CN110438318A - A kind of large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise and system - Google Patents
A kind of large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise and system Download PDFInfo
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- CN110438318A CN110438318A CN201910659928.3A CN201910659928A CN110438318A CN 110438318 A CN110438318 A CN 110438318A CN 201910659928 A CN201910659928 A CN 201910659928A CN 110438318 A CN110438318 A CN 110438318A
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- C—CHEMISTRY; METALLURGY
- C21—METALLURGY OF IRON
- C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
- C21D1/00—General methods or devices for heat treatment, e.g. annealing, hardening, quenching or tempering
- C21D1/62—Quenching devices
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- C—CHEMISTRY; METALLURGY
- C21—METALLURGY OF IRON
- C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
- C21D11/00—Process control or regulation for heat treatments
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- C—CHEMISTRY; METALLURGY
- C21—METALLURGY OF IRON
- C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
- C21D9/00—Heat treatment, e.g. annealing, hardening, quenching or tempering, adapted for particular articles; Furnaces therefor
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Abstract
The invention discloses a kind of large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise and systems, this method uses the Hybrid Heating mode of two sections of switchings, it merges total power and controls the two-way advantage of two kinds of heating methods of power, by establishing minimum temperature allowance solving model, the minimum temperature margin value for guaranteeing heating process non-overshoot is obtained；Based on this minimum temperature allowance and convection current-radiation Evolution Mechanism, derive Optimal Temperature switching point when two kinds of heating method switchings, it solves the technical issues of prior art can not realize the heating of glowing furnace non-overshoot steepest under the requirement of least energy consumption, can guarantee forging heating non-overshoot and smoothly steepest heats up.
Description
Technical field
The present invention relates to heat treatment temperature control technology field, in particular to a kind of large-scale vertical glowing furnace low energy consumption steepest
Method for controlling temperature rise and system.
Background technique
High-strength aluminum alloy die casting is the aerospaces such as aircraft crossbeam, keel, rocket, guided missile end ring, engine cylinder body
Device important component.Its annealing device large-scale vertical glowing furnace is that one kind is typically used for production high-strength aluminum alloy forging very much
The periodic heat furnace of part.Process flow are as follows: it is (eutectiferous molten that aluminum alloy forge piece is first heated to desired temperature in furnace
Point), melt the hardening constituent in alloy into aluminum substrate, formed using aluminium as the solid solution of base, is then made after heat preservation two hours or more
Solvable phase in alloy sufficiently dissolves, formation α supersaturated solid solution, chilling in 60-100 DEG C of water of then quickly quenching, thus
So that strengthen constituent element obtains fixed to greatest extent save in the alloy.By the heat temperature raising of large-scale vertical glowing furnace, uniformly
Heat preservation and three technical process of rapid quenching carry out solution treatment to aluminum alloy forge piece, and to improve the hardness of forging, intensity is resistance to
Mill property, the mechanical properties such as corrosion resistance.
In entire quenching technical, heating up process consumes energy more than 85%, for the link that most consumes energy.Since glowing furnace belongs to
Heat-flash inertial device, can the speed of heating rate is directly determined regulate and control to prevent forging temperature super by uniform holding stage
It adjusts.Therefore, the heating up process control of glowing furnace is just particularly important.But due to glowing furnace heating space scale is big,
Aluminum alloy forge piece is wide in variety, batch is small, and product quality requires the reasons such as changeable, and leading to glowing furnace temperature-rise period, there is only strong non-
Linearly, strong jamming, the features such as complicated and changeable and distribution scale is big, and strong metal thermal inertia existing for inside, so that in minimum energy
Realize that the heating of glowing furnace non-overshoot steepest is extremely difficult under the requirement of consumption.This is mainly due to there is a pair of of core in temperature-rise period
Contradiction: if heating is too fast, metal fever effect of inertia influences product quality it is easier that overshoot occurs in forging temperature；If reducing heating
Rate, then the heating-up time extends, and energy consumption increases, and production efficiency reduces.Therefore, low energy consumption, non-overshoot, the heating to heat up fastly are studied
Process temperature field method for optimally controlling improves product qualification rate to energy consumption is reduced, and realizes large-scale vertical glowing furnace Precise control
It is most important.
For the contradiction in glowing furnace temperature-rise period between energy consumption and product quality, main control strategy is roughly divided into three
Major class: one, heating whole process is all made of heating with full power mode, and forging is warming up to set temperature；Two, heating whole process is all made of control
Power heating method processed, is warming up to set temperature for forging；Three, the leading portion of heating uses heating with full power mode, when reaching certain
It is heated up again using controlled power heating method after one temperature.From the point of view of the result that industry spot is attempted: whole total power adds
Though hot mode heating duration is obviously shortened, product qualification rate is lower, and production cost does not reduce；And whole controlled power heating
Mode, though product qualification rate significantly improves, the heating-up time is elongated, and energy consumption increases, and production cost is not optimum state；And it adopts
The third heating method mixed with two kinds, due to being difficult to determine the suitable temperature switching point of two kinds of heating methods, and when selection
Unsuitable temperature switching point, the duration that heats up and product qualification rate cannot significantly improve, instead result in and be produced into
This and energy consumption rise, and this case, in processed forging model, material transitivity parameter frequent fluctuation, further
Deteriorate.
Patent No. CN1896703A discloses the measurement method of large-scale vertical glowing furnace workpieces processing surface temperature, is based on
Heat balance principle establishes radiation in furnace-convection current complex heat transfer process mathematical model, utilizes Monte Carlo number numerical method
Radial thermo parameters method in furnace is calculated, the temperature compensation curve between actual spot of measurement and tested point is obtained.According to temperature-compensating
Curve obtains correction value in conjunction with distance between sensor position and workpiece surface to be heated, calculates workpiece surface temperature.But
It is that this patent models for temperature field is complicated, only considered radial temperature profile in furnace, have ignored axial temperature gap, do not meet
Actual condition, so that temperature field information actual use error is big.
Patent No. CN103820631A discloses a kind of new upright quenching furnace member temperature field distribution detection system.Benefit
It is given with temperature acquisition system, collecting work chamber interior walls thermo-electric couple temperature data and by the temperature information using communications system transmission
Computer temperature field compensation system.Computer temperature field compensation system, by the numerical solution to component heat transfer mechanism model,
Member temperature field distribution information is converted by collected temperature information, and real-time online is shown.The obvious patent is existing
Field staff provides more accurate member temperature field distribution information, but there is no the heat treatment process heat exchange sides to glowing furnace
Formula and process mechanism are analysed in depth, the component partial temperature generated when being changed to glowing furnace by the temperature rise period to holding stage
Overshoot is spent, causes member temperature to be unevenly distributed and burning part, underburnt part occurs, make scrap of the product, waste of resource etc. is a series of
Problem, there is no substantive research achievements.
Patent No. CN105087882A discloses a kind of upright quenching furnace heat treatment stages division methods, vertical by establishing
Formula glowing furnace member temperature field prediction model calculates component surface convection heat and radiations heat energy, further established glowing furnace
The mechanism model that interior the quantity of heat convection and Radiant exothermicity develop, the heat convection of component surface is obtained using this model in real time
The case where quantitatively being developed between amount and Radiant exothermicity.According to 2 times of gap principles of the quantity of heat convection and Radiant exothermicity, will quench
The furnace treatment reason stage is quantitatively divided into temperature rise period, transition stage and holding stage.The patent successfully realizes vertical quenching
Furnace carries out the differentiation of the amount in each stage in heat treatment process to large aluminum alloy component, can effectively avoid glowing furnace by heating up
The series of problems such as the component partial temperature overshoot that the stage generates when changing to holding stage.But there is no study such as the patent
Under the premise of where avoiding temperature overshoot, realize that glowing furnace steepest is warming up to the steepest heating problem of temperature set-point.I.e. for
Contradiction between the heating duration and energy consumption of temperature-rise period, is not solved.
Therefore, in glowing furnace temperature-rise period, it is badly in need of a kind of completely new heating that can balance heating duration and product qualification rate
Control strategy the problems such as existing a large amount of randomnesss and artificial blindness, is quenched with overcoming in existing control strategy with realizing to improve
Stove product qualification rate shortens its duration that heats up, energy saving, purpose for reducing production cost.The heating control of low energy consumption steepest
Route map is as shown in Figure 1.
Summary of the invention
A kind of large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise provided by the invention and system, solve existing
Technology can not realize the technical issues of glowing furnace non-overshoot steepest heating under the requirement of least energy consumption.
The controlling party in order to solve the above technical problems, a kind of large-scale vertical glowing furnace low energy consumption steepest proposed by the present invention heats up
Method includes:
The energy for obtaining forging heating reaches steepest heating mode, can specifically refer to forging can be made to be warming up to up to steepest heating mode
The steepest heating mode of predetermined target value；
According to thermal inertia present in glowing furnace temperature-rise period, determine that minimum allowance, minimum allowance are that glowing furnace heated up
Cheng Zhong, under the premise of guaranteeing forging temperature non-overshoot and energy consumption the smallest steepest heating, when the heating method of glowing furnace is from can reach
When steepest heating mode switches to stopping heating, required minimum temperature safety allowance；
Based on minimum allowance, the optimum control of forging low energy consumption steepest heating is realized.
It further, can be specially heating with full power mode up to steepest heating mode.
Further, based on minimum allowance, realize that the optimum control of forging low energy consumption steepest heating includes:
Based on minimum allowance and forging heating back segment heating method, obtains and forging heating back segment heating method is corresponding most
Excellent temperature switching point, wherein forging heats up leading portion using heating with full power mode；
Using Optimal Temperature switching point as the switching point of forging heating leading portion and back segment heating method, to realize that forging is low
The optimum control of energy consumption steepest heating.
Further, it is determined that minimum allowance includes:
The forging models for temperature field of minimum allowance is established, specifically:
Wherein, u (x, y, t) represents forging internal temperature field, u0The forging models for temperature field that (x, y) represents minimum allowance is fixed
The primary condition of solution, u (x, y, 0) represent the forging initial temperature at t=0 moment, and u (0, y, t) is represented at t moment x=0, that is, forged
Forging surface temperature on the left of part longitudinal section, u (2R, y, t) are represented at t moment x=2R, i.e., forging surface temperature on the right side of forging longitudinal section
Degree, uy(x, 0, t) represents t moment forging bottom surface temperature, uy(x, l, t) represents top surface temperature on t moment forging, D (t) is represented
The cooling function that electrothermal resistance silk cools down since limiting temperature, 2R represent the basal diameter of forging, and λ represents the heat transfer system of forging
Number, ρ represent forging density, and c represents the specific heat capacity of forging, and Ω represents the computational domain where forging, and l represents forging height；
Forging models for temperature field based on minimum allowance obtains minimum allowance.
Further, minimum allowance are as follows:
Tr=Ts-u0(d,ys)
Wherein, TrRepresent minimum allowance, TsThe target temperature of forging heating is represented, d represents diameter of forgings, ysRepresent forging
Highly, u0(d,ys) represent stop heating when, forging is in (d, ys) at temperature.
Further, it is based on minimum allowance and forging heating back segment heating method, is obtained and forging heating back segment heating side
The calculation formula of the corresponding Optimal Temperature switching point of formula:
Wherein, TfFor temperature safety allowance, TsFor the target temperature of forging heating, TcFor Optimal Temperature switching point, TrFor most
Small allowance, C are the specific heat capacity of forging, and M is the quality of forging, EuFor the energy that control amount generates, u is control input quantity.
Further, forging heating back segment heating method is specially controlled power heating method.
A kind of large-scale vertical glowing furnace low energy consumption steepest heating control system proposed by the present invention includes:
Memory, processor and storage on a memory and the computer program that can run on a processor, processor
The step of realizing large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise of the invention when executing computer program.
Compared with the prior art, the advantages of the present invention are as follows:
Large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise provided by the invention and system, by obtaining forging liter
The energy of temperature reaches steepest heating mode, can specifically refer to the steepest liter that forging can be made to be warming up to predetermined target value up to steepest heating mode
Warm mode determines that minimum allowance, minimum allowance are glowing furnace temperature-rise period according to thermal inertia present in glowing furnace temperature-rise period
In, under the premise of guaranteeing forging temperature non-overshoot and energy consumption the smallest steepest heating, when the heating method of glowing furnace is from can reach most
When fast heating mode switches to stopping heating, required minimum temperature safety allowance, and based on minimum allowance, realize that forging is low
The optimum control of energy consumption steepest heating, glowing furnace non-overshoot can not be realized most under the requirement of least energy consumption by solving the prior art
The technical issues of speed heating, can guarantee forging temperature non-overshoot and the smallest steepest heating of energy consumption, thus real based on minimum allowance
Existing temperature-rise period low energy consumption steepest heating target.
Detailed description of the invention
Fig. 1 is the low energy consumption steepest heating control route map of the embodiment of the present invention；
Fig. 2 is the flow chart of the large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise of the embodiment of the present invention one；
Fig. 3 is the flow chart of the large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise of the embodiment of the present invention two；
Fig. 4 is the glowing furnace two dimension vertical section structure rough schematic view of the embodiment of the present invention two；
Fig. 5 is the minimum temperature allowance and temperature switching point schematic diagram of the embodiment of the present invention two；
Fig. 6 is the large-scale vertical glowing furnace low energy consumption steepest heating control system block diagram of the embodiment of the present invention.
Appended drawing reference:
10, memory；20, processor.
Specific embodiment
To facilitate the understanding of the present invention, the present invention is made below in conjunction with Figure of description and preferred embodiment more complete
Face meticulously describes, but the protection scope of the present invention is not limited to the following specific embodiments.
The embodiment of the present invention is described in detail below in conjunction with attached drawing, but the present invention can be defined by the claims
Implement with the multitude of different ways of covering.
Embodiment one
Referring to the large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise that Fig. 2, the embodiment of the present invention one are provided, packet
It includes:
Step S101, the energy for obtaining forging heating reach steepest heating mode, can specifically refer to make up to steepest heating mode
Forging is warming up to the steepest heating mode of predetermined target value；
Step S102 determines that minimum allowance, minimum allowance are quenching according to thermal inertia present in glowing furnace temperature-rise period
In furnace temperature-rise period, under the premise of guaranteeing that forging temperature non-overshoot and the smallest steepest of energy consumption heat up, when the heating side of glowing furnace
Formula from can up to steepest heating mode switch to stopping heating when, required minimum temperature safety allowance；
Step S103 realizes the optimum control of forging low energy consumption steepest heating based on minimum allowance.
Large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise provided in an embodiment of the present invention, by obtaining forging liter
The energy of temperature reaches steepest heating mode, can specifically refer to the steepest liter that forging can be made to be warming up to predetermined target value up to steepest heating mode
Warm mode determines that minimum allowance, minimum allowance are glowing furnace temperature-rise period according to thermal inertia present in glowing furnace temperature-rise period
In, under the premise of guaranteeing forging temperature non-overshoot and energy consumption the smallest steepest heating, when the heating method of glowing furnace is from can reach most
When fast heating mode switches to stopping heating, required minimum temperature safety allowance, and based on minimum allowance, realize that forging is low
The optimum control of energy consumption steepest heating, glowing furnace non-overshoot can not be realized most under the requirement of least energy consumption by solving the prior art
The technical issues of speed heating, can guarantee forging temperature non-overshoot and the smallest steepest heating of energy consumption, thus real based on minimum allowance
Existing temperature-rise period low energy consumption steepest heating target.
Embodiment two
Referring to Fig. 3, large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise provided by Embodiment 2 of the present invention, packet
It includes:
Step S201 determines that heating with full power mode reaches steepest heating mode as the energy of forging heating leading portion.
Specifically, three-dimensional transient temperature heat-transfer mechanism model of the present embodiment based on forging in glowing furnace, will heat up speed
Contradiction between rate and energy consumption is converted into the boundary Control optimization problem of steepest heating.By the solution of Optimal Control Problem, obtain
It is the steepest heating mode that can be reached to heating with full power mode.Concrete thought are as follows: when the heating method of selection glowing furnace is provided
Heating amount u, when being the boundary Control variable of above-mentioned optimization problem, then can quantitative description above-mentioned optimization problem, wherein forging
Three-dimensional transient temperature is conducted heat shown in boundary Controlling model such as formula (1), wherein and Ω represents the entire warming space inside forging,
Time t value existsOn, it is assumed that quenching stove heating occurs on forging surface region Γ and forging surface is other than Γ
SurfaceIt is insulation, and
Wherein, y0≥0,u≥0,y(t；y0, u) and it is boundary Control problem u ∈ UMSolution, UMIt is reachable
Domination set, y0>=0 is the initial temperature of forging.In entire heating process, boundary Control amount u >=0,I.e.
Control amount only makes forging heat temperature raising, and is unable to refrigeration cool-down.Based on above-mentioned forging three-dimensional transient temperature heat transfer boundary Control
Model, then the boundary Optimal Control Problem of above-mentioned steepest heating can be described as shown in formula (2),
t*For optimal heating-up time, y*∈L2(Ω) and y*>=0 is the set target value of heating, B (y*, ε) then representative can nothing
The neighborhood for approaching set target value thoroughly, can be described as:
UMTo indicate all control duration sets for being able to achieve forging bulk temperature and reaching near setting value up to domination set,
Shown in its definition such as formula (4),
Obviously, it is found that obtain the total power that can be reached from the mathematical description for the boundary Optimal Control Problem that steepest heats up
Steepest heating heating method, needs to meet: one, for shown in controllable system such as formula (1), there are at least one optimal control u*∈
UM, so that y (t*；y0,u*)∈B(y*, ε) and Time Optimal Control Problem on Time such as formula (2) shown in, at least exist one solution so that should
Control amount is that can reach steepest heating mode；Two, for meeting the optimum control amount u of conclusion one*, should also have bangbang (stick
Stick) characteristic, that is, meet formula (5) constraint, to meet the heating mode as heating with full power mode.
| u (x, t) |=M for a.e. (x, t) ∈ Γ × (0, t*) (5)
Following four steps of proposed adoption are solved, specifically:
Step 1: the reachable set A for meeting the control amount composition of Time Optimal Control Problem on Time (2) is convex set, wherein A such as formula
(6) shown in,
Α={ y (t*；y0,u)|u∈UM} (6)
Two elements, i.e. y (t are arbitrarily taken in set A*；y0,u1),y(t*；y0,u2) ∈ Α, wherein u1,u2∈UM, it is clear that
y1≡y(t*；y0,u1) be equation (1) solution, formula (7) can be obtained by being substituted into
WhereinIt is y1In boundary pointThe exterior normal derivative at place, similarly for y2≡y(t*；y0,
u2) be also equation (1) solution, substituted into obtain formula (8),
Affine arithmetic is carried out to above-mentioned equation (7) and (8) and meets formula (9) then to arbitrary α ∈ (0,1)
I.e. it will be noted that y from equation (9)αIt is the solution of equation (1), yαExpression formula such as formula (10) shown in,
yα≡[αy1+(1-α)y2](t；y0,αu1+(1-α)u2) (10)
Formula (11) can be obtained by being substituted into equation (1),
Again according to UMDefinition can obtain, α u1+(1-α)u2∈UM, it therefore follows that yα∈ A, so that reachable set A is convex set.
Step 2: reachable set A and target set point y*Neighborhood B (y*, ε) and intersect at B (y*, ε) boundary on, whereinIt is one with y*Centered on, radius closes ball for ε's.
It converts above problem equivalence to and solves following two problems (a), (b) while meeting:
(a)And if only if there are u ∈ UMSo that Eq. (1) has and only one solution y (t*；y0,u)∈
B(y*,ε)。
(b)And if only if t*It is optimal, whereinIt is one with y*Centered on,
Radius is kicking off for ε.
Problem (a) obviously meets, because reachable set A is convex set, and neighborhood B (y*, ε) and to close ball, while as shown in formula (1)
System is constrained according to quenching technical, must be controllable system, then (a) is centainly set up.
Reduction to absurdity is used for problem (b), it is assumed that there areSo that formula (12) is set up,
So existSo thatSinceTo Mr. Yu r > 0, existMake
It enablesSoObviouslyFor the solution of equation (1), then there is formula
(13) it sets up,
Convolution (12) can obtain formula (14) establishment using green theorem,
eΔtIt is the semigroup generated by Δ, G (x, q, τ) isInGreen's function, with zeroth order Di Like
Thunder boundary condition, χΓIt is the characteristic function of boundary Γ.Using the canonical parabola criterion of standard, then there is C=C (n, γ) to meet formula
(15),
Wherein,And t > s >=γ.BecauseSelect γ > 0 sufficiently small, so thatAlso sufficiently small and formula (16) is set up,
It is so desirable | t-s | it is sufficiently small, so that following formula is set up,
Formula (18) establishment then can be obtained in convolution (16), (17),
And because | t-s | it is sufficiently small, and work as t > s >=γ, it can be taken by formula (19)
Again because of θ > 0, then it can derive that formula (20) are set up,
When θ is sufficiently small, must then there be formula (21) establishment using above formula,
Obviously, using formula (21), this and optimal time t can be obtained*It contradicts.Therefore reachable set A and target set point y*'s
Neighborhood B (y*, ε) centainly intersect at B (y*, ε) boundary on, meet (b) requirement.
Step 3: there are η*∈L2(Ω)-{ 0 } makes inequalityIt sets up.
Due to set Α and B (y*, ε) and it is all convex set, then Convex Set is utilized, then there will necessarily be function f ∈ (L2
(Ω))*So that formula (22) is set up,
Riesz representation theorem is utilized again, and there are η*∈L2(Ω) meetsFor all ξ ∈ L2(Ω), so that
F (ξ)=< ξ, η*> set up, therefore formula (23) exists.
Step 4: optimum control amount u*, there is bangbang characteristic, meet the constraint of formula (5).
Due to control amount u*For the timing-optimal control of equation (1), then there must be formula (24) establishment,
y(t*；y0,u*)∈Α∩B(y*,ε) (24)
Again because of reachable set A and target set point y*Neighborhood B (y*, ε) and intersect at B (y*, ε) boundary on, then must have
Inequality formula (25) is set up,
Combining reachable set A again is the definition of convex set, then has formula (26) establishment,
Assume againFor following equations (27) solution that is,
Must then there be formula (28) establishment,
The expansion of upper formula can be obtained formula (29) to set up,
And utilize green theorem, then formula (30) establishment can be obtained,
And becauseSubstitution formula (30), simplification can obtain formula (31),
Therefore, the necessary and sufficient condition set up by formula (26) can derive formula (32) establishment,
Then to arbitrary c ∈ [0, M], (x0,t0)∈Γ×(0,t*), ζ > 0 defines u by formula (33)c(x, t),
Wherein, B ((x0,t0), ζ) it indicatesOn, with (x0,t0) centered on, it is the ball of radius with ζ > 0, and convolution
(33) then there is formula (34) establishment,
As ε → 0, Lebesgue point u is utilized*Formula (35) establishment can be obtained,
And becauseFormula (36) establishment can then be obtained by observability inequality for the solution of formula (27),
Formula (37) can have been released using formula (36) to set up,
Wherein Μ is any measurable set on the Γ of boundary, meets Hn-1(Μ) ≠ 0, wherein Hn-1(Μ) is on Μ
Hausdorff estimates, and can see inequality also with formula (36), obtainThis can be indicated
It can not set up, because of η*≠ 0, contradiction is generated, therefore formula (38) is set up,
|u*(x, t) |=Μ for a.e. (x, t) ∈ Γ × (0, t*) (38)
Therefore optimum control amount u is acquired*, there is bangbang characteristic, and meet the constraint of formula (5).
By aforementioned four step, the available heating with full power mode of the solution procedure of Optimal Control Problem is glowing furnace
The steepest heating mode that can be reached.It is found that glowing furnace can when being heated up using heating with full power mode during this Optimization Solution
The temperature reached is setting value y*Spheric neighbo(u)rhood B (y*, ε) boundary on.Although it is assumed that ε can use arbitrarily small positive real number, but quenching
In the practical heating process of stove, since glowing furnace heater can not freeze, so that there are obvious strong metal heat in heating process
Inertia, and quenching technical requires temperature-rise period, that is, non-overshoot steady again, this results in the value of ε not only to have smallest limit,
And there is the most suitable value for meeting process requirements.Therefore, the ε most lower limit value that can use is defined as minimum allowance, and its is most suitable
Value be defined as most desirable temperature switching point.As long as determining minimum allowance and reasonable temperature switching point, and design suitable control
Temperature-rise period low energy consumption steepest heating target can be realized in system strategy.
At least there is an optimal control u by solving controllable system in the present embodiment*∈UM, so that y (t*；y0,u*)∈B
(y*, ε) and Time Optimal Control Problem on Time at least there is a solution so that the control amount is can be and optimal up to steepest heating mode
Control amount u*Also there is bangbang characteristic, solving obtain total power system for the first time is a kind of steepest heating mode that can be reached.Base
In the conclusion, it, up to steepest heating mode, is forging that the present embodiment, which selects heating with full power mode as the energy of forging heating leading portion,
Low energy consumption steepest heating based theoretical and technical support, ensure that the realization of forging low energy consumption steepest heating.
Step S202 determines that minimum allowance, minimum allowance are quenching according to thermal inertia present in glowing furnace temperature-rise period
In furnace temperature-rise period, under the premise of guaranteeing that forging temperature non-overshoot and the smallest steepest of energy consumption heat up, when the heating side of glowing furnace
Formula from can up to steepest heating mode switch to stopping heating when, required minimum temperature safety allowance.
It is that energy consumption is minimum and forging is whole by step S201 it is found that glowing furnace heating whole process is all made of heating with full power mode
Temperature can reach the steepest heating mode near setting value.But glowing furnace in temperature-rise period there are apparent thermal inertia,
Forging is heated to set temperature using such heating method by whole process, necessarily results in forging temperature more than setting value, overshoot occurs
Phenomenon causes forging burning, product quality decline.Therefore, when adding the constraint of non-overshoot to glowing furnace temperature-rise period, it is necessary to
Before forging bulk temperature reaches setting value, there are some temperature safety allowances to stop heating, and then utilizes glowing furnace itself
Thermal inertia forging is just warming up to setting value.The temperature safety allowance of the guarantee not overshoot reserved is previously mentioned
The most lower limit value of ε is minimum allowance.Based on this, can provide the definition of minimum allowance here: minimum allowance, which refers to, to quench
In furnace temperature-rise period, under the premise of guaranteeing that forging temperature non-overshoot and energy consumption steepest as small as possible heat up, when glowing furnace
When heating method switches to stopping heating from heating with full power mode, required minimum temperature safety allowance.To further clarify
The meaning of minimum allowance is illustrated in conjunction with glowing furnace temperature-rise period from the angle of the conservation of energy: when whole process uses heating with full power
Mode is supplied to from the perspective of energy at this time if stopping the temperature safety allowance reserved when heating and being less than minimum allowance
The energy of forging heating is greater than energy needed for forging is warming up to set temperature, and according to the conservation of energy, forging temperature must will surpass
Cross the temperature of setting, the overshoot so that forging temperature is bound to；On the contrary, the temperature safety allowance reserved is greater than minimum allowance, at this time
The energy for being supplied to forging heating is less than energy needed for forging is warming up to set temperature, then must also need to use it at this time
Its heating method injects new energy, so that forging reaches set temperature；And when the temperature safety allowance reserved is abundant equal to minimum
Amount, the energy for being supplied to forging heating at this time is exactly equal to energy needed for forging is warming up to set temperature, as long as so at this time
It can reach setting value by thermal inertia.Therefore the definition of minimum allowance is combined, in theory, when glowing furnace heating strategy
When forging being integrally warming up to apart from setting value minimum allowance, then to stop heating, finally first with heating with full power mode
When forging to be just heated to setting value using the thermal inertia of glowing furnace, then this heating strategy must be all glowing furnaces heating plans
In slightly, the smallest steepest heating strategy of forging temperature non-overshoot, heating energy consumption.Based on this, in practical glowing furnace warming temperature,
Optimal heating strategy should be divided into three phases: first stage, and heating leading portion is heated up using heating with full power mode, with
Guarantee that heating rate is most fast, energy consumption is minimum；Second stage, the determination of heating method switching point, by used by analysis back segment
Heating method and minimum allowance, determine Optimal Temperature switching point corresponding with heating method, to guarantee to reserve enough temperature peaces
Full allowance prevents forging temperature overshoot；Three phases, heating back segment is by selecting suitable power control mode to quench to meet
Stationarity requirement of the stove to temperature-rise period.It can be found from above-mentioned optimal heating strategy, the determination of minimum allowance, to entire
The tactful determination that heats up is most important.
The definition of minimum allowance according to the present embodiment determines that the key of minimum allowance is that glowing furnace heat in temperature-rise period is used
The size of property.To accurately calculate minimum allowance, the physical mechanism that thermal inertia is formed need to be understood fully.Analyze electrothermal resistance silk heating mechanism and
Basic heat transfer theory, when forging quenching heat treatment process starts, the electrothermal resistance silk of each heating zone after powered up, be rapidly heated to
The limiting temperature T of electrothermal resistance silkmax, i.e. electrothermal resistance silk temperature reaches TmaxAfterwards, continue energization electrothermal resistance silk temperature no longer to become
Change；And after the power-off of electrothermal resistance silk, the temperature of electrothermal resistance silk can't jump, and the temperature of electrothermal resistance silk is much higher than at this time
Forging temperature, the heat that electrothermal resistance silk provides continue to heating forging, form forging temperature and continue the thermal inertia phenomenon risen.
From this thermal inertia phenomenon it is found that when glowing furnace using heating with full power mode heat up when, electrothermal resistance silk stop heating after, when and
Only after the forging temperature in the electrothermal resistance silk temperature and rising in decline reaches set temperature simultaneously, thermal inertia is to forging temperature
The influence of overshoot will disappear.This critical condition is to calculate the main foundation of minimum allowance.Based on this foundation, minimum allowance
Calculating thinking can be described as: after stopping heating, forging temperature when first stopping undetermined being heated, and electrothermal resistance silk temperature is calculated simultaneously
Degree drops to the time of set temperature；It recycles forging to be warming up to this condition of set temperature just within this time, calculates
Forging undetermined stops the temperature at heating moment out；The temperature at stopping heating moment is finally subtracted using set temperature
Acquire minimum allowance.Following reasonable assumption is done based on the above thinking in order to calculate the convenience of minimum allowance:
A) ignore between chamber walls and forging that there are space lengths, it is assumed that electrothermal resistance silk directly heats the appearance in forging
Face.Although the hypothesis will not cause minimum allowance calculated value less than normal, influence so that minimum allowance calculated value is bigger than normal slightly
Less, it can be ignored；
B) in view of the good conductor that aluminum alloy forge piece is heat, and forging shape is cylindrical body, therefore ignores heat radially
Conduction, that is, think radially forging temperature be it is identical, so as to which the shape of forging is equivalent to a two-dimensional rectangle；
C) according to the principle of heat transfer, temperature be from forging surface to forging inside conduct, therefore, forging surface when heating
Temperature be higher than forging internal temperature；According to quenching technical, there is slight overshoot simultaneously in the temperature short time of forging outmost surface
Product quality is not influenced, therefore using the surface at forging outmost surface 1mm as the plane of reference for calculating minimum allowance, is represented
The temperature of forging；
D) according to multi-portion heating mode, electrothermal resistance silk is to heat from top to bottom around forging, all heating electrothermal resistance silks
Power is identical with model, and locating environment is almost the same, it is therefore assumed that the electrothermal resistance silk heated on boundary, from limit temperature
Spend TmaxThe cooling function for starting cooling is unrelated with position, only related with the time.
Based on above-mentioned it is assumed that can be reduced to glowing furnace structure in the stove as shown in Figure 4.In figure rectangle the right and left be etc.
The two dimension heating boundary of the glowing furnace of effect, borderline HEATING FUNCTION is the cooling letter that electrothermal resistance silk cools down since limiting temperature
Number D (t) (function can be fitted using the temperature data of measurement and be obtained by carrying out pull-down test to heating electrothermal resistance silk)；Square
The bottom surface and top surface of the upper following equivalent glowing furnace of shape, have been generally acknowledged that in the top bottom surface of glowing furnace as adiabatic boundary.D=in figure
Two dotted line sides at 0.01m are on equivalent glowing furnace two-dimensional surface for calculating plane of reference when minimum allowance, l=31m
For the height of forging, 2R is the basal diameter of forging.Therefore, after glowing furnace switches to stopping heating from heating with full power mode,
The forging models for temperature field for solving minimum allowance is established as shown in (39):
Wherein, u (x, y, t) represents forging internal temperature field, u0(x, y) is the primary condition that model undetermined solves surely, table
Show that glowing furnace switches to the temperature of forging when stopping heating from heating with full power mode.For the solving model formula of minimum allowance
(39), since the primary condition in the definite condition of this equation is, so the numerical solution of this equation can not be solved, to need to fixed condition
Find out its analytic solutions.Above-mentioned modular form (39) is the two-dimensional heat equation with non-odd times boundary condition, is needed first that its is non-
Odd times boundary carries out homogeneous partial differential operation, and constructor v (x, y, t)-D (t)=u (x, y, t), then above formula (39) can be converted into formula
(40):
Observation type (40), boundary condition shown in third equation are First Boundary Condition, and shown in the 4th equation
Boundary condition be second kind boundary condition.Therefore, when being solved using Method of expansion in terms of eigenfunctions, Fu such as formula (41) is selected
Vertical leaf transformation:
Using formula (41) Solution of Initial Value Problems of First-order Ordinary Differential can be converted by desired partial differential equation:
Wherein:
Using the solution formula of ODE, the solution of formula (11) can be written as follow the form of formula (48):
Further according to the inverse transformation of Fourier transform in formula (10), inversion is carried out to formula (43), equation (40) can be solved,
Shown in its form such as formula (49) solved:
Wherein:
The condition generated using minimum allowance constructs equation group shown in formula (52):
Wherein D (2R, y, t)=D (0, y, t)=D (t).In above-mentioned equation group (52), as selected variable y=ys, m=
(y when 1, n=1sRepresent the height that forging is arbitrarily designated), then containing only there are three known variables t, u in equation0(d,ys),u0(2R-
d,ys), due to u0(d,ys)=u0(2R-d,ys), equation group only has two independent variables, two independent equations, so equation
Group can solve.Forging temperature is u when can find out stopping heating0(d,ys), y=y can be solvedsThe minimum allowance T at placer=Ts-
u0(d,ys)。
Step S203 is based on minimum allowance and forging heating back segment heating method, obtains and forging heating back segment heating side
The corresponding Optimal Temperature switching point of formula, wherein forging heats up leading portion using heating with full power mode.
The definition of minimum allowance according to the present embodiment, when switching heating method, as long as the temperature safety allowance reserved is big
In minimum allowance, so that it may to prevent forging overshoot from reserving enough regulation spaces in forging temperature-rise period.But the temperature reserved
Safety allowance is spent closer to minimum allowance, and glowing furnace heats up, and duration is shorter, and energy consumption is also fewer, then the regulation to heating rate is empty
Between it is also fewer.When temperature safety allowance is equal to minimum allowance, after switching heating method at this time, to prevent overshoot, Suo Youjia
Hot device must go stopping for electric heating, this makes the heating rate of forging apparent jump occur, i.e. heating slope will appear obviously
The case where decline, this forging heating curve slope jumps suddenly, does not meet quenching technical heating stationarity requirement；In addition,
The temperature safety allowance reserved can not arbitrarily select in the range for being greater than minimum allowance, because in the mistake of selection safety allowance
Cheng Zhong also needs the influence for considering glowing furnace heat transfer type in temperature-rise period.If glowing furnace heat exchange side in temperature-rise period
There is transformation in formula, will lead to forging bulk temperature and small frequent fluctuation occur, need to just switch heating method, intervention control in time at this time
The heating method of power processed, to guarantee the stationarity of heating.But premature switching heating method, can make the safety reserved abundant
Amount is too big, although the regulation space of heating rate is sufficient enough, ensure that the stationarity of heating well, at this time glowing furnace liter
The warm time extends, and energy consumption increases.It based on above-mentioned analysis, is the stationarity for guaranteeing glowing furnace temperature-rise period, in the temperature that selection reserves
When spending safety allowance, it is considered as the following:
It a), should be according to glowing furnace heat treatment process usually under the premise of the temperature safety allowance reserved is greater than minimum allowance
In convection current-radiation evolution process, temperature safety allowance is set as in temperature-rise period, heat transfer type becomes multiple in glowing furnace
Temperature value when miscellaneous guarantees the gentle of heating curve；
B) selecting suitable temperature safety allowance, i.e., after Optimal Temperature switching point determines, subsequent control power heating
The temperature control system of mode must satisfy a constraint condition: glowing furnace heating system passes to the energy of forging, is equal to forging
Part from temperature switching point be warming up to set temperature value needed for heat subtract the heat that all electrothermal resistance silk thermal inertias provide, to protect
Forging not overshoot is demonstrate,proved, and can be rapidly heated and reach set temperature；
Based on above-mentioned analysis, in conjunction with glowing furnace convection current-radiation Evolution Mechanism and heat treatment stages three-stage division methods
It is found that in the temperature-rise period of glowing furnace, when forging temperature is greater than TcWhen, TcIt is furnace heat transfer mode by thermal convection and heat transfer
It accounts for leading role and is changed into thermal convection, heat radiation and the coefficient heat exchange mode of heat transfer, that is, the stage that is rapidly heated is to transition
The temperature value in stage.Obviously, the diabatic process in glowing furnace is in TcThe complexity become later, therefore it is T that temperature switching point, which may be selected,c,
As shown in Figure 5.Obtaining the temperature safety allowance that should be reserved simultaneously is Tf=Ts-Tc> Tr.So, using controlled power heating side
When formula heats up, control amount u should meet the constraint condition being shown below,
Wherein, C is the specific heat capacity of forging, and M is the quality of forging, EuThe energy generated for control amount.
Step S204, using Optimal Temperature switching point as the switching point of forging heating leading portion and back segment heating method, thus
Realize the optimum control of forging low energy consumption steepest heating.
Optimal switching point once it is determined that, the optimal heating strategy of glowing furnace can be provided are as follows: heating leading portion use total power
Heating method heats up；When being warming up to temperature switching point TcWhen, it is switched to control power heating method, and guarantee to add simultaneously
The energy of the control amount of hot mode meets the constraint of formula (53), and forging is finally warming up to set temperature.The heating strategy is
Guarantee forging heating non-overshoot and stable steepest heating strategy.
The control object of large-scale vertical glowing furnace heat treatment process is that have non-linear, time lag, the temperature of distributed nature
Field model, the presence of metal thermal inertia make between temperature rise period heating rate and overshoot that there are contradictions.If quick heating, thermal inertia
Meeting is acted on so that control effect can not embody immediately, overshoot is easy to appear, influences product quality；If reducing heating rate, heating
Time increases, and energy consumption increases, and production efficiency reduces.To solve this problem, it is based on the multi-period aluminum alloy forge piece temperature field mould of multi-region
Type will heat up the contradiction between phase temperature overshoot and energy consumption and be converted into optimizing temperature field control and ask in conjunction with boundary Control problem
Topic, obtains this Optimal Control Problem by Optimization Solution process and meets bang-bang characteristic, and there are at least one optimal controls
The conclusion of amount processed；And heating with full power mode is obtained, the duration that not only heats up is shorter and to can guarantee that the arrival of forging bulk temperature is set
Energy near definite value is up to control, on this basis, proposes the glowing furnace low energy consumption steepest heating switching control based on minimum threshold doseag
Strategy.The control strategy uses the Hybrid Heating mode of two sections of switchings, fusion total power and control two kinds of heating methods of power
Two-way advantage obtains the minimum temperature margin value for guaranteeing heating process non-overshoot by establishing minimum temperature allowance solving model；
Based on this minimum temperature allowance and convection current-radiation Evolution Mechanism, Optimal Temperature switching when two kinds of heating method switchings is derived
Point realizes the target of low energy consumption steepest heating to guarantee the stationarity in temperature field.
Key inventive point of the invention is:
(1) by the solution of Optimal Control Problem, obtaining heating with full power mode is the steepest heating mode that can be reached；
(2) consider that glowing furnace, there are apparent thermal inertia, proposes to reach setting in forging bulk temperature in temperature-rise period
Before value, the temperature safety allowance for guaranteeing not overshoot is reserved, i.e., minimum allowance；
(3) foundation and solution of the forging models for temperature field of minimum allowance；
(4) it based on minimum allowance and forging heating back segment heating method, obtains corresponding with forging heating back segment heating method
Optimal Temperature switching point；
(5) optimal heating strategy, i.e. guarantee forging heating non-overshoot have been determined based on forging temperature-rise period temperature switching point
And smoothly steepest heating is tactful.
Referring to Fig. 6, the large-scale vertical glowing furnace low energy consumption steepest heating control system of proposition of the embodiment of the present invention, comprising:
Memory 10, processor 20 and it is stored in the computer journey that can be run on memory 10 and on processor 20
Sequence, wherein processor 20 realizes the large-scale vertical glowing furnace low energy consumption steepest liter that the present embodiment proposes when executing computer program
The step of warm control method.
The specific work process of the large-scale vertical glowing furnace low energy consumption steepest heating control system of the present embodiment and work are former
Reason can refer to the course of work and working principle of the large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise in the present embodiment.
These are only the preferred embodiment of the present invention, is not intended to restrict the invention, for those skilled in the art
For member, the invention may be variously modified and varied.All within the spirits and principles of the present invention, it is made it is any modification,
Equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (8)
1. a kind of large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise, which is characterized in that the described method includes:
The energy for obtaining forging heating reaches steepest heating mode, described up to steepest heating mode to specifically refer to that the forging liter can be made
Temperature to predetermined target value steepest heating mode；
According to thermal inertia present in glowing furnace temperature-rise period, determine that minimum allowance, the minimum allowance are that glowing furnace heated up
Cheng Zhong, under the premise of guaranteeing forging temperature non-overshoot and energy consumption the smallest steepest heating, when the heating method of glowing furnace is from described
When can switch to stopping heating up to steepest heating mode, required minimum temperature safety allowance；
Based on the minimum allowance, the optimum control of forging low energy consumption steepest heating is realized.
2. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 1, which is characterized in that described
It can be specially heating with full power mode up to steepest heating mode.
3. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 2, which is characterized in that be based on
The minimum allowance realizes that the optimum control of forging low energy consumption steepest heating includes:
Based on the minimum allowance and forging heating back segment heating method, obtain corresponding with forging heating back segment heating method
Optimal Temperature switching point, wherein forging heat up leading portion use heating with full power mode；
Using the Optimal Temperature switching point as the switching point of forging heating leading portion and back segment heating method, to realize forging
The optimum control of part low energy consumption steepest heating.
4. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 1 to 3, feature exist
In determining minimum allowance includes:
The forging models for temperature field of minimum allowance is established, specifically:
Wherein, u (x, y, t) represents forging internal temperature field, u0What the forging models for temperature field that (x, y) represents minimum allowance solved surely
Primary condition, u (x, y, 0) represent the forging initial temperature at t=0 moment, and u (0, y, t) is represented at t moment x=0, i.e., forging is vertical
Cross-sectional left forging surface temperature, u (2R, y, t) are represented at t moment x=2R, i.e. forging surface temperature on the right side of forging longitudinal section,
uy(x, 0, t) represents t moment forging bottom surface temperature, uy(x, l, t) represents top surface temperature on t moment forging, and D (t) represents electric heating
The cooling function that resistance silk cools down since limiting temperature, 2R represent the basal diameter of forging, and λ represents the coefficient of heat conduction of forging, ρ
Forging density is represented, c represents the specific heat capacity of forging, and Ω represents the computational domain where forging, and l represents forging height；
Based on the forging models for temperature field of the minimum allowance, minimum allowance is obtained.
5. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 4, which is characterized in that described
Minimum allowance are as follows:
Tr=Ts-u0(d,ys)
Wherein, TrRepresent minimum allowance, TsThe target temperature of forging heating is represented, d represents diameter of forgings, ysForging height is represented,
u0(d,ys) represent stop heating when, forging is in (d, ys) at temperature.
6. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 5, which is characterized in that be based on
The minimum allowance and forging heating back segment heating method, obtain optimal temperature corresponding with forging heating back segment heating method
Spend the calculation formula of switching point:
Wherein, TfFor temperature safety allowance, TsFor the target temperature of forging heating, TcFor Optimal Temperature switching point, TrIt is minimum abundant
Amount, C are the specific heat capacity of forging, and M is the quality of forging, EuFor the energy that control amount generates, u is control input quantity.
7. large-scale vertical glowing furnace low energy consumption steepest method for controlling temperature rise according to claim 6, which is characterized in that described
Forging heating back segment heating method is specially controlled power heating method.
The control system 8. a kind of large-scale vertical glowing furnace low energy consumption steepest heats up, the system comprises:
Memory (10), processor (20) and it is stored in the computer that can be run on memory (10) and on processor (20)
Program, which is characterized in that the processor (20) realizes any institute of the claims 1 to 7 when executing the computer program
The step of stating method.
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