27)
f EFx ＝-σ x (y+2δy) (28)
after finishing, the following can be obtained:
according to the geometrical relationship:
after being collated, the modified Kalman differential equation is as follows:
wherein, K p ＝1.155σ s Is the plane deformation resistance of the material, unit MPa; "+" is the back slide zone and "-" is the front slide zone.
And step 5.2: substituting the friction stress distribution obtained in the step 4 into an improved Kalman differential equation, and integrating to obtain the rolling force fluctuation quantity delta P caused by the vertical vibration of the roller 1 ；
Substituting the friction stress distribution obtained in the step 4 into the improved Kalman differential equation obtained in the step 5.1, and integrating the friction stress distribution along a deformation area to obtain a dynamic rolling force P caused by the vertical vibration of the roller d The rolling force fluctuation amount delta P caused by the vertical vibration of the roll 1 Can be expressed as:
ΔP 1 ＝P d -P s (32)
wherein, P s Is v is y The steady state rolling force at =0 is in kN.
And 6: calculating the variation of post tension caused by vibration and the fluctuation delta P of rolling force caused by the variation of post tension according to the tension relation between frames 2 Specifically, the method comprises the following steps:
step 6.1: calculating the post tension variation caused by vibration according to the tension relation between the frames;
the vibration of the roller can cause the speed of the strip steel inlet to change, and further, the tension relationship between the frames causes the change of the post tension, and the change quantity delta sigma of the post tension b The expression of (c) is as follows:
wherein E is s The elastic modulus of the strip steel is 2.1 multiplied by 10 11 Pa; l is the distance between the racks and takes the value of 5m; v. of in,i The current frame entrance speed is in m/s; v. of out,i-1 Is the exit velocity of the previous frame in m/s.
Step 6.2: calculating the fluctuation quantity delta P of the rolling force caused by the change of the post tension 2 ；
Rolling force fluctuation amount delta P caused by post tension variation 2 Comprises the following steps:
wherein Q is p Is the stress state coefficient, and w is the width of the rolled piece, and the value is 1000mm.
And 7: according to the stress relation among all parts of each rolling mill and the total fluctuation quantity delta P = delta P of the rolling force 1 +ΔP 2 And establishing a vertical vibration dynamic equation of the rolling mill system and solving to obtain the displacement and speed response of the roller, thereby predicting the stability of the rolling process.
Step 7.1: according to the one-half simplified model of the six-roller cold rolling mill illustrated in (b) in fig. 4, the stress relationship among the rollers, the rolled piece and the housing windows is combined with the mechanical vibration theory to establish the vertical vibration dynamic equation of the rolling mill system as follows:
in the above formula, M s 、M b 、M im And M w Respectively the mass of the memorial archways at the upper half part of the rolling mill, the mass of a supporting roller, the mass of a middle roller and the mass of a working roller in kg; c b 、C im And C w Respectively supporting roll damping, intermediate roll damping and working roll damping, and the unit is N.s/m; k s 、K b 、K im And K w Respectively setting the rigidity of the memorial archways at the upper half part of the rolling mill, the rigidity of a supporting roll, the rigidity of a middle roll and the rigidity of a working roll in a unit of N/m; x is a radical of a fluorine atom s 、x b 、x im And x w Respectively displacement of the upper half part of the housing of the rolling mill, displacement of a supporting roller, displacement of a middle roller and displacement of a working roller in a unit m;
and
respectively the speed of the upper half memorial archway of the rolling mill, the speed of a supporting roller, the speed of a middle roller and the speed of a working roller in m/s;
and
respectively the acceleration of the upper half of the memorial archway of the rolling mill, the acceleration of a supporting roller, the acceleration of a middle roller and the acceleration of a working roller in the unit of m/s 2 (ii) a Δ P is the total rolling force fluctuation in kN.
And 7.2: solving a vertical vibration dynamic equation of the rolling mill system by adopting a Newmark-Beta method; the vertical speed of the roller is used as the input quantity of the calculation process at the next moment; the vertical displacement of the roller is used as a basis for judging the stability of the rolling mill, 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 predicted effect of the stability of the rolling mill under different process parameters is shown in fig. 5. In fig. 5 (a), the roll displacement curve changes from convergent to divergent as the reduction increases, the mill is unstable and self-excited vibration occurs; in fig. 5 (b), the increase in post-tension makes the roll displacement curve converge, improving the stability of the rolling mill, but the effect is not significant; in fig. 5 (c) and (d), both the reduction in roughness and the increase in viscosity increase the lubricity of the rolling interface, which in turn reduces the frictional energy dissipation capacity of the interface, resulting in instability of the rolling mill; in fig. 5 (e), the roll displacement curve changes from converging to constant amplitude to diverging with increasing rolling speed, indicating that an increase in rolling speed destabilizes the mill. Therefore, the method can judge whether the formulated rolling schedule is reasonable or not through simulation calculation before production, thereby avoiding the problems of production accidents, equipment damage and the like.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art; the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions as defined in the appended claims.
Claims (8)
1. A rolling stability prediction method of a six-roller cold rolling mill is characterized by comprising the following steps:
step 1: collecting related parameters including strip steel parameters, lubricating oil parameters, rolling process parameters and rolling mill structure parameters;
and 2, step: calculating the dynamic contact arc length of a deformation area according to the parameters of the strip steel, the roll diameter of the roll and the vertical vibration speed of the roll, carrying out discretization treatment on the deformation area along the rolling direction, and calculating the average deformation resistance of each infinitesimal body obtained after the discretization treatment;
and step 3: calculating the thickness of the dynamic inlet oil film by using a one-dimensional Reynolds equation;
and 4, step 4: calculating the friction stress distribution of a deformation region by combining the dynamic inlet oil film thickness obtained in the step 3 and the Christensen roughness distribution hypothesis;
and 5: improving the Kalman differential equation, substituting the friction stress distribution of the deformation region obtained in the step 4 into the improved Kalman differential equation to solve the rolling force fluctuation quantity delta P caused by the vertical vibration of the roller 1 ；
Step 6: calculating the variation of post tension caused by vibration and the fluctuation delta P of rolling force caused by the variation of post tension according to the tension relation between frames 2 ；
And 7: according to the stress relation among all parts of each rolling mill and the total fluctuation quantity delta P = delta P of the rolling force 1 +ΔP 2 And establishing a vertical vibration dynamic equation of the rolling mill system and solving to obtain the vertical displacement and speed response of the roller, 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, characterized in that the strip steel parameters include: the grade of the strip steel, the width of the strip steel and the thickness of hot rolling incoming materials; the lubricating oil parameters comprise lubricating oil viscosity and viscosity-pressure coefficient; the rolling process parameters comprise: front and back tension between the racks, rolling speed of each pass, entrance speed of strip steel of each pass and thickness of an entrance and an exit of the strip steel of each pass; the structural parameters of the rolling mill comprise: the mass of the roller, the material of the roller, the diameter of the roller, the length of the roller, the rigidity coefficient of the rolling mill, the damping coefficient of each part of the rolling mill and the mass of the housing; the rigidity coefficient of the rolling mill comprises a rigidity coefficient of a roller and a rigidity coefficient of a housing.
3. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, characterized in that the step 2 further comprises the steps of:
step 2.1: solving the dynamic contact arc length of a deformation area according to the thickness of the strip steel inlet and outlet, the roll diameter of the roll and the vertical vibration speed of the roll;
step 2.2: discretizing the deformation area along the rolling direction to obtain a plurality of microelements;
step 2.3: and calculating the average deformation resistance of each infinitesimal body by using a deformation resistance model according to the material quality of the strip steel and the thickness of the infinitesimal body.
4. The rolling stability prediction method of a six-roll cold rolling mill according to claim 3, characterized in that 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 flattening radius of the roller, and the unit is mm; y is in And y out The thickness of the strip steel inlet and outlet is in mm; theta is the bite angle variation, in units rad; v. of y The vertical vibration speed of the roller is positive, and the unit is m/s; v. of out Is the strip steel outlet speed in m/s.
5. The rolling stability prediction method of a six-roll cold rolling mill according to claim 1, wherein the method for calculating the dynamic inlet oil film thickness by using the one-dimensional Reynolds equation in the step 3 is as follows:
the one-dimensional Reynolds equation, which takes into account the squeezing effect, is shown below:
in the above formula, h 1 The thickness of an oil film in an inlet area is in mm; x is the number of f The distance between any position in the inlet area and the junction of the inlet area and the deformation area is unit mm; p is rolling pressure distribution in a deformation region, and the unit is MPa; eta is the viscosity of the lubricating oil under different pressures, and the unit Pa & s;
the average speed of the strip steel and the roller is in m/s; t is time, unit s;
because the oil film pressure in the inlet area is small, the lubricating oil viscosity formula adopts a Barus formula as follows:
η＝η 0 e γp (12)
introducing a dimensionless parameter phi:
in the above formula, γ is the viscosity-pressure coefficient of Barus formula, unit MPa -1 (ii) a p is rolling pressure distribution in a deformation region, and the unit is MPa; eta 0 Is the lubricating oil viscosity at atmospheric pressure, in Pa · s units;
integrating the one-dimensional Reynolds equation and using the vertical vibration velocity v of the roller y The steady state result when =0 replaces the integration constant, one can get:
in the above formula, α is the bite angle, unit rad;
is the bite angle change rate, unit rad/s; sigma b The post tension of the strip steel is in unit MPa; sigma s Is the average deformation resistance in MPa;
the change rate of the thickness of the oil film at the inlet is in mm/s; h is a total of 0 The thickness of the inlet oil film at the steady state is unit mm;
when x is f When the pressure tends to infinity, the lubricating oil film pressure tends to be 0, and therefore the following boundary condition 1 can be obtained:
x f ＝∞,h 1 ＝∞，φ＝1 (15)
substituting boundary condition 1 into
And the expression of (A) and the arrangement can obtain:
wherein σ s Is the average deformation resistance in MPa; r is the flattening radius of the roller and is in mm;
according to the Tresca yielding criterion p = σ available at the intersection of the entry zone and the deformation zone s -σ b The following boundary conditions 2 can be obtained by calculating the lubricating oil film pressure:
substituting the boundary condition 2 into the expression of phi and arranging to obtain:
wherein, the first and the second end of the pipe are connected with each other,
the change rate of the thickness of the oil film at the inlet is in mm/s; h is 0,d Is the dynamic inlet oil film thickness in mm; Δ t is the time step, unit s; h is 0 The inlet oil film thickness at steady state, in mm, can be determined by:
wherein v is in The strip steel inlet speed is in the unit of m/s; v. of r Is the rolling speed, unit m/s; l 0 The length of the deformation zone in the steady state is in mm; sigma s Is the average deformation resistance in MPa; r is the flattening radius of the roller in mm.
6. The rolling stability prediction method of a six-roll cold rolling mill according to claim 1, characterized in that the method for calculating the friction stress distribution of the deformation region in step 4 is:
according to the dynamic inlet oil film thickness and volume invariance principle obtained in the step 3, the oil film thickness distribution h (x) in the deformation region can be represented by the following formula:
in the above formula, h (x) is the oil film thickness distribution in the deformation region, and the unit is mm; x is the distance between any position in the deformation area and the junction of the entrance area and the deformation area, and the unit is mm; v. of r Is the rolling speed, unit m/s; v. of in The strip steel inlet speed is in the unit of m/s; v. of s The speed distribution of the strip steel along the rolling direction is in the unit of m/s; h is 0,d Is the dynamic inlet oil film thickness in mm;
from the Christensen roughness profile assumption, the actual contact area ratio A c And average oil film thickness h t Can be respectively expressed as:
in the above formulaδ is the roughness distribution, in μm; z = h (x)/3R q Is a dimensionless parameter; r is q The unit is the comprehensive surface roughness of the strip steel and the roller; f (δ) is a probability density function, which can be expressed as:
in the above formula, R q The unit is the comprehensive surface roughness of the strip steel and the roller;
finally, the deformation zone frictional stress distribution τ can be expressed as:
in the above formula, τ is the total friction stress distribution in the deformation zone, in MPa; tau is a Friction stress generated by rough contact, unit MPa; tau is f Friction stress generated by fluid lubrication, unit MPa; k is the shear strength of the material, in MPa; eta is the viscosity of the lubricating oil under different pressures, unit Pa · s.
7. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, characterized in that the step 5 further comprises the steps of:
step 5.1: analyzing the stress of the deformation area infinitesimal body, and then aligning a static equilibrium relation equation of the deformation area infinitesimal body along the rolling direction, and obtaining an improved Kalman differential equation by the static equilibrium relation equation;
and step 5.2: substituting the friction stress distribution obtained in the step 4 into an improved Kalman differential equation, and obtaining the rolling force fluctuation quantity delta P caused by the vertical vibration of the roller after integration 1 。
8. The rolling stability prediction method of a six-high cold rolling mill according to claim 1, characterized in that the step 7 comprises the steps of:
step 7.1: establishing a vertical vibration kinetic equation of a rolling mill system according to a half simplified model of a six-roller cold rolling mill and the stress relation among a roller, a rolled piece and a housing window and by combining a mechanical vibration theory;
step 7.2: solving a vertical vibration dynamic equation of a rolling mill system by adopting a Newmark-Beta method, taking the vertical speed of the roller as the input quantity of the calculation process at the next moment, taking the vertical displacement of the roller as the basis for judging the stability of the rolling mill, wherein if the vertical displacement curve of the roller is converged, the rolling mill is stable, and if the vertical displacement curve of the roller is diverged, the rolling mill is unstable.
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