CN111651891B - Dynamic Modeling Method for Analysis of Horizontal Self-excited Vibration of Work Rolls in Hot Rolling Finishing Mills - Google Patents

Abstract

The invention provides a dynamic modeling method for analyzing horizontal self-excited vibration of a working roll of a hot rolling finishing mill, which comprises the following steps: a. calculating the dynamic speed of the rolled piece according to the principle that the flow volume of the rolled piece in the deformation area is not changed

To obtain a neutral angle

Horizontal vibration speed of roller

A differential equation; b. based on the principle that the rolled piece satisfies the plastic fluid mechanics in the rolling process, the average shear stress applied to the rolled piece in the rolling process is calculated

(ii) a c. Calculating stress state coefficient of rolled piece when upper and lower rollers of rolling mill move asymmetrically

(ii) a d. Obtaining a calculation formula of the dynamic rolling force P of the hot rolling; e. establishing a horizontal dynamic model of the working roll; f. and obtaining a dynamic analysis equation of the horizontal self-excited vibration of the working roll of the hot finishing mill. The invention has important significance for improving the product quality and the production safety.

Description

Dynamic Modeling Method for Analysis of Horizontal Self-excited Vibration of Work Rolls in Hot Rolling Finishing Mills

technical field

The invention relates to the field of rolling mill vibration analysis, in particular to a dynamic modeling method for analyzing the horizontal self-excited vibration of a work roll of a hot rolling finishing mill.

Background technique

With the development of large-scale, high-load, and high-speed rolling equipment in the iron and steel industry, the dynamic effect of the rolling mill during the rolling process has also become prominent, and the vibration problem of the rolling mill has also become obvious, especially the horizontal self-excited vibration of the work roll. very frequently. Violent vibration not only threatens the safe production of rolling mills, but also reduces the surface quality of strip steel, and even causes major equipment accidents, becoming a bottleneck that plagues strip steel production and new product development.

Due to the structural gap in the horizontal direction of the work rolls in the rolling mill system, the restraint strength is low, so the horizontal vibration of the work rolls is the most severe. The horizontal self-excited vibration frequency of the work rolls is 40-80Hz, and the vibration directions of the upper and lower work rolls are opposite. In order to explore the vibration mechanism and solve the vibration problem, scholars have carried out a series of studies on the horizontal vibration of the rolling mill. Although these studies can reveal some vibration phenomena of the rolling mill from different angles, they all take the single roll as the research object or assume the motion state of the upper and lower rolls. research under the same conditions. In practice, the movement of the upper and lower work rolls of the rolling mill is a reverse vibration phenomenon. On the one hand, the reverse vibration of the upper and lower work rolls will cause a change in the direction of the force of the rolling stock on the rolls, and on the other hand, it will also cause the difference in the friction state of the upper and lower surfaces of the rolling stock in the deformation zone, making the neutral angle positions of the upper and lower surfaces different. The rolling area will be derived, and the stress state is more complicated. The dynamic derivation of the rolling zone makes the deformation zone produce a new damping mechanism, changes the stability of the rolling deformation zone, and has a great impact on the stability of the rolling mill system, resulting in the hot rolling finishing mill rolling high-strength thin-gauge strips Severe self-excited vibration of work rolls frequently occurs when steel is used.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a dynamic modeling method for analyzing the horizontal self-excited vibration of the hot rolling mill work rolls in the rolling deformation zone during unsteady rolling, so as to solve the problem of rolling in the hot rolling finishing mill. When making high-strength and thin-gauge strip steel, the problem of severe self-excited vibration of work rolls frequently occurs.

The present invention is realized as follows: a dynamic modeling method for analyzing the horizontal self-excited vibration of work rolls of a hot-rolling finishing mill, comprising the following steps:

a. Based on the principle that the flow volume of the rolling piece in the deformation zone remains unchanged, the dynamic velocity v _x of the rolling piece is calculated, and the calculation formula of v _x is:

Among them, v ₀ is the entry velocity of the rolled piece, _ve is the horizontal vibration velocity of the roll, H is the thickness of the entry of the rolled piece, and h _x is the thickness of the rolled piece at the position x on the contact arc between the roll and the rolled piece;

Taking the neutral angle θ _n as the boundary condition of formula (1), the following formula is obtained:

Arrange the formula (2) to obtain the differential equation between the neutral angle θ _n and the horizontal vibration velocity _ve of the roll:

Among them, R is the radius of the work roll, and v _r is the rolling speed;

b. Based on the principle that the rolled piece satisfies the plastic hydrodynamics during the rolling process, calculate the average shear stress τ _m that the rolled piece is subjected to during the rolling process. The calculation formula of τ _m is:

Among them, v _x1 is the flow velocity of the upper surface of the rolling stock at position x, v _x2 is the flow velocity of the lower surface of the rolling stock at position x, v _e1 is the horizontal vibration velocity of the upper work roll, v _e2 is the horizontal vibration velocity of the lower work roll, ξ is the flow viscosity of the rolling piece, k is the metal deformation resistance, and l is the length of the contact area between the rolling piece and the roll;

搓轧区轧件的应力状态系数为定值；计算轧机上下轧辊非对称运动时轧件的应力状态系数η_σ，η_σ的计算公式为：c. Assuming that the stress state coefficients of the front and rear sliding zones vary linearly along the contact line between the rolling stock and the roll; ignoring the effect of tension, the stress state coefficients of the rolling stock at the entrance and exit are

The stress state coefficient of the rolling piece in the rolling area is a fixed value; the calculation formula of the stress state coefficient η _σ of the rolling piece when the upper and lower rolls of the rolling mill move asymmetrically, the calculation formula of η _σ is:

Among them, θ _n1 is the neutral angle of the upper work roll during dynamic time, θ _n2 is the neutral angle of the lower work roll during dynamic time, and η _σmax is the maximum stress state coefficient in the deformation zone;

From formula (3) we get:

Substitute formula (6) into formula (5) to get:

The calculation formula of η _σmax in formula (5) and formula (7) is:

Among them, h is the thickness of the rolled piece at the entrance, h _n is the thickness of the rolled piece at the neutral angle position, and e is the reduction ratio;

The formula for calculating the reduction rate e is:

The calculation formula of θ _n in formula (8) is:

The calculation formula of h _n in formula (8):

d. The formula for calculating the rolling force P of hot rolling is:

Substituting Equation (4), Equation (7), Equation (8), Equation (9), Equation (10) and Equation (11) into Equation (12), we get:

e. The horizontal dynamic model of the work roll is:

Among them, m is the mass of the work roll and its bearing and bearing housing, cx is the damping coefficient of the horizontal movement of the roll, _kx is the stiffness coefficient of the horizontal movement of the roll, _x1 is the horizontal displacement _of the upper work roll, _x2 is the lower work roll the horizontal displacement;

是计算公式为：in formula (14)

is the calculation formula:

In formula (15), μ is the friction coefficient of the deformation zone, and its calculation formula is as follows:

为x的一阶导数；Among them, μ _s is the static friction coefficient, χ is the frictional negative damping coefficient, μ is the friction coefficient in the deformation zone,

is the first derivative of x;

sin β in equation (14) is calculated by:

Among them, x ₁ is the horizontal displacement of the upper work roll; x ₂ is the horizontal displacement of the lower work roll;

f. Subtract the two formulas in formula (14) and bring formula (15), formula (16) and formula (17) into, and obtain the dynamic analysis equation of the horizontal self-excited vibration of the work roll of the hot rolling finishing mill ,which is:

为x₁的一阶导数，

为x₂的一阶导数，

为x₁的二阶导数，

为x₂的二阶导数，P为由公式(13)计算的轧制力；in,

is the first derivative of x ₁ ,

is the first derivative of x ₂ ,

is the second derivative of x ₁ ,

is the second derivative of x ₂ , and P is the rolling force calculated by formula (13);

The length l of the contact area of the rolling stock can be calculated according to the following formula:

l=R*α (19)

where α is the bite angle.

The invention proposes a dynamic modeling method for analyzing the horizontal self-excited vibration of the work roll of a hot-rolling finishing mill. The method considers factors comprehensively and realistically, and establishes a more reliable model. Based on this method, the generation mechanism of the horizontal self-excited vibration of the hot rolling finishing mill can be analyzed, and the influence law of the rolling mill structure parameters and rolling process parameters on the self-excited vibration can be analyzed. Vibration measures to ensure the stable production of rolling mills are helpful to solve the problem of self-excited vibration of work rolls that have plagued the production site for a long time, and are of great significance to improving product quality and production safety.

Description of drawings

Figure 1 is a schematic diagram of the horizontal vibration of the upper and lower work rolls.

Figure 2 is a diagram showing the force relationship in the rolling deformation zone when the upper and lower work rolls move asymmetrically.

Figure 3 is the dynamic response diagram of the speed difference between the upper and lower work rolls with different inlet thicknesses.

Figure 4 is the dynamic response diagram of the speed difference between the upper and lower work rolls at different outlet thicknesses.

Figure 5 is the dynamic response diagram of the speed difference between the upper and lower work rolls under different deformation resistance.

Figure 6 is the dynamic response diagram of the speed difference between the upper and lower work rolls with different structural damping.

Detailed ways

As shown in Figure 1 and Figure 2, a dynamic modeling method for analyzing the horizontal self-excited vibration of a hot rolling finishing mill work roll of the present invention includes the following steps:

a. In the case of considering the horizontal vibration speed of the upper and lower work rolls, the dynamic speed of the rolling stock v _x and v _x can be calculated according to the following formulas based on the principle of the constant flow volume of the rolling stock in the deformation zone:

Among them, v ₀ is the entry velocity of the rolled piece, _ve is the horizontal vibration velocity of the roll, H is the thickness of the entry of the rolled piece, and h _x is the thickness of the rolled piece at the position x on the contact arc between the roll and the rolled piece;

Taking the neutral angle θ _n as the boundary condition of the dynamic velocity formula of the rolling stock, the following formula is obtained:

The neutral angle is the angle between the interface between the front slip zone and the back slip zone and the vertical line of the roll's gravity;

After finishing the above formula, the differential equation between the neutral angle θ _n and the horizontal vibration velocity _ve of the roll is obtained:

Among them, R is the radius of the work roll, and v _r is the rolling speed.

b. Based on the principle that the rolled piece satisfies the plastic hydrodynamics during the rolling process, calculate the average shear stress τ _m that the rolled piece is subjected to during the rolling process. The calculation formula of τ _m is:

为轧件粘度,k为金属变形阻力，l为轧件与轧辊的接触区长度；Among them, v _x1 is the flow velocity of the upper surface of the rolling stock at position x, v _x2 is the flow velocity of the lower surface of the rolling stock at position x, v _e1 is the horizontal vibration velocity of the upper work roll, v _e2 is the horizontal vibration velocity of the lower work roll,

is the viscosity of the rolling piece, k is the metal deformation resistance, and l is the length of the contact area between the rolling piece and the roll;

l Calculated according to the following formula:

l=R*α

where α is the bite angle.

搓轧区轧件的应力状态系数为定值；计算轧机上下工作辊非对称运动时轧件的应力状态系数η_σ，η_σ的计算公式为：c. Assuming that the stress state coefficients of the front and rear sliding zones vary linearly along the contact line between the rolling stock and the work roll; ignoring the effect of tension, the stress state coefficients of the rolling stock at the entrance and exit are

The stress state coefficient of the rolling piece in the rolling area is a fixed value; the calculation formula of the stress state coefficient η _σ of the rolling piece when the upper and lower work rolls of the rolling mill move asymmetrically, the calculation formula of η _σ is:

Among them, θ _n1 is the neutral angle of the upper work roll during dynamic time, θ _n2 is the neutral angle of the lower work roll during dynamic time, and η _σmax is the maximum stress state coefficient in the deformation zone

From the differential equation between the neutral angle and the horizontal vibration velocity of the roll, it can be obtained:

Substitute the above formula into the calculation formula of η _σ :

_ησmax in the above formula can be calculated according to the following formula:

Among them, h is the thickness of the rolled piece at the entrance, h _n is the thickness of the rolled piece at the neutral angle position, and e is the reduction ratio;

The reduction rate e can be calculated according to the following formula:

The neutral angle θ _n can be calculated according to the following formula:

The thickness h _n of the rolled piece at the neutral angle position can be calculated according to the following formula:

d. The formula for calculating the rolling force P of hot rolling is:

Substituting the above formula into the rolling force formula, we get:

e. The horizontal dynamic model of the work roll is:

Among them, m is the mass of the work roll and its bearing and bearing housing, cx is the damping coefficient of the horizontal movement of the roll, _kx is the stiffness coefficient of the horizontal movement of the roll, _x1 is the horizontal displacement _of the upper work roll, _x2 is the lower work roll the horizontal displacement;

可根据以下公式计算：in,

It can be calculated according to the following formula:

μ is the friction coefficient of the deformation zone, which can be calculated according to the following formula:

为x的一阶导数；Among them, μ _s is the static friction coefficient, χ is the frictional negative damping coefficient, μ is the friction coefficient in the deformation zone,

is the first derivative of x;

sinβ can be calculated by the following formula:

Among them, x ₁ is the horizontal displacement of the upper work roll; x ₂ is the horizontal displacement of the lower work roll;

By subtracting the two equations in the horizontal dynamic model of the work roll, and substituting each parameter formula, the dynamic analysis equation of the horizontal self-excited vibration of the work roll of the hot rolling finishing mill is obtained, namely:

为x₁的一阶导数，

为x₂的一阶导数，

为x₁的二阶导数，

为x₂的二阶导数，P为由公式计算的轧制力。in,

is the first derivative of x ₁ ,

is the first derivative of x ₂ ,

is the second derivative of x ₁ ,

is the second derivative of _x2 , and P is the rolling force calculated by the formula.

Based on the established dynamic analysis model, the dynamic response of the speed difference between the upper and lower work rolls was simulated and analyzed when the inlet thickness was 13.5mm, 14.0mm, and 14.5mm, respectively. The simulation results are shown in Figure 3.

Based on the established dynamic analysis model, the dynamic response of the speed difference between the upper and lower work rolls was simulated and analyzed when the outlet thickness was 6.8 mm, 7.0 mm, and 7.2 mm, respectively. The simulation results are shown in Figure 4.

Based on the established dynamic analysis model, the dynamic response of the speed difference between the upper and lower work rolls was simulated and analyzed when the deformation resistance was 160MPa, 170MPa, and 180MPa, respectively. The simulation results are shown in Figure 5.

Based on the established dynamic analysis model, when the structural damping of simulation analysis is 6×10 ⁵ N/(m/s), 8×10 ⁵ N/(m/s), and 10×10 ⁵ N/(m/s), respectively The dynamic response of the speed difference between the upper and lower work rolls, the simulation structure is shown in Figure 6.

It can be seen from the simulation results that when the thickness of the exit of the rolling stock is constant, the greater the thickness of the entrance, the greater the vibration intensity of the work rolls; when the thickness of the entrance of the rolling stock is constant, the greater the thickness of the exit, the smaller the vibration intensity of the work rolls; other parameters When it remains unchanged, the greater the deformation resistance of the rolling stock, the greater the vibration intensity of the work rolls; when other parameters remain unchanged, the greater the structural damping of the rolling mill, the smaller the vibration intensity of the work rolls. In actual production, the greater the rolling reduction, the greater the deformation resistance of the rolled piece, the smaller the structural damping, and the easier the horizontal self-excited vibration of the work roll occurs. The simulation results are consistent with the actual production phenomenon. Therefore, a dynamic modeling method for analyzing the horizontal self-excited vibration of the work roll of a hot rolling finishing mill proposed by the present invention is effective.

Claims (2)

1. A dynamic modeling method for analyzing horizontal self-excited vibration of a working roll of a hot rolling finishing mill is characterized by comprising the following steps:

a. calculating the dynamic speed v of the rolled piece according to the principle that the flow volume of the rolled piece in the deformation area is not changed_x，v_xThe calculation formula of (2) is as follows:

wherein v is₀For the entry velocity of the product, v_eIs the horizontal vibration speed of the roller, H is the inlet thickness of the rolled piece, H_xThe thickness of a rolled piece at the x position on the contact arc of the roller and the rolled piece;

at neutral angle theta_nAs a boundary condition of the formula (1), the following formula is obtained:

wherein h is_nThe rolled piece thickness at the neutral angular position;

the neutral angle theta is obtained by processing the formula (2)_nWith horizontal vibration speed v of the rolls_eDifferential equation:

wherein R is the work roll radius, v_rIs the rolling speed;

b. based on the principle that the rolled piece satisfies the plastic fluid mechanics in the rolling process, the average shear stress tau borne by the rolled piece in the rolling process is calculated_m，τ_mThe calculation formula of (2) is as follows:

wherein v is_x1For the flow velocity, v, of the upper surface of the product at the x position_x2For the flow velocity, v, of the lower surface of the product in the x position_e1For horizontal vibration speed of upper working roll, v_e2The horizontal vibration speed of a lower working roll is set, xi is the flow viscosity of a rolled piece, k is the metal deformation resistance, and l is the length of a contact area between the rolled piece and a roll;

c. the stress state coefficient of the front and rear sliding areas is assumed to change linearly along the contact line of the rolled piece and the roller; neglecting the effect of tension, the stress state coefficients of the rolled pieces at the inlet and outlet are

The stress state coefficient of the rolled piece in the rolling area is a fixed value; calculating stress state coefficient eta of rolled piece when upper and lower rollers of rolling mill move asymmetrically_σ，η_σThe calculation formula of (2) is as follows:

wherein, theta_n1At dynamic upper work roll neutral angle, θ_n2Neutral angle of lower working roll, eta, in dynamic state_σmaxThe maximum stress state coefficient of the deformation zone;

from equation (3):

substituting formula (6) into formula (5) yields:

eta in the formulae (5) and (7)_σmaxThe calculation formula of (2) is as follows:

wherein h is the inlet thickness of the rolled piece, h_nThe thickness of the rolled piece at the neutral angle position is shown, and e is the reduction rate;

the reduction rate e is calculated by the formula:

h in formula (8)_nThe calculation formula of (2):

theta in the formula (10)_nThe calculation formula of (2) is as follows:

d. the calculation formula of the dynamic rolling force P of the hot rolling is as follows:

substituting formula (4), formula (7), formula (8), formula (9), formula (10), and formula (11) into formula (12) yields:

e. the horizontal dynamic model of the working roll is as follows:

wherein m is the mass of the working roll and its bearings and bearing seats, c_xDamping coefficient, k, for horizontal movement of rolls_xThe stiffness coefficient, x, for horizontal movement of the rolls₁For horizontal displacement of the upper work rolls, x₂Horizontal displacement of the lower working roll;

the calculation formula is as follows:

mu in the formula (15) is the friction coefficient of the deformation region, and the calculation formula is as follows:

wherein, mu_sIs static friction coefficient, chi is negative friction damping coefficient,

is the first derivative of x;

sin β in formula (14) is calculated by the following formula:

wherein x is₁Is the horizontal displacement of the upper working roll; x is the number of₂Horizontal displacement of the lower working roll;

f. subtracting the two equations in the equation (14) and substituting the equations (15), (16) and (17) to obtain a kinetic analysis equation of the horizontal self-excited vibration of the work rolls of the hot finishing mill, that is:

wherein,

is x₁The first derivative of (a) is,

is x₂The first derivative of (a) is,

is x₁The second derivative of (a) is,

is x₂P is the rolling force calculated by the formula (13).

2. The dynamic modeling method of analyzing hot finishing mill work roll horizontal self-excited vibrations as set forth in claim 1, characterized in that the rolled piece contact zone length/, is calculated according to the following formula:

l＝R*α (19)

where α is the bite angle.

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