CN109359429A - A kind of board rolling is advancing slip value calculating method and device - Google Patents
A kind of board rolling is advancing slip value calculating method and device Download PDFInfo
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Abstract
The invention discloses a kind of advancing slip value calculating methods of board rolling, comprising: roll gap deformed area is divided into zone of slippage on the entry side and zone of slippage on the delivery side, establishes the unit width rolling pressure differential equation and average level stress model in each region；Judge the friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet, calculates each area unit draught pressure distribution under corresponding friction condition；The distribution of roll elastic flattening amount is calculated, and establishes deformation roll profile curve model and roll gap thickness distributed model；It iterates and roll gap thickness distribution curve is calculated；The rolled piece thickness and the slope of curve from neutral surface are obtained from roll gap thickness distribution curve, and advancing slip value is thus calculated.The present invention also provides a kind of advancing slip value calculation apparatus of board rolling.The invention has the benefit that principle of the invention clear and definite, assuming that few with simplified condition, roll gap deformational behavior can be more accurately simulated, computational accuracy is high, and calculated result, which can be used as, formulates rolling procedure, selection main motor capacity and the foundation for checking motor load.
Description
Technical field
The invention belongs to rolling technical fields, and in particular to a kind of board rolling is advancing slip value calculating method and device.
Background technique
It is sliding after rolled piece metal particle is formed to inlet side during rolling deformation, it is flowed to outlet side before being formed
It is sliding, therefore the horizontal component of the bar rolling speed in roll gap everywhere and roll linear velocity and unequal (except neutral surface), but deposit
In certain gap.This characteristic indicates with advancing slip value f, is defined as:V in formulahFor rolled piece muzzle velocity, vr
For roll linear velocity.
Advancing slip value is one of most important parameter of rolling mill practice, is on the one hand needed when formulating rolling procedure in known roll
Rolled piece muzzle velocity is accurately determined under conditions of linear velocity, provides reasonable mill speed setting value for automatic control system,
To guarantee to be rapidly achieved steady production；On the other hand it needs when rolling mill main motor lectotype selection and load are checked in known rolling
Roll linear velocity is determined under conditions of speed, accurately to obtain reasonable main motor parameter.
Advancing slip value is generally calculated using the advancing slip formula of Fink or the advancing slip formula of Ekelund at present, the two formula belong to
Analytic function space formula has been all made of a large amount of hypothesis and simplified condition in derivation process, and computational accuracy is lower, calculates error and reaches
To 30% or more.With the continuous improvement of mill speed, the two formula have been unable to satisfy engineering calculation required precision.Therefore it needs
Further to develop the advancing slip value computation model of high-precision.
Summary of the invention
It is an object of the present invention in view of the deficiencies of the prior art, provide a kind of advancing slip value calculating method of board rolling and
Computing device, to solve the problems, such as that existing advancing slip value model computational accuracy is low, be unable to satisfy engineering calculation required precision.
A kind of the technical solution adopted by the present invention are as follows: advancing slip value calculating method of board rolling, comprising the following steps:
Step 1: roll gap deformed area is divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet, and establish each area
The unit width rolling pressure differential equation and average level stress model in domain；
Step 2: judging the friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet, and calculate each region under corresponding friction condition
Unit width rolling pressure distribution；
Step 3: calculating the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and establish deformation roll wheels
Wide curve model and roll gap thickness distributed model；
Step 4: being iterated and roller being calculated by unit width rolling pressure distributed model and deformation roll profile curve model
Stitch thickness distribution curve；
Step 5: obtaining the rolled piece thickness and the slope of curve from neutral surface from roll gap thickness distribution curve, thus calculate
Obtain advancing slip value.
According to the above scheme, the unit width rolling pressure differential equation in each region is
The average level stress model is
Wherein, positive sign "+" indicates zone of slippage on the entry side, and negative sign "-" indicates zone of slippage on the delivery side；pxAbscissa is that the unit at x rolls pressure
Power, MPa；txIt is the friction stree between the rolled piece and working roll at x, MPa for abscissa；σxFor the average water that abscissa is at x
Horizontal stress, MPa；K is deformation of rolled wire drag, K=1.15 σs, σsFor yield strength, MPa；hxFor the rolled piece thickness that abscissa is at x
Degree, mm；
In step 3, the roll elastic flattening amount distributed model is
The deformation roll profile curve model is
The roll gap thickness model is
The x-axis of the coordinate system of above-mentioned foundation is located at the interior thickness position of rolled piece, and y-axis is located on roll line of centres,
Middle h0Rolled piece inlet thickness, unit mm；h1Rolled piece exit thickness, unit mm；R- roller radius, unit mm；Value that f- is advancing slip；hr-
Rolled piece thickness at neutral surface, unit mm；Roll gap thickness distribution curve slope at neutral surface；x0Arc-shaped roll wheels
Rolled piece inlet abscissa, unit mm when wide (i.e. initial roll profile)；x1Rolled piece inlet abscissa after roll flattening, it is single
Position mm；xnRolled piece exit abscissa (i.e. deformation roll profile lowest point abscissa), unit mm after roll flattening；δ (x)-is mono-
Abscissa caused by the draught pressure of position is the roll elastic flattening amount at x, unit mm；Deformation roll profile is bent before y- moves down roll
Line ordinate, unit mm；yminRoll profile lowest point ordinate, unit mm are deformed before moving down roll；E1Roll material elasticity
Model, units MPa；v1Roll material Poisson's coefficient；P (s)-abscissa is the unit width rolling pressure at s, units MPa；
In step 5, the calculation formula of the advancing slip value is
According to the above scheme, in step 2, the friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet includes sliding friction and adhesion
Friction, whenWhen be sliding friction condition, at this time tx=μ px, μ coefficient of friction between working roll and rolled piece；It rubs in sliding
The unit width rolling pressure differential equation under the conditions of wiping is
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side；
WhenWhen be sticking friction condition, at this timeUnit width rolling pressure under the conditions of sticking friction is micro-
Point equation is
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side.
According to the above scheme, the acquisition methods of roll gap thickness distribution curve are as follows:
1) initial roll contour curve, is set, and determines rolled piece entry position:
2) each section of zone of slippage on the entry side unit width rolling pressure, is calculated from entrance to outlet: using zone of slippage on the entry side formula from entrance to outlet
It calculates, judges the partitioning scenario of sliding friction and sticking friction, and calculate separately each section of zone of slippage on the entry side unit under corresponding friction condition
Draught pressure；
3) each section of zone of slippage on the delivery side unit width rolling pressure, is calculated from outlet to entrance: using zone of slippage on the delivery side formula from entrance to outlet
It calculates, judges the partitioning scenario of sliding friction and sticking friction, and calculate separately each section of zone of slippage on the delivery side unit under corresponding friction condition
Draught pressure；
4) unit width rolling pressure distribution, is calculated by initial roll contour curve；
5) new roll contour curve, is calculated using unit width rolling pressure distribution；
6) whether the roll contour curve for, judging that front and back is calculated twice restrains；
7), twice roll profile curve convergence when roll gap thickness distribution curve is calculated, roll contour curve is not twice
Enter next round iterative calculation when convergence until roll profile curve convergence；
8) the rolled piece thickness and the slope of curve from neutral surface, are obtained from roll gap thickness distribution curve, are calculated advancing slip
Value.
According to the above scheme, in step 4 1) in, initial roll contour curve is arc-shaped, δ (x)=0, roll contour curve
It is discrete in deformed area: deformed area to be divided into n sections, the roll gap thickness model equation under arc-shaped roll profile isWherein x (i) is i-th section of abscissa, and h (i) is i-th section of rolled piece thickness, x
(n)=0, h (n)=h1,Discrete segment length
According to the above scheme, in step 4 2) in, the specific of each section of zone of slippage on the entry side unit width rolling pressure is calculated from entrance to outlet
Method are as follows:
Entrance unit width rolling pressure under the conditions of sliding friction is calculated by average level stress model formula:
In formula, T0For entrance tension, unit N；B
For rolled piece width, unit mm；
P (1) is solved using iterative methodb_ sli judges (1) μ p at entranceb_ sli withSize is divided into two kinds of situations:
(i) whenWhen, the unit width rolling pressure p (1) of entranceb=p (1)b_sli；Utilize sliding friction
Under the conditions of the unit width rolling pressure differential equation of zone of slippage on the entry side successively calculate the unit width rolling pressure of the 2nd section, the 3rd section ..., and
μ p (i) is all judged at each sectionb_ sli withSize, specifically:
It is obtained by the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sliding friction:
The friction stree of zone of slippage on the entry side under the conditions of sliding friction are as follows: t (i)b_ sli=μ p (i)b_sli；
A: when being all satisfied from entrance to outlet sectionWhen, calculated each section using zone of slippage on the entry side formula
Unit width rolling pressure are as follows: p (1)b=p (1)b_sli、p(2)b=p (2)b_sli…p(n)b=p (n)b_sli；
B: exist when at m sectionsWhen, then it is sticking friction to outlet since m sections, switchs to
M sections, m+1 sections ... n-th section are successively calculated using the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction
Unit width rolling pressure, specifically:
It is obtained by the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction
The friction stree of zone of slippage on the entry side is under the conditions of sticking friction
The calculated each section of unit width rolling pressure of zone of slippage on the entry side formula is utilized at this time are as follows: p (1)b=p (1)b_sli、p(2)b=p
(2)b_sli…p(m-1)b=p (m-1)b_sli、p(m)b=p (m)b_sti、p(m+1)b=p (m+1)b_sti…p(n)b=p
(n)b_sti；
(ii) whenWhen, then the unit width rolling pressure of entranceUsing viscous
The unit width rolling pressure differential equation of zone of slippage on the entry side successively calculates the 2nd section under friction condition, the 3rd section ... n-th section of unit is rolled
Pressing pressure p (1)b=p (1)b_sti、p(2)b=p (2)b_sti……p(n)b=p (n)b_sti；
Step 4 3) in, it is p (1) using the calculated each section of unit width rolling pressure of zone of slippage on the delivery side formulaf、p(2)f……p
(n)f。
According to the above scheme, in step 4 4) in, the calculation method of unit width rolling pressure distribution are as follows: be compared with zone of slippage on the delivery side public affairs
Formula and the calculated two groups of unit width rolling pressure p (1) of zone of slippage on the entry side formulaf、p(2)f……p(n)fAnd p (1)b、p(2)b……p
(n)b, find that difference is r sections the smallest, then this section is the interface segment namely neutral surface of zone of slippage on the delivery side and zone of slippage on the entry side, x (r)=x
(1)+(r-1)ΔX；Retain p (1)f、p(2)f……、p(r-1)f、p(r)fOr p (r)b、p(r+1)b……p(n)b, specify roll
Unit width rolling pressure under profile is distributed as p (1)=p (1)f, p (2)=p (2)f..., p (r-1)=p (r-1)f, p (r)=p
(r)fOr p (r)=p (r)b, p (r+1)=p (r+1)b... p (n)=p (n)b。
According to the above scheme, in step 4 5) in, the side for calculating roll contour curve h (i) is distributed using unit width rolling pressure
Method are as follows: it introduces smoothing factor e and is iterated calculating,
That is pm+1(i)=ep (i)+(1-e) pm(i), 0 < e < 1,
P (i) is the draught pressure distribution under calculated specified roll profile；pm(i) what is used when being the m times iteration rolls
Pressing pressure distribution；pm+1(i) the draught pressure distribution used when being the m+1 times iteration；
Utilize the unit width rolling pressure distribution p after relaxationm+1(i) the elastic flattening deflection δ (x (j)) for calculating roll, by
The method of accumulation summation calculates the roll elastic flattening amount that abscissa is the place x (j)
siFor unit draught pressure pm+1(i) corresponding abscissa；
Finding out deformation roll profile curve distribution is
Roll gap thickness is distributed as
In formula, y (x (j))minFor the corresponding ordinate in deformation roll contour curve lowest point, mm.
According to the above scheme, in step 4 7) in, the calculation method of roll gap thickness distribution are as follows:
It is corresponding with unit width rolling pressure distribution, roll profile is handled, i.e.,
hm+1(j)=eh (j)+(1-e) hm(j),
Wherein, h (j) is calculated each section of roll profile；hm(j) each section of roll profile used when being the m times iteration；
hm+1(j) each section of roll profile used when being the m+1 times iteration；Using new roll profile curvilinear equation according to above-mentioned identical
Method solves the distribution of the unit width rolling pressure under the roll profile, loop iteration, until roll profile curve convergence again.
In step 4 8) in, the rolled piece thickness h (r) and the slope of curve from neutral surface are obtained from roll gap thickness distribution curve
For
Advancing slip value, which is calculated, is
The present invention also provides a kind of advancing slip value calculation apparatus of board rolling, including be sequentially connected partition modeling module,
Friction condition determination module, roll contour curve modeling module, iterative calculation module and advancing slip value computing module, wherein described
Partition modeling module is used to that roll gap deformed area to be divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet, and establishes each area
The unit width rolling pressure differential equation and average level stress model in domain；The friction condition determination module is for judging zone of slippage on the entry side
The friction condition met with zone of slippage on the delivery side, and calculate the distribution of each area unit draught pressure under corresponding friction condition；The roll
Contour curve modeling module is used to calculate the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and establishes deformation and roll
Roll profile curve model and roll gap thickness distributed model；The iterative calculation module be used for by unit width rolling pressure distributed model and
Deformation roll profile curve model, which iterates, is calculated roll gap thickness distribution；The advancing slip value computing module is used for from roll gap
The rolled piece thickness and the slope of curve at neutral surface are obtained on thickness distribution curve, and advancing slip value is calculated.
The invention has the benefit that advancing slip value computation model of the present invention belongs to numerical method model, pass through theory point
Analysis establishes the roll gap deformed area unit width rolling pressure differential equation for taking into account sliding friction and sticking friction condition and deformation roll
Contour curve model, according to given technological parameter (including rolled piece entrance and exit thickness, rolled piece width, rolled piece yield strength,
Roller diameter, coefficient of friction, entrance and outlet tension etc.), for by the unit width rolling pressure differential equation and deformation roll profile
Curve model, which iterates, is calculated roll gap thickness distribution, and then calculates advancing slip value using the method for diff；This hair
Bright the method clear principle is clear, it is assumed that and simplified condition is few, can more accurately simulate roll gap deformational behavior, calculates essence
Degree is high, and calculated result, which can be used as, formulates rolling procedure, selection main motor capacity and the foundation for checking motor load.
Detailed description of the invention
Fig. 1 is the flow chart of heretofore described method.
Fig. 2 is roll gap subregion and micro unit stress diagram in the present invention.
Fig. 3 is the flow diagram of roll profile curve acquisition method in the present invention.
Fig. 4 is the micro unit stress diagram after the roll gap deformed area in the present invention is discrete.
Fig. 5 be full sliding friction under the conditions of utilize the calculated friction stree distribution schematic diagram of zone of slippage on the entry side formula.
Fig. 6 is illustrated to be distributed under the conditions of sliding friction and sticking friction using the calculated friction stree of zone of slippage on the entry side formula
Figure.
Fig. 7 be full sticking friction under the conditions of utilize the calculated friction stree distribution schematic diagram of zone of slippage on the entry side formula.
Fig. 8 be full sliding friction under the conditions of utilize the calculated friction stree distribution schematic diagram of zone of slippage on the delivery side formula.
Fig. 9 is illustrated to be distributed under the conditions of sliding friction and sticking friction using the calculated friction stree of zone of slippage on the delivery side formula
Figure.
Figure 10 be full sticking friction under the conditions of utilize the calculated friction stree distribution schematic diagram of zone of slippage on the delivery side formula.
Figure 11 is the normalization roll gap thickness distribution curve of 5 kinds of example operating conditions of heretofore described method.
Figure 12 is the unit width rolling pressure distribution curve of 5 kinds of example operating conditions of heretofore described method.
The friction stree distribution curve of 5 kinds of example operating conditions of the heretofore described method of Figure 13.
Figure 14 is the structural schematic diagram that tabularium of the present invention rolls advancing slip value computing module.
Specific embodiment
For a better understanding of the present invention, the present invention is further described in the following with reference to the drawings and specific embodiments.
The advancing slip value calculating method of a kind of board rolling as shown in Figure 1, specifically includes the following steps:
Step 1: as shown in Fig. 2, roll gap deformed area is divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet,
And establish the unit width rolling pressure differential equation and average level stress model in each region, the unit width rolling pressure in each region
The differential equation are as follows:
In above formula, positive sign "+" indicates zone of slippage on the entry side, and negative sign "-" indicates zone of slippage on the delivery side；
The average level stress model is；
In above formula, pxAbscissa is the unit width rolling pressure at x, MPa；txFor the rolled piece and working roll that abscissa is at x
Between friction stree, MPa；σxFor the average level stress that abscissa is at x, MPa；K is deformation of rolled wire drag, K=1.15
σs, σsFor yield strength, MPa；hxFor the rolled piece thickness that abscissa is at x, mm.
Step 2: judging the friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet, and calculate each region under corresponding friction condition
Unit width rolling pressure distribution, specifically:
The friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet includes sliding friction and sticking friction, whenWhen for sliding
Friction condition, at this time tx=μ px, μ coefficient of friction between working roll and rolled piece；Unit width rolling pressure under the conditions of sliding friction
The differential equation are as follows:
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side；
WhenWhen be sticking friction condition, at this timeUnit width rolling pressure under the conditions of sticking friction is micro-
Divide equation are as follows:
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side；
Step 3: calculating the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and establish deformation roll profile
Curve model and roll gap thickness distributed model, the roll elastic flattening amount distributed model are
The deformation roll profile curve model isThe roll gap thickness model is
In formula, h0For rolled piece inlet thickness, mm；h1For rolled piece exit thickness, mm；R is roller radius, unit mm；hrFor in
Rolled piece thickness at property face, unit mm；For the roll gap thickness distribution curve slope at neutral surface；x0For arc-shaped roll wheels
Rolled piece inlet abscissa, unit mm when wide (i.e. initial roll profile)；x1It is single for rolled piece inlet abscissa after roll flattening
Position mm；xnFor rolled piece exit abscissa after roll flattening (i.e. deformation roll profile lowest point abscissa), unit mm；δ (x) is
Abscissa caused by unit width rolling pressure is the roll elastic flattening amount at x, unit mm；Y is to deform roll wheels before moving down roll
Wide curve ordinate, unit mm；yminTo move down deformation roll profile lowest point ordinate before roll, unit mm；E1For roll material
Expect elastic model, units MPa；v1For roll material Poisson's coefficient；P (s) is that abscissa is unit width rolling pressure at s, unit
MPa；
Step 4: being iterated and roller being calculated by unit width rolling pressure distributed model and deformation roll profile curve model
Stitch thickness distribution curve；
Step 5: obtaining the rolled piece thickness and the slope of curve from neutral surface from roll gap thickness distribution curve, thus calculate
Advancing slip value is obtained, the calculation formula of the advancing slip value is
In formula, f is advancing slip value；hrFor the rolled piece thickness at neutral surface, mm；For the roll gap thickness distribution at neutral surface
The slope of curve.
In step 4, the acquisition methods of roll gap thickness distribution curve the following steps are included:
1, initial roll contour curve is set, and determines rolled piece entry position:
Assuming that roll is undeformed, it is arc-shaped, δ (x)=0；It is discrete to deformed area: as shown in figure 4, deformed area is divided into n
Section (such as taking n=1000), the roll gap thickness model equation under arc-shaped roll profile are
Wherein x (i) is i-th section of abscissa, and h (i) is i-th section of rolled piece thickness, x (n)=0, h (n)=h1, thereforeDiscrete segment length
2, each section of zone of slippage on the entry side unit width rolling pressure is calculated from entrance to outlet, specifically:
It is calculated using zone of slippage on the entry side formula from entrance to outlet, and judges the partitioning scenario of sliding friction and sticking friction:
Entrance (paragraph 1) unit under the conditions of sliding friction is calculated by average level stress model formula and rolls pressure
Power:
P (1) is solved using Aitken iterative methodb_
sli。
In formula, T0For entrance tension, unit N；B is rolled piece width, unit mm；
Judge (1) μ p at entranceb_ sli withSize is divided into two kinds of situations:
If (i)Then illustrate that entrance is sliding friction, the unit width rolling pressure p (1) of entranceb=
p(1)b_sli.The 2nd section, the 3rd are successively calculated using the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sliding friction
The unit width rolling pressure of section ..., and μ p (i) is all judged at each sectionb_ sli (1≤i≤n) withSize.Specifically:
Write the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sliding friction as difference form:
It arranges:
The friction stree of zone of slippage on the entry side under the conditions of sliding friction are as follows: t (i)b_ sli=μ p (i)b_sli
There are two kinds of situations again in calculating process:
If 1) be all satisfied from entrance (paragraph 1) to outlet section (n-th section)Then say
The bright unit width rolling pressure differential equation using zone of slippage on the entry side under the conditions of sliding friction is cunning when being calculated from the inlet to the outlet
Dynamic friction, as shown in Figure 5.The calculated each section of unit width rolling pressure of zone of slippage on the entry side formula is utilized at this time are as follows: p (1)b=p (1)b_
sli、p(2)b=p (2)b_sli…p(n)b=p (n)b_sli。
If 2) have at m (1 < m≤n) section:Then explanation is viscous to outlet since m sections
Friction, as shown in Figure 6.Switch to successively to calculate the using the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction
M sections, m+1 sections ... n-th section of unit width rolling pressure.Specifically:
Write the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction as difference form:
It arranges:
The friction stree of zone of slippage on the entry side under the conditions of sticking friction are as follows:
The calculated each section of unit width rolling pressure of zone of slippage on the entry side formula is utilized at this time are as follows: p (1)b=p (1)b_sli、p(2)b=p
(2)b_sli…p(m-1)b=p (m-1)b_sli、p(m)b=p (m)b_sti、p(m+1)b=p (m+1)b_sti…p(n)b=p
(n)b_sti。
(ii) ifThen illustrate that entrance is sticking friction, and is viscous from entrance to outlet section
Friction, as shown in Figure 7.The unit width rolling pressure of entranceAfter under the conditions of sticking friction
The unit width rolling pressure differential equation of skating area successively calculates the 2nd section, the 3rd section ... n-th section of unit width rolling pressure.
It is at this time p (1) using the calculated each section of unit width rolling pressure of zone of slippage on the entry side formulab=p (1)b_sti、p(2)b=p
(2)b_sti……p(n)b=p (n)b_sti。
3, each section of zone of slippage on the delivery side unit width rolling pressure is calculated from outlet to entrance, method is similar to zone of slippage on the entry side calculation method,
Specifically:
It is calculated using zone of slippage on the delivery side formula from outlet to entrance, and judges the partitioning scenario of sliding friction and sticking friction:
Outlet section unit width rolling pressure under the conditions of sliding friction is calculated by average level stress model formula:
P is solved using Aitken iterative method
(n)f_sli。
In formula, T1To export tension, unit N；
Judge μ p (n) at outlet sectionf_ sli withSize:
If (i)Then illustrate that outlet section is sliding friction, the unit width rolling pressure of outlet section is p (n)f
=p (n)f_sli；(n-1)th section, are successively calculated using the unit width rolling pressure differential equation of zone of slippage on the delivery side under the conditions of sliding friction
N-2 sections ... of unit width rolling pressure, and μ p (i) is all judged at each sectionf_ sli (1≤i≤n) withSize, specifically:
Write the unit width rolling pressure differential equation of zone of slippage on the delivery side under the conditions of sliding friction as difference form:
It arranges:
It adopts
P (i) is solved with Aitken iterative methodf_sli；
The friction stree of zone of slippage on the delivery side under the conditions of sliding friction are as follows: t (i)f_ sli=- μ p (i)f_ sli, negative sign indicate zone of slippage on the delivery side
Friction stree direction towards entrance side (opposite with rolling direction),
There are two kinds of situations again in calculating process:
A: if being all satisfied from outlet section to entranceThen illustrate to utilize sliding friction
Under the conditions of the unit width rolling pressure differential equation of zone of slippage on the delivery side be sliding friction from entrance is exported to when being calculated, such as Fig. 8 institute
Show.The calculated each section of unit width rolling pressure of zone of slippage on the delivery side formula is utilized at this time are as follows: p (1)f=p (1)f_sli、p(2)f=p (2)f_
sli…p(n)f=p (n)f_sli。
B: if having at s (1 < s≤n) section:Then explanation is viscous to entrance since s sections
Friction, as shown in Figure 9.Switch to successively to calculate the using the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction
The unit width rolling pressure of s sections, s-1 sections ... paragraph 1.Specifically:
Write the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction as difference form:
It arranges:
The friction stree of zone of slippage on the entry side under the conditions of sticking friction are as follows:
Successively using the calculated each section of unit width rolling pressure of zone of slippage on the delivery side formula at this time are as follows: p (1)f=p (1)f_sti、p
(2)f=p (2)f_sti…p(s)f=p (s)f_sti、p(s+1)f=p (s+1)f_sli…p(n)f=p (n)f_sli。
(ii) ifThen illustrate that outlet section is sticking friction, and is from outlet section to entrance
Sticking friction, as shown in Figure 10.The unit width rolling pressure of outlet sectionUtilize sticking friction condition
The unit width rolling pressure differential equation of lower zone of slippage on the entry side successively calculates the unit width rolling pressure of (n-1)th section, the n-th -2 sections ... paragraph 1,
It is at this time p (1) using the calculated each section of unit width rolling pressure of zone of slippage on the delivery side formulaf=p (1)f_sti、p(2)f=p
(2)f_sti……p(n)f=p (n)f_sti。
4, each section of unit width rolling pressure of roll gap deformed area is determined:
It is more above-mentioned to utilize zone of slippage on the delivery side formula and the calculated two groups of unit width rolling pressure p (1) of zone of slippage on the entry side formulaf、p
(2)f……p(n)fAnd p (1)b、p(2)b……p(n)b, the smallest section of difference (being assumed to be r sections) is found, then before the section is
The interface segment (i.e. neutral surface) of skating area and zone of slippage on the entry side, x (r)=x (1)+(r-1) Δ X.Retain p (1)f、p(2)f……、p(r-1)f、p
(r)fOr p (r)b、p(r+1)b……p(n)b.So far the unit width rolling pressure distribution under specified roll profile, i.e. p are had calculated that
(1)=p (1)f, p (2)=p (2)f..., p (r-1)=p (r-1)f, p (r)=p (r)fOr p (r)=p (r)b, p (r+1)=p (r
+1)b... p (n)=p (n)b。
5, it is distributed using unit width rolling pressure and calculates roll contour curve h (i), but in order to guarantee to restrain, introduced here
Smoothing factor (relaxation factor) e makes each section of unit width rolling pressure smooth variation iterated to calculate out of front and back 2 times.
That is pm+1(i)=ep (i)+(1-e) pm(i), 0 < e < 1,
P (i) is the draught pressure distribution under calculated specified roll profile；pm(i) what is used when being the m times iteration rolls
Pressing pressure distribution；pm+1(i) the draught pressure distribution used when being the m+1 times iteration.
Utilize the unit width rolling pressure distribution p after relaxationm+1(i) the elastic flattening deflection δ (x (j)) for calculating roll, by
The method of accumulation summation calculates the roll elastic flattening amount that abscissa is the place x (j)J=1,2,3 ... n, siIt rolls and presses for unit
Power pm+1(i) corresponding abscissa.
Then deformation roll profile curve distribution is found out are as follows:
Roll gap thickness distribution are as follows:
In formula, y (x (j))minFor the corresponding ordinate in deformation roll contour curve lowest point, mm.
6, whether the roll contour curve for judging that front and back is calculated twice restrains.
7, roll gap thickness distribution is calculated when restraining, otherwise enters next round iterative calculation until roll contour curve is received
It holds back:
It is corresponding with unit width rolling pressure distribution, " relaxation " processing, i.e. h are carried out to roll profilem+1(j)=eh (j)+(1-e)
hm(j)
H (j) is calculated each section of roll profile；hm(j) each section of roll profile used when being the m times iteration；hm+1
(j) each section of roll profile used when being the m+1 times iteration.
Utilize new roll profile (hm+1(j)) unit under the roll profile is solved again according to above-mentioned same procedure to roll
Pressing pressure distribution, such loop iteration, until convergence.The condition of convergence are as follows: front and back each section of roll profile differences of 2 calculated correspondences
Value is less than accuracy value, i.e. h (j)-hm(j)≤η × h (j), η are convergence precision, such as take η=0.001.
8, after iteration convergence, the rolled piece thickness h (r) and the slope of curve from neutral surface are obtained from roll gap thickness distribution curveThus advancing slip value is calculated
It is calculated below by the actual measurement floor data of certain five rack continuous hot-rolling mill of steel mill to using the present embodiment method
The accuracy of advancing slip value verified.Take 5 groups of actual measurement floor datas of the unit rolling procedure, the technological parameter measured
Have: rolled piece inlet thickness, exit thickness, rolled piece width, rolled piece yield strength, roller diameter, entrance tension and outlet tension, tool
Body is as shown in table 1.For this five embodiments, relevant presetting parameter is taken as respectively: the discrete number of segment n=1000 of roll gap, is put down
Sliding coefficient e=0.3, roll profile convergence precision η=0.001.
1 Examples 1 to 5 of table surveys floor data
Technological parameter and above-mentioned presetting parameter using the example operating condition in upper table, are counted according to the present embodiment method
It calculates, can be obtained the advancing slip calculated value under each rolling operating condition after iteration convergence, calculated result is as shown in the column of table 1 the 10th.It is calculating
Normalization roll gap thickness distribution curve, unit width rolling pressure distribution curve and the friction stree distribution of each example obtained after convergence
Curve is respectively as shown in Figure 11, Figure 12 and Figure 13.The corresponding abscissa of the peak value of every curve is each example work in Figure 12
The neutral surface position of condition, peak value left side are zone of slippage on the entry side, are zone of slippage on the delivery side on the right side of peak value.The mutated site of every curve is (vertical in Figure 13
Coordinate becomes negative value from positive value) corresponding abscissa be also each example operating condition neutral surface position, (friction on the left of mutated site
Stress is positive value) it is zone of slippage on the entry side, (friction stree is negative value, and negative value indicates friction stree direction and rolling side on mutated site right side
To on the contrary) it is zone of slippage on the delivery side, in addition it can also be seen that the zone of slippage on the delivery side and zone of slippage on the entry side of each example operating condition respectively include sliding friction
Area and sticking friction area (horizontal line part), meet sliding friction condition and sticking friction condition respectively.
On the other hand, roll actual speed N can be measured by the encoder being mounted in roller transmission shaft, further may be used
It is converted into the practical peripheral speed v of rollr(for conversion method to be known in the industry, and will not be described here in detail), by being mounted on rack outlet
The laser velocimeter at place can measure rolled piece muzzle velocity vh, in this way according to the definition of advancing slip valueI.e.
Can be calculated advancing slip value indirectly, it is this by the actual measurement speed of roll and rolled piece indirectly calculated advancing slip value be equivalent to it is advancing slip
The measured value of value.Calculated result is as shown in the column of table 2 the 4th, it can be seen that present invention method calculated result and advancing slip value are real
Measured value is very close, and error meets engineering calculation requirement within 10%.
Value calculated value error that 2 Examples 1 to 5 of table is advancing slip
The present invention also provides a kind of advancing slip value calculation apparatus of board rolling, including be sequentially connected partition modeling module,
Friction condition determination module, roll contour curve modeling module, iterative calculation module and advancing slip value computing module, wherein described
Partition modeling module is used to that roll gap deformed area to be divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet, and establishes each area
The unit width rolling pressure differential equation and average level stress model in domain；The friction condition determination module is for judging zone of slippage on the entry side
The friction condition met with zone of slippage on the delivery side, and calculate the distribution of each area unit draught pressure under corresponding friction condition；The roll
Contour curve modeling module is used to calculate the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and establishes deformation and roll
Roll profile curve model and roll gap thickness distributed model；The iterative calculation module be used for by unit width rolling pressure distributed model and
Deformation roll profile curve model, which iterates, is calculated roll gap thickness distribution；The advancing slip value computing module is used for from roll gap
The rolled piece thickness and the slope of curve at neutral surface are obtained on thickness distribution curve, and advancing slip value is calculated.
Preferably, the friction condition determination module includes zone of slippage on the entry side computing unit and zone of slippage on the delivery side computing unit, zone of slippage on the entry side
Computing unit is used to calculate using the zone of slippage on the entry side unit width rolling pressure differential equation from entrance to outlet, and judges the sliding of zone of slippage on the entry side
The partitioning scenario of friction and sticking friction, and calculate the distribution of the zone of slippage on the entry side unit width rolling pressure under corresponding friction condition；Zone of slippage on the delivery side
Computing unit is used to calculate using the zone of slippage on the delivery side unit width rolling pressure differential equation from outlet to entrance, and judges the sliding of zone of slippage on the delivery side
The partitioning scenario of friction and sticking friction, and calculate the distribution of the zone of slippage on the delivery side unit width rolling pressure under corresponding friction condition.
Preferably, the iterative calculation module includes roll profile calculation unit, convergence judging unit and roll gap thickness point
Cloth computing unit, the roll profile calculation unit are used to calculate new roll contour curve by unit width rolling pressure distribution；It receives
Hold back whether roll contour curve of the judging unit for judging that front and back is calculated twice restrains；Roll gap thickness is distributed computing unit
For calculating roll gap thickness distribution after restraining, otherwise enter next round iterative calculation until roll profile curve convergence.
Finally it should be noted that these are only the preferred embodiment of the present invention, it is not intended to restrict the invention, although
Referring to embodiment, invention is explained in detail, for those skilled in the art, still can be to aforementioned
Technical solution documented by each embodiment is modified or equivalent replacement of some of the technical features, but it is all
Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in protection of the invention
Within the scope of.
Claims (10)
1. a kind of advancing slip value calculating method of board rolling, which comprises the following steps:
Step 1: roll gap deformed area is divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet, and establish each region
The unit width rolling pressure differential equation and average level stress model；
Step 2: judging the friction condition that zone of slippage on the entry side and zone of slippage on the delivery side meet, and calculate each area unit under corresponding friction condition
Draught pressure distribution；
Step 3: calculating the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and it is bent to establish deformation roll profile
Line model and roll gap thickness distributed model；
Step 4: being iterated by unit width rolling pressure distributed model and deformation roll profile curve model is calculated roll gap thickness
Spend distribution curve；
Step 5: obtaining the rolled piece thickness and the slope of curve from neutral surface from roll gap thickness distribution curve, thus it is calculated
Advancing slip value.
2. the advancing slip value calculating method of board rolling as described in claim 1, which is characterized in that in step 1, each area
The unit width rolling pressure differential equation in domain is
The average level stress model is
Wherein, positive sign "+" indicates zone of slippage on the entry side, and negative sign "-" indicates zone of slippage on the delivery side；pxAbscissa is the unit width rolling pressure at x, MPa；
txIt is the friction stree between the rolled piece and working roll at x, MPa for abscissa；σxFor the average level stress that abscissa is at x,
MPa；K is deformation of rolled wire drag, K=1.15 σs, σsFor yield strength, MPa；hxFor the rolled piece thickness that abscissa is at x, mm；
In step 3, the roll elastic flattening amount distributed model is
The deformation roll profile curve model is
The roll gap thickness model is
The x-axis of the coordinate system of above-mentioned foundation is located at the interior thickness position of rolled piece, and y-axis is located on roll line of centres, wherein h0-
Rolled piece inlet thickness, unit mm；h1Rolled piece exit thickness, unit mm；R- roller radius, unit mm；Value that f- is advancing slip；hrIt is neutral
Rolled piece thickness at face, unit mm；Roll gap thickness distribution curve slope at neutral surface；x0Arc-shaped roll profile is (i.e.
Initial roll profile) when rolled piece inlet abscissa, unit mm；x1Rolled piece inlet abscissa after roll flattening, unit mm；
xnRolled piece exit abscissa (i.e. deformation roll profile lowest point abscissa), unit mm after roll flattening；δ (x)-unit is rolled
Abscissa caused by pressing pressure is the roll elastic flattening amount at x, unit mm；Deformation roll contour curve is vertical before y- moves down roll
Coordinate, unit mm；yminRoll profile lowest point ordinate, unit mm are deformed before moving down roll；E1Roll material springform
Type, units MPa；v1Roll material Poisson's coefficient；P (s)-abscissa is the unit width rolling pressure at s, units MPa；
In step 5, the calculation formula of the advancing slip value is
3. the advancing slip value calculating method of board rolling as described in claim 1, which is characterized in that in step 2, zone of slippage on the entry side and
The friction condition that zone of slippage on the delivery side meets includes sliding friction and sticking friction, whenWhen be sliding friction condition, at this time tx=
μpx, μ coefficient of friction between working roll and rolled piece；Unit width rolling pressure differential equation under the conditions of sliding friction is
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side；
WhenWhen be sticking friction condition, at this timeUnit width rolling pressure differential side under the conditions of sticking friction
Cheng Wei
Wherein, positive sign "+" indicates zone of slippage on the entry side；Negative sign "-" indicates zone of slippage on the delivery side.
4. the advancing slip value calculating method of board rolling as described in claim 1, which is characterized in that in step 4, roll gap thickness
The acquisition methods of distribution curve are as follows:
1) initial roll contour curve, is set, and determines rolled piece entry position:
2) each section of zone of slippage on the entry side unit width rolling pressure, is calculated from entrance to outlet: being calculated using zone of slippage on the entry side formula from entrance to outlet,
Judge the partitioning scenario of sliding friction and sticking friction, and calculates separately each section of zone of slippage on the entry side unit rolling pressure under corresponding friction condition
Power；
3) each section of zone of slippage on the delivery side unit width rolling pressure, is calculated from outlet to entrance: being calculated using zone of slippage on the delivery side formula from entrance to outlet,
Judge the partitioning scenario of sliding friction and sticking friction, and calculates separately each section of zone of slippage on the delivery side unit rolling pressure under corresponding friction condition
Power；
4) unit width rolling pressure distribution, is calculated by initial roll contour curve；
5) new roll contour curve, is calculated using unit width rolling pressure distribution；
6) whether the roll contour curve for, judging that front and back is calculated twice restrains；
7), twice roll profile curve convergence when roll gap thickness distribution curve is calculated, roll contour curve is not restrained twice
When enter next round iterative calculation until roll profile curve convergence；
8) the rolled piece thickness and the slope of curve from neutral surface, are obtained from roll gap thickness distribution curve, and advancing slip value is calculated.
5. the advancing slip value calculating method of board rolling as claimed in claim 4, which is characterized in that in step 4 1) in, initially roll
Roll profile curve is arc-shaped, and δ (x)=0, roll contour curve is discrete in deformed area: deformed area being divided into n sections, arc-shaped
Roll gap thickness model equation under roll profile isWherein x (i) is i-th
Section abscissa, h (i) are i-th section of rolled piece thickness, x (n)=0, h (n)=h1,It is discrete
Segment length
6. the advancing slip value calculating method of board rolling as claimed in claim 5, which is characterized in that in step 4 2) in, from entrance
Each section of zone of slippage on the entry side unit width rolling pressure is calculated to outlet method particularly includes:
Entrance unit width rolling pressure under the conditions of sliding friction is calculated by average level stress model formula:
In formula, T0For entrance tension, unit N；B is to roll
Part width, unit mm；
P (1) is solved using iterative methodb_ sli judges (1) μ p at entranceb_ sli withSize is divided into two kinds of situations:
(i) whenWhen, the unit width rolling pressure p (1) of entranceb=p (1)b_sli；Utilize sliding friction condition
The unit width rolling pressure differential equation of lower zone of slippage on the entry side successively calculates the unit width rolling pressure of the 2nd section, the 3rd section ..., and every
One section all judges μ p (i)b_ sli withSize, specifically:
It is obtained by the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sliding friction:
The friction stree of zone of slippage on the entry side under the conditions of sliding friction are as follows: t (i)b_ sli=μ p (i)b_sli；
A: when being all satisfied from entrance to outlet sectionWhen, utilize the calculated each section of unit of zone of slippage on the entry side formula
Draught pressure are as follows: p (1)b=p (1)b_sli、p(2)b=p (2)b_sli…p(n)b=p (n)b_sli；
B: exist when at m sectionsWhen, then it is sticking friction to outlet since m sections, switchs to utilize
The unit width rolling pressure differential equation of zone of slippage on the entry side successively calculates the unit of m sections, m+1 sections ... n-th section under the conditions of sticking friction
Draught pressure, specifically:
It is obtained by the unit width rolling pressure differential equation of zone of slippage on the entry side under the conditions of sticking friction
The friction stree of zone of slippage on the entry side is under the conditions of sticking friction
The calculated each section of unit width rolling pressure of zone of slippage on the entry side formula is utilized at this time are as follows: p (1)b=p (1)b_sli、p(2)b=p (2)b_
sli…p(m-1)b=p (m-1)b_sli、p(m)b=p (m)b_sti、p(m+1)b=p (m+1)b_sti…p(n)b=p (n)b_
sti；
(ii) whenWhen, then the unit width rolling pressure of entranceIt is rubbed using adhesion
The unit width rolling pressure differential equation of zone of slippage on the entry side successively calculates the unit rolling pressure of the 2nd section, the 3rd section ... n-th section under the conditions of wiping
Power p (1)b=p (1)b_sti、p(2)b=p (2)b_sti……p(n)b=p (n)b_sti；
Step 4 3) in, it is p (1) using the calculated each section of unit width rolling pressure of zone of slippage on the delivery side formulaf、p(2)f……p(n)f。
7. the advancing slip value calculating method of board rolling as claimed in claim 6, which is characterized in that in step 4 4) in, unit is rolled
The calculation method of pressing pressure distribution are as follows: be compared with zone of slippage on the delivery side formula and the calculated two groups of unit width rolling pressures of zone of slippage on the entry side formula
p(1)f、p(2)f……p(n)fAnd p (1)b、p(2)b……p(n)b, find that difference is r sections the smallest, then the section is zone of slippage on the delivery side
With the interface segment namely neutral surface of zone of slippage on the entry side, x (r)=x (1)+(r-1) Δ X；Retain p (1)f、p(2)f……、p(r-1)f、p
(r)fOr p (r)b、p(r+1)b……p(n)b, the unit width rolling pressure under roll profile is specified to be distributed as p (1)=p (1)f、p(2)
=p (2)f..., p (r-1)=p (r-1)f, p (r)=p (r)fOr p (r)=p (r)b, p (r+1)=p (r+1)b... p (n)=p
(n)b。
8. the advancing slip value calculating method of board rolling as claimed in claim 6, which is characterized in that in step 4 5) in, utilize list
The method that position draught pressure distribution calculates roll contour curve h (i) are as follows: it introduces smoothing factor e and is iterated calculating,
That is pm+1(i)=ep (i)+(1-e) pm(i), 0 < e < 1,
P (i) is the draught pressure distribution under calculated specified roll profile；pm(i) the rolling pressure used when being the m times iteration
Power distribution；pm+1(i) the draught pressure distribution used when being the m+1 times iteration；
Utilize the unit width rolling pressure distribution p after relaxationm+1(i) the elastic flattening deflection δ (x (j)) for calculating roll, by accumulating
The method of summation calculates the roll elastic flattening amount that abscissa is the place x (j)
siFor unit draught pressure pm+1(i) corresponding abscissa；
Finding out deformation roll profile curve distribution is
Roll gap thickness is distributed as
In formula, y (x (j))minFor the corresponding ordinate in deformation roll contour curve lowest point, mm.
9. the advancing slip value calculating method of board rolling as claimed in claim 6, which is characterized in that in step 4 7) in, roll gap is thick
Spend the calculation method of distribution are as follows:
It is corresponding with unit width rolling pressure distribution, roll profile is handled, i.e.,
hm+1(j)=eh (j)+(1-e) hm(j),
Wherein, h (j) is calculated each section of roll profile；hm(j) each section of roll profile used when being the m times iteration；hm+1
(j) each section of roll profile used when being the m+1 times iteration；Using new roll profile curvilinear equation according to above-mentioned same procedure
Again the unit width rolling pressure distribution under the roll profile, loop iteration, until roll profile curve convergence are solved.
In step 4 8) in, rolled piece thickness h (r) and the slope of curve from roll gap thickness distribution curve from acquisition neutral surface are
Advancing slip value, which is calculated, is
10. a kind of advancing slip value calculation apparatus of board rolling, which is characterized in that including be sequentially connected partition modeling module, friction
Condition criterion module, roll contour curve modeling module, iterative calculation module and advancing slip value computing module, wherein the partition
Modeling module is used to that roll gap deformed area to be divided into zone of slippage on the entry side and zone of slippage on the delivery side from rolling entrance to outlet, and establishes each region
The unit width rolling pressure differential equation and average level stress model；The friction condition determination module is for judging zone of slippage on the entry side with before
The friction condition that skating area meets, and calculate the distribution of each area unit draught pressure under corresponding friction condition；The roll profile
Curve modeling module is used to calculate the distribution of roll elastic flattening amount according to unit width rolling pressure distribution, and establishes deformation roll wheels
Wide curve model and roll gap thickness distributed model；The iterative calculation module is used for by unit width rolling pressure distributed model and deformation
Roll profile curve model, which iterates, is calculated roll gap thickness distribution；The advancing slip value computing module is used for from roll gap thickness
The rolled piece thickness and the slope of curve at neutral surface are obtained on distribution curve, and advancing slip value is calculated.
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| CN113145653A (en) * | 2021-04-13 | 2021-07-23 | 东北大学 | Forward slip value calculation and rolling speed distribution method in asynchronous continuous rolling process of steel strip |
| CN113441558A (en) * | 2021-06-29 | 2021-09-28 | 杭州电子科技大学 | Rolling mill rolling interface friction coefficient measuring device based on forward sliding method |
| CN114192588A (en) * | 2021-12-14 | 2022-03-18 | 杭州电子科技大学 | Cold rolling mill rolling interface friction coefficient and friction force measuring device based on rolled piece forced braking method |
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