CN109926456A - A kind of draught pressure forecast method under mixed lubricating state - Google Patents
A kind of draught pressure forecast method under mixed lubricating state Download PDFInfo
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Abstract
The present invention provides a kind of draught pressure forecast method under mixed lubricating state comprising Kalman's unit pressure differential equation S1, following steps: is obtained using Cai Likefu solution；Unsteady thermal stresses dynamical roll gap friction stree under S2, mixed lubricating state；Draught pressure forecast under S3, mixed lubricating state, determines forecasting model；S4, the precision of prediction of forecasting model is verified and is analyzed.The invention proposes a kind of draught pressure forecast methods under mixed lubricating state, it is contemplated that generally existing dry friction or boundary lubrication friction and hydrodynamic lubrication friction and the mixed lubrication Frotteurism deposited in the actual production process.By combining the total friction stree of mixed lubrication with Kalman's unit pressure differential equation, a kind of draught pressure forecast model for being more conform with actual production situation is established.
Description
Technical field
The present invention relates to flat cold-rolled sheet manufacturing technology fields, pre- more particularly to the roll-force under a kind of mixed lubricating state
Reporting method.
Background technique
Strip is one of most common product in rolling field.In recent years, with the rapid development of the national economy, arriving greatly
Aerospace, high-speed rail motor-car, all trades and professions such as computer small to mobile, household electrical appliance are increasing to the demand of Strip, this
It is just more harsh to the quality of Strip and required precision.With the continuous development and automatic technology of electronic computer industry
Increasingly complete, mill speed is also greatly improved, so that there has also been no small raisings for the yield of Strip.
But because tandem mill equipment more falls behind, no matter Strip is from quantity, there are also all work as far from satisfaction in quality
Under the economic level that increases rapidly.With the continuous improvement of mill speed, quality of the rolling mill vibration to cold rolling equipment and Strip
Bring negative effect is more and more very important, therefore also becomes a very important research class to the inhibition of rolling mill vibration
Topic.Instantly, because the decline of Strip quality caused by rolling mill vibration has become the serious problem that domestic major steel mill faces；
Equally, rolling mill vibration also results in the repairing of certain important parts and replaces more frequent.Certain enterprises are fast using rolling is reduced
The method of degree cuts down amplitude, to reduce the generation of chatter mark, will obviously reduce production efficiency in this way, is a less desirable side
Method.Also have by the way of replacement important part, using liner etc., but can not all handle vibration problem well completely.
One of an important factor for foundation of roll-force mathematical model is analysis and processing rolling process stability.Accurately roll
Power mathematical model processed can accurately show the alteration trend of gross pressure in rolling vibration processes, this just vibrates and improve to inhibition
The quality of Strip has highly important meaning.For a long time, the cold and hot Rolling Force Modeling rolled is all in rolling area research
A big hot spot, many of them is all on the basis ofs Bland-Ford hill formula, karman formula, orowan formula etc.
What deduction obtained.But they only considered dry friction (or boundary lubrication friction) state a bit, some are only dynamic in fluid
The conclusion obtained under hydrodynamic lubrication state, is obviously not enough to react in this way the complex situations of rolling roll gap, and some forecasting models
Precision does not reach requirement.Their shortcoming is mainly reflected in the following aspects:
One, DRY SLIDING is only accounted for, fails to probe into conjunction with the case where lubrication friction.Some rolling force models
DRY SLIDING is only only accounted for, that is, thinks that the Frotteurism between rolled piece and roll submits to Coulomb friction.So rubbing
Wipe the product that stress is equal to the coefficient of sliding friction and unit pressure, it may be assumed that tx=μ px.The conclusion obtained can thus be made more
It is unilateral.
Two, lubrication friction condition is only accounted for, fails to probe into conjunction with the case where dry friction.And some models then only consider
Lubrication friction condition, that is, think that the Frotteurism between rolled piece and roll submits to certain lubrication friction conditions, such as
Newtonian liquid law of friction etc..Also just could not equally it make in view of the situation for the dry friction that roll and rolled piece directly contact in this way
The conclusion obtained is more unilateral, and convincingness is insufficient.
Three, theory deduction is not deep enough, and the precision of prediction of gained mathematical model is not good enough.Although some models apply mixed
Lubrication friction principle is closed, that is, include dry friction also includes lubrication friction, or to stick together friction and sliding friction etc. multiple
Miscellaneous unstable state friction, lubrication state.But since derivation process is not rigorous enough, there is no profound understanding theoretical knowledge, these mathematical modulos
Ideal precision of prediction is not achieved in type, so the mathematical model of roll-force need to be further improved.
Summary of the invention
The aspect considered mostly based on existing roll-force mathematical model is more single, and general in the actual production process
The mixed lubrication Frotteurism for being all dry friction and lubrication friction and depositing.In order to make roll-force mathematical model closer to practical feelings
Condition, and further increase the precision of prediction of its mathematical model, and the draught pressure forecast under the conditions of proposing a kind of mixed lubrication
Method.
Specifically, the present invention provides a kind of draught pressure forecast method under mixed lubricating state comprising following steps:
S1, Kalman's unit pressure differential equation after line is obtained using Cai Likefu solution；
S2, the unsteady thermal stresses dynamical roll gap friction stree calculation formula under mixed lubricating state is obtained；
S3, the roll-force under mixed lubricating state is forecast, determines forecasting model；
S4, the precision of prediction of forecasting model is verified and is analyzed.
Preferably, Kalman's unit pressure differential equation after line is obtained in the step S1 using Cai Likefu solution
Step specifically:
S11, the unit pressure differential equation is determined:
Unit pressure fundamental differential is initial are as follows:
Ignore the processing hardening, temperature of rolled piece and the influence of deformation velocity in degeneration area, then resistance of deformation K value is approximately
Above formula is become following form by constant:
S12, according to Cai Likefu's it is assumed that using cross deformed area terminal make vertical line as y-axis, using rolled piece central axes as x-axis, then
A point coordinate isB point coordinate isWherein, l is deformed area contact arc length；H and h be respectively rolled piece entrance and
Exit thickness then passes through the straight line equation of A and B two o'clock are as follows:
It is obtained after carrying out differential to above-mentioned formula:
Or
It is solved using Cai Likefu, it will be in Kalman's unit pressure differential equationWithReplacement, after obtaining linearisation
Kalman's unit pressure differential equation it is as follows:
Wherein: pxIt is unit normal pressure of the roll to rolled piece, MPa；txIt is the unit frictional force between roll and rolled piece, N；Δh
It is drafts；Positive sign indicates that zone of slippage on the entry side, negative sign indicate zone of slippage on the delivery side.
Preferably, the formula of unsteady thermal stresses dynamical roll gap friction stree calculates under mixed lubricating state described in step S2
Method specifically includes the following steps:
The typical expression formula of S21, total friction stree are as follows:
τ=A τa+(1-A)τb
Wherein, τaIt is boundary lubrication friction stree, τbIt is hydrodynamic lubrication friction stree, A is surface real contact area
Than；
Assuming that roughened contacting surface boundary lubrication friction stree τaIt can be calculated according to adhesion friction theory: τa=k, wherein k
It is the shear strength of material, the hydrodynamic lubrication friction stree τ generated by the shear action of lubricating oilbIt can be by following formula meter
It calculates:
Wherein, ε0It is lubricating oil viscosity, u (x) is bar rolling speed, hxIt is the oil film thickness of workspace any position；
S22, total friction stree expression formula under mixed lubricating state is obtained based on step S21 are as follows:
In formula, k is the shear strength of material, ε0It is lubricating oil viscosity, v is mill speed, h0It is entrance oil film thickness, u1
It is rolled piece entrance velocity, ε is reduction ratio, and A is real contact area ratio.
Preferably, h in the step S21xWith entrance oil film thickness h0The flow condition of continuity need to be met i.e.:
Wherein, bar rolling speed u (x) are as follows:
Wherein, rolled piece entrance velocity u1Are as follows:
Wherein, μ represents the coefficient of friction between roll gap, is indicated with Roberts formula, it may be assumed that
K in formula1、K2It is frictional behavior coefficient, K1=1.08；K2=0.001；D is work roll diameter.
Preferably, the entrance oil film thickness h0Calculating use following formula:
In formula, α is inlet angle,It is average surface speed, γ1It is pressure coefficient of viscosity, μ0It is viscous under atmospheric pressure
Degree, σ is the yield stress of rolled piece material, qhIt is rolled piece backward pull.
Preferably, the expression formula of the real contact area ratio A is as follows:
In formula, hmIt is the gap of two contact surfaces, RqIt is r.m.s. roughness.
Preferably, the step S3 forecasts the roll-force under mixed lubricating state, determines that forecasting model specifically wraps
Include following steps:
S31, deformed area general rolling force P, zone of slippage on the entry side unit pressure p are determined-And zone of slippage on the delivery side unit pressure p+Expression formula:
The initializer of deformed area rolling gross pressure P are as follows:
The expression formula of zone of slippage on the entry side unit pressure are as follows:
The expression formula of zone of slippage on the delivery side unit pressure are as follows:
S32, the expression formula based on front and back skating area unit pressure correct the expression formula of deformed area general rolling force P are as follows:
In formula, B is the width of operation of rolling tabularium material, xnIt is the abscissa of neutral surface, qHIt is rolled piece forward pull；
S33, above formula is substituted into total friction stree expression formula obtained in step S2, and the item for being unable to proper integral is adopted
It is handled with Taylor series approximation, because shaped likeFunction can not proper integral obtain original function, so will
Molecule ln (mx+n) expands into the multinomial of x with Maclaurin series, approximate can thus acquire the original function of above-mentioned integral.
Arrangement can obtain:
In formula:Wherein Wherein
Above formula is the draught pressure forecast model under mixed lubricating state, and friction stree a part is roughened contacting surface
The directly boundary lubrication friction stree of contact generation, another part are that the fluid that pressure lubrication oil generates in contact surface groove is dynamic
Hydrodynamic lubrication friction stree.
It preferably, is specially that roll-force is calculated according to model in the step S4, by the calculated result of model and practical life
It produces data to compare, obtains prediction error within ± 4.25%.
Compared with prior art, the invention has the following advantages:
The invention proposes a kind of draught pressure forecast methods under mixed lubricating state, it is contemplated that in the actual production process
Generally existing dry friction (or boundary lubrication friction) and hydrodynamic lubrication friction and the mixed lubrication Frotteurism deposited.Pass through
The total friction stree of mixed lubrication is combined with Kalman's unit pressure differential equation, one kind is established and is more conform with actual production
The draught pressure forecast model of situation.And can accurate forecast roll-force size, can instruct to roll to a certain extent
The optimization of technological parameter in journey guarantees the quality of Strip product.
Detailed description of the invention
Fig. 1 is the flow chart of a kind of draught pressure forecast method under mixed lubricating state；
Fig. 2 is the differentiation element body stress analysis schematic diagram of contact in rolling；
Fig. 3 is the contact schematic diagram of Christensen surface roughness；
Fig. 4 is that remaining parameter remains unchanged in embodiment, when only changing friction factor, the situation of change of unit pressure p；
Fig. 5 is that remaining parameter remains unchanged in embodiment, when only changing friction factor, the situation of change of general rolling force P；
Fig. 6 is that remaining parameter remains unchanged in embodiment, when only changing reduction ratio, the situation of change of unit pressure p；
Fig. 7 is that remaining parameter remains unchanged in embodiment, when only changing reduction ratio, the situation of change of general rolling force P；
Fig. 8 is that remaining parameter remains unchanged in embodiment, when only changing flow stress, the situation of change of unit pressure p；
Fig. 9 is that remaining parameter remains unchanged in embodiment, when only changing flow stress, the situation of change of general rolling force P；
Figure 10 is that remaining parameter remains unchanged in embodiment, when considering roll flattening, the situation of change of unit pressure p；With
And
Figure 11 is the increase in embodiment with the number of iterations, the situation of change of general rolling force P.
Specific embodiment
Below with reference to the attached drawing exemplary embodiment that the present invention will be described in detail, feature and aspect.It is identical attached in attached drawing
Icon note indicates element functionally identical or similar.Although the various aspects of embodiment are shown in the attached drawings, unless special
It does not point out, it is not necessary to attached drawing drawn to scale.
To be more easily understood technical solution of the present invention, with reference to the accompanying drawings of the specification, to technical side of the invention
Case progress clearly, explicitly describes.Based on the embodiment of the present invention, those of ordinary skill in the art are being unable to get creation
Property the fruit of labour under conditions of acquired whole other embodiments, protection scope of the present invention all should belong to.
As shown in Figure 1, the invention discloses a kind of draught pressure forecast method under mixed lubricating state, this method is mainly wrapped
It includes:
Step 1: the Cai Likefu of Kalman's unit pressure differential equation is solved；
Step 2: the unsteady thermal stresses dynamical roll gap friction stree under mixed lubricating state；
Step 3: a kind of draught pressure forecast method under mixed lubricating state；
Step 4: the precision of prediction verifying and analysis of this forecasting model.
The draught pressure forecast method under a kind of mixed lubricating state of the present invention is explained in detail below.
(1) the Cai Likefu solution of Kalman's unit pressure differential equation
1.1 Kalman's unit pressure differential equation
As shown in Fig. 2, by dynamic balance condition, writing out equilibrium equation step 1: take differential volume in deformed area.In ac
Average normal pressure is set on section as σx+dσx, and the value of depth of section is y+dy.Then to the power on the face ac on the left of differential body are as follows:
2(σx+dσx)(y+dy) (1)
In zone of slippage on the entry side, the floor projection of roll effect resultant force on this differential body unit width are as follows:
Act on the summation of each power floor projection on differential body are as follows:
WhereinIt may be expressed as:And both sides with multiplied byAndAnd ignore second order infinitesimal, then
The equilibrium equation of differential body into zone of slippage on the entry side are as follows:
In zone of slippage on the delivery side, it will be slided along roll surface along roll rotation direction on differential body with the particle of roll contact.It is micro- at this time
Seperated equilibrium condition is similar to zone of slippage on the entry side, and only direction is opposite.Then in zone of slippage on the delivery side differential body equilibrium equation
Are as follows:
In formula: pxIt is unit pressure of the roll to rolled piece, MPa；txIt is the unit frictional force between roll and rolled piece, N；
Step 2: quoting the plasticity equation under the conditions of plane deformation to solve equation (5) and (6):
Assuming that the principal stress σ on considered differential body1And σ3For vertical stress and horizontal stress, then:
Section 2 its value compared with first item is very small in above formula bracket, can be omitted, then: σ1=pxWith σ3=σx,
Wherein σxFor the average compression principal stress on differentiation element body section.It can thus be concluded that: px-σx=K, rolls in degeneration area if ignoring
The influence of the processing hardening, temperature and deformation velocity of part, resistance of deformation K value is approximately constant, then:
Above formula is the general type of Kalman's unit pressure differential equation equation.
1.2 Cai Likefu equations
Contact arc is regarded as string by Cai Likefu, makes y and x linear function relationship, then the differential equation has solution, to obtain outlet
Property equation.As shown in Fig. 2, according to Cai Likefu's it is assumed that using cross deformed area terminal make vertical line as y-axis, be x with rolled piece central axes
Axis, then A point coordinate beB point coordinate isWherein, l is deformed area contact arc length；H and h is that rolled piece enters respectively
Mouth and exit thickness then pass through the straight line equation of A and B two o'clock are as follows:
After differential:
The linearisation of 1.3 deformed area unit pressure equations
Cai Likefu equation after differential, which is substituted into Kalman's unit pressure differential equation, to be obtained:
Above formula is exactly the unit pressure differential equation after linearisation.Wherein: pxIt is unit normal pressure of the roll to rolled piece,
MPa；txIt is the unit frictional force between roll and rolled piece, N；Δ h is drafts；Positive sign indicates that zone of slippage on the entry side, negative sign indicate zone of slippage on the delivery side.
(2) the total friction stree of dynamical roll gap under mixed lubricating state
The typical expression formula of 2.1 total friction strees
Under mixed lubricating state, the load and frictional force a part on joint surface are undertaken by roughened contacting surface, another
Part is undertaken by the pressure lubrication oil in contact surface groove, at this time the typical expression formula of total friction stree are as follows:
τ=A τa+(1-A)τb (12)
Wherein τaAnd τbRespectively boundary lubrication friction stree and hydrodynamic lubrication friction stree, A are surface actual contacts
Area ratio.Assuming that roughened contacting surface boundary lubrication friction stree τaIt can be calculated according to adhesion friction theory: τa=k, k are materials
Shear strength.The hydrodynamic lubrication friction stree τ generated by the shear action of lubricating oilbIt can be calculated by following formula:
Wherein ε0It is lubricating oil viscosity, u (x) is bar rolling speed, and v is roller surface linear velocity, hxIt is workspace any position
Oil film thickness.
2.2 real contact area ratios
Due to the surface roughness of roll, rolled piece be it is non-uniform, generally assume that rolled piece and roll surface roughness height
It is distributed as Gaussian Profile, therefore can estimate its real contact area ratio A.For convenience's sake, Christensen proposes one
The approximation simplified is come approximate instead of Gaussian Profile, i.e., the probability density function f (z) of a certain certain height z are as follows:
In formulaIt is r.m.s. roughness, Rq1And Rq2It is the surface roughness of roll, rolled piece respectively.
In conjunction with Fig. 3, can be acquired by being integrated to probability density function in the real contact area ratio A of a certain certain height:
As z > 3RqWhen, f (z)=0 is then apparent from:And then above formula first half has been left behind, calculating can
:
In formula, hmIt is the gap of two contact surfaces, also known as nominal oil film thickness.RqIt is r.m.s. roughness.
2.3 workspace any position oil film thicknesses
hxWith entrance oil film thickness h0The flow condition of continuity need to be met i.e.:
In formula, u1It is rolled piece entrance velocity, u (x) is bar rolling speed.
Rolled piece entrance velocity u1It can be exported by following methods.It can be obtained according to the equal principle of metal mass flow:Its
Middle u2For rolled piece muzzle velocity.It is rule of thumb apparent from: u2=v (1+sh), wherein shFor advancing slip value.Then:Here
Taking lengthening coefficient λ is 1.3.Advancing slip value shModel uses following empirical equation:
For bar rolling speed u (x), can be determined by following formula:
Wherein y (x) is workspace rolled piece thickness, it may be assumed that
Wherein, ε is reduction ratio, then bar rolling speed u (x) are as follows:
Wherein rolled piece entrance velocity u1Are as follows:
Wherein, μ represents the coefficient of friction between roll gap, approximate can be indicated with Roberts formula, it may be assumed that
K in formula1、K2It is frictional behavior coefficient, K1=1.08；K2=0.001；D is work roll diameter.
Entrance oil film thickness h0Calculating use Wilson and Walowit formula, under isothermal situation consider after tensile stress
Influence:
In formula, α is inlet angle, γ1It is pressure coefficient of viscosity, μ0It is the viscosity under atmospheric pressure, σ is bending for rolled piece material
Take stress, qhIt is rolled piece backward pull,It is average surface speed.
2.4 total friction strees
In conclusion total friction stree expression formula under mixed lubricating state are as follows:
In formula, k is the shear strength of material, ε0It is lubricating oil viscosity, v is mill speed, h0It is entrance oil film thickness, u1
It is rolled piece entrance velocity, ε is reduction ratio, and A is real contact area ratio.
(3) a kind of draught pressure forecast method under mixed lubricating state
By the t in formula (11)xIt can be obtained with total friction stree τ replacement:
The 3.1 zone of slippage on the entry side unit pressure differential equations
Use p-Instead of px, convolution (9), and both sides can be obtained with dx is multiplied:
Integral can obtain:
According to boundary condition, at inlet section, as x=l, p-=K-qH, wherein qHTensile stress before indicating, in substitution
Formula can solve:
It can to sum up obtain, the expression formula of zone of slippage on the entry side unit pressure are as follows:
The 3.2 zone of slippage on the delivery side unit pressure differential equations
Use p+Instead of px, can similarly obtain, the zone of slippage on the delivery side unit pressure after integral are as follows:
According to boundary condition, at Outlet Section, as x=0, p+=K-qh, wherein qhTensile stress after expression, in substitution
Formula can solve:
It can to sum up obtain, the expression formula of zone of slippage on the delivery side unit pressure are as follows:
Draught pressure forecast model under 3.3 mixed lubricating states
Deformed area rolls gross pressure are as follows:
In conjunction with the expression formula of front and back skating area unit pressure, can obtain:
In formula, B is the width of operation of rolling tabularium material, it is assumed that ignore and spreads, xnFor the abscissa of neutral surface, qHIt is to roll
Part forward pull.
Total friction stree τ is substituted into, and the item for being unable to proper integral is handled using Taylor series approximation, arrangement can obtain:
In formula:Wherein Wherein
Here it is a kind of draught pressure forecast method under mixed lubricating state, friction stree a part is by Rough Contact
Surface directly contacts the boundary lubrication friction stree of generation, and another part is generated by pressure lubrication oil in contact surface groove
Hydrodynamic lubrication friction stree.
(4) the precision of prediction verifying and analysis of this forecasting model
The verifying of 4.1 precision of predictions
Used data source Mr. Yu produces the cold rolling mill of sheet band steel strip.Material data and rolling parameter such as following table institute
Show.
4.1 coil of strip data information of table
Table 4.1 Data information of the roll steeling
Each passage coil of strip rolling data information of table 4.2 and this model calculation compare
Table 4.2 Comparison of the data of rolling data of each pass and the
calculation result of this model
From the point of view of the comparison of production real data and the calculated result of this forecasting model above, actual measurement roll-force and this rolling
The prediction error of power model is maintained within ± 4.25%.This has turned out this draught pressure forecast method prediction essence with higher
Degree, can preferably be close to industrial actual conditions.So this draught pressure forecast method can be applied to actual industrial
In production, thus the forecast to instruct roll-force in cold-rolled plate and strip production process, for the verification and production technology of milling train equipment
Parameter optimization provide guidance.
Influence of 4.2 coefficient of frictions to unit normal pressure and roll-force
As shown in figure 4, unit normal pressure increases with the increase of coefficient of friction, and maximum is obtained at neutral point
Value.Same coefficient of friction is bigger, and the peak value of unit normal pressure is also higher.But when coefficient of friction is more than after 0.3, unit is just
The increase of pressure becomes slowly.This is because lubrication friction proportion is smaller, entirely as what coefficient of friction was got over becomes larger
Lubricating status is closer to dry friction.As shown in figure 5, becoming larger with coefficient of friction, general rolling force is also increasing.Equally,
When coefficient of friction is more than after 0.3, the increase of general rolling force also becomes slowly.In this simulation example, when friction is
Number from 0.05 rise to 0.2 when, roll-force has the significant growth close to 20%.So if adequate measures can be taken to improve
Lubrication friction situation in the operation of rolling, reduces coefficient of friction, and the roll-force of finishing mill can effectively reduce.
Influence of 4.3 reduction ratios to unit normal pressure and roll-force
As shown in fig. 6, unit normal pressure increases with the increase of reduction ratio, and the unit normal pressure at neutral point is
It is maximum in deformed area each point.Same reduction ratio is bigger, and the peak value of unit normal pressure is higher, and deformed area arc length has apparent increasing
Long, the value at neutral point also slightly increases.With becoming larger for reduction ratio, the increasing degree of unit normal pressure is also increasingly
Greatly.As shown in fig. 7, becoming larger with reduction ratio, general rolling force is increasing, and the increasing degree of general rolling force is also got over
Come bigger.
Influence of 4.4 flow stresses to unit normal pressure and roll-force
The variation range of flow stress is from 80Mpa to 180Mpa.As shown in figure 8, unit normal pressure is with flow stress
Increase and increase, and it obtains peak value at neutral point.Same flow stress is bigger, and the peak value of unit normal pressure is also got over
It is high.As shown in figure 9, becoming larger with flow stress, general rolling force is increasing, and general rolling force is almost with flowing
The increase of stress and linearly increase.
Influence of 4.5 roll flattenings to unit normal pressure and roll-force
Consider the flattening effect of roll, use the most common dynamic roll flattening radius formula herein:
In formula, R' is the roller radius after flattening, and R is original radius,It is roll flattening coefficient, vrWith
E is respectively the Poisson's ratio and elasticity modulus of roll, generally takes C0=2.2 × 10-5.P is general rolling force, and B is rolled piece width, Δ h
For drafts.
Figure 10 illustrates the unit normal pressure distribution situation before and after roll flattening, it can be seen that before considering roll flattening
Afterwards, the variation of zone of slippage on the delivery side unit normal pressure is unobvious, and the peak value of zone of slippage on the entry side original position pressure and unit normal pressure all slightly increases,
And position and the also slightly increase of deformed area arc length of neutral point.
To realize the decoupling between roll-force and roll flattening formula, need roll-force formula and roll flattening formula it
Between iterate, in this simulation example, each iteration all correspond to a rolling pass.The condition of iteration ends is phase
The deviation of adjacent rolling force data twice is less than 0.1%.As shown in figure 11, the initial data of roll-force is 3723.877kN, repeatedly
Five realizations of Dai convergence, the roll-force after restraining is 3858.860kN, about increases 3.6%.This illustrates roll
The flat stress of deformed area in vertical direction that will lead to of roll-in increases, and equally can also cause the increase of each micro unit body length,
Will finally general rolling force be made to become larger.
Finally, it should be noted that above-described embodiments are merely to illustrate the technical scheme, rather than to it
Limitation；Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should understand that:
It can still modify to technical solution documented by previous embodiment, or to part of or all technical features into
Row equivalent replacement；And these modifications or substitutions, it does not separate the essence of the corresponding technical solution various embodiments of the present invention technical side
The range of case.
Claims (8)
1. a kind of draught pressure forecast method under mixed lubricating state, it is characterised in that: itself the following steps are included:
S1, Kalman's unit pressure differential equation after line is obtained using Cai Likefu solution；
S2, the unsteady thermal stresses dynamical roll gap friction stree calculation formula under mixed lubricating state is obtained；
S3, the roll-force under mixed lubricating state is forecast, determines forecasting model；
S4, the precision of prediction of forecasting model is verified and is analyzed.
2. the draught pressure forecast method under mixed lubricating state according to claim 1, it is characterised in that: the step S1
The step of middle Kalman's unit pressure differential equation obtained using Cai Likefu solution after line specifically:
S11, the unit pressure differential equation is determined:
Unit pressure fundamental differential is initial are as follows:
Ignore the processing hardening, temperature of rolled piece and the influence of deformation velocity in degeneration area, then resistance of deformation K value is approximately normal
Number, becomes following form for above formula:
S12, according to Cai Likefu's it is assumed that using cross deformed area terminal make vertical line as y-axis, using rolled piece central axes as x-axis, obtain A
Putting coordinate isB point coordinate isWherein, l is deformed area contact arc length；H and h be respectively rolled piece entrance and
Exit thickness then passes through the straight line equation of A and B two o'clock are as follows:
Differential calculation is carried out to above formula, is obtained:
Or
It is solved using Cai Likefu, it will be in Kalman's unit pressure differential equationWithReplacement, the karr after being linearized
The graceful unit pressure differential equation is as follows:
Wherein: pxIt is unit normal pressure of the roll to rolled piece, MPa；txIt is the unit frictional force between roll and rolled piece, N；Δ h is pressure
Lower amount；Positive sign indicates that zone of slippage on the entry side, negative sign indicate zone of slippage on the delivery side.
3. the draught pressure forecast method under mixed lubricating state according to claim 1, it is characterised in that: described in step S2
The calculation formula for obtaining unsteady thermal stresses dynamical roll gap friction stree under mixed lubricating state specifically includes the following steps:
The typical expression formula of S21, total friction stree are as follows:
τ=A τa+(1-A)τb
Wherein, τaIt is boundary lubrication friction stree, τbIt is hydrodynamic lubrication friction stree, A is surface real contact area ratio；
Assuming that roughened contacting surface boundary lubrication friction stree τaIt can be calculated according to adhesion friction theory: τa=k, wherein k is material
The shear strength of material, the hydrodynamic lubrication friction stree τ generated by the shear action of lubricating oilbIt is calculated by following formula:
Wherein, ε0It is lubricating oil viscosity, u (x) is bar rolling speed, hxIt is the oil film thickness of workspace any position；
S22, total friction stree expression formula under mixed lubricating state is obtained based on step S21 are as follows:
In formula, k is the shear strength of material, ε0It is lubricating oil viscosity, v is mill speed, h0It is entrance oil film thickness, u1It is to roll
Part entrance velocity, ε are reduction ratios, and A is real contact area ratio.
4. the draught pressure forecast method under mixed lubricating state according to claim 3, it is characterised in that: the step
H in S21xWith entrance oil film thickness h0The flow condition of continuity need to be met i.e.:
Wherein, bar rolling speed u (x) are as follows:
Wherein, rolled piece entrance velocity u1Are as follows:
Wherein, μ represents the coefficient of friction between roll gap, is indicated with Roberts formula, it may be assumed that
K in formula1、K2It is frictional behavior coefficient, K1=1.08；K2=0.001；D is work roll diameter.
5. the draught pressure forecast method under mixed lubricating state according to claim 4, it is characterised in that: the entrance oil
Film thickness h0It is calculated using the following equation:
In formula, α is inlet angle,It is average surface speed, γ1It is pressure coefficient of viscosity, μ0It is the viscosity under atmospheric pressure, σ is
The yield stress of rolled piece material, qhIt is rolled piece backward pull.
6. the draught pressure forecast method under mixed lubricating state according to claim 4, it is characterised in that: described really to connect
The expression formula for touching area ratio A is as follows:
In formula, hmIt is the gap of two contact surfaces, RqIt is r.m.s. roughness.
7. the draught pressure forecast method under mixed lubricating state according to claim 1, it is characterised in that: the step S3
Roll-force under mixed lubricating state is forecast, determine forecasting model specifically includes the following steps:
S31, deformed area general rolling force P, zone of slippage on the entry side unit pressure p are determined-And zone of slippage on the delivery side unit pressure p+Expression formula:
The initializer of deformed area general rolling force P are as follows:
Zone of slippage on the entry side unit pressure p-Expression formula are as follows:
Zone of slippage on the delivery side unit pressure p+Expression formula are as follows:
S32, the expression formula based on front and back skating area unit pressure correct the expression formula of deformed area general rolling force P are as follows:
In formula, B is the width of operation of rolling tabularium material, xnIt is the abscissa of neutral surface, qHIt is rolled piece forward pull；
S33, total friction stree expression formula obtained in step S2 is substituted into above formula, and the item for being unable to proper integral uses
Taylor series approximation processing, obtains the expression formula of final deformed area general rolling force P:
In formula:Wherein Wherein
Above formula is the draught pressure forecast model under mixed lubricating state, and friction stree a part is that roughened contacting surface is direct
The boundary lubrication friction stree generated is contacted, another part is the fluid dynamic profit that pressure lubrication oil generates in contact surface groove
Sliding/friction stress.
8. the draught pressure forecast method under mixed lubricating state according to claim 1, it is characterised in that: the step S4
In be specially according to model calculate roll-force, the calculated result of model and actual production data are compared, obtain prediction mistake
Difference is within ± 4.25%.
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