CC BY
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Investigation of combustion in titanium-ferrosilicon system
0,5
Avarage particle size, mm
Fig.
6. Relationship between combustion rate and titanium powder particle size in titanium-ferrosilicon system
Thus, these investigations have shown that SHS-technology can be applied to obtain ferro silico titanium with high titanium content. It is possible to obtain alloys with various titanium content and various densities by varying of initial mixture and particle size of initial powders. Moreover, lack of waste and electricity consumption will bring low cost and provide high competitiveness of products. At the same time, producing of new alloy in inert gas atmosphere will increase the purity of end product.
Investigations results were used for developing the experimental-industrial technology of ferro silico titanium production by SHS-method. Specifications for optimal SHS-ferro silico titanium composition are developed (Table 2).
Table 2
Conclusions
The process of obtaining ferro silico titanium with high titanium content (to 75%) by self-propagating high-temperature synthesis was investigated. The relationships between combustion rate, combustion temperature and initial components ratio, titanium powder particle size were obtained. As it turned out, temperature depends weakly on initial components ratio and titanium powder particle size and remains at the same level (about 1720 ± 50°K). Combustion rate is also weakly depends on titanium powder particle size, but we can see, that combustion rate reduces when titanium content both increases and reduces. Maximum combustion rate was obtained on the compound with 72% titanium. Based on these data, experimental-industrial technology of obtaining ferro silico titanium by SHS-method was developed.
1,5
References
Chemical composition of SHS-ferro silico titanium
Grade Ti Si C S P O N H
max
FST 70 61-74 18-27 0,15 0,005 0,009 0,1 0,05 0,005
Lyakishev N.P., Pliner, U.L., Lappo S.I. Legiruyuschie splavy i stali s titanom. [Alloys and alloying steel with titanium]. M.: Metallurgiya, 1985, 230 p. Gasik M.I. Teoriya i tekhnologiya proizvodstva ferrosplavov. [Theory and technology of production of ferroalloys]. Moscow: Metallurgiya, 1988, 340 p. Sarkisyan A.R. and other. Some laws of combustion of mixtures of transition metals with silicon and silicide synthesis. Fizika goreniya i vzryva. [Physics of combustion and explosion]. 1977, no. 3, pp. 34-40. Azatyan T.S. Some laws of combustion of titanium with silicon. Fizika goreniya i vzryva. [Physics of combustion and explosion]. 1978, no. 1, pp. 44-49. Novikov N.P., Borovinskaya I.P., Merzhanov A.G. Thermodynamic analysis of self-propagating high-temperature synthesis reactions. Protsessy goreniya vkhimicheskoy tekhnologii i metallurgii. [Combustion Processes in Chemical Technology and Metallurgy: Proceedings]. Ed. A.G. Merzhanov. Chernogolovka, 1975, pp. 174-188. Bukreev A.E., Manashev I.R., Nikiforov B.A., Bigeev V.A. New nitrogen-containing chrome nitride based alloys, obtained by SHS. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2008, no. 1, pp 49-51.
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Parsunkin B.N., Andreev S.M., Akhmetov T.U., Mukhina E.Y.
OPTIMAL ENERGY-EFFICIENT COMBUSTION PROCESS CONTROL IN HEATING FURNACES OF ROLLING MILLS
Abstract. Considering continuous energy price rising, energy- efficient combustion process control is of current interest because circa 15% of the consumed firing is expended in rolling production for metal heating.
Effective solution of this problem is possible by using the automated systems of optimal control, based on optimizing control algorithms of search type. Such management systems have the ability to provide search and to maintain the maximum value of the optimized parameters under uncertainty and the lack of accurate quantitative model of the processing. Keywords: temperature, air volume control, objective variable, extremal control, combustion control.
In iron and steel industry circa 15% of the consumed firing is expended in rolling production in metal heating. Therefore, energy-efficient combustion process control is of current interest, especially considering continuous energy price rising.
Optimal energy-efficient combustion process control is a difficult task in continuous furnaces of modern highperformance hot rolling mills, when their operating rate varies from 100 up to 1000 t / h, and the initial temperature of continuous cast billets, feeding to heating, ranges
from 0 to 600°C. Effective solution of this problem is possible by using optimal control automated systems, based on the principles of search optimizing algorithms. Such extreme control systems possess a unique ability to provide effective control under uncertainty and absence of accurate quantitative model of the optimizing processing.
In automatic combustion process controlling, under plant conditions, method of volumetric flow rate of firing and air is frequently used. This method provides target value stabilization of air flow rate - a3A in accordance with the following condition:
VA(r)
a„ =•
VF (t) • Lo
- = const,
where VF (r) is the current air flow, m3 / h; VF (r) is the current firing rate, m3 / h; t is the current time, s; LO is a coefficient, defining required air quantity for complete combustion of one unit measure of used fuel.
The combustion process investigation showed that there is individual dependency of value aA on the gas flow, when the best energy firing conditions are provided for each type of combustion units (burners) and for each zone of heating furnace.
For example, rational values aA dependency on gas flow for top zones №1, 3, 5 of a modern highperformance 10-zone continuous furnace № 1at Mill 2000 OJSC «MMK» with walking beams, with roof top and side lower natural gas firing, designed for continuous cast billet heating with 250 mm thickness and from 5000 to 12000 mm length is shown in Fig. 1 [1].
Overstated air flow under low gas flow rates is determined by the necessity to maintain the required kinetic energy of the gas-air jet in order to provide the flow «sticking» to the flat furnace roof surface. Under high gas flow rate, less air flow is required in comparison with theoretically calculated one, since oxygen in intensive mixing enters gas jet from the workspace by means of inleakage, where the oxygen content is 5-8%.
Gas flow. xlQ m3/h3
Fig. 1. Dependencies of rational values of air flow rate aA on the gas flow for the upper zones №1, 3, 5 of continuous furnace № 1 at the Mill 2000 OJSC «M
Target value a3A maintaining on required rational value involves constant operator intervention into combustion process control mode in each gas flow changing. It is physically impossible under non-steady furnace operation behavior. Therefore, overstated aA (r) is set for all flow-rates in zones. This reduces the efficiency of fuel combustion process control and increases discharge intensity.
Energy-saving automated system is effectually used to implement the optimal fuel combustion process control. This system should independently (without operator intervention) define and maintain that sort of aA value, which enables firing to cause maximum thermal effect, with furnace characteristics and external influences changing accidentally.
The obligative and necessary functioning condition of this optimal fuel combustion process control system is unimodal (one-extreme without derivative breaking) type of optimization process steady-state characteristic [1].
The experimental dependencies of top zones workspace temperatures of continuous furnace №1 at the Mill 2000 OJSC «MMK» on value aA in each zone are presented in Fig. 2.
1400
o
1300
1200
1100
1000
0,8 0,9
Air flow coefficient.
Fig.2. Dependency of workspace temperature in the top welding zones according to zone thermal couple readings upon air flow rate: 1) zone №3, Vtc = 1020m3 / h, and 2) zone №3, Vtc = 2600m3 / h, and 3) zone №5, Vtc = 1100m3 / h
Dependencies analysis obtained proves the ability and expediency to use optimal fuel combustion process control system in each top zone of fired continuous furnaces.
Long-term practice of automatic optimization systems (AOS) using under real operation conditions showed that such systems should be two loop circuit [1,7].
The first loop is stabilizing, providing volumetric gas and air flow proportion, realizes fast but rough firing and air flow ratio. This allows the control system to response
quickly to deep technological indignation, when changing firing rate and temperature.
The second loop is optimizing, begot on extreme control principles, allows to carry out, within a dedicated work area for this circuit, more sensitive optimal condition adjustment of combustion process, but more slowly.
Block diagram of two-loop automatic control system of optimum combustion process is shown in Fig. 3.
The stabilizing loop, implementing standard PI or PID controller theory, includes firing rate FS and air rate AS sensors with rate transmitters VF and VA. Functional generator composes the required air flow rate VA (r) in accordance with the expected rational air flow Vp(z) = F [Vf(t)] (see Fig. 1). The value F [Vf(t) ] is compared in comparison element CE with the current air flow rate value VA (r) . The signal A VA (r) is generated at comparison element output.
AVa (t) = F[VF (T)]-Va (T) ,
=
al(t),if AVa(t) >AVa3 (t) o2(T),if AVa(t) <AVa3 (t),
where ct1(t), ct2(t) are the switching functions, defining the current travel direction of the actuating unit (AU), that changes the air flow accordingly to stabilizing or optimizing loops in accordance with the following expression:
Va(t) = Va, +ct,(T) • К a
i = 12,
where F [VF(r)] = VF (r) • LO -«A ("0 is required current «target» air flow into a zone.
Signal A VA (r) is fed to the input of switch control unit SCU.
At the same time, signal A VA (t) , which is formed by a setting device SD and defines target work area of optimizing loop, is fed to the SCU input.
The switch control unit switches over the control of the air flow actuating unit AU in accordance with the following condition:
where VAI is the initial value of the air flow; <ji (r) e (+1, — 1) is the current direction of the air flow rate changing; KAU is constant speed of the actuating unit (AU), according to technical characteristics.
Optimizing loop involves a heating area temperature detector TE, a rate converter RC and an optimizer, begot on the extreme control principle, providing the detection and maintenance of optimal combustion conditions within a set zone A VA (t) in accordance with the extreme type dependency t°C=9(aA (r)), (see Fig. 2).
Under normal operating conditions, type of steady-state extreme characteristics and extremum location in the field «control action - optimizing variable» have not been defined. Therefore, the using of continuous extreme control system with the remembering of optimized parameter speed extremum and with actuating unit stop at the moment of maximum speed changing is the most acceptable.
Dynamics of a searching process in such automatic management optimization system (AMOS) of combustion process is determined by the equations set and logical conditions [5,6]:
Y [ X (t) ] = a0 + a1 X (r) + a2 X 2(r) +... + anXn (r) TodZ (t)/ dr + Z1(t) = Y [ X (r)]; T, dZ (t)/ dr+ Z (t) = Z1(t).
Fig. 3. Block diagram of two-loop system of combustion process control optimization in the workspace
of industrial furnaces
t , r dZ(r) „ In the case oi -— > 0
dr
U (t) =
+1,ifZ(r) - Z (T)max + Z (t) J > 0; 0, if Z (t) - Z (r)max Z (t) j < 0.
dZ (t) • . n
In the case of -= Z (r) < 0
dz
U(t) = —1, if z(t) + z(t)j < 0.
If U(t) = +1, then c2 (t + 1) = ct2 (t) . If U(t) = 0, then ct2(t + 1) = 0. If U(t) = -1, then ct2(t + 1) = -<t2(t) , where (r — 1) , r, (t +1) denote the past, current, posterior time intervals respectively; X (r) = VA(r) is the current value of the control parameter; Z (r),
Z(t) are current values of optimizing parameter and its change rate over time respectively; Y [X(r)] is
the set optimizing parameter point in accordance with the steady-state characteristic of the optimized
process; T0 = Tobj + TL is the equivalent object
time coefficient, characterizing optimizing process
persistence - Tobj and lagging - TL ; TF is the
smoothing filter time coefficient, used for high frequency information signal interference rejection • •
Z(r); Z (r -1) is the maximum rate changing value of the optimized parameter, achieved in the
search cycle; 3-4 elapsed time of optimizing loop after AU forced reverse; 4-5 conditioning period before the next cycle of search, etc.
The time interval rC - conditioning before verifica-tory forced reverse is required for the accumulation of information about optimizing process current state.
Engineering implementation of two-loop AMOS of combustion process on the basis of domestic CJSC Mek-hanoremontny Komplex (Mechanical Repair Shop) is examined in detail in [2].
The property of this extremum search method is the absence of AMOS operation periodic mode and considerably high accuracy in the extremum error less than 5%.
& JS
M
70-
65-
60-
55-
50-
45-
40J
¡3 'm
18
15
0,3
J_
1 2 3 4 5 5 7
2
(V
by-past time period; Al Z(r) I is the optimizing
V / DZ
loop dead zone.
The value Z (r -1) is formed by a memory unit in accordance with the following condition:
if Z(r) > Z(t - 1)max , then Z(t - 1U = Z?(t) ;
if zZ(T) < zZ(T - 1)max , then zZ(T - 1)max = zZ(t - 1)max .
The study was made of the automatic optimization system efficiency on the laboratory setup [1,4], under conditions close to real.
The trajectories of changing Z(r), Z(r) and X(r) parameters over time, during search operation mode of automatic management optimization system AMOS of combustion process, in using this extremum search method, are presented in Fig. 4.
The following time intervals are identified in Fig. 4: 0-1 elapsed time of stabilizing loop, 1-2 elapsed time of optimizing loop; 2-3 conditioning period before the next
150
300
Time, s
450
600
750
Fig. 4. Change over time Z(t), Z(r), X(t) in introducing AMOS of combustion process in the furnace workspace: 1 - relative changing of temperature detector; 2 - air flow changing, 3 - temperature changing rate
The utilization of the introduced software-programmable optimization technology of control energy-intensive process of combustion in industrial furnaces workspace enables 1.5-2.5% reduction of firing discharge intensity. That becomes possible due to more effective and operational control of air flow under heating furnaces nonsteady behavior.
Moreover, combustion process stabilization will lead to the stabilization of thermal state of heating billets and will permit to improve calculation accuracy of the strip thermal state during rolling [8]. Such firing combustion control systems are applicable for almost all thermal energy consuming units, operating in nonsteady mode, in which gaseous firing is used as the source of heat [9].
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3
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References
1. Parsunkin B.N., Andreev S.M., Akhmetov U.B. Optimization of processing control in metallurgy. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2006. 198 p.
2. Kazakevitch V.V., Rodov A.B. The automatic optimization systems. Moscow: Energy, 1977, 288 p.
3. Parsunkin B.N., Andreev S.M. Processing control optimization of fuel combustion in heating furnaces workspace. Steel. 2000, no. 5, pp. 48-52.
4. Parsunkin B.N., Andreev S.M., Obukhova T.G. Study of optimum energy efficient fuel combustion process in metallurgical furnaces workspace. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2005, no. 4, pp. 28-36.
5. Parsunkin B.N., Bushmanova M.V., Andreev S.M. Calculations of automatic systems of processing optimization in metallurgy: Textbooks. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2003, 267 p.
6. Sayrov A.M. Optimization of thermal management in heating furnace workspace. Automated technologies and production: Collection of Scientific Papers. Ed. Parsunkin B.N. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2013. no. 5, pp. 296-301.
7. Parsunkin B.N., Andreev S.M. Ways to improve the efficiency and noise immunity of processing control automatic optimization. Automated technologies and production: Collection of Scientific Papers. Ed. Par-sunkin B.N. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2013. no. 5, pp. 277-290.
8. Rumyantsev M.I., Shubin I.G., Nosenko O.U. Model designing to calculate the temperature of low-alloy steels in hot rolling. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2007, no. 1, pp. 54-57.
9. Zadonskaya T.A., Shvetsova E.S., Koptsev V.V. Firing of high-speed streams of natural gas. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2009, no. 3, pp. 67-68.
Antsupov A.V., Antsupov A.V. (jun), Antsupov V.P.
DESIGNED ASSESSMENT OF MACHINE ELEMENT RELIABILITY DUE TO EFFICIENCY CRITERIA
Abstract. The universal method of reliability assessment of mechanical system loaded elements at the design stage as a sequence of steps within the procedure of constructing physical and probabilistic models of parametric failure formation based on various criteria is suggested. The methodology of forecasting durability of parts by kinetic strength is represented and an example of its implementation is shown.
Keywords: methodology, forecasting, reliability, dependability, durability, failure, damage susceptibility, gamma-percent life.
The main problem of the reliability theory is behavior prediction of mechanical system parts and components in supposed conditions of external loading, when it becomes possible to evaluate their reliability and durability in early stage design. In this case, the assessment of system element behavior and their parameters changing over time in future running is carried out on the dynamic, physical and probabilistic models [1].
A single, universal methodological approach to probability forecasting of trouble-free operation and resource characteristics of loaded elements of mechanical systems according to various criteria of their performance was stated in this paper, on basis of mathematical formaliza-tion of reliability theory basic concepts of engineering objects (GOST 27.002-89), and general concept of their gradual failure formation [2-4].
To describe theoretically the objective formation of technical product failures during their damageability (degradation) under external affecting, the suggested approach is stated as a series of rules of their parameter reliability dynamic models designing.
This approach is presented in a probabilistic form, and is a combination of the following steps.
I. Selection of object state basic parameter.
Parameter Xt (a random variable) is selected for the testing product type, according to the standard (GOST 20911-89) definition of «object state». Variable changing over time simulates the parameter behavior (state changing) during the entire operation period under certain external affecting conditions.
II. The equation formulation of object state.
Random function (dependency) elaboration or choosing, that describes parameter Xt increasing (+) or decreas-
ing (-) changing over time, and models the product state changes in aging (degradation) during the operation can be written as the following:
t
Xt = X0 ±J Xt ■ dt, (I)
o
where X0 is Xt parameter distribution at time T = t0 characterizing the initial object state; Xt = dXt / dt denotes random variable current distribution of object damageability rate at time T = t;
If a random variable of object damageability rate does not change over time - Xt = X = const, then the conditions (I) can be written as follows:
Xt = X0 + X ■ t (I.a)
Equations (I) simulate object damageability over time.
III. The formulation of object efficiency condition.
In accordance with the standard definition of «object performance capability», according to GOST 27.002-89, the condition of its performance is mathematically formulated in the form of one possible inequality:
t
Xt = X0 + J Xt ■ dt < xL or
0
t (II)
Xt = X0 -J Xt • dt > Xl ,
0
where xL is a limit value of Xt parameter, established in
