MMSE Journal Vol.2 2016

Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954

MMSE Journal. Open Access www.mmse.xyz

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Sankt Lorenzen 36, 8715, Sankt Lorenzen, Austria

Mechanics, Materials Science & Engineering Journal

January 2016



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Mechanics, Materials Sciences & Engineering Journal, Austria, Sankt Lorenzen, 2015

Mechanics, Materials Science & Engineering Journal (MMSE Journal) is journal that deals in peer-reviewed, open access publishing, focusing on wide range of subject areas, including economics, business, social sciences, engineering etc.

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CONTENT

I. MATERIALS SCIENCE ................................................................................................ 5

THE CARBON-FLUORINE ADDITIVES FOR WELDING FLUXES ......................................... 5

INFLUENCE VOLTAGE PULSE ELECTRICAL DISCHARGE IN THE WATER AT THE

ENDURANCE FATIGUE OF CARBON STEEL ................................................................... 15

ALUMINUM COMPOSITES WITH SMALL NANOPARTICLES ADDITIONS: CORROSION

RESISTANCE.................................................................................................................. 25

II. MECHANICAL ENGINEERING & PHYSICS ............................................................. 31

PERFORMANCE OPTIMIZATION OF A GAS TURBINE POWER PLANT BASED ON ENERGY

AND EXERGY ANALYSIS .............................................................................................. 31

CERTAIN SOLUTIONS OF SHOCK-WAVES IN NON-IDEAL GASES .................................. 44

ANALYTICAL MODELING OF TRANSIENT PROCESS IN TERMS OF ONE-DIMENSIONAL

PROBLEM OF DYNAMICS WITH KINEMATIC ACTION .................................................... 57

ON INFLUENCE OF DESIGN PARAMETERS OF MINING RAIL TRANSPORT ON SAFETY

INDICATORS ................................................................................................................. 62

VIII. Information Technologies .............................................................................. 70

THE ASSESSMENT OF THE STABILITY OF THE ELECTRONICS INDUSTRY FACILITY IN THE

MAN-MADE EMERGENCIES WITH THE USE OF INFORMATION TECHNOLOGY .............. 70

X. Philosophy of Research and Education .............................................................. 78

TEACHING REITLINGER CYCLES TO IMPROVE STUDENTS’ KNOWLEDGE AND

COMPREHENSION OF THERMODYNAMICS .................................................................... 78

MULTIMEDIA TUTORIAL IN PHYSICS FOR FOREIGN STUDENTS OF THE ENGINEERING

FACULTY PREPARATORY DEPARTMENT ....................................................................... 84

PETRUS PEREGRINUS OF MARICOURT AND THE MEDIEVAL MAGNETISM ..................... 90

DEPLETION GILDING: AN ANCIENT METHOD FOR SURFACE

ENRICHMENT OF GOLD ALLOYS .................................................................................. 98



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I. Materials Science

The Carbon-Fluorine Additives For Welding Fluxes

R.Е. Kryukov1, O.А. Kozyreva

1,a, N.А. Kozyrev

1,b

1 – Federal State Budgetary Educational Institution of Higher Professional Education «Siberian State Industrial

University», Research and Development Center «Welding Processes and Technologies», 654007, Russia,

Novokuznetsk, 42, Kirov str.

a – [email protected]

b – [email protected]

Keywords: welding, flux, metal, slag, gas-forming compounds.

ABSTRACT. Is carried out the thermodynamic estimation of the probability of the flow of the processes of the removal

of hydrogen from the weld with the welding in the fluorine-bearing flux in the standard states in the range of

temperatures 1700 – 2200 K. In this case, as the standard states for the substances – of reagents they were selected:

Na3AlF6L, SiO2L, SiF4g, NaAlO2s, Na2SiO3l, CaF2l, CaSiO3l, H2g, SiF2g, HFg, O2g, SiFg, Hg. As a result the calculations of

standard energy of Gibbs and equilibrium constants of reactions it is determined, that from the reactions of the direct

interaction of ftoragentov of slag with hydrogen and oxygen of the metal most probable appears the reaction with the

cryolite. In the mechanism of more complex interaction with the participation in the reaction, besides ftoragentov, silica

of slag and by the possible formation of the intermediate product of SiF4g more probable is the process with fluorite.

Calculations showed the expediency of using the connection Na3AlF6 together with fluorite for the removal of hydrogen

with the submerged welding. The carried out calculations became the basis of the development of the compositions of

the new flux- additives, protected by patents RF.

Introduction. The issue of new fluxes and their additives development has been attracting much

attention currently, as well as research into their influence on welding and technological characteristics

of a weld and on the concentration of oxygen and non-metallic impurities in a weld [1-5].

Submerged arc welding is attended by intensive mass transfer of liquid molten metal and slag,

forming from welding flux. Reactions of oxidation and deoxidation of manganese, ferrum, and

silicon, i.d. exchange processes involving oxygen are typical for this process. The most grades of

domestically produced fluxes, which are applied for welding low-alloyed steels are oxidizing ones

and ground on silicon-manganese oxidation-reduction processes. Here, the products of these

reactions are oxide compounds of silicon, manganese, ferrum, aluminum etc., which often can’t

surface and assimilate to slag, forming from welding flux, the level of impurity of weld metal by

non-metallic admixtures increases consequently; as the result, the complex of physical and

mechanical characteristics deteriorates. Apparently, restoratives, which form gaseous products of

reactions, are advisable to apply in order to avoid impurity of weld metal. It is carbon that can be a

restorative of this kind, and forms gaseous compounds CO2 and CO when reacting with oxidizers.





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Materials and methods of research. Shielding is usually provided through pushing atmospheric

gases aside from weld zone by forming gases CO2 (CO); that helps to reduce or even exclude the

probability of molten metal saturation with oxygen, nitrogen or hydrogen from atmosphere. Gas-

forming compounds of carbonates like CaCO3, MgCO3, FeCO3, MnCO3 and their derivatives are

usually used for this purpose. Gas shielding is possible due to CO2 as high-temperature

decomposition of carbonates takes place according to the following reactions and temperatures [6]:

CaCO3 → CaO + CO2 (900-1200 ºC), (1)

MgCO3 → MgO + CO2 (>650 ºC), (2)

FeCO3 → FeO + CO2 (280-490 ºC), (3)

MnCO3 → MnO + CO2 (330-500 ºC) (4)

According to stoichiometric calculations the results of decomposition are as follows: 1 kg CaCO3 –

0.224 m3 CO2, 1 kg MgCO3 – 0.267 m

3, 1 kg FeCO3 – 0.192 m

3, 1 kg MnCO3 – 0.194 m

3.

Without taking into account the costs of carbonates decomposition, MgCO3 and CaCO3 are the most

optimal components, which help to get most CO2 when decomposing 1 kg of material, succeeded

by MnCO3 и FeCO3.

Furthermore, when decomposing CaCO3 and MgCO3 basic oxides CaO and MgO are formed and

improve basicity of welding flux, and that of a forming slag, respectively, whereas, when MnCO3

and FeCO3 decomposing oxides FeO and MnO are formed, which raise the degree of oxidation in

slag systems and oxygen concentration in a weld. The latter causes all negative consequences –

increasing level of impurity by non-metallic oxide components in a weld and deterioration of

mechanical properties.

Having followed all mentioned pre-conditions we have developed a flux – ANK additive, protected

it by a patent of the Russian Federation and applied in production process at Open Joint Stock

Company “Novokuznetsk Plant of Reservoir Metalware named after N.E. Kryukov” [7]. For its

manufacturing ferrosilicon FS75 (GOST 1415-78), marble М92- М97 (GOST 4416-73 (92-97%

СаСО3)), and liquid glass (GOST 13078-81) were used. Production technology was as follows.

Marble and ferrosilicon were grinded to less than 1 mm fraction. Grinded marble and silicon were

mixed in 50 to 50% mass proportion. It was dried at temperature 100-200 0С for 10 - 20 minutes,

succeeded by grinding and size grading to 2.5 mm. 3-5% of additive was introduced into fluxes.

Before a flux with an additive is used its 40 – 60 minutes annealing in the furnace is recommended

at temperature 250-350 0С.

This additive is used for roll welding of tanks. The technology involves assembling, welding,

controlling and rolling plates of tanks walls, all the processes are performed on special roll facilities

with upper and down rolling. Two-side submerged arc welding of butt joints of wall plates is

applied in the process, first on the upper tier, then on the lower one, after the plate is rolled. An

additive helped to avoid pore formation and improve quality of welds.

However, shielding gases CO and CO2 can form due to carbon, added to the flux, according to the

reactions:

(C) + [O2] = {CO2}, (6)



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(C) + ½[O2] = {CO} (7)

Here 1.863 m3 CO2 and 1.864 m

3 CO release per each kg of carbon (in normal conditions).

The second important issue is that of weld metal dehydrogenization. As a rule, it is carried out by

introducing fluorine-containing additives (fluorite or cryolite), hydrogen combines with fluorine

and is further removed as a compound HF.

The following chemical transformations can be considered as probable reactions of removal:

1/2 (CaF2)+ [H]+ 1/2 [O] = 1/2(CaO) + HFg, (8)

1/6(Na3AlF6)+ [H]+ 1/2 [O] = 1/6NaAlO2 s+ HFg + 1/6(Na2O), (9)

As well as reactions:

2(CaF2) + 3(SiO2) = 2CaSiO3 s + SiF4g, (10)

2/3(Na3AlF6) + 5/3(SiO2) = SiF4g + 2/3NaAlO2 s + 2/3 (Na2SiO3), (11)

succeeded by reactions of dehydrogenization with SiF4:

1/2 SiF4g + [H] = 1/2SiF2 g+ HFg (12)

1/4 SiF4g + [H]+ 1/2 [O] = 1/4 (SiО2) + HFg (13)

1/3 SiF4g + [H] = 1/3SiFg + HFg (14)

1/2 SiF4g + [H] = 1/2 SiF2g + HFg (15)

Thermodynamical characteristics in standard conditions [∆rН°(Т), ∆rS°(Т), ∆rG°(Т)] needed to

assess reaction probability were calculated by well-known methods [8] in the temperature range of

welding processes 1700 – 2200 К [9] in terms of thermodynamic properties of reagents [[Н°(Т)-

Н°(298,15 K)], S°(Т), ∆fH°(298,15 K)] [10,11]. Here, chemical states Na3AlF6l, SiO2l, SiF4g,

NaAlO2 s,Na2SiO3l, CaF2l , CaSiO3 s, H2г, SiF2g, HFg, О2g, SiFg, Hg were selected as standard ones

for substances – reagents in the range 1700 – 2200 К according to fact aggregate states of phases in

the system under consideration.

The results of calculations are provided in the Table 1.

Table 1 demonstrates that reaction (9) is thermodynamically the most probable (cryolite

dehydrogenization), the second one is reaction (8) (fluorite dehydrogenization), followed by

reactions (10, 11), where silicon tetrafluoride is formed as an intermediate product of further

reactions (12) - (15); the latter result in formation of gaseous compound HF. Here, reaction (13) is

thermodynamically the most probable (SiF4 combines with hydrogen and oxygen). The

stoichiometric reactions (15), (12), (14) are the least probable ones.



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Table 1. Standard Gibbs energy of reactions (8) – (15) and reaction equilibrium constants

according to temperature

Reaction

∆rG°(Т), kJ

К(Т)

1700К 1800К 1900К 2000К 2100К 2200К

8 -16,22 -18,61 -20,93 -23,17 -25,36 -27,47

3,2 3,5 3,8 4,0 4,3 4,5

9 -32,32 -33,82 -35,20 -36,46 -37,62 -38,68

9,8 9,6 9,3 9,0 8,6 8,3

10 41,80 35,98 30,62 25,71 21,22 17,18

0,05 0,09 0,14 0,21 0,30 0,39

11 82,41 76,11 70,40 65,22 60,56 56,38

0,003 0,006 0,012 0,020 0,031 0,046

12 86,62 78,13 69,68 61,27 52,90 44,57

0,002 0,005 0,012 0,025 0,048 0,087

13 -90,16 -89,83 -89,51 -89,21 -88,91 -88,63

589,5 404,5 289,1 213,8 162,8 127,2

14 113,04 104,93 96,86 88,82 80,80 72,82

0,0003 0,0009 0,0022 0,0048 0,0098 0,0187

15 -38,07 -40,60 -43,08 -45,49 -47,84 -50,14

14,78 15,08 15,29 15,42 15,49 15,51

Therefore, Na3AlF6 is the most reasonable to use for dehydrogenization when submerged arc

welding as if compared with fluorite.

Having taken into account the aforementioned preconditions, we have developed a technology of

submerged arc welding with carbonaceous additives. As the basis of carbon and fluorine containing

additive we took metallurgical production wastes. It was dust with the following chemical

composition (mass %): Al2O3 = 21 – 46.23; F = 18 – 27; Na2O = 8 – 15; К2O = 0.4 – 6; CaO = 0.7 –

2.3; SiO2 = 0.5 – 2.48; Fe2O3 = 2.1 – 3.27; C = 12.5 – 30.2; MnO = 0.07 – 0.9; MgO = 0.06 – 0.9; S

= 0.09 – 0.19; P = 0.1 – 0.18. Mineralogical makeup of dust was determined according to the data

of X-ray structural analysis made by difractometer DRON-2 in the mode: Fe – K α radiation,

voltage 26 kV, electrical current 30 mA.

The research into the dust of electrostatic precipitators revealed that the material consisted of bi-

dimensionally ordered carbon (d0O2=3.47Å, Lc=45.8Å), X-ray amorphous substance, cryolite,

corundum, hyolithe, and various admixtures. Diffraction patterns of roasted at 700°С material

demonstrate no indication of graphite, that is caused by nearly complete burning out of carbon-

containing mass in this temperature range, as well as significant curve flattering on the diffraction

pattern, and decrease in X-ray amorphous substance. The reason of the latter is probably chemical



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composition of X-ray amorphous substance, which carbon compounds are main components of. At

700°С the change in indication intensity of mineralizing components (cryolite, corundum, X-ray

amorphous substance, fluorite, hematite and various admixtures) was recorded.

From the theoretical point of view the additive makes possible: 1) dehydrogenization by fluorine-

containing compounds (like Na3AlF6,), decomposing at the temperatures of welding processes and

isolating fluorine, which combines with dissolved in steel hydrogen and forms gaseous HF; 2)

intensive carbon “boiling” due to forming CO and CO2, when fluoric carbon CFx (1 ≥x>0)

combines with dissolved in steel oxygen, here, as carbon is in a bound state steel carbonization is

hardly possible; 3) improvement of arc stability due to potassium and sodium, facilitating ionization

in arc column.

To make an additive to flux carbon and fluorine containing substance was mixed with liquid glass,

then this mixture was dried, cooled down and grinded. Afterwards this additive was mixed with flux

in a special mixer according to a definite, strictly determined proportion. АN-348А, АN-60, АN-67

fluxes were taken as basic ones and their mixtures with flux-additives.

The experiments were carried out on 200500 mm 09Mn2Si steel samples 16 mm in thickness.

Fay welding of butt joints was made on two sides, as when welding wall plates of tanks on roll

facility. Sv-08Mn wire 5 mm in diameter was used as a filler metal.

Submerged arc welding of samples was made in similar modes. The samples were cut of welded

plates and subject to the following tests: X-ray spectral analysis of weld metal chemical

composition, metallographic tests of welds; total concentration of oxygen in welds, mechanical

properties, strength of joint welds and impact strength of welds were determined at temperatures -

20°С and -40°С. Concentration of carbon, sulphur, phosphorus was determined in chemical

composition of weld metal by chemical methods in terms of GOST 12344-2003, GOST 12345-

2001, and GOST 12347-77, respectively. Concentration of alloying elements in weld metal; that of

calcium oxide, silicon, manganese, aluminum, magnesium, ferrum, potassium, sodium and fluorine-

compounds in fluxes with additives and slag, obtained after welding was determined by

SHIMADZU roentgen-fluorescent spectrometer XRF-1800.

The experiments demonstrated that maximum 6% carbon and fluorine containing additive provided

carbon concentration in weld similar to its concentration in original metal (Figure 1), whereas

concentration of oxygen, hydrogen and nitrogen dropped (Figures 2, 3, 4).

Fig. 1. Influence of carbon and fluorine containing additive on carbon concentration in a weld



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Metallographic research into polished sections of joint welds was carried out by optical microscope

OLYMPUS GX-51 in bright field and zooming ×100, ×500. The microstructure of metal was found

out by etching in 4 % HNO3 solution in ethanol. The structure of base metal in all samples consists

of ferrite grains and lamellar pearlite (4-5 µm). In base – to – added metal zone a fine-grain

structure occurs (1-2 µm), which was formed as the result of re-crystallizing when heating in course

of welding. In the microstructure of a weld there are ferrite grains stretched towards heat rejection

because of heating and speeded up cooling down. Structures of welds didn’t differ much

irrespectively of used fluxes. The level of impurity by non-metallic substances decreased in

samples, which were welded with fluxing agents, containing carbon and fluorine additives; it was

caused by reduction of total oxygen concentration.

Fig. 2. The change in oxygen in dependence on carbon and fluoride containing additive concentration

Fig. 3. The change in hydrogen in dependence on carbon and fluorine containing additive

The research into mechanical properties (yield point, strength, modulus of elongation, impact

strength at temperatures below zero) carried out on cut according to GOST 6996-66 samples,

demonstrated that the level of properties went beyond the values required in GOST 31385-2008 and



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increased as the concentration of carbon and fluorine containing additive rose. Increasing impact

strength KCV and KCU at temperatures -20°С and -40°С, respectively (Figures 5, 6) is worth

mentioning. Flux-additives, which were developed, have been protected by the Russian Federation

patents [12, 13].

Fig. 4. The change in nitrogen in dependence on carbon and fluorine containing additive

Fig. 5. The change in impact strength KCV at temperature -20°С in dependence on carbon and

fluorine containing additive.

Summary. 1. On the ground of made calculations and carried out experiments we can conclude that carbon

containing additives to welding fluxes are possible and promising ones in order to improve welding and

technological characteristics of welded metalware.

2. The probability of dehydrogenization of a weld in fluorine containing submerged arc welding has

been assessed thermodynamically in the temperature range 1700 – 2200 К. Here, Na3AlF6l, SiO2l,

SiF4g, NaAlO2s, Na2SiO3l, CaF2l, CaSiO3 s, H2г, SiF2g, HFg, О2g, SiFg, Hg. were selected as standard

states for substances - reagents. In terms of calculation of standard Gibbs energy reactions it has

been found out that the reaction of gaseous hydrogen fluorine direct formation by cryolite is

thermodynamically the most probable one, the second probable is the group of reactions resulting in



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formation of silicon tetrafluoride as an intermediate product for further HF formation. In this group

the most thermodynamically probable reaction is that of SiF4 with hydrogen and oxygen. In terms

of calculations Na3AlF6 is more reasonable to use for dehydrogenization when submerged arc

welding in comparison to fluorite.

Fig. 6. The change in impact strength KCV at temperature -40°С in dependence on carbon and

fluorine containing additive

3. Introduction of developed carbon and fluorine containing additive into fluxes АN-348А, АN-60

and АN-67 reduces gas content of a weld, the level of impurity by oxide non-metallic substances,

and improves required mechanical properties and impact strength (at temperatures below zero,

especially).

References

[1] Study of the relationship between the composition of a fused flux and its structure and

properties/ Amado Cruz Crespoa, Rafael Quintana Puchola, Lorenzo Perdomo Gonzáleza, Carlos R.

Gómez Péreza, Gilma Castellanosa, Eduardo Díaz Cedréa & Tamara Ortíza / Welding International.

– 2009. - Volume 23. - №2. - p. 120-131

[2] Using a new general-purpose ceramic flux SFM-101 in welding of beams/ Yu. S. Volobueva, O.

S. Volobueva, A. G. Parkhomenko, E. I. Dobrozhelac & O. S. Klimenchuk // Welding

International.– 2012.- Volume 26. - №8. - p. 649-653

[3] Special features of agglomerated (ceramic) fluxes in welding / V. V. Golovko & N. N.

Potapov // Welding International. – 2011.- Volume 25. - №11. - p. 889 - 893.

[4] The influence of the air occluded in the deposition layer of flux during automatic welding: a

technological aspect to consider in the quality of the bead / Rafael Quintana Puchola, Jeily

Rodríguez Blancoa, Lorenzo Perdomo Gonzaleza, Gilma Castellanos Hernándeza & Carlos Rene

Gómez Péreza // Welding International. – 2009.- Volume 23. - №2. - p. 132-140.

[5] Obtaining a submerged arc welding flux of the MnO–SiO2–CaO–Al2O3 – CaF2 system by

fusion / A.C. Crespoa, R.Q. Puchola, L.P. Goncaleza, L.G. Sanchezb, C.R. Gomez Pereza, E.D.



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Cedrea, T.O. Mendeza & J.A. Pozola//Welding International.– 2007.- Volume 21. - №7. - p. 502-

511.

[6] Reaction of non-organic substances / R.А. Lidin, V.А. Molochko, L.L. Andreeva – М.: Drofa,

2007. – 637 p.

[7] Manufacture of vertical bulk –oil storage tanks for northern climates using special welding

materials/ Kryukov N.E., Koval'skii I.N., Kozyrev N.A., Igushev V.F., Kryukov R.E.// Steel in

Translation. -2012. - Т. 42. -№ 2.-P. 118-120.

[8] Thermodynamical properties of substances: Reference book. V.1. Issue 1 / Edited by V.P.

Glushko, L.V. Gurvich et al. M.: Nauka, 1978. pp. 22.

[9] Welding materials for arc welding: СReference book in 2 volumes. V. 1. Shielding gases and

welding fluxes: Konishchev B.P., Kurlanov S.А., Potapov N.N. et al. / Edited by Potapov N.N. -

М.: Machinebuilding, 1989 – pp. 104.

[10] John L. Haas, Jr., Gilpin R. Robinson, Jr., and Bruse S. Hemingway // J. Phys. Chem. Ref.

Data. – 1981. – Vol. 10. – № 3. – P. 575 – 669.

[11] NIST-JANAF Thermochemical Tables 1985. Version 1.0 [Electronic resource] : data compiled

and evaluated by M.W. Chase, Jr., C.A. Davies, J.R. Dawney, Jr., D.J. Frurip, R.A. Mc Donald, and

A.N. Syvernd. – Available at: http://kinetics.nist.gov/janaf.

[12] Patent 2467853 RF, МPК 8 V23 К35/362 Ceramic flux-additive / Kryukov N.Е., Kovalsky

I.N., Kozyrev N.А., Igushev V.F., Krykov R.Е.; Open Joint Stock Company ОАО «Novokuznetsk

Plant of Reservoir Metalware» named after N.E. Kryukov.- № 201112341602/02(034654),

Application 08.06.2011.

[13] Patent 2484936 PF, МPК 8 V23 К35/362 Ceramic flux-additive / Kozyrev N.А., Igushev V.F.,

Kryukov R.Е., Goldun S.V.; FSBEI HPE “Siberian State Industrial University”.-

№2012104939/02(007484), Application 13.02.2012.

http://elibrary.ru/contents.asp?issueid=1035678

http://elibrary.ru/contents.asp?issueid=1035678

http://elibrary.ru/contents.asp?issueid=1035678&selid=17986531

http://kinetics.nist.gov/janaf



14

Influence Voltage Pulse Electrical Discharge In The Water at the Endurance

Fatigue Of Carbon Steel

I.A. Vakulenko1, a

, A.G. Lisnyak2, b

1 – Department of Materials Technology, Dnepropetrovsk National University of Railway Transport named after

Academician V. Lazarian. Street. Lazarian, 2, Dnepropetrovsk, Ukraine, 49010, Tel. 38 (056) 373 15 56, ORCID 0000-

0002-7353-1916

2 – Department "The technology of mining machinery" Dnepropetrovsk National Mining University, pr. Karl Marx, 19,

Dnepropetrovsk, Ukraine, 49027, Tel. 38 (0562) 46 99 81, ORCID 0000-0001-6701-5504



Keywords: hardness, distribution, impuls pressures, electric digit, limited endurance

ABSTRACT. Effect of pulses of electrical discharge in the water at the magnitude of the limited endurance under

cyclic loading thermally hardened carbon steel was investigated. Observed increase stamina during cyclic loading a

corresponding increase in the number of accumulated dislocations on the fracture surface. Using the equation of Cofino-

Manson has revealed a decrease of strain loading cycle after treatment discharges. For field-cycle fatigue as a result of

processing the voltage pulses carbon steel structure improvement, followed by growth of limited endurance decrease

per cycle of deformation. With increasing amplitude of the voltage loop gain stamina effect on metal processing voltage

pulses is reduced. The results can be used to extend the life of parts that are subject to cyclic loading.

Introduction. In the process of cyclic loading of carbon steel, the extent, to which the cycle

amplitude exceeds fatigue limit, affects the character of structural change considerably [2]. For this

reason, the rate of increase in the number of crystalline defects, and evenness of their distribution in

the metallic matrix are the determinants of the conditions of the fatigue damage sites formation in

metals and alloys [14]. Considering that, dislocations are basic carrier units of plastic deformation

[3], the possibility of purposeful control over the process of their growth and redistribution under

the fatigue loading can be considered a promising direction of development of the measures on

improvement of the finite life. The information on the use of electric pulse effects [6, 10] in the

carbon steel after a certain degree of plastic deformation can serve as example. As a result, there

was such a change in the internal structure of a metallic material, which was required to achieve a

desired set of properties.

Status of the problem. At the certain stage of the development of metal materials processing

technology, in the production of complex shapes, especially of plate stock of considerable size, they

detected certain difficulties in the implementation of the technical solutions. One of the ways to solve

this problem was the proposal to use the shock wave resulted by an electric discharge in liquid [4].

Based on numerous studies [4‒8], it was found that this technology allows not only the

manufacturing of products by the formation of a complex deformed state but also managing a range

of properties. Based on this, we can confidently assume that the value of the energy of pulse

loading, its momentum distribution [7, 13] may significantly change the result to be achieved.

Considering the existence of a certain threshold dependence of the impulse of voltage being formed,





15

it is possible to obtain the result of different quality, ranging from the reinforcing effect to the metal

weakening [4, 11, 12]. In most cases, the effect of hydraulic shock caused by the electric discharge

in liquid for many metallic materials has reinforcing nature [4, 5], which is supposed to be followed

by the change in the number of accumulated dislocations. Thus, if the effect has reinforcing nature,

the increase in the dislocation density may be expected. Considering that the result depends on a

large number of individual factors, the cumulative effect often leads to qualitatively opposite

results. For example, the rise of the stress wave amplitude increases the number of dislocations [4].

On the other hand, the pulse length largely determines the conditions for the movement of the

dislocation structures. Most of the known experimental data concerns the study of the influence of

the electric discharge shock waves in liquid on the properties of metallic materials under static

loading [5]. Based on this, we can confidently assume that the assessment of the impact of this

effect on the behavior of the metal under the fatigue is quite an important issue.

Purpose. Assessment of the impact of voltage impulses of the electric discharge in liquid on the

behavior pattern of carbon steel under fatigue loading.

Methodology. The carbon steel of the railway wheel pair axle with 0.45% carbon content was the

material under research. The content of other chemical elements corresponded to the grade

composition. The samples for alternating bending test under symmetric loading cycle were metal

sheets of 1 mm thick, 15 mm wide and 180 mm length. The samples were subjected to martensite

quenching and tempering at 300°C, for 1h. The analysis of the fracture surfaces was performed

using a scanning electron microscope and fractography techniques; the dislocation density was

evaluated by X-ray methods [1].

Metal fatigue testing was performed under alternating bending under symmetric loading cycle by

means of the ten-station test machine “Saturn-10”. Electrical discharge impulse action on the

samples of steel in water was performed by the “Iskra-23”, with the amplitude of the voltage to a

maximum of 2 GPa. The total number of pulses was about 104, at the frequency of 2-3 Gts.

Results. Selection of the structural state of steel after martensite quenching and subsequent

tempering at 300°C was driven by the possibility of achieving, under the high density of

dislocations, enhanced values of fatigue resistance of a metal under cyclic loading. From the

analysis of the internal structure of the metal, it follows that after quenching and tempering at

300°C, there the stages occur in the process of dispersed carbide particles liberation at the

dislocations, both in the middle and at the boundaries of martensite laths. Besides, as follows from

the results of studies [9], the development of dislocation recombination processes resulting in a

decrease in their total amount should always result in the lowering of their mobility. Therefore, we

can confidently assume that most of the dislocations that have appeared in the metal as a result of

mentioned thermal treatment are immobile to different extents.

The analysis of the shock stress treatment effect on the fatigue behavior of a metal was carried out

in a particular sequence. Fatigue curve was build first, for the samples that had undergone the

thermal treatment (Fig. 1, curve 1), by which the finite life of the metal was determined. Further, the

newly prepared samples were loaded, under the corresponding amplitudes of the cycle to the level

of 0.6‒0.7 of the value of the finite life. Then they were subjected to the shock stress. Further, the

cyclic loading continued until the final destruction of the samples. Finite life value is the total

number of cycles including the number of cycles before the shock stress treatment and after it, up to

the final destruction of the sample (Fig. 1, curve 2).

The analysis of fatigue curves shows the expected difference in the evolution of the fine crystalline

structure of the metal depending on the treatment applied. Indeed, for the similar amplitudes of

loading there is a clear increase in the fatigue resistance of the metal that has been subjected to the

shock wave impulse.



16

a ,

iN 610 cycle.

Fig. 1. The diagrams of cyclic loading steel 45 after tempering and annealing at 300C (♦) and

after treatment of SS (■).(Stress straik).

To explain the observed increase in the finite life of the metal, the dislocation density was estimated

by the interference (110) and (211) on the fracture surfaces of the samples.

Regardless of the treatment (before and after the shock stress), the decrease in the amplitude of the

cycle is followed by the accumulation of the amount of dislocations in the volume of metal under

plane-strain loading. The absolute values of )(hkl are of great interest. Thus, during cyclic loading

at high amplitude the absolute values of the dislocation density at the fracture surface of the samples

are almost the same. It can be explained by the fact that under high cyclic overstress the formation

of elementary shifts within the structural element of steel causes significant plastic deformations

localization, simultaneously with the rapid transition of the metal to the plane-strain condition.

Further, during the subsequent decrease of a the increase in the accumulated number of

dislocations occurs, with the rate of increase 211 that is significantly higher than the corresponding

value 110 (Fig. 2, a).

The nature of the changes of 211 and 110 (Fig. 2, a) corresponds to the known experimental data

for metal loading under unidirectional static and cyclic loading [2].

By treatment of the metal that had been subjected to the preliminary cyclic loading (up to 0.6-0.7 of

the value of the finite life with certain a ) by shock wave impulses, we have received the

qualitative differences in the nature of the change of the dislocation density on the investigated

interference (Fig. 2, b). The received level of absolute values: 211 is less than 110 , and their

change rate with the decrease of a appeared quite unexpected.

In order to explain the nature of the observed effect of the shock stress on the finite life under cyclic

loading, we analyzed the fracture surface of the samples.

Ряд1; 0,2; 110

Ряд1; 0,25; 93

Ряд1; 0,35; 75

Ряд1; 0,7; 60

Ряд2; 0,2; 120

Ряд2; 0,25; 100

Ряд2; 0,35; 90

Ряд2; 0,7; 80 1

2



17

210

),( 10 смhkl

a ,

а)

210

),( 10 смhkl

a ,

b)

Fig.2. The change of dislocations density, estimated on interferences (110) - ♦ and (211) - ■

depending on amplitude of cyclic loading and preliminary treatment: without SS (a) and after SS

(b).

The general analysis of fracture pattern in the samples after 256 310 cycles with the amplitude of

950 MPa (Fig. 3) shows that the surface of fracture was formed by a mixed mechanism. It is

indicated by the presence of chips inside grains (Fig. 3, A) and formation of the faceted surfaces of

intergranular fracture (Fig. 3, B) at the fracture surface.

The mechanism of formation of the chips inside grains is associated with the high overload along

the cycle. The first phase of structural changes caused by the emergence of elementary shifts within

Ряд1; 120; 13

Ряд1; 100; 10

Ряд1; 90; 15

Ряд1; 80; 21

Ряд2; 120; 10 Ряд2; 100; 10 Ряд2; 90; 11

Ряд2; 80; 14



18

the individual grains due to the movement of the unevenly distributed dislocations. Randomly

oriented shifts lead to the rapid partition of the grain into pieces, the boundaries of which are the

series of microcavities. The fatigue microcracks appear and extend along the specified boundaries

due to the local low resistance of the metal [15]. In the case of discrepancy of surfaces of the

simultaneously growing microcracks, in the places where they meet, a step or another boundary

appears that separates the other fragments (light lines in Fig. 3).

Fig.3. Fractographic investigation of the sample after the 260x. 310 cycles at an amplitude of

950 MPa.

Formation of the facets of intergranular fracture has a different mechanism. Instead of the chip

within the grain, due to the reduction of the cyclic overload in individual grains, the microcavities

appear near the angle boundaries, which reduces the bond between individual grains in the metal.

Moreover, the movement of dislocations near the large angular boundaries for several

crystallographic systems results in a series of vacancies. Under the influence of cyclically varying

loads in the metal, the areas accumulating the vacancies near the grain boundaries turn into volumes

with high concentrations of microcavities, along which the fatigue crack grows. The more detailed

analysis shows additional features, which indicate the participation of other failure mechanisms in

the formation of the fracture. In fact, there are dimples ( F ) on the fracture surface. These elements

of the structure of the fracture surface explain the emergence of a significant number of microcracks

( E ), which grow mostly at the ferrite grain boundaries. Based on this, it can be assumed that the

sample loading conditions with an amplitude of 950 MPa correspond to low-cycle fatigue, with the

finite life of 256 thousand of cycles.

The reduction of the amplitude to 750 MPa is followed by the expected prolongation of finite life

(up to 350 thousand of cycles). The analysis of the fracture surface (Fig. 4) testifies to the mixed

mechanism of fracture just as under higher amplitude of loading. While under 950 MPa, the fracture



19

surface is formed mainly due to the chips inside grains and formation of the faceted surfaces of

intergranular fracture, under 750 MPa the chips inside grains do not appear (Fig. 4, в, A label).

Fig.4. Fractographic investigation of the sample after 370 x10 3

cycle at an amplitude of 750 MPa.

The formation of the separation areas with the crests, which look like the light lines (Fig. 4,

A label), and the intergranular fracture facets (B label) with a significant dispersion should be

considered the dominating mechanism of the fracture surface formation. The sign that confirms the

fatigue resistance improvement is the fewer number of decompositions and microcracks. At the

same time, the number of pits of different sizes and shapes increased; this indicates an increase in

the number of microcavities in the plane of the growing crack. Moreover, on the surface of the

fracture, the occurrence of the sites with an equidistant arrangement of lines can be observed. The

lines have external characteristics similar to fatigue striations (C label). Based on the analysis of the

fracture it can be assumed that under the loading amplitude of 750 MPa the behavior of the sample

corresponds to the conditions of low-cycle fatigue with the signs explaining the increase in the

number of cycles to failure.

After the shock stress processing of the samples, the fracture surfaces have a slightly different

structure (Fig. 5).

According to the external characteristics, the elements of the fracture surface (Fig. 5) has been

formed by the mixed mechanism with almost the same range of particle dimensions as compared

to the sample that has not undergone the shock stress (Fig. 3). The fracture pattern analysis

(Fig. 5) shows the absence of the signs indicating the chip formation within the grains, which was

observed in Fig. 3. At the same time, a considerable part of the fracture surface is occupied by the

facets of intergranular fracture (Fig. 5, A label). There is approximately the same number of

micro-cracks as in the sample that has not undergone the shock stress (Fig. 3), which are located

along the grain boundaries (Fig. 5, B label), decompositions (C), separation areas with the crests

(D) and dimples (F).



20

Fig. 5. The fracture surface of the sample with an amplitude 1000 MPa, after the total number of

260 x10 3 cycle with UN interim treatment.

As for the presence of the fatigue striations as in the case of the sample shown in Fig. 3, it is quite

difficult to determine uniquely, although there are similar sections (E). By means of the

comparative analysis of the fracture surfaces and the obtained level of finite life, it is quite difficult

to determine the influence of shock stress for the high-stress low-cycle region. On the other hand, it

is known that in proportion to the degree of cyclical overload the influence of the static component

on the development of fatigue phenomena increases. The static component that determines the

effect of the deformation and precipitation hardening treatment on the structural changes, in fact,

can mask the effect of the shock stress treatment. The confirmation of the above explanations may

be received under the lower degree of the cyclic overload.

Fig. 6 presents the fracture pattern of the sample that survived 370 thousand cycles at an amplitude

of 900 MPa, which has undergone the intermediate shock stress processing. In comparison to the

sample with the same number of cycles to failure but without shock stress treatment (Fig. 4), the

degree of dispersion of the fracture elements that has undergone the shock stress is higher. Firstly,

the facets formed on the fracture surface have a more equiaxial shape (Fig. 6, a, A label). Compared

to the fracture surface of the sample shown in Fig. 4, there are large areas with very small dimples

(Fig. 6, b, B label); their formation mechanism is based on the coagulation of microcavities [2]. At

the same time, there is a certain number of facets with crests of separation (C) and equidistant

arrangement of the metal decomposition (D), with a low number of the facets of intergranular

fracture (E). In the case of reduction of the test results to the equal cycle amplitude, the finite life of

the metal after the shock stress treatment increases by about 30 %.

Summary. The voltage impulse treatment of metal produced by the electric discharge in water

contributes to the increase of finite life of the carbon steel under cyclic loading. With the rise of the

cycle amplitude, the gain in fatigue resistance resulted by the shock stress declines.



21

а)

b)

Fig. 6. The fracture surface of the sample with an amplitude of 900 MPa, after the total number of

370 x103 cycle with UN interim treatment.

References

[1] Gine A. Rentgenografiya kristallov [Roentgenography of crystals]. Moscow, Gosudarstvennoye

izdatelstvo fiziko-matematicheskoy literatury Publ., 1961, 604 p.



22

[2] Nott Dzh.F. Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow,

MetallurgiyaPubl., 1978. 256 p.

[3] Yefremenko V.G., Murashkin A.V., Ivanchenko Ye.P. Sovershenstvovaniye sostava i

termicheskoy obrabotki staley dlya nozhey kholodnoy rezki listovogo prokata [Improvement of

composition and heat treatment of steels for knives for cold cutting of sheet metal]. Stal – Steel,

2007, no. 1, pp. 75-77.

[4] Meyers M.A., Murr L.B. Udarnyye volny i yavleniya vysokoskorostnoy deformatsii metallov

[Shock waves and phenomena of high-rate deformation of metals]. Moscow, Metallurgiya Publ.,

1984. 510 p.

[5] Chachin V.N. Elektrogidravlicheskaya obrabotka mashinostroitelnykh materialov [Electro-

hydraulic processing of engineering materials]. Minsk, Nauka i tekhnika Publ., 1978. 184 p. [In

Russian]

[6] Yao K-F., Wang J., Zheng M. A research on electroplastic effects in wire-drawing process of an

austenitic stainless steel. Scripta Materialia, 2001, vol. 45, issue 15, pp. 533-539. doi:

10.1016/s1359-6462(01)01054-5.

[7] Ait Aissa K., Achour A., Camus J. Comparison of the structural properties and residual stress of

AIN films deposited by dc magnetron sputtering and high power impulse magnetron sputtering at

different working pressures. Thin Solid Films, 2014, vol. 550, pp. 264-267. doi:

10.1016/j.tsf.2013.11.073.

[8] Conrad H. Effects of electric current on solid state phase transformations in metals. Materials

Science and Engineering : A, 2000, vol. 287, issue 2, pp. 227-237. doi: 10.1016/s0921-

5093(00)00780-2.

[9] Dhadeshia H.K.D.H. Bainite in Steels. Cabridge, The University Press Publ., 2001. 454 p.

[10] Vakulenko I.A., Nadezdin Yu.L., Sokirko V.A. Electric pulse treatment of welded joint of

aluminum alloy.Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho

universytetu zaliznychnoho transportu– Science and Transport Progress. Bulletin of Dnipropetrovsk

National University of Railway Transport,2013, no. 4 (46), pp. 73-82. doi:10.15802/stp2013/16584.

[11] Tang G., Zhang J., Zheng M. Experimental study of electroplastic effect on stainless steel wire

304L.Materials Science and Engineering : A, 2000, vol. 281, issue 1-2, pp. 263-267. doi:

10.1016/s0921-5093(99)00708-x

[12] Morgan W.L., Rosocha L.A. Surface electrical discharges and plasma formation on electrolyte

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[13] Razavian S.M., Rezai B., Irannajad M. Numerical simulation of high voltage electric pulse

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[14] Vakulenko I.A., Proydak S.V. The Influence Mechanism of Ferrite Graine Size on Strength

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10.15802/stp2014/22668 [In Russian].



23

Aluminum Composites With Small Nanoparticles Additions: Corrosion

Resistance

L.E. Agureev1a

, V.I. Kostikov2, Zh.V. Eremeeva

2, A.A. Barmin

3, S.V.Savushkina

4, B.S. Ivanov

5

1 – Researcher, Department of Nanotechnology, Keldysh Research Center, Russia

2 – Doctor of Science, Associate Professor, Moscow State University of Steel and Alloys, Russia

3 – Ph.D., Leading Researcher, Department of Nanotechnology, Keldysh Research Center, Russia

4 – Ph. D., Senior Researcher, Department of Nanotechnology, Keldysh Research Center, Russia

5 – Engineer, Department of Nanotechnology, Keldysh Research Center, Russia


Keywords: nanometric particles, aluminum composites, PM method, corrosion resistance. corrosion rate

ABSTRACT. Research of corrosion resistance of the aluminum powder composites containing microadditives (0.01 –

0.15% is executed about.) zirconium oxide nanoparticles. Extreme dependence of speed of corrosion of aluminum

composites in 10-% solutions of sulfuric and nitric acid from the maintenance of nanoadditives is shown. It has been

shown the dynamics of mass loss of aluminum composites with nanoparticles of ZrO2 during corrosion tests in acids

solutions. The lowest corrosion rate of 3.36 mm/a of nitric acid was observed in the sample containing ZrO2 0.01 vol.%

nanoparticles. For the case of sulfuric acid with the best result of 2.21 mm/a showed the material with 0.05 vol.% nano-

additive.

Introduction. Nanotechnologies allow to create the strong and lightweight materials steady against

various aggressive influences. Influence of nanoparticles on structure of material is caused by high

superficial energy. There is a huge number of the works devoted to creation of composite materials,

both with metal, and with a ceramic matrix, the nanoparticles strengthened by various concentration

[1-7]. The light and strong materials, like aluminum alloys, for creation of various bearing designs

of spacecraft have high value For astronautics [8-11]. In many works, the researchers conducted the

development of aluminum composites containing nanoparticles of different nature in concentrations

of more than 5 vol.%. It is rarely possible to find work devoted to low concentrations of nano-

additives in aluminum [12-18]. This work is dedicated to the creation of aluminum composites with

small amounts (0.01-0.15 %vol.) of nano-oxide ZrO2 by powder metallurgy techniques.

Attention to small concentrations of the nanoparticles was based on the following provisions:

– high surface energy of nanoparticles;

– ease of uniform distribution of small amounts of nanoparticles and their disaggregation within the

matrix;

– high impact of nanoparticles on the structure and properties of interfacial layers (matrix-MFS-

nanoparticle).

The theory of irreversible processes and catastrophe theory say that small changes of operating

parameters can jump the most important characteristics of the system [19,20]. Nanoparticles

possessing high superficial energy, brings it in material and to interphase layer, influencing




24

functional characteristics of composite in one direction or another. In this regard, a researcher

separate issue is the determination of threshold effects of nanoparticles on the material and the

search for the optimal technology of its receipt, depending on performance requirements.

The objective of the work was creation of aluminum composites, hardened with small additions of

metal oxide nanoparticles like ZrO2, and determination of its corrosion resistance in acids solutions.

According to ideas of a number of famous scientists on the structure and properties of an interphase

layer in solids nanoparticles having a high surface energy and making changes to structure of a

matrix, even at very small concentration at the level of 0.001-0,. about. % can cardinally change

characteristics of material [21-24]. In tab. 1 influence of nanoparticles on properties of materials is

briefly explained.

1. Experimental procedure. The charge used: as a matrix - aluminum powder with mean diameter

of 4 μm (ASD-4, "SUAL", Russia), as reinforcer - nanopowder of zirconia (dav = 50 nm, Ssp = 32

m2/g), Keldysh Research Center, Russia). The technology of preparation of composites consisted in

the following. At the beginning aluminum powder was sieved through a sieve with a cell of 14

microns, then mixed with alcohol in a ratio of 1:4. Then, placed in an ultrasonic bath while stirring

the mixture by rotary stirrer. Nanoparticles dispersed in ultrasound, after which the dispersion was

added to the stirred alumina powder in alcohol. Quantity of nanoadditives varied from 0.01 to 1.5

vol.% Mixing lasted for 20-40 min. Drying of suspensions took place on air at a temperature of 60 °

C within 24 hours. The resulting blend compressed into a cylindrical mold with a pressure of 400

MPa. Next, sintering was performed in forevacuum at 640 ° C during 120-180 minutes.

The corrosion resistance was measured as follows. The total exposure time of samples was 15

hours. Samples were weighed prior to the experiment and during the measurements on scales up to

4-th sign. Samples were immersed in 10% solution acid (nitric acid or sulfuric acid). The difference

in mass (primary - to experiment and obtained by checkweighing) was determined by mass loss of

samples and plotted on it. At each check weighing and date recorded.

By results of tests of samples of aluminum composites for corrosion resistance values of speed of

corrosion (γ) on a formula were calculated [25]:

1000

24365

x, mm/a,

where x1 – mass loss rate, g/(m2∙h);

ρ – density of material, g/cm3.

2. Results and discussions. The results are shown in Fig. 1-4. Particularly interesting is the results

on corrosion resistance in a solution of nitric acid. The lowest rate of mass loss of 3.36 mm/a was

observed in the sample containing nanoparticles of ZrO2 0.01 vol.% . For the case of sulfuric acid

with the best result of 2.21 mm/a showed the material with 0.05 vol.% of the nano-additive.

The worst level of resistance in H2SO4 showed a sample with 0.15 vol.% of nanoparticles. Perhaps

this is due to the number and size of the brought defects (cavities) by mixing aluminum powder

with nano-additives . Nevertheless, it should be noted that all of the samples in comparison with

pure aluminum sintered showed considerably greater resistance to corrosion in both acid solutions.

While first (pure aluminum) at all dissolved in nitric acid after 15 hours and in sulfuric through 10.



25

Fig. 1. The dependence of the aluminum composites corrosion rate of the content nanoparticles

ZrO2 (test in a 10-% nitric acid solution).

Fig. 2. Composites mass loss over time in a solution of nitric acid.

Summary. Samples of aluminum composites with ZrO2 nanoparticles were examined for corrosion

resistance in 10-% solutions of nitric acid and sulfuric acid. The lowest corrosion rate of 3.36 mm/a

of nitric acid was observed in the sample containing ZrO2 0.01 vol.% nanoparticles. For the case of

sulfuric acid with the best result of 2.21 mm/a showed the material with 0.05 vol.% nano-additive.

Acknowledgements. Authors thank collectives NITU "MISIS" and Keldysh Research Center for

the help in development of aluminum composites.



26

Fig. 3. The dependence of the aluminum composites corrosion rate of the content nanoparticles

ZrO2 (test in a 10-% sulfuric acid solution)

Fig. 4. Composites mass loss over time in a solution of sulfuric acid.

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kompozicionnyh materialov i konstrukcij, 2004, t. 10, №3, s. 596-612.- Samples IF, Lurie SA,

Belov PA et al. Basic theory of the interfacial layer. Mechanics of Composite Materials and

Structures, 2004, v. 10, №3, p. 596-612. [In Russian]

[22] Tajra S., Otani R. Teorija vysokotemperaturnoj prochnosti materialov. –M.: Metallurgija,

1986. -280 s.- Taira S., R. Otani theory of high-strength materials. -M .: Metallurgy, 1986. -280 p.

[In Russian]

[23] Chuvil'deev V.N. Neravnovesnye granicy zjoren v metallah. Teorija i prilozhenija. –M.:

FIZMATLIT, 2004. -304 s.- Chuvildeev VN Non-equilibrium grain boundaries in metals. Theory

and Applications. -M .: FIZMATLIT, 2004. -304 p. [In Russian]

[24] Ohji T., Jeong Y.-K., Choa Y.-H., Niihara K. Strengtheing and toughening mechanisms of

ceramic nanocomposites .// Journal of American Ceramic Society. - 1998. - №81. - P. 1453-1460.

[25] Handbook of Corrosion Data / Ed. by B.D.Craig, D.S.Anderson. – Ohio: ASM International,

998 p.



29

II. Mechanical Engineering & Physics

Performance Optimization of a Gas Turbine Power Plant Based on Energy and

Exergy Analysis

Ghamami M.1, a

, Fayazi Barjin A.1, Behbahani S.

1

1 – Department of Mechanical Engineering, Isfahan University Technology, Isfahan, Iran


Keywords: Gas turbine, Exergy, Multi-objective, optimization, Fireflies algorithm, thermoflow.

ABSTRACT. The purpose of this study is energetic and exergetic analysis of combined cycle power plant, study of the

variables that affect the efficiency and performance and provide a solution to improve the efficiency and performance of

the gas turbine. Therefore, after modeling gas cycle, the impact of environmental conditions and performance of gas

turbine cycle will be checked, eventually we achieve two objective optimization of gas cycle that optimized by firefly

algorithm in six cold months of the year. The objective functions are exergy efficiency and cost of the gas cycle

maintenance, fuel cost and destroyed exergy cost. The proposed optimized result show increase in net output power of

the gas cycle, energy and exergy efficiency and decrease in air pollution amount.

Introduction. Gas turbine is one of the power generating machines that have been widely used in

various industries such as power plants, refineries and oil and gas industries. Since a high

percentage of the power requirements of the country, is provided in the gas power plants and due to

the fact that fossil fuels are the energy requirements of these power plants, thus the performance

improvement of these power plants is very important. From about 70 years before gas turbines have

been used to generate electricity, in the last twenty years the production of these type of turbines

has increased by twenty times. Thermodynamic Simulator of gas cycle and combined cycle, is a

useful tool to predict the behavior of each components of the cycle, by which the basic parameters

of the processes in the cycle can be obtained. Exergy analysis is a good way to evaluate the quality

of the energy with the aid of laws of conservation of mass and the first law of thermodynamics, and

is on the basis of the second law of thermodynamics. The tool is used for design, analysis and

optimization of thermal systems. The main objective of exergy analysis, finding solutions to

eliminate or reduce thermodynamic defects in the processes. We can reduced exergy destruction by

identifying the irreversibility factors and situation. Many studies have been done in this field,

research done in this field can be mentioned the following:

Siddiqui et al. [1] In their article they simulated a 100 MW gas cycle of one of the power plants in

Iran is hot and dry regions ,by thermoflow software ,and investigated the effect of steam injection

into the combustion chamber based on the exergy concept in order to improving gas turbine cycle.

Sadeghi et al. [2] they studied and simulated the effects of light and heavy fuel on operational

parameters of the gas turbine and combined cycle in Kazeroon power plant.

Kim and Hwang [3] examined the performance of a gas turbine with recovery in half-load situation,

by considering and comparing different mechanisms to control the turbine. Salary et al. [4] have

studied exergy analysis of 112 MW Power Plant in Ahvaz Zergan. They optimized the cycle by




30

increasing the turbine inlet temperature in terms of energy and exergy. Abdul Khaliq [5], used

exergy method to analyze gas turbine cycle with inlet air cooling and has shown that most exergy

destruction occurs in the combustion chamber, he also showed that by use of cooling the

compressor inlet air, energy efficiency and the cycle Exergy will be increased. Ehyaei et al. [6] at

the same time studied exergic, economic and enviromental analysis affected by Fog cooling system

in the gas cycle of Rajayee power plant. Sanaye and Jafari [7] work in optimizing field, they have

examined effect of inlet air cooling in gas turbine cycle by absorption refrigeration. The two-

objective optimization of the system is done by the genetic algorithm. kaviri et al. [8] have done

thermodynamic modeling and two-objective optimization of a combined cycle power plant. Ahmadi

[9] study on thermodynamic analysis of a gas cycle power plant and obtained best design

parameters by using multi-objective optimization.

In this study, energetic and exergetic analysis of gas turbine power plants have done and solutions

to improve efficiency and performance of gas turbine are suggested. Factors affecting the efficiency

of power plants have been studied and finally variables to improve the efficiency of power plants

have been selected.

Exergy (or ability to perform work). The maximum work that a system may do during a

reversible process from initial state to reach a dead end is called exergy. Exergy of a system in a

given state depends on environmental conditions and system properties, and for a control volume,

it’s equal to or reversible work with a dead end. Exergy has potential, physical and chemical

components. For the steady flow devices, kinetic and potential exergy can be assumed to be zero.

The sum of physical and chemical exergy, is called thermal exergy [10].

Ph Chex ex ex (1)

Physical exergy is defined by Equation 2.

( ) ( )Ph o o oex h h T s s

(2)

Chemical exergy of mixtures is obtained from equation (3) [11].

∑ ( ) ∑

( )

, (3)

(4)

Exergy analysis by using of the first and second laws of thermodynamics on the components of a

system, makes it possible to identify the place and production of irreversibility and unfavorable

thermodynamic process of the system, In this way, in addition to evaluate the different components

of thermodynamic cycle, approaches to increase efficiency and output are identified [13].

Efficiency of Thermodynamic Second Law (Exergic efficiency). The first law efficiency is

defined by an ideal isentropic process that never happens in practice. It makes no mention of the

best case, and isn't sufficient to measure the actual system performance alone. To assess the

deviation from the best possible processes, second law efficiency is defined. The second law

efficiency determines how much work ability or potential used in a process [11]. In fact, it

determines how much of exergy given to the system, by a process is achieved and how much of it is

wasted in the form of irreversibility. The second law efficiency is defined the ratio of useful exergy



31

to exergy input and output intensity of irreversibility is defined as (5) the difference between output

exergy and input exergy [13].

(5)

(6)

Thermodynamic Modeling of gas cycle and power plant. Thermodynamic modeling of gas cycle

power plant have been done by using thermodynamic relations. Plant that studied in this paper,

included 4 gas unit manufactured by Mitsubishi Japan MW-701D models with nominal capacity of

each is 128.5 MW and in total 514 megawatts. By installation of 4 retriever boilers and two steam

turbo generator that each has nominal capacity of 100 MW, power plant Transformed to combined

cycle power plant. In order to simulate the combined cycle power plant, we set the data related to

environmental conditions (Table 1).

Table 1. Environmental condition in power plant

Value Environmental condition

31 centigrade Temperature

0.8964 bar Pressure

RH=29% Relative humidity

1022 meter Above sea level

Thermoflow software is one of the most powerful software in design and analysis of power plant

cycles, which is capable to model various stages of the power plant, including thermodynamic

analysis, engineering design and simulating equipment. Combined cycle block consists of two gas

turbines, two recovery boilers and a steam turbine. By choosing Siemens W701 D engine which is

available in the software engines, combined cycle block is simulated in normal loads and in

software. Table 2 shows the software output.

Table 2. Power plant output in normal times (90%)

Gas oil Natural gas Type of gaseous fuel cycle

520844 526576 Net power output of the plant

(kW)

7948 7894 Plant heat rate (kJ/kWh)

45.3 45.6 Plant thermal efficiency (%)

In order to verify the results of the software simulation, the values obtained from the simulation and

actual data are compared in Table 3.

Figure 3 shows the flow of incoming and outgoing energy to one block in combined cycle of power

plant, also, it shows where the input fuel energy is intended in terms of heat value of fuel. Input

energy consists of latent and sensible energy of air and chemical energy of fuel. Most thermal losses

is related to the condenser, because discharges the heat taken from the cooling water to the

environment. After condenser most heat losses is related to the exhaust flue gas that is at about 118

Celsius degrees, which enters too much heat into the environment without using them.



32

Fig. 1. Operating parameters plant in case of 90% load

Fig. 2. Performance and placement components of HRSG plant in case of 90% load

In tables 3, net output power is expressed in kilowatts (kW) scale and heat rate is expressed in kJ /

kWh scale. The rate is expressed on a scale of kilograms per second (kg/s). By comparing the study

results provided by the simulation and power plant results it can be seen that there is a good

adaption between the results. In six cold months (October to the end of April), due to a dramatic

reduction in household electricity consumption compared with six warm months of the years, the

demand for electricity from power plants in the country declined. The main priority in the six cold

months, is increase in exergy efficiency of gas cycle and reduce the annual cost.



33

Fig. 3. Diagram of Energy flow (input and output plant power)

Table 3. Data comparing of power plant in case of 90% load

Error )%( Power

plant

Software

simulation Parameter

+1.08

526576 532250 Net power output

-0.14 7894 7883 Heat Rate

+0.15 45.6 45.67 Thermal efficiency (%)

+0.11 6.35 6.361 Fuel flow

0.11 338 339.1 Air flow

0.57 12.2 12.27 The compressor pressure ratio

0.8 11.2 11.29 Turbine pressure ratio

0.21 1385 1387.9 Turbine inlet gas temperature (K)

With the increase in air temperature, the gas turbine and the compressor's power reduces, due to the

more steep decline of power in gas turbine compared with the compressor, the net output power of

the gas cycle is reduced. With the increase in air temperature, mass flow of gas turbine exhaust

gases reduces, less steam is produced in the recovery boiler and there will be a total loss in power of

steam turbine. By reducing the power of steam-gas cycle, the net output of power plant appear with

declined more sharply. For one degree Celsius rise in ambient air temperature, pure output power of

the gas cycle, steam turbine and power plant will averagely reduce 0.63 and 0.27 and 0.53,

respectively. Comparison between output powers with respect to temperature is shown in Figure 4.



34

Fig. 4. Special compressor pressure ratio and can shift with ambient temperature

Optimization. After reviewing the parameters affecting the performance of plants, defining

optimization problem based on target functions and parameters can be done. Optimization problem

in finding answers or solutions on a set of possible options aimed at improving the standard or

standards of the issue. Multi-objective optimization problem arise from the decision-making

methods in the real world that one decision maker faces a set of contradictory and conflicting

objectives and criteria. In these types of issues, unlike the single-objective optimization problems

and because of the multi-purpose (often conflicting), rather than just a solution optimized set of

questions arises.

In the multi-objective optimization, after the introduction of design variables and determine the

objective functions, optimal points are determined and the impact of design on objective functions

are provided. Many factors affect the performance of gas turbine, therefore, gas turbine cycle has

many ways to improve the performance of the industry. Each of these methods has different effects

on output power, efficiency and specific consumption of fuel. The selection of a particular method

according to plant type, climatic conditions, work area, how it affects the performance of the project

cycle, and measures will be considered. Some of the most important factors affecting the operation

of the gas turbine are:

• Pressure ratio

• Compressor inlet temperature

• Compressor efficiency

• The compressor intake

• Turbine inlet temperature

• Turbine efficiency

• Output power of turbine

• Fuel air ratio

• Mass flow rate

As can be seen in Figure 5, with increasing ambient air temperature, compressor pressure ratio

reduces. As well as the temperature increases, air density decreases, resulting in a greater volume of

air should be particularly dense, and the special power of compressor will increase.

315

320

325

330

335

340

345

350

355

360

365

5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40

Ma

ss f

low

ra

te o

f a

ir e

nte

rin

g

the

com

pre

sso

r [k

g/s

]

Environment temperature [C]



35

Fig. 5. Change in net output power cycle gas and steam turbine power plants with ambient

temperature

For one degree Celsius increase in temperature, compressor pressure ratio and special averaged

power increases 0.24 percent and 0.25 percent respectively. Gas turbine is power generation system

at constant volume. By increasing the ambient air temperature and constant air pressure in a fixed

volume, density and mass flow rate of air flow is reduced, resulting in reduced compressor inlet

mass. Figure 6 shows the compressor inlet air mass flow changes to show the changes in ambient

temperature. For one degree Celsius rise in temperature, compressor inlet air flow is reduced by an

average of 0.24 per cent.

Fig. 6. Chart compressor inlet air mass flow changes with temperature

With the increase in air temperature, gas turbine inlet gas temperature increases due to the reduced

amount of fuel and increase in air to fuel ratio. With increasing temperature due to increased

temperature of the exhaust gases from the gas turbine inlet air temperature for cooling turbine

blades increases. For one degree Celsius rise in temperature ambient air, intake and exhaust gas

330

335

340

345

350

355

360

365

370

375

380

11,4

11,6

11,8

12

12,2

12,4

12,6

12,8

13

13,2

5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40

Sp

ecia

l p

ow

er c

om

pre

sso

rs

[kW

/ k

g /

s]

Co

mp

ress

or

pre

ssu

re r

ati

o


Pressure ratio Special power

530

532

534

536

538

540

542

544

546

548

550

1110

1111

1112

1113

1114

1115

1116

1117

1118

1119

5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40 Exh

au

st t

urb

ine

gas

tem

per

atu

re [

C]

Tu

rbin

e in

let

gas

tem

per

atu

re [

C]


TIT TET



36

temperature of the turbine by an average of 0.4 degrees Celsius, respectively 0.17 ° C decrease and

increase. Figure 7 shows the change in gas turbine inlet and outlet gas temperature than the ambient

temperature shows.

Fig. 7. Gas turbine exhaust gas temperature changes graph input and ambient temperature

Differences between the energy and exergy system can be expressed as follows [12].

1. Energy just relates to the system condition and the mass flow but exergy in addition to those

conditions is dependent on environmental conditions.

2. The amount of energy in the dead system may also have an amount, but the exergy in a dead

system is always zero.

3. Energy for all the processes are subject to the law of survival, and is stated in the form of the first

law of thermodynamics but exergy is subject to survival only in reversible processes. In irreversible

processes, always exergy a destroyed. Exergy, applies a combination of the first and second laws of

thermodynamics to the review process.

4. Energy is only a quantitative measure for evaluating processes but exergy is both quantitative and

qualitative measure.

5. Energy can be calculated with respect to each case assumptions but exergy basis mode is

determined by environmental conditions.

After reading the parameters and variables on power plant performance optimization, optimization

process takes place. Because of the simultaneous search of multiple points, no need for an explicit

mathematical relationship between objective functions, the need for direct measurement and

mathematical calculations needed to optimize the methods of analysis and generalization of random

search algorithms, optimization of problem is done by random search algorithms.

The objective function. To compare the achieved considerable optimization problems we need to

have a selection criterion. Such a measure, which plan is optimized and is a function of design

variables, standard function, is called advantage function or objective function. In this study, the

objective functions, exergy efficiency and costs related to gas cycle, and the optimal points

represent the highest efficiency and lowest costs. Relation 6 and 7 show the first and second

objective function, respectively.

75

78

81

84

87

90

93

96

99

102

105

108

111

240

250

260

270

280

290

300

310

5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40

Net

po

wer

ou

tpu

t (G

T-S

T)

MW

Net

po

wer

ou

tpu

t (P

lan

t)

MW


Plant Net Power GT GrossPower ST Gross Power



37

OF1:Max

(7)

OF2: Min (8)

( ) (9)

(10)

Net Output power of the gas cycle can be obtained as above.

Decision variables. Thermodynamic modeling inputs are decision variables and numbers represent

degrees of freedom of the system. Decision variables change during the optimization process, but

the parameters are fixed, but some parameters, are dependent parameters which is determined on

the amount of basis of the decision variables. The variables which are specified in Table 4, are

selected as the decision variables. In order to stay in the recovery boiler circuit, the gas turbine load

is considered higher than 55%. Using thermoflow and EES software and range change in

environmental conditions, according to the decision of the six variables in Table 1 and also taking

into account the load percentage of the gas turbine in the range of 55 to 100% has been obtained.

Firefly algorithm. Firefly optimization algorithm or FA for short is inspired of the natural behavior

of fireflies which live together in large collections, and was introduced for the first time in late 2008

by Xin-She Yang [14], this multi-agent algorithms can be a solution of hard optimization problem

and it is a very efficient algorithm for solving combinatorial optimization problems.

In summary, the performance of the algorithm is that the number of artificial fireflies (initial

population) are randomly distributed in the range and then emits light of a firefly which intensity is

proportional to the amount of optimality point Firefly is that it is located. The light intensity of each

firefly regularly intensity compared to other fireflies and fireflies brighter too faint to be absorbed.

At the same time the brightest fireflies also aims to increase the chances of finding the optimal

solution is the global accidentally move. In this algorithm, exchange information with each other

through the light emission occurs. The composition of this combined action makes the overall trend

towards a more efficient is fireflies.

Table 4. Optimization variables and their ranges

Variable Variable interval

Compressor pressure ratio

Isentropic efficiency turbine

Isentropic efficiency compressor

Compressor inlet mass flow rate (kg/s)

The output of the gas turbine

combustion pressure (bar)

( ) Gas turbine inlet temperature (K)

Optimization Results. Given the equations required optimization objective functions according to

the decision made and the six variables in MATLAB fireflies algorithm code was used to optimize



38

the objective function. The primary population for the first generation is considered 200. In the

multi-objective optimization instead of an optimal point, we have an optimal solution that is

optimized to the famous pareto point and the set of these points are called pareto front. Figure 8

shows the pareto front of the optimization objective functions, including optimal points. As can be

seen by increasing the efficiency of the gas cycle exergy, it also increases annual costs.

Fig. 8. Pareto Front of the first objective functions (cost) for six months

Selection the desired optimization of energy systems based on multi-objective optimization

decision-making ideas happen after the search. Each individual decision-maker may be due to

considerations in mind, their own scenario is to select the optimal point. Pareto front of the

optimization objective function shows that the costs for the six months is considered. The results,

show minimal costs during the year should be paid for a certain exergy efficiency, and most exergy

efficiency that can be achieved for a certain fee during the year. Figure 9 shows the net profit for the

six months according to exergy efficiency. Net profit, the difference between the proceeds from the

sale of electricity and the cost of the cycle ( TotC ) is obtained. The price of electricity purchased from

power plants 0.15 Dollar/kWh is considered [13]. Pareto front of net profit of the previous stage

results are plotted in Figure 9.

In Figure 10, the net profit in the six months according to exergy efficiency has been showed in gas

cycle power plant. The price of electricity purchased from power plants is intended 0.3 Dollar/kWh.

Table 5 Three optimal point A, B and C compared with each other. Given the priority of each

objective function optimal point can be selected.

In table 5, net output power and destroyed exergy are in megawatts scale (MW) and amounted net

profit is expressed in millions of dollars scale for both 0.15 and 0.3 dollar per Kilowatt hours

(dollar/kWh) of generated electricity.

Summary. The main goal of this study was to evaluate and improve the performance of gas cycle

power plant in different environmental conditions. The analysis results show that the greatest

destruction exergy of gas cycle power plant is happening in the combustion chamber. That reason is

high temperature difference between the temperature of the flame and fluid. Much of this

destruction exergy is inevitable that cannot be reduced, so exergy efficiency of power plants has

been studied and other ways use to reduce the exergy destruction.

4

4,2

4,4

4,6

4,8

5

5,2

5,4

5,6

5,8

6

6,2

6,4

6,6

6,8

0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35

(Mil

lio

ns

of

do

lla

rs)

cost

s

Exergy efficiency (%)

A

B

C



39

Fig. 9. The change in net profit with electricity prices 0.15 Dollar/kWh

Fig. 10. The change in net profit with electricity prices 0.3 Dollar/kWh

Table 5. Comparison of the optimum

Point C Point B Point A

34.5 31.3 26.7 Exergy efficiency (%)

34.9 32.5 27.5 Efficiency (%)

114 90.7 68 Net output power

6.4 4.9 4.3 Price Six months (millions of dollars)

141 120 104 Exergy destroyed

0.9 0.9 0.05 Net profit price of electricity: 0.3

8.3 6.7 4.4 Net profit price of electricity: 0.15

0

0,2

0,4

0,6

0,8

1

1,2

0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35

(Mil

lio

ns

of

do

lla

rs)

net

pro

fit


A

B

C

3

4

5

6

7

8

9

10

0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35

(Mil

lion

s of

doll

ars

) n

et p

rofi

t


A

B

C



40

Firefly algorithm has been optimization algorithm in gas cycle power plant. Objective functions are

exergy efficiency and cost, cost include the gas cycle maintenance costs, fuel cost and the cost of

exergy demolition, highest efficiency exergy and lowest cost are requirements. The results show

that by increasing the efficiency of the gas cycle exergy, its cost also increased. Lower temperature

reduces emissions and steam quality in the recovery boiler and steam turbine power output is

reduced as a result. To remedy this problem, the use of gas turbine exhaust duct burner is

recommended. In this case, the temperature of the exhaust gas from the turbine should exceed the

temperature of HRSG design.

The study achievements can be cite to use of meta-heuristic algorithm in large search space, non-

linear variables and objective functions such as firefly algorithm. Because that limited studies have

been done for examine ability and capabilities of this algorithms, this study is an opportunity to

investigate the algorithm and its ability. Multi-objective optimization process has its own challenges

and advantages. In the multi-objective optimization not only efficiency but also exergy cycle costs,

including the cost of repair and maintenance, the cost of fuel and the cost of destruction exergy have

been studied. Time-consuming optimization process is very important. Less computational time and

iteration means less computational cost, by using of the optimal response of optimization algorithm,

the net power output of the gas cycle power plants by as much as 11.15 and 8.08 percent, energy

efficiency and exergy cycle gas 3.64 and 3.61 respectively percent and air emissions, 0.77 percent

decrease. This study also examines changes in environmental conditions and levels of load on the

gas cycle power plant, Technical and economic assessment, energy and exergy analysis using the

first and second law of thermodynamics can be mentioned. As well as alternative ways to reduce

destruction exergy and increase exergy efficiency are reviewed.

Thermoflow Software can calculate the pollutions of the turbine gas output. It is suggested that the

impact of changing load levels and the effect of cooling system of air entering to compressor will be

investigated in order to predict exhaust pollutions of gas turbines.

Reference

[1] Siddiqi H, Bayati Gh,Tvakoli A, Fotoohi D, "simulated cycle 100 MW gas and steam injection

into the combustion chamber 'exergetic analysis and energetic", conferences energy efficiency,

conferences Institute of Technology, Tehran, (2010).

[2] Sadeghi H, Haghighi khoshkhor V, Tanasan M, Moosavian M, "Simulation of the

thermodynamic effects of non-gaseous fuels on the performance and efficiency of combined cycle

power plant", the twenty-seventh International Conference on Electric Power Research Institute,

Inc. Tavanir, Tehran, (2012).

[3] Kim T, Hwang S.H, “Part load performance analysis of recuperated gas turbines considering

engine configuration and operation strategy”, J.of.Energy, 31, pp. 260-277, (2006),

doi: 10.1016/j.energy.2005.01.014

[4] Salari M, Hashemi Sh, Zayer noori M, "Exergy and Exergy Economic Analysis Zargan Gas

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[6] Ehyaei M. and Mozafari A. and Alibiglou M, “Exergy, economic & environmental (3E) analysis

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[7] Sanaye S, Jafari s, "Optimizing the objective cycle gas turbine inlet air cooling by absorption

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[8] Kaviri A. and Jaafar M. and Lazim th, “Modeling and multi-objective exergy based optimization

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2529-2540, (2011), doi:10.1016/j.applthermaleng.2011.04.018

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42

Certain Solutions Of Shock-Waves In Non-Ideal Gases

Kanti Pandey1, a

& Kiran Singh1

1 – Department of Mathematics & Astronomy, Lucknow University, Lucknow, 226007, India


Keywords: Shock waves, Non-ideal medium, AMS Classification

ABSTRACT. In present paper non similar solutions for plane, cylindrical and spherical unsteady flows of non-ideal gas

behind shock wave of arbitrary strength initiated by the instantaneous release of finite energy and propagating in a non-

ideal gas is investigated. Asymptotic analysis is applied to obtain a solution up to second order. Solution for numerical

calculation Runga-Kutta method of fourth order is applied and is concluded that for non-ideal case there is a decrease in

velocity, pressure and density for 0th and II-nd order in comparison to ideal gas but a increasing tendency in velocity,

pressure and density for Ist order in comparison to ideal gas. The energy of explosion J0 for ideal gas is greater in

comparison to non-ideal gas for plane, cylindrical and spherical waves.

1. Introduction. The assumption that the medium is an ideal gas is no more valid when the flow

takes place in extreme conditions. Anisimov & Spiner [1] studied a problem of point explosion in

low density non ideal gas by taking the equation of state in a simplified form which describes the

behaviour of medium satisfactorily. Robert’s & Wu [2] studied the gas that obeys a simplified

Vander Waal’s equation of state.

Vishwakarma et al. [3] have investigated the one dimensional unsteady self-similar flow behind a

strong shock, driven out by a cylindrical or spherical piston in a medium which is assumed to be

non-ideal and which obey the simplified Vander-Waal’s equation of state as considered by Robert’s

& Wu [2]. However, they have assumed that the piston is moving with time according to law given

by Steiner & Hirschler [4]. Madhumita & Sharma [5] have considered the model equation for a low

density gas, which describes the behavior of the medium satisfactorily for implosion problems

where the temperature for implosion problems were the temperature attained by the gas motion in

the strong shock limit is very high. Pandey & Pathak [6] have discussed growth and decay of sonic

waves in non-ideal gases. In present paper using asymptotic expansion an attempt is made to obtain

non-self similar solution of shock-waves in non-ideal gas. For numerical calculation Runge Kutta

method is applied .In preparation of graphs Origin 7.5 is used.

2. Basic Equations

The basic equations describing a cylindrically symmetric (α= 1) or a spherically symmetric (α = 2)

motion of a non-ideal gas can be written as:

( )0

u u

t r r

, (2.1)

10

u u pu

t r r

, (2.2)

( ) { ( )}0

r E r u E p

t r

, (2.3)




43

where ρ is the gas density, u is the fluid velocity, p is the pressure and

2

2

uE e

, (2.4)

is the total energy density with e being the internal energy density, the independent variables are the

space co-ordinate r and time t: The equation of state characterizing the non-ideal medium is taken to

be of the form

(1 )

RTp

b

,

where b is the internal volume of the gas molecules which is known in terms of the molecular

interaction potential in high temperature gases, it is a constant with b ρ << 1. The gas constant R

and the temperature T are assumed to obey the thermodynamic relations p VR C C and Ve C T ,

where ( 1)

V

RC

is the specific heat at constant volume and γ is the ratio of specific heats. Thus

in view of these thermodynamic relations, the equation of state can be written as

( 1)

(1 )

ep

b

. (2.5)

Expression for E, in view of equation (2.5) assumes the form

2(1 )

( 1) 2

p b uE

.

Using above value of E in equation (2.3), we have

0(1 )

p p p u uu

t r b r r

. (2.6)

Here α=0,1,2 corresponds to planar, cylindrical and spherical geometries respectively. The

assumption of the instantaneous release of constant energy 0E at time t = 0 yields the energy

balance equation:

20 0

0

00

(1 )1 (1 ){ }

2 ( 1)

Sp bu p b

E K r dr

,



44

where Kα= 2, 2π, 4 π for α= 0, 1, 2 and S represents the shock radius which is assumed to be zero at

t = 0.

From Lagrangian equation of continuity we have 1

00( 1)

SS

r dr

. Thus energy balance

equation transform into:

120 0

0

0

(1 )(1 )

2 ( 1) ( 1)( 1)

S K S p bu p bE K r dr

. (2.7)

The conservation relations across the shock for the present problem can be written as:

0 1 1( )U U u , (2.8)

2 2

0 0 1 1 1( )p U p U u , (2.9)

22

0 0 0 1 1 1 1

0 0 1 1

(1 ) (1 ) ( )

( 1) 2 ( 1) 2

p p b p p b U uU

, (2.10)

where subscripts 1 and 0 refer to values immediately behind and ahead of the shock respectively

and represents the shock velocity.

dSU

dt ,

In following section we introduce the dimension less variables.

3. Transformation of Fundamental Equations in Non-Dimensional Form

To transform fundamental equations, we consider principal of similarity & introduces new variables

x and y in place of r and t as defined by 7Sakurai

rx

S (3.1)

0

2

2y

U

, (3.2)

u=Uf(x ,y ), (3.3)

2

0

0(1 ) ( , )U

p b g x y

, (3.4)

0 ( , )h x y , (3.5)

where



45

2 0

0

0 0(1 )

p

b

, r Sx dr Sdx . (3.6)

Thus

1

r S x

, (3.7)

( )D U

f x yDt S x y

, (3.8)

where

dy

dSSy

(3.9)

and λ is a function of y alone.

Substituting equations (3.1) to (3.8) in to fundamental equations (2.1), (2.2), (2.6), (2.7) and

boundary conditions (2.8, 2.9, 2.10), equations (2.1), (2.2), (2.6) become

( )h h f f

f x y hx y x x

, (3.10)

0(1 )( )

2

bf f f gh f x y

x y x

, (3.11)

. (3.12)

Equation (2.7) now become

1 1 220 0 0 0

0

(1 )(1 ) (1 )

2 ( 1) ( 1)( 1)

S g b h b b yhfy x dx

S

, (3.13)

where

1

10

0 2

0 0

ES

K

. (3.14)

Equations (2.8), (2.9), (2.10) now become as

0

( )(1 )

g g g f fg f x y

x y b h x x



46

0 0

1(1, )

1 2 2 (1 )h y

b y b

, (3.15)

(1, ) 1(1, )

(1, )

h yf y

h y

, (3.16)

0

0

(1 )(1, ) (1, )

(1 )

b yg y f y

b

. (3.17)

Differentiating equation (3.11) with respect to y and using expression,

1 20 0

0

(1 )(1 )

2 ( 1)

g b h bhfx dx J

, (3.18)

defined in equation (3.9) is given by

2

0(1 )( 1)

( 1)

b yJ

dJJ y

dy

. (3.19)

4. Construction of Solution in Power series of y. While the shock waves are strong, the velocity

U is large and y can be considered as small there, so that the quantities f; g; h can be expanded in

rapidly convergent series of powers of y in following manner:

(0) (1) 2 (2) ...........f f yf y f (4.1)

(0) (1) 2 (2) ...........g g yg y g (4.2)

(0) (1) 2 (2) ..........h h yh y h (4.3)

where ( ) ( ) ( ), , i i if g h , (i = 0,1, 2,………) are all functions of x only . Inserting equations (4.1, 4.2,

4.3) in the expression (3.18), we have

0 1 21 .....J J y y , (4.4)

where



47

2(0)1 (0) (0) (0)(0)

0 0 0

0

0

(1 ) (1 )

2 ( 1) ( 1)

b g b b h gh fJ x dx

, (4.5)

1 (1) (0) (1) (1) (0)(1) (0)(0) (0) (1) 0 0 0 0 0

1 0

0

(1 ) (1 ) (1 )

2 ( 1) ( 1) ( 1)

g b b h g b b h g bh fJ h f f x dx

(4.6)

2 2

10(0) (0) (2) (0) (1) (0) (1) (1) (0) (2) (2) (0) (2) (1) (1) (0) (2)

2 0 0 0 0

0

(1 )1[ 2 2 ]2 ( 1)

bJ h f f h f f f h f h g b h g b g h b g h x dx

(4.7)

Using equation (4.4),the equation (3.13)becomes

1 2

20 0

0 1 2

0

(1 )1 ...

( 1)( 1)

S by J y y

S J

, (4.8)

Or in view of (3.1)

2 1 2 42

0 0 0 0 0

0 1 2

0

(1 )1 .....

( 1)( 1)

S bJ

U S J U U

. (4.9)

Equation (4.9) is in form of power series in

2

0

U

, which gives a relation between propagation

velocity U and the position of shock front S. If 0 and iJ are known can be expanded in

following form

2

20

1 2

0

(1 )( 1) 1 2 ....

( 1)( 1)

by y

J

. (4.10)

If we use, for simplicity , the expressions

2

0

1 1

0

(1 )

( 1)( 1)

b

J

, (4.11)

2 22 . (4.12)

Equation(4.10)can be written as

2

1 2( 1)(1 .....)y y . (4.13)



48

Now, substituting equations (4.1, 4.2. 4.3) and (4.13) in equation (3.10, 3.11, 3.12) and Comparing

the Coefficients of the same powers of y on both sides of (3.10), ( 3.11), (3.12) we get the following

system in equations:

For zero-th power of y (Ist Approximation)

(0) (0)

(0) (0) (0) (0)0(1 ) ( 1)( )

2

bf gh f x f h

x x

, (4.14)

(0) (0)

(0) (0) (0) (0)( )f h

h f x f hx x x

, (4.15)

(0) (0)

(0) (0) (0) (0) (0) (0) (0) (0)

0 0( ) (1 ) ( 1) ( 1)f g

g f x b h b g h g f gx x x

, (4.16)

For the first power of y (IInd

Approximation)

(1) (1) (0)(0)

(0) (0) (0) (1) (0) (0) (1) (0) (0)0

1

(1 ) ( 1) ( 1) ( 1)( ) ( )

2 2 2

bf g f ff x h h f f f x h f h

x x x x

, (4.17)

(1) (1) (0) (0)(0) (0)(0) (0) (1) (1)( ) ( 1)

f h h h f fh f x f h

x x x x x x

, (4.18)

(1) (0) (1) (0) (0)(0) (1) (0) (1)(0) (0) (1) (0) (1) (0) (1) (0) (1)

1 0 0(0)

0

1( 1) ( ) ( ) ( 1)

(1 )

g g f f g f f g gg f x f g g f x b h b g h

x x x x x x xb h

2

(2) (1) (0) (2) (1) (0) (0) (0) (1)

(0) (0) (0) (1) (0) (2) (0) (1) (0) (1) (1) (2) (0) ( 2) (1)

(2)2( 1)

f f f f f f f f fh f h f h f h x h f h f h f h x h x

x x x x x x x x x

f

(2)

(0) (1) (0) (1) (1) (0) (2) (1) (1) (2) (0) 0

1

(1 )( 1) ( 1) ( 1)( 1) ( 1)

2 2 2

b gh f h f h h f h f h f

x

(4.19)

For the second power of y (IIIrd

Approximation)

2

(2) (1) (0) (2) (1) (0)

(0) (0) (0) (1) (0) (2) (0) (1) (0) (1) (1)

(0)

(2) (2) (0) (1) (0) (1) (1)

1

( 1)2( 1) ( 1) ( 1)

2

f f f f f fh f h f h f h x h f h f

x x x x x x

fh x f h f h f h

x

(2) (0) (1) (1)

(2)

(0) (2) 0

( 1)

2

(1 )( 1)

2

f h f h

b gf h

x

, (4.20)

(2) (1) (0) (2) (2)

(0) (1) (2) (2) (1) (0)

1

(1) (0) (0) (2) (1) (1) (2) (0)(1) (2)

2( 1) ( 1)

2

h h h h ff f f x h h h

x x x x x

f f h f h f h fh h

x x x x

, (4.21)



49

(0) (1) (0) (0) (2)

(0) (2) (0) (1) (1) (1) (2) (0)

0 0 0 0

(2)

2 (2) (1) (1) (1) (0) (1) (1)

0 0 0 1 0( 1) ( 1) ( 1) ( 1) 2(

g g g g gb f h b f h b f h b xh f

x x x x x

gx b h b h g b h g b h g

x

(2)

(2) (1) (0)

(1) (0) (1) (2)

1

1)

( 1)

g

f f fg g g g

x x x

(4.22)

In similar manner substituting equations (4.1, 4.2, 4.3) into equations (3.15, 3.16, 3.17), we have

(0) (0) (0)0

0

2(1 ) 2 1(1) , g (1) , h (1)

1 1 1 2

bf

b

, (4.23)

(1) (1) (1)0 0

2

0

2(1 ) 2( 1)(1 )1(1) , g (1) , h (1)

1 1 ( 1 2 )

b bf

b

, (4.24)

2

(2) (2) (2) 0

3

0

4( 1)(1 )(1) 0, g (1) 0 , h (1)

( 1 2 )

bf

b

, (4.25)

If we take b=0, equations (4.14 – 4.16) with condition (4.23) coincides with the results obtained by

Sakurai [7].

Fig. 1. Variation of velocity for zeroth order solution (plane wave)



50

Fig. 2. Variation of velocity for zeroth order solution (cylindrical case)

Fig. 3. Variation of velocity for zeroth order (Spherical case)



51

Fig. 4. Variation of pressure for zeroth order solution (plane case)

Fig. 5. Variation of pressure for zeroth order solution (cylindrical case)



52

Fig. 6. Variation of pressure for zeroth order (spherical case)

Fig. 7. Variation of density for zeroth order



53

Fig. 8. Variation of velocity for the first order solution

Fig. 9. Variation of pressure for the first order solution



54

Fig. 10. Variation of density for the first order solution

Fig. 11. Variation of velocity for the second order solution

5. Result and Conclusion

1. For constant solutions, velocity, pressure and density varies linearly and for non-ideal case there

is a decrease in comparison to ideal gas.



55

Fig. 12. Variation of pressure for the second order solution

Fig. 13. Variation of density for the second order solution

2. For first order solution velocity, pressure density all varies linearly, but as value of m (= bρ0)

increases they are increasing in comparison to ideal gas.

3. For second order solution variation of velocity is linear. In plane case it is same for ideal as well

as non-ideal case but as m increases there is a slight decrease for cylindrical and spherical case.



56

4. The energy of explosion J0 for ideal gas is greater in comparison to non ideal gas for plane,

cylindrical and spherical wave.

Fig. 14. Variation of energy of explosion

References

[1] S. I. Anisimov and O. M. Spiner, Motion of an almost ideal gas in the presence of a strong point

explosion, J. Applied Maths, Vol.36(No.5) (1972), pp.883-887.

[2] P. H. Robert and C.C. Wu, Shock wave propagation in a sonolu-minescing gas bubble, The

American physical Society, Vol. 70 (No. 22) (1933), pp.3424-3427.

[3] J. P. Vishwakarma, Self-similar solution of a shock propagation in a non ideal gas. Int. J. of

Applied Mech and Engineering, Vol. 12 (No.3) (2007), pp.813-829.

[4] H. Steiner and T. Hirschler, A self similar solution of a shock propagation in a dusty gas, Eur. J.

Mech. B/Fluids, Vol. 21 (No.3) (2002), pp.371-380.

[5] Madhumita and Sharma, Imploding cylindrical and spherical shock waves in a non-ideal

medium, Journ. of Hyperbolic dif. eq., Vol. 1(No.3) (2004), pp.521-530.

[6] K. Pandey and P. P. Pathak, Growth and Decay of sonic waves in non-ideal gases

(Communicated for publication).

[7] A. Sakurai, On the propagation and structure of the Blast wave I, Journal of the Physical Society

of Japan, Vol. 8 (No.5) (1953), pp.662-669.



57

Analytical Modeling of Transient Process In Terms of One-Dimensional

Problem of Dynamics With Kinematic Action

V.Kravets1a

, K.Bas1, T.Kravets

2 & L. Tokar

1

1 – State Higher Educational Institution “National Mining University”, Dnipropetrovsk, Ukraine

2 – Dnipropetrovsk National University of Railway Transport, Dnipropetrovsk, Ukraine


Keywords: material system, kinematics action, mathematical model, analytical solution, characteristic equation,

dynamic design

ABSTRACT. One-dimensional dynamic design of a component characterized by inertia coefficient, elastic coefficient,

and coefficient of energy dispersion. The component is affected by external action in the form of time-independent

initial kinematic disturbances and varying ones. Mathematical model of component dynamics as well as a new form of

analytical representation of transient in terms of one-dimensional problem of kinematic effect is provided. Dynamic

design of a component is being carried out according to a theory of modal control.

Introduction. Analytical modeling is the essential stage of technical system dynamic design

followed by computational and full-scale experiment [0, 0]. Analytical modeling of dynamic

systems is based upon traditional mathematical methods of solutions of differential equation

systems [0], theory of modal control [0], root-locus technique [0], and root-locus method [0].

Free motion dynamics of one-dimensional mechanical system experiences analytical study in a

work by Kravets [0]; forced motion dynamics in terms of external dynamic effect was considered in

a work by Kravets [0]. The paper models forced motion dynamics in terms of external kinematic

effect.

Formulation of the problem. Fig.1 demonstrates dynamic scheme of one-dimensional mechanical

system.

Fig. 1. Dynamic scheme of kinematic effect problem

Here М and m are interacting masses, с is coefficient of elasticity, µ is damping coefficient.

It is assumed that M>>m. m mass is finite and specified. ( ) motion of m mass cannot effect a(t)

motion of М mass. Notion of М mass is supposed as specified function of ( ) time. For example:

( ) = V0t where V0 is М mass velocity.




58

It is required to develop ( ) analytical solution modeling stable transient and determining steady

motion of m mass depending upon such running design parameters of mechanical system as µ and

c.

Mathematical model. Continuous dynamic model with single degree of freedom is described with

the help of following matrix differential equation:

‖ ‖ ‖

‖ ‖

‖ ‖ ( )

( )‖ (1)

where ( ) ; ( ).

For mechanical system under consideration, the equation coefficients are determined as follows:

= -

, = -

, (2)

= 1, = 0 .

Power function for kinematic effect is identified in the form of:

( )

( )

( ) (3)

f2(t) = 0 .

Analytical solution. Following normalized form for analytical solution x(t) determining motion of

mass m is as follows:

( ) =

| | +

∑

( )

( )

∑

( )

( ) (4)

| |

∑

( )

( )

∑

( )

( ).

Here analytical solution is represented in the form of dependence on the roots of characteristic

equation: ; specified initial disturbances ; specified external power effect within the

initial time period f(0) and current one f(t).

Analytical modeling. If external kinematic effect is specified as: ( ) then considering

( ) that both function and its derivatives are:

f(t) =

V0 +

V0t , f(0) =

V0 , (5)

(t) =

V0 , (0) =

V0 ,

(t) = 0 , ( ).

Hence:

∑

( )

( ) ; ∑

( )

( ) ; (6)



59

∑

( )

( ) ( ); ∑

( )

( ) ( ).

Substituting the results into general formula and performing simple transformations we obtain

laconic analytical representation of transient:

( ) =

+

(V0 – ) + V0t . (7)

In case of complex roots of characteristic equation: 1,2 = α ±iβ transient is modeled by means of

following function:

( ) = [|

|

] –

t . (8)

According to the given different forms of transient records, following particular cases of root

distribution are being modeled:

1. , = 0;

2. = , 3. =±iβ , = 0.

In the context of particular case one, transient is modeled as:

( )

( - V0) +

(V0 - + λx0) + V0t. (9)

In the context of particular case two assuming 1→ 2 or →0, i.е. ∆ →0 and considering

that:

(10)

We obtain following transient:

( ) = eλt[( ) ] (11)

Assuming that β→0 , i.е. 1= 2=α and considering that:

(12)

We obtain transient in its equivalent record:



60

( ) = [|

| ] + t. (13)

In the context of case three transient is described with the help of following time function:

( )=[|

| ]

t. (14)

Analytical design. Dynamic design of mechanical systems is to select running design parameters

depending upon required transient quality: aperiodic transient or vibration one; degree of stability;

oscillation frequency and amplitude; control time etc. Transient performance depends on

distribution of characteristic equation roots within complex plane. Adequate distribution of

characteristic equation roots is achieved by selection of running parameters of mechanical system.

For linear dynamic systems analytical selection is possible.

Characteristic equation of one-dimensional dynamic system is:

02221

1211

аа

аа (15)

Roots of characteristic equations depend on coefficients of differential equations as follows:

= + , = |

| . (16)

For the involved mechanical system running parameters are directly determined by the formulas:

( ) (17)

In terms of complex roots we obtain:

c ( ) (18)

where α is degree of stability; and β is factor of natural frequency.

In the context of particular case one we determine:

c=0, (19)

i.е. elastic element is not available in the mechanical system.

In the context of particular case two we determine:



61

(20)

or

(21)

In the context of particular case three we determine:

µ = 0, с = mβ2, (22)

i.е. damping component is not available in the mechanical system.

Summary. New record of analytical solutions of linear differential equations in harmonic form is

proposed. The form is applied for analytical modeling and design of one-dimensional dynamic

system in terms of kinematic effect. Qualitatively different forms of transients within one-

dimensional mechanical system as well adequate running design parameters of elastic and damping

elements have been obtained.

References

[1] Khachaturov, A.A. 1976. Dynamics of a road-railcar-driver system (in Russian). – Moscow:

Mechanical Engineering, 535 P.

[2] Hubka, W. 1987. Theory of technical systems (translation from German language).– Moscow:

Mir, 208 P.

[3] Smirnov, V.I. 1974. A course of higher mathematics (in Russian).– Moscow: Nauka V.2, 656 P.

[4] Kuzovkov, N.T. 1976. Modal control and monitoring facilities (in Russian). – Moscow:

Mechanical Engineering, P. 184.

[5] Udermann, E.Т. 1972. Root-locus method in the theory of automatic systems (in Russian). –

Moscow: Nauka, 448 P.

[6] Kravets, V.V. 1978. Dynamics of solid bodies system in the context of complex control (in

Russian). – Kyiv: Applied Mechanics, Issue 7, P. 125-128.

[7] Kravets, V.V.., Bas К.М., Kravets, Vl.V. 2012. Dynamic design of the simplest vehicle

component (in Russian). – Sevastopol: Messenger of SebNTU, Issue 135, P. 188-191.

[8] Kravets, V.V.., Bas К.М., Kravets, Vl.V., Burov, V.S. 2014. Analytical method of the simplest

vehicle component dynamic design in terms of external effect (in Russian). – Sevastopol: Scientific

Messenger of the First Ukrainian Marine Institute, Issue 1, P. 79-82.



62

On Influence Of Design Parameters Of Mining Rail Transport On Safety

Indicators

Ziborov Kirill1, Protsiv Volodimir

2a, Fedoriachenko Serhii

3b, Verner Illya

4

1 – Associated professor, Head of the Machinery Design Fundamentals Department, National Mining University,

Ukraine.

2 – Professor, Head of the Mining Engineering Department, National Mining University, Ukraine.

3 – Associated professor, Machinery Design Fundamentals Department, National Mining University, Ukraine.

4 – Head of the Computational Engineering Laboratory, Machinery Design Fundamentals Department, National Mining

University, Ukraine.



Keywords: tractive effort, safety, mining locomotive, rolling stock, hard rock, mathematical simulation, principal

scheme

ABSTRACT. The influence of design parameters of mining rail transport on safety indicators is defined in the paper.

The mining locomotive ЭШК-10 is studied. Substantiated, that during constant locomotive speed V, variation of the

tangential component Qx occurs when the increment speed of the boundary layers of friction pair materials δV leads to

energy loss in the contact area. This provokes unstable state of the electromechanical system. To increase stability and

safety, reduce the load on the bogie, as well as on the rail track, additional movability of the kinematic connection of its

links can be used. Basing on the thrust forces equations subject to adhesion and permissible power for definite

conditions, we can determine the values of engine voltage Uc as a function of the locomotive speed.

Introduction. The large tonnage hard rock mines, either coal or copper etc., use underground rail.

South and Central America, Canada, China, South Africa, Ukraine these are may be the biggest

regions using mining rail transport [0]. Almost each region has its own suppliers of mining

locomotives and rolling stock. There is a tendency, that mining rolling stock suppliers focusing on

the locomotive rebuilds and refurbishment of old locomotives and rolling stock [0]. However, the

economical conditions of the mining regions are different and the development of a new locomotive

has its own strategy from region to region.

The Ukrainian locomotive ЭШК-10, that has been developed by the team of scientists from

National Mining University, has a lot of specific features, which allows using this loco worldwide

from mine to mine.

This happens due to comprehensive mathematical models and usage of sophisticated 3D simulation.

Research results. During the rock mass and coal transportation by the mining rail transport along

the mining shafts, the rail’s functions are not only carrying static loads, but to transmit the

dynamical stress and bogie mass to the rail track structure as well. The interaction area between

wheel and rail facilitates transmitting braking and tractive forces. In order to increase the

productivity of the mining rolling stock, an adhesion weight of the modern mining locomotives

increases either and now achieves 10-28 tons. This mass allows hauling heavier mining tub with

significantly increased static loads on the rail track on the steeper slopes. Due to the fact, that

existing mining rail tracks have been designed for much lower locomotives’ weight, increased axial

loading on the rail track elements rocketed up to 1,5-2,5 times and for mining tub 7 times more.




63

However, increased adhesive weight did not solve the problem insufficient friction properties of

rolling stock that caused unreasonable energy loss, reduction of its exploitation characteristics.

Exploitation indexes of railway transport show, that to overcome friction up to 30 % of all

consuming energy is necessary, and loss of material of friction pair amounts 15 % of producing

metal [0].

Each of mining drifts has its own climate environment, rail track profile and plan, bending radii,

track incline, admissible haulage speed and braking distance etc. All these factors dependence on

both economic and exploitation indexes, and on transport system reliability in general. Thus, study

of the rail, wheel and their interaction surface as a standalone system elements, wheel-rail

interaction control, allow optimizing their work during difficult motion regime.

Modern design methods [0], which base on the scientific simulation and research approaches,

facilitate definition of the location and character of arising dynamical loading and prevent their

growth during forming within the mining vehicle chassis.

This prevents the following dynamical load transfer on the bolster structure. Thus, the structure

selection and selection of mining machines parameters, which bases on the detailed analysis of

running processes, might be an essential part of energy-mechanical system and its scheme

development during development [0].

The purpose of the paper is to define the influence of design parameters of mining rolling stock on

the rational tractive regimes with high exploitation indexes and low energy loss.

As it is known, the frictional surfaces move across the interaction area with tangential velocities V1

and V2. The bodies have the components of angular rotation velocity relatively to the base tangent

to the surface. Different relations of the wheel set line speed V1 and speed of rotational motion V2 is

characterized by the sliding velocity V .

After each wheel’s turn on the interaction area resilient and plastic deformations arise. As a result,

the friction elements wheel-rail start negotiate through the finite size area. Taking into account

existing rail track imperfections and imperfections of contact area, let assume nominal and real

contact areas. All force interactions of frictional pair wheel-rail are carrying within the real contact

area. Therefore, the tangent reaction xyQ is formed with elementary forces xyiQ , which act on each

i-th point of the real contact area (fig. 1). Thus, during analytical research we need to proceed from

the elementary contacting area of the interacting bodies.

The wheel, moving along the rail, can be either in free (Qxy= 0), tractive (Qxy> 0) or braking (Qxy<

0) regimes (fig. 2, b).

Fig. 1. Real contact areas of interacting bodies

These forces are directed opposite to the sliding velocity of i-th point iV in the contact area (fig.

2) in dependence on motion regime. The total force, in the case when doesn’t independent on



64

iV direction, acts in the direction opposite to the wheel’s slipping velocity, and their scalar

product VQxy defines the power of dissipative forces in the contact area.

Thus:

i

k

izixy QQ cos

1

(1)

where k – amount of the contact points in the slipping area;

– coefficient of friction limit.

During mining locomotive motion along the mining drifts, the wheel contacts rolls both on the inner

and outer rails, which have different curvature and gage width. This fact induces the lateral

displacement of the contact area though its width. The worn wheel tread profile represents the total

envelope profile of all rails that are contacting with tread [0]. The tread areas, which contact with

rails most often, expose to intensive sliding, high contact stress and significant wear in comparison

to other tread areas. Mine drifts with big amount of straight track segments lead to wear

concentration on the rolling area at the center of the wheel tread. In this case the wear of the flange

is minimal. Otherwise, motion on the curvilinear rail track segments (most often case for coalmines)

causes significant flange wear.

a) b)

Fig. 2. The calculation scheme of forces and velocities. а) tractive regime (Qxy> 0); b) braking

regime (Qxy< 0)

As a result, of frictional interaction of the wheel and rail, a clearance between contact surfaces forms.

Uncontrollable growth of the clearances provokes additional dynamical forces, acting on the bogie

and track, that reduce the exploitation characteristics of the machine.

However, there is possible to revise the machine design and additional kinematical movability either

to reduce the duration of nonstationary motion regime. This is essential for mining conditions, which

is marked by lots of unfavorable factors [4]. To provide the smooth wear of coupled kinematical

members a coupling with local movability can be applied [4].



65

For example, locomotive of the module scheme, that includes a few sections. It allows for

development of the vehicle with different trailing weight, energy supply system and necessary

exploitation indexes. The distinguish feature of such locomotives is kinematical coupling between

bogie and tractive section (Fig. 3).

Such connection provides necessary relative movability and transmits vertical loading from frame

to bogie, horizontal lateral forces – centrifugal force, reaction of overrunning rail, which has

geometrical imperfections in all surfaces. Movability around the vertical axis is necessary for

tractive bogie turn and in order to avoid odd couplings, because the pin does not carry the chassis

weight; around lateral axis – for correct weight distribution between locomotive axles and reduction

influence on the rail track; longitudinal movability is absent because the tractive effort transmits in

this direction.

a) b)

Fig. 3. Pin joint locomotive (a); Locomotive joint (b)

In order to define relations between kinematical and dynamical characteristics of mine rollingstock

we need to provide the analysis of rail and wheel interaction, and to evaluate locomotives tractive

and safety properties.

The obtained data allows for assessment of the safety index, which is used to describe by safety

coefficient [0]:

1tg1

tg

y

z

Q

QSF

(2)

where – angle of wheel flange;

– friction coefficient;

zQ – normal rail reaction under ongoing wheel, N;

yQ – guiding force on the ongoing wheel, N.

Local and regular rail imperfections lead to additional growth of guiding force yQ that can cause

the derailment at some certain critical value (Fig. 4, 5, b). Reduction of guiding force can improve

stability and predict derailment (Fig. 4, 5, a).



66

The most complex motion regime is driving through curvilinear rail track with wheel flange climbing

by both rear and front axles. This induces the rotation of tractive bogie in relation to mass center (Fig.

4, 5). Simultaneously, the middle section rotates around pin joint. At axial displacement of the wheels,

a reaction force arises at the point of flange contact, which acts flatwise to motion direction. A sudden

growth of these forces appears while wheel misalignment. To reduce reactive forces an additional local

movability of kinematical pair coupling is necessary.

a) b)

Fig. 4. The forces on the wheel flange while straight motion (a) and along bend rail segment (b)

а) b)

Fig. 5. The creep forces between rail and wheel during straight motion (a) and in the bend rail

segment (b)

The usage of mathematical simulation facilitates the designing and dynamical interconnection of

mine rolling stock. The study of mining vehicle dynamics is provided via developed system of

differential equations.

Thus, we have obtained several relations of dynamic forces and safety factor (SF) indexes (Fig. 7).

As mentioned above, the characteristics of contact surfaces, and the pressing force define friction

properties at the contact point. When the position of the wheel set in the rail track cannot be

achieved through the friction forces, there is a two-point contact appears and lateral forces on the



67

flange, which protects the wheel set from derailment (Fig. 4 а, b). At the same time, an additional

resistance force arises. However, the forces on the flange are connected with frictional components,

which may lead to force reduction in the contact area. Thereby it facilitates the wheel climbing on

the rail, especially on curved track sections of small radius.

Fig. 6. General scheme of tractive bogie rotation in relation to mass center during wheel climbing

(1- tractive bogie; 2 – middle section; 3 – pin joint)

To enhance the stability and safety, reduce load on the vehicle’s chassis and the track and to reduce

motion resistance become possible while the usage of a new kinematical design where the

kinematical pairs will have an additional local movability. Thus, it will reduce the number of

redundant links with shortage of the unnecessary weight. To determine the appropriate value of

mobility, providing the necessary performance, we can use modern means of computer simulation

interoperability of mine transport and track.

Fig.7. Safety factor relation to track curvature subject to structural scheme. V=4 m/s - - - -

sectional pin-joint locomotive; –– conventional locomotive

Taking into account the denoted above approach of wheel and rail interaction evaluation, the motor torque,

reduced to the wheel set with rigid connection between the wheels, as a function of absolute motion

velocity V and relative velocity of the boundary layers iV of the frictional pair wheel-rail, defines as

N

ixyiдв RQM

1. The value xyiQ for each wheel calculates according to [4]. Each point of the grip

characteristics is corresponded by its distinguish energy state of interaction process of the pair wheel-rail.

Thus, alteration of the grip accompanies by a change of the state. At a constant locomotive speed V

alteration of the tangent component xyQ takes place during increase of the boundary layer displacement of

frictional pair material iV , which leads to energy loss in the contact area and unstable state of the



68

eletromechanical system. Such combination of adverse factors can evoke skidding (during tractive regime)

or blocking wheels (during braking).

The critical velocity can be determined by equating the limit values for traction grip and power to each

other. The maximum permissible torque, at which there will be no grip disruption, can be defined from the

expression of .двM after substitution the relative velocity V [4]. Using the relation between torque and

angular velocity of tractive motor, we can determine the voltage CU as a function of the speed V for these

conditions and formulate requirements for tractive motor (braking) control algorithm.

However, the operator of the loco can lose the driving control in hard mining environment. As a result the

wheels can be slipping or skidding, which will significantly increase the braking distance (especially on

the 50 ‰ slopes). As a result, the necessity of automated control ABS (anti-block system) system

appeared.

The main purpose of the ABS is to predict the wheel blocking and skidding adjusting tractive and braking

characteristics of the locomotive [7]. The ABS must connect to different systems: electromechanical

power-train and braking hydraulic systems. The principal electrical-hydraulic ABS system has been

developed subject to [8] and is depicted on the fig. 8.

Fig. 8. The general electric-hydraulic scheme of automated control system against skidding and wheel

blocking of mining pin-joint loco.

Summary. While constant locomotive speed V variation of the tangential component Qx occurs

when the increment speed of the boundary layers of friction pair materials δV leads to energy loss in

the contact area and the unstable state of the electromechanical system. To increase stability and

safety, reduce the load on the vehicle and chassis, as well as on the rail track, additional movability

of the kinematic connection of its members can be used. Basing on the thrust forces equations

subject to adhesion and permissible power for definite conditions we can determine the values of

engine voltage Uc as a function of the locomotive speed. To improve tractive and braking



69

characteristics of mining pin-joint locomotive a special ABS system has been developed and

described in the paper.

References

[1] Moore P. (2012), Mine locomotion, International Mining, Vol. 3, pp. 88-96.

[2] Isaev I.P., Lujhnov Ju., (1985), Problems of locomotive’s traction grip, Mashinostroenije, 238 P.

[3] Ziborov K.A., Protsiv V.V., Fedoriachenko S.A. (2013), Application of computer simulation

while designing mechanical systems of mining rolling stock, Scientific Bulletin of NMU, №6, pp.

55-59.

[4] Ziborov K.A., Fedoriachenko S.A. (2014), The frictional work in pair wheel-rail in case of

different structural scheme of mining rolling stock, Progressive technologies of coal, coalbed

methane and ores mining, Netherlands, pp. 517 - 521., doi: 10.1201/b17547-87

[5] Ziborov K.A. (2014), Characteristics of Friction Pair "Wheel—Rail" of Mining Locomotive

with Kinematical and Power Imperfections, mining Equipment and Electromechanics, №3 (100),

pp.26-32.

[6] Garg V.K., Dukkipaty R.V. (1988), Dynamics of rail transport, New-York, 391 P.

[7] Protsiv V.V., Gonchar O.Ye. (2010), Проців В. В. On the usage of automated system,

prevented wheel blocking and skidding of mining pin-joint locomotive, Mining electro-mechanics

and automatics, Vol. 84, pp. 116 – 125.

[8] Protsiv V.V. Indicators of arising skid during braking with limited frictional force on the wheel,

Scientific bulletin of NMU, Vol. 5, pp.106 – 112.



70

VIII. Information Technologies

The Assessment of the Stability Of the Electronics Industry Facility In the Man-

Made Emergencies With the Use Of Information Technology

Hancharyk A.V.1 and Kizimenko V.V.

1

1 – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

Keywords: evaluation method, system sustainability, electronic industry object, hazard prediction, mathematical model,

risk.

ABSTRACT. The object of study is the enterprise (object) of the electronics industry. By industrial object means

engineering-technical complex, which includes buildings, structures, power systems, equipment, automated systems,

equipment, tools, etc. By the stability of the industrial object we mean ability to produce specified types of products in

required quantities in a case of variety of emergency situations, as well as the willingness to self-repairing in if the

object proves in the affected area of weak or medium damages. For the stable operation of the facility, in addition to the

stability of the object, the security of workers and employees must be ensured, as well as individual and collective

protection equipment have to be provided. One of the important indicators for assessing the sustainability of industrial

facilities in emergencies is an evaluation of the probability of occurrence of internal and external emergencies and their

impact on the operability of the industrial facility. The estimation of probability of occurrence internal and external

emergency situation is characterized by a measure of the risk. By the risk means a value, which includes both the

probability of accidents and damage from them [1]. The development of criteria for evaluating the stability of the object

in the man-made disaster is often identified with the risk. The stability of the facility's operation in the man-made

disaster is estimated by the highest acceptable risk. There are the following methods for determining the risk: statistical,

model, expert and sociological. Currently, the software «SKEVIA» has been developed, which allows estimating the

damage caused by man-made emergencies for a particular industrial facility. Scientific novelty lies in the development

of new criteria for sustainable operation of the enterprises of electronic industry. The practical significance lies in the

implementation of software «SKEVIA» at the enterprises of electronic industry of Belarus.

Introduction: In this paper, we will consider the work of the facilities of electronic industry in

emergency situations. To ensure stable operation of the facility in emergency situations it becomes

necessary to increase the level and effectiveness of preventive measures to reduce the scale and

impact of disasters. Until recently, the highest priority in solving the problems of protection of the

population and territories from emergency situations was paid to eliminate the consequences of

accidents, i.e. rapid response to emergencies. However, as time has shown, it is economically

feasible to direct limited resources to reduce probability of occurrence of emergencies and to ensure

human security, rather than to pay huge costs for covering damage caused by emergencies.

Carrying out activities to identify hazards and the monitoring the probabilities of disaster on the

potentially dangerous facilities will prevent the growth and magnitude of the consequences of

natural and man-made disasters. The implementation of the complex preventive measures will

reduce the cost of the emergency response by 10-15 times in comparison with the avoided damage,

and in some cases - to completely avoid them. [2]

A rapid change of the conditions of emergency situations significantly complicates quick reaction

and the development of adequate measures to eliminate their consequences. Therefore urgent task is



71

a minimization the amount of raw data and the development of a rapid method of predicting not

only the areas of contamination and damages with a minimum number of parameters, but also

assessment of the risks, which can lead to complete loss of the stability of the facility in the

situation of man-made disaster [3].

In order to reduce and optimize the processing time to predict the impact of sources of emergency

on the production staff and processes, and for development of measures to prevent man-made

disaster (and in case of emergency - in order to minimize the damage) is needed to create a software

product for operational use by the head of safety department of the facility.

Analysis of recent publications and researches in this area. A great contribution to the

development and introduction of methods of assessment of emergency situations have made

Akimov V.A., Bariev E.R., Belov P.G., Vetoshkin A.G., Ermin V.G., Mikhnyuk T.F., Kozlachkov

V.I., Kukin G.Sh., Safronov A.G., Frolov A.B., Shadsky I.P. and others.

As it was previously mentioned, the criteria for assessing the sustainability of the enterprise are

associated with the risk indicator. Currently, there are following methods for determining the risk

[1]:

– Statistical: based on the statistical analysis of data on accidents;

– Model: model of the impact of harmful factors on the production staff, the process and the

environment of the facility is built. Such models can describe as a normal mode of operation of

the enterprise, as well as damage from an accident on it;

– Expert: the risk of accidents, the connection between them and the consequences are determined

not by calculation, but by the results of the survey of experienced experts;

– Sociological: the danger level is determined by the results of sociological surveys of various

large groups of people, which work on the facility.

The probabilities of events, calculated on the basis of information accumulated over a certain period

of time in the past can be extrapolated to the future using the law of distribution of random variables

in time.

The random variable ζi, which distribution function corresponds to the probability of occurrence of

z-th accident scenario, has a compound distribution, calculated by the formula (1):

ζi=ξi+γi+ηi, (1)

where ξi – random variable distributed according to an exponential law and is responsible for the

probability of failure due to technical problems;

γi – random variable which is responsible for the accident as a result of natural disasters;

ηi – random variable is responsible for accidents involving the "human factor".

Distribution of the last two variables is established empirically.

Known methods for evaluating the sustainability of enterprises in emergency situations can be

divided into some main approaches.

By the first approach the assessment is made using as a criterion the generalized criteria which

includes certain indicators. The difficulty and complexity of the application of these methods of

assessment lies in the fact that the number of indicators and their significance of these methods are

significantly different for different authors, in addition, given values of parameters are not

supported by the regulatory documents.



72

The second approach is to identify the most vulnerable links in the system, and evaluation of

stability for these links, which will be the assessment of the stability of the whole system.

The third approach is to identify and develop integral evaluation criterion the stability of the

facility. Moreover, this approach can be divided into two groups. The first group includes methods

of evaluation using the generalized criterion on the basis of partial indicators. The second group

involves the development or the search for a universal integral criterion, which will replace partial

ones.

Analysis of information sources has showed that the most promising methods of evaluating and

predicting the sustainability of facilities in a man-made disaster are methods which use criteria

Multiple-discriminant analysis based on the use of multifactor criteria.

It should be noted that there are several problems in application of known methods in practice, and

the main of them is the mismatch in the specificity of the functioning and development of certain

industries and their facilities.

Forecasting technological disaster is based on an assessment of the technical state of the object, its

equipment and the assessment of the human factor and the environment. The result of the prediction

of any man-made disaster is the determination of the risk of its occurrence, which depends on many

factors. Let us consider accounting these factors on the example of an estimation of industrial

structures and technological equipment, the accident on which usually can led to the disaster. [4].

The essence of the research

The following main features were used in research:

– The technogenic hazard is considered to be the main hazard;

– All hazards are probabilistic by the inherently;

– All sources of technogenic hazards, leading to emergencies, are divided into three classes by the

nature of occurrence: 1) the human factor; 2) Technical (technological) factor; 3) factor of the

environment;

– Risk is a measure of hazard. It simultaneously takes into account the possibility of a disaster and

an estimate of the risk;

– The stability of control system is interpreted as ability to to perform specified functions, not only

in normal conditions but also in emergency situations.

The risk of death in the industry is estimated at 10-6 or less per person per year [5]. Thus, during the

process of design the operation of technical devices the risk at the level 10-6 per person per year can

be accepted valid when the following requirements for risk analysis are provided: the problem of

the risk was analysed; i.e. probability of occurrence of adverse events and the probability of it

escalating into a emergency was estimated; all factors affecting emergency were considered, etc.

– Analysis carried out before making a decision and confirmed by the available data in a certain

time interval;

– Analysis and conclusion about the risk, obtained on the basis of the available data do not change

after the occurrence of an adverse event;

– Analysis and the results of control all the time show that the threat cannot be reduced at the cost

of acquitted costs.

As a result of research the algorithm for estimating the stability of the industrial facility in the

emergency was considered. (see Fig.1). [3]

Estimation of the stability of the object is provided consistently in relation to the effects of each

striking factor that may have a significant damaging effect on one or another element. The

sustainability of object's element is characterized by the practical value of a factor, when the



73

element is not broken and does not fail. However, in order to be able to predict the stability of the

facility in the man-made disaster, it is required to calculate the risk of damaging factor and compare

it to an acceptable risk.

In this paper we focus on the development of the block "Assessment of probability of occurrence

internal and external emergencies and their impact on the working process of the facility."

A special software product «SKEVIA» has been developed (the developers are Alena Hancharyk

and Viacheslav Kizimenko) in order to reduce and optimize processing time for the prediction of

effect of emergency sources on production personnel and technological process. «SKEVIA» has a

very simple and convenient user interface.[2]

Fig. 1. Algorithm for estimating the sustainability of the industrial facility in emergency situations

Estimation of the stability of

the object

Estimation of the probability

of internal and external

disaster and its impact on the

performance of the enterprise

объекта

Estimation of protection of

facility's personnel

Estimation of the control

system stability

Estimation of the physical

stability of the buildings, and

other systems

Estimation of the stability of

the logistics and industrial

links

Estimation of the

readiness object to the

restoration of impaired

production



74

«SKEVIA» is designed for predicting possible consequences of man-made emergencies on the basis

of a single industrial enterprise for one personal work place; it does not presuppose work via the

Internet or LAN. This condition is required due to the protection of confidential information of the

industrial enterprise. For the image of the program, see Fig. 2.

Fig. 2. The image of «SKEVIA»

The application deals with two possible ways of emergency development. The first way of

emergency development is the explosion of a tank with propane at the railway station near the

object (see Fig.3).

Fig. 3. Damage area



75

Damage areas are displayed as concentric circles where the centre is in the explosion point. They

show the geographic position of the points that are affected by various values of manometric

pressure (heavy damage – 0,4 kg/sm2 = 39,24 kPa – within a radius of 306 m, average damage –

0,3 kg/sm2 = 29,43 kPa, light damage – 0,2 kg/sm2 = 169,6 kPa). Calculation results are shown in

Fig. 3-4.

Fig. 4. Zones of gas-air mixture explosion base

The second way is the emission of the chemically hazardous substance (ammonia) at the processing

industry object that is situated nearby (see Fig.5).

Fig. 5. Zones of chemical contamination



76

It is possible to estimate death toll after exposure to poisonous substances. After entering the

number of the staff of the enterprise, the total number of victims as well as the number of people

with minor and moderate injury and the number of the dead is calculated. Graphic construction is

made on the cartographic basis loaded by the user. For user convenience it is possible to press any

two points of the map and see the distance in meters below the map. All the objects the location of

which is considered in the program as well as the distance between them are displayed on the map

after clicking “Objects”. Saving of the maps that contain the data of calculations is done by clicking

“Save” that creates a temporary file with the extension .bmp in the work directory of the PC. The

program is undemanding towards the processor resources, it is easy to use as it does not require

special skills apart from Windows interface basic work skills.

Thus, we have developed the system that significantly facilitates the work of an expert who deals

with safety of industrial enterprise personnel. Output graphic information allows to imagine the

scale of consequences after man-made catastrophes and to take rapid measures that are necessary

for people’s safety.

Currently, with the development of information technologies software «SKEVIA» is being

upgraded, which will provide more detailed development of the block algorithm, the stability of the

industrial facility in an emergency (Fig. 1) "The evaluation of the probability of internal and

external emergencies and their impact on the working process of the facility".

The following risks of man-made disaster will be analyzed:

1. The risk of unacceptable physical stability of buildings and structures;

2. The risk of failure of process equipment;

3. The risk of error in the work of administrative and management personnel and engineers;

4. The risk of errors in the work of service personnel;

5. The risk of failure of power supply systems;

6. The risk of unpreparedness of logistics;

7. Risk of influence of negative factors and working environment;

8. The risk of errors in the work of main production staff;

9. The risk of failure in the management systems;

10. The risk of failure in the systems of telecommunications.

All of these risks affect on the occurrence of man-made disaster at the facilities of electronic

industry. If the values of three criteria are higher than acceptable risk, the calculation of the rest can

be ignored. These criteria are: the limit of resistance to the shock wave, the limit of resistance to

light radiation, as well as the limit of stability to the electromagnetic field (EMF). The novelty is a

new criterion for the stability limit to EMF. If it exceeds the limit, then the entire electronic

apparatus fails, control systems, which consist of electronic devices, will be denied, as well as

technologies and equipment, i.e. the risk will exceed the permissible, therefore further payment

other risks impractical.

In case the risk values are within an acceptable risk, we calculate the remaining risks. The worst

option of these is selected, and its value will be the criterion for assessing the stability of the object

of electronic industry.

Currently, the program units to the software «SKEVIA» are developed, taking into account all

described risks, but there are practical difficulties in debugging these additions, as the majority of

facilities of electronic industry in Belarus today are not able to conduct testing and debugging this

changes.



77

References

[1] Kolodkina, V.M. (2001) Quantitative risk assessment of chemical accidents / V.M. Kolodkin,

Murin A.V., Petrov A.K., Gorsky V.G. / Izhevsk: Publishing House "Udmurtia University", 2001 -

228 p. ISBN 5-7029-0260-2

[2] Levkevich, V.E. (2004) Environmental risk - patterns of development, forecasting and

monitoring. Minsk.

[3] Dorozhko, S.V. (2008) Protecting the population and facilities in an emergency. Radiation

safety: manual. Part 1. Emergency situations and their prevention/ Dorozhko S.V., Rolewicz I.V.,

Poustovit V.T. / 2nd ed. - Minsk, 2008. - 284 p.

[4] Dorozhko, S.V. (2008) Protecting the population and facilities in an emergency. Radiation

safety: manual. In 3 hours. Part 2. The system of survival of the population and territories protection

in emergencies / Dorozhko S.V., Poustovit V.T., Morzak G.I., Murashko V.F. /2nd ed., - Minsk,

2008. - 400 p.

[5] Medvedev, V.T. (2002) Environmental Engineering / Ed. by V.T. Medvedev. M., 2002.



78

X. Philosophy of Research and Education

Teaching Reitlinger Cycles To Improve Students’ Knowledge And

Comprehension Of Thermodynamics

Amelia Carolina Sparavigna1

1 – Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy

Keywords: Thermodynamics, Thermodynamic cycles, Regenerative cycles, Thermal efficiency.

ABSTRACT. The second law of thermodynamics puts a limit on the thermal efficiency of heat engines. This limit

value is the efficiency of the ideal reversible engine represented by the Carnot cycle. During the lectures on physics, the

emphasis on this cycle is generally so strong that students could be induced to consider the Carnot cycle as the only

cycle having the best thermal efficiency. In fact, an entire class of cycles exists possessing the same maximum

efficiency: this class is that of the regenerative Reitlinger cycles. Here we propose to teach also these cycles to the

engineering students of physics classes, to improve their knowledge and comprehension of thermodynamics.

Introduction: Generally, the Carnot cycle is the only thermodynamic cycle that, during the lectures

on physics, is discussed as having the maximum possible thermal efficiency. This happens because

Carnot cycle is directly connected to the second law of thermodynamics, which puts a limit on the

thermal efficiency of heat engines. This limit value is the efficiency of the ideal reversible engine

cycle represented by the Carnot cycle. Sometimes, an approach considering only Carnot engines

with emphasis on their efficiency, could yield the following result: it is unknown that an entire class

of cycles exists, having a thermal efficiency which is the same of that of Carnot cycle. This is the

class of the regenerative Reitlinger cycles. Of course, since a large part of engineering students will

be required as engineers to deal with relatively simple thermodynamic problems, a discussion of

Reitlinger cycles could appear as unnecessary. However, it is unquestionable that a proper

knowledge of the fundamentals of thermodynamics is necessary for engineers as well as for

scientists in general. For this reason, in the following discussion, we will propose some notes

suitable for teaching these cycles to students of physics classes, to improve their knowledge and

comprehension of thermodynamics.

Reitlinger cycles. The Reitlinger cycles consist of two isothermal and two polytropic processes of

the same kind [1,2], so that the heat which is absorbed during a polytropic, is exactly the same that

it is rejected on the other polytropic process. Therefore, if we have a perfect regeneration of heat, by

means of which the heat rejected during the polytropic is transferred to a thermal storage (the

regenerator) and then transferred back to the working fluid, the thermal efficiency of the Reitlinger

cycle equals that of the Carnot cycle (in fact, it is a Reitlinger cycle too).

Of all the Reitlinger cycles, the Carnot cycle is unique in requiring the least regeneration, namely,

none at all because its polytropics are adiabatics [1]. Let us note that the mechanical work of the

Carnot cycle is not the best we can obtain between extremal states. We can easily evidence this fact

from the diagram in Figure 1, which is comparing Carnot and Stirling cycles, having the same

temperature and volume extremes [1]. In the Figure 2, we can see how, in general, a Reitlinger



79

cycle can be different from a Carnot cycle, in a p-V diagram. Working between the same

isothermals, with the same thermal efficiency, a regenerative Reitlinger cycle can give more work

or less work, depending on the polytropic process the cycle is performing between the same

extremal states.

Fig. 1. The figure (adapted from Ref.1) shows a Carnot cycle inscribed in a Stirling cycle in a p-V

diagram. The optimum constant buffer pressure is also shown. The work of the Stirling cycle ABCD

is greater than the work of Carnot cycle AB’CD’

Let us note that the ideal Stirling cycle is also a Reitlinger cycle, having as polytropics two

isochoric segments. It is the most popular example of a cycle having the same thermodynamic

efficiency of the Carnot cycle; however, to attain this result, the Stirling cycle makes quite heavy

demands on the process of regeneration [3].

Fig. 2. The figure shows how a Reitlinger cycle can be different from a Carnot cycle, in a p-V

diagram. Working between the same isothermals, with the same thermal efficiency, a regenerative

Reitlinger cycle AB’’CD’’ can give more work or less work, depending on the polytropic process

the cycle is performing between the same extremal states

As observed in [6], there are ten elementary power cycles which follow from the combinations of

five typical thermodynamic changes of state. In the Figure 3, we can see them and the names of

their inventors (for other cycles, see [7]). In [6], Carnot, Ericsson and Stirling cycles are

distinguished from the Reitlinger cycles, which have the most general form in idealized cycles



80

[4,5], because they have a specific importance in thermodynamics. In these cycles we have, besides

the two isothermal processes, the two polytropic regenerative processes realized by adiabatics,

isochoric and isobaric processes, respectively.

Fig. 3. The elementary thermodynamic cycles (figure adapted from [6])

Thermal Efficiency: For any thermodynamic cycle, reversible or irreversible, after one cycle, the

working fluid is again in its initial state and thus the change of its internal energy is zero. In this

manner, the first principle of thermodynamics tells us that the mechanical work produced by the cycle

is the difference of input heat energy Qin minus the energy dissipated in waste heat Qout. Heat engines

transform thermal energy into mechanical energy or work, W, so that W = Qin − Qout. We can calculate

the thermal efficiency of the cycle as the dimensionless performance measure of the use of thermal

energy. The thermal efficiency of a heat engine is the percentage of heat energy which is transformed

into work, so that:

inQ

W (1)

For a Carnot engine, it is η = 1−TC/TH, where TH,TC are the temperatures of the furnace and of the

cold sink, respectively. Let us discuss the thermal efficiency of the Stirling cycle. Using a p-V

diagram, the cycle appears as in the Figure 4. In the same figure, the Ericsson cycle and Reitlinger

cycle are also shown.

Fig. 4. Stirling, Ericsson and Reitlinger cycles in p-V diagrams.



81

The work can be easily calculated as:

A

B

V

VTTnRW ln21 (2)

In (2), n is the number of moles and R the universal gas constant. Heat is gained by the

thermodynamic system from the reversible isochoric transformation from D to A and during the

isothermal path AB. During isochoric process, heat gained is: 21 TTnCQ Visoc . CV is the molar

specific heat for an isochoric process. During isothermal process, the heat gained is

)/(ln1 ABisot VVnRTQ .

Let us note that, during the isochoric process, the fluid is obtaining heat from an infinite number of

thermal reservoirs [8]. This same amount of heat is lost during the isochoric cooling process, with a

thermal exchange with the same reservoirs. Then, for each of the infinite thermal reservoirs that we

meet during the isochoric reversible process, it happens what we see in the Figure 5. In this figure,

we have two thermal machines that must have the same efficiency, to satisfy the second principle of

thermodynamics. Let us suppose the efficiency of the right machine larger than that of the left one.

Let us consider the same work W produced by the two machines, and operate the machine on the

left in reversed manner. It is easy to see that, if we consider the net result of these two machines

operating together, we have that some heat is transferred from the low temperature reservoir to the

high temperature reservoir, violating the Clausius statement of the second principle of

thermodynamics. We have the same result if we consider the efficiency of the left machine larger

than that of the right one, and operate this last machine in reversed manner.

Fig. 5. The two reversible cycles in the figure have the same efficiency. If it were not so, we should

violate the second principle of thermodynamics. Let us suppose the efficiency of the right machine

larger than that of the left one. Let us consider the same work W produced by the two machines,

and operate the machine on the left in reversed manner. It is easy to see that the net result of these

two machines operating together is that of transferring some heat from the low temperature

reservoir to the high temperature reservoir, violating the Clausius statement of the second principle

of thermodynamics. We have the same result, supposing the efficiency of the left machine larger

than that of the right machine

Calculating efficiency of working fluid with regeneration: If we consider a regenerative Stirling

cycle from an engineering perspective, we have in it the regenerator which is storing the heat.

Therefore the abovementioned thermal reservoirs are not involved. Consequently, considering the

system made of working fluid and regenerator, the thermal efficiency is:



82

1

2

1

21

1

ln

ln

T

T

V

VnRT

V

VTTnR

Q

W

A

B

A

B

(3)

In (3), Q is the heat the system receives during the high temperature isothermal process, because the

heat received from the regenerator is that lost by the fluid during cooling isochoric process. This

efficiency is equal to that of a Carnot cycle which is working between the same two isothermal

processes. We can repeat the calculation for the Ericsson cycle. The work is:

A

B

A

B

A

B

A

B

B

A

A

B

C

D

A

B

C

DP

A

BP

V

VnRT

V

VnRT

nRTV

VnRTnRT

V

VnRT

p

pnRT

V

VnRT

nRTp

pnRTnRT

V

VnRT

V

VnRTTTnC

V

VnRTTTnCW

lnlnlnln

lnlnlnln

ln)(ln)(

211

121

212

221

221121

(4)

In (4), Cp is the molar specific heat at constant pressure. It is clear that the heat lost and gained

during the two isobaric processes is the same. Therefore, the thermal efficiency, in the case of a

perfect regeneration, is given by:

1

2

1

21

1

ln

ln

T

T

V

VnRT

V

VTTnR

Q

W

A

B

A

B

(5)

In (5), Q is the heat the system receives during the high temperature isothermal process. Let us

conclude with a Reitling cycle, where polytropics are given by equations constpV and

constTV 1 . The molar specific heat of such polytropic process is Cα. Let us note that from

polytropic equation we have (see Figure 4):

12

11

12

11

CB

DA

VTVT

VTVT (6)

Therefore, we have:

C

D

B

A

C

D

B

A

V

V

V

V

V

V

V

V

1

1

1

1

(7)

Then:

A

B

A

B

C

D

A

B

V

VnRT

V

VnRT

V

VnRTTTnC

V

VnRTTTnCW

lnln

ln)(ln)(

21

221121

(8)



83

Again, we find a thermal efficiency of the system (fluid and regenerator), which is equal to that of

the Carnot engine. Therefore, since the polytropic index α can have any value, we have an infinite

number of thermodynamic cycles that have the same value of thermal efficiency, equal to that of the

Carnot cycle when operating between the same two isothermal processes. Let us stress that these

cycles incorporate a regenerative heat transfer process, in place of adiabatic compression and

expansion of the Carnot cycle [5], or, if preferred, an infinite number of mono-thermal processes,

not influencing the efficiency of the cycle. Moreover, during lectures, it is better to remark that the

fact of possessing the same thermal efficiency does not mean that the same work is obtained from

different reversible cycles, when they are operating between the same extremal states.

References

[1] J.R. Senft, Mechanical Efficiency of Heat Engines, Cambridge University Press, 2007.

[2] I. Kolin, The Evolution of the Heat Engine, Longman, 1972.

[3] J.R. Senft, An Introduction to Stirling Engines, Moriya Press, 1993.

[4] J. Reitlinger, Uber Kreisprozesse zwischen zwei isothermen. Z. Ost. Ing. Arch. Ver. 1876.

[5] G. Walker, Cryocoolers, Part 1: Fundamentals, Plenum Press 1983.

[6] I. Kolin, S. Koscak-Kolin, M. Golub, Geothermal Electricity Production by means of the Low

Temperature Difference Stirling Engine, Proceedings World Geothermal Congress 2000, Kyushu -

Tohoku, Japan, May 28 - June 10, 2000 , 3199-3203.

[7] J.Selwin Rajadurai, Thermodynamics and Thermal Engineering, New Age International, 2003.

[8] P. Mazzoldi, M. Nigro, C. Voci, Fisica, S.E.S. 1991.



84

Multimedia Tutorial In Physics

For Foreign Students Of the Engineering Faculty Preparatory Department

P. G. Matukhin1a

, S. L. Elsgolts1b

, E. V.Pevnitskaya1c

, O. A. Gracheva1d

, E. A. Provotorova1e

1 – People’s Friendship University of Russia



c – [email protected]

d – [email protected]

e – [email protected]

Keywords: engineering education, multimedia tutorial, foreign students, manual, presentation, tests, OneDrive

ABSTRACT. Foreign students study physics and Russian as a foreign language at the preparatory Department. They

are to be trained to study different courses. During only one year the teachers of physics and Russian should help

students from Asia, Africa and Latin America to get ready to study in the university. To help students in a short time to

learn physical terms, to understand physics by ear, to read and write, teachers are developing the online multimedia

tutorial. It is placed on the cloud OneDrive. Tutorial includes the main themes in the Mechanics. They are physical

processes and phenomena, units, physical quantities, kinematics, laws of mechanics and others. The Power Point

presentation slides contain information on the topics. These slides help students learn to read Russian texts on physics.

There are hyperlinks to sound files on slides. Listening to those recordings, students gain the skills of physical texts

listening. After each module we placed the test. Students can prepare for it using the simulator. Tests and exercise

equipment made in the form of EXCEL spreadsheets. We provide our students the opportunity to view, read and listen,

the tutorial files via their own mobile devices. Thus they can study physics in Russian in the classroom, or at home, but

in the library, in the Park etc. Also they have access to it when they are not in Russia, and in their native countries. The

tutorial presented seems to be considered as the first attempt to develop the online multimedia aimed to assist foreign

students to get success in their efforts to study physics in Russian. It helps our students to learn physics in Russian faster

and better. Determined are the directions of further development and improvement of the tutorial.

Introduction. The elements and the structure of the online multimedia manual in physics are the

basics for the organization of educational communication in natural and engineering sciences with

elements of smart and BYOD technologies and webinars at the preparatory Department of the

University. Here we observe a number of the main prospects of the MS OneDrive Internet resource

as an IT platform to support the complex solution of the tasks of the formation and development of

basic competences of foreign students in Russian language of physics as a foreign language, in

physics and in modern information technologies for education including mobile access.

Foreign students come to the preparatory faculty of the University to get the Pre-university training

to enter at the faculties with increased demands on natural-scientific disciplines. Its goal is to build

a solid educational competent scope as the profile of science and in the language sector of the

educational and professional communication. Teachers of physics develop advanced smart

multimedia learning tools complex in collaboration with colleagues of the Russian language as a

foreign language (RFL) department and IT experts. Compressed terms of training and the need to

ensure wide access to the complex and it’s components faced developers the necessity to use

Internet technologies. It is supposed to use the elements of smart technologies, webinars and mobile

access. The vast opportunities of cloud Internet resources, such as MS OneDrive, make them








85

adjustable for use as an IT environment for preparation, loading, storage, access and application of

interactive tools to support learning in online mode. Simultaneously the problem of the increase of

IT competency of all participants of educational communication was solving.

Components Of the Multimedia Tools Complex For Enhanced Training Of Foreign Students

In Physics. One of the main items for future engineering-ditch of any specialty is physics. Teachers

in physics on the preparatory level at the Russian Language and Basic Education Department

dealing with foreign students coming to study at PFUR face a very complex problem. Despite the

fact that foreign students already have some basic education in physics, their earlier knowledge

needs to be adjusted to Russian educational standards. At the same time they are undergoing

intensive training in Russian of science as a foreign language. Thus, the task of training at the

preparatory faculty is not only bringing in accelerated mode of level of preparation of students on

the subject in compliance with the standards of the Russian Federation on secondary education

taking into account, that the level of knowledge of students from different countries varies greatly.

It is also attended by teachers of profile disciplines in the formation of the basic professional

educational competences of students in the Russian as a foreign language for scientific and physical

purposes and in the sector of application of information technologies in natural science education.

The aim of such an integrated approach is to achieve a level of preparation of students adjusted to

enter the University and to study physics, and other engineering disciplines in Russian language as a

foreign language of science based on modern means of in-formation technologies successfully

along with native Russian students.

One of the ways to achieve these goals is to use modern information technologies in the educational

and professional communication [3-5]. In particular, their application creates interactive electronic

training manuals, intended for the use not only offline, but also Internet-resources based. This will

allow us to include in the program of training a set of smart elements of online communication [6],

such as students’ self-training, including the self-test, mobile access, or conducting exercises with

elements of webinars.

It is the ambitious idea to develop the project of multimedia manual complex in physics for foreign

students, focused on special training on Russian language of physics as a foreign language. The

basis for elaboration includes the principle of providing the wide access to and open use of

components of the complex in different modes, including offline, on-line system with Internet

access and in mo-bile mode. Multifunctional use of the complex presupposes how to work with the

audience and for the students’ self-work. It also provides for the classroom and outdoor control of

the level of training and learning of students. Mediacomplex includes audited presentation

correlated with the adopted textbook [1] and applications for this tutorial [2] and a set of test tools

for the preparation and monitoring of the level of training.

Test system consists of the set of the issues in physics (300 questions) and Russian language of

physics as a foreign language (200 items), computer simulators, and tests. Elements of the set are

performed in the mode of the table processor Excel files [7] and web pages designed under the

specialized training tests environment Hot Potatoes [8].

Audited presentation on the course of «Physics» for for-eign students of the preparatory Department

forms is the basis of the mediacomplex. It is intended for training on the topics in mechanics. Slides

of the presentation are designed to suit the requirements of the existing educational standards and in

accordance with the level of education and language training of foreign students. Each slide

contains the header, illustrations, definitions, physical formula. Audio records associated with slides

allow students to listen fragments of the manual in Russian language. To increase the efficiency of

media complex as a mean to support the training process the presentation is equipped with built-in

elements of self-control. These mini tests are designed in the form of interactive web pages, which

are prepared under the tests constructor HOT POTATOES environment. They contain the question,

variants of the answer and the field to point the correct answer. They have a built-in check module

and the test result display. Mini tests are embedded in a presentation after each section. They serve



86

as training elements for self control in personal studies. Assembly of different HP tests can be used

both as training engines as well as means of the periodical and remote control in the online mode,

including for self teaching on physics and for webinar studies. This is covered further in [5].

Computer training tools are included in the media complex formed as Excel tables are intended for

self control in the process of the presentation study and for preliminary training, as well as for

official testing procedures. Training tools are developed not only to be built-in the individual

paragraphs, but also for practical topics of the course «Physics» for foreign students. Files of tests

simulators are placed on the MS OneDrive network share. Hyperlinks on the test modules are

available in its final part of each section of the presentation. They can be used by students

themselves outside-taken in person and on the lessons in the computer class.

Using the test generator and the set of questions, everyone can create an unlimited number of

control issues. They can include a number of questions for the control of both the audience and

extracurricular. Possibilities and information about the IT support of the media complex built-in

testing subsystem are presented in the papers [5-8].

Multimedia Manuals On Rlfs In the Physical Education Of Foreign Students. The need of the

development of the broad access online media complex to support preparation for the application of

foreign students of engineering and scientific areas, chosen their degree mastering in Russian

language, was highlighted by the way of understanding of teachers of Russian language, Physics

and Informatics of the difficulties faced by foreign students who participate in the core disciplines

in parallel with beginning studies of the Russian as a foreign language and a language of the

physical science at a basic level.

The problems in the grammar of Russian language are well-known. This is first of all specific

syntax and its implementation with flexible word order, distinctive design, character of links

between words in a sentence, case-case system of nouns and adjectives.

Modern realities in the language of engineering and natural Sciences compared with common

language have their own specific features in terms of grammar, and in terms of vocabulary, which

requires for elaboration of special technologies for correct educational content presentation and

fastening. Therefore the main task of the media complex in conjunction with the apparatus of built-

in tests on Russian language of physics as a foreign language is to create a foreign language

students framework on the subject of «Physics». To solve the problem, the developers of media

tutorial focused on the implementation of the following linguistic tasks:

1) Development of lexical physical terms compatibility;

2) Development of the case system and verbal forms in a scientific context;

3) Development of syntactic structures and their implementations in scientific language.

Implementation of these tasks was following by the tests of number of types:

1) Tests for approval kind and number of adjectives and nouns;

2) Tests on the use of prepositions, participating together with the endings in the formation of case

grammatical values;

3) Tests to determine the cases of nouns in the syntactic context;

4) Tests for the presence of the verbal word form;

5) Run on understanding the functioning of words and word collocations on «Basic concepts in

mechanics».

To support the solution of the above described tasks of teaching foreign students on Russian as a

foreign language of science media complex includes interactive elements for training and

monitoring of the achieved level of mastering the current language-acoustic material. It is



87

completing the mini tests embedded in slides, simulators, tests on the topics of the manual and sets

options for mid-term and final testing.

Language mini tests are included in the presentation in parallel with tests in physics. Their presence

allows us to combine the specialist training with the language in the mode of unity. This approach

through is quite important for teaching of the contingent of foreign students of the preparatory

faculty. And it allows provide the synergy effect from combination of two educational directions –

study of physics and language training.

EXCEL kits of tests for the preparation, organization and holding of the computer training and

testing on scientific language of physics at the level of Russian as a foreign strange similar to those

described above sets of test in physics. Base of 200 questions is also the basis of the simulator and

test generator. Using these tools, a set of options with a given number of issues, and embedded

environments tools verification is to be designed. Sets of test tools on scientific language of physics

are de-signed in such a way that they could be posted online. They may be downloaded and used in

standalone mode or when placing on Internet services such as MS-OneDrive, apply for webinars

and self-control, including mobile access. These tests are extremely important and useful for

training in Russian language because foreign students translate grammatical phenomena from their

language into Russian language, making countless mistakes. The instructor provides tests which

help to reorient the foreign students from grammar realities of their native language to realities of

Russian language. So online tests seem to be indispensable for providing foreign students the

necessary time to reflect specific grammar of Russian language and give the opportunity of constant

training at a convenient mode, including removed access. Therefore, the advantage of the system of

allocation and access for the media complex and built-in tests on the Internet resource MS

OneDrive is the fact that it can be used as taken in personal and outside of the classroom, self study

language training of foreign students.

The means of IT support of training, similar to that described above, and their components may be

effectively used in achieving the goal of preparing foreign students for the core disciplines,

combined with enhanced language training under such conditions as the maximum availability and

functionality. Solution of such tasks faces a number of certain difficulties.

The first and foremost is the problem of IT competence of the developers. Usually they are

extremely well-educated experts in their field of knowledge and have extensive experience with a

contingent of foreign students in pre-University stage. But they should not always be considered to

be professionals in the field of information technologies, although master them at a level above the

advanced computer user level. Thus, one of the tasks of the development and application of

informational and methodological support of training is the best free choice of software tools and

platforms for placement of their products, educational purpose. On the one hand, the instrument

used should provide effective solution of these problems; on the other hand, they should not require

significant time and effort on their study.

In the course of analysis of modern network resources and software tools, the aim was to choose the

most appropriate subject to the following requirements indicated:

• Accessibility;

• Reliability;

• Easy to use;

• Functionality;

• Compatibility;

• Prospects and some others.

Several different platforms including corporate net-work of the University, some of Internet hosting

and cloud services were explored. Most appropriate up-to-day tools taking into account the above



88

requirements in our opinion is the Internet-resource MS OneDrive, which is a subsystem of the

portal service provided by the Microsoft Company [9].

The structure of catalogues for placing the media complex components based on this resource was

created, including test simulators and sets of option tests. Methods of organizing the system of

storage simplicity, its identity to the standard file system of Windows allowed developers of the

tutorial in short terms to configure the main directory and file management operations under the

OneDrive environment control. The Built-in component of the MS OFFICE-online package enables

them to create and edit the elements of the complex using the collective mode of remote access. The

advantage of the OneDrive resource is availability of developing the access control system. It

provides the ability to assign different rights to different groups of users. Developers have the

highest access level. They have the right to place components of the complex in the directory, edit

them and provide access to users. Users have the right to view the available files and copy them to

their computer or mobile device.

The OneDrive performs the function of file storage. This store is a reliable transmission element of

educational information in computer mediated communication among teachers and students. Active

resource options allow us to organize the direct communication and feedback in this process. The

training materials and tests move in the for-ward direction from the teacher to the students. In the

opposite direction — filled tests and results of their processing come toward a teacher. Thus, the

OneDrive tools provide the opportunity to organize interaction without the chronotop restrictions of

the communication. Apparatus for short links makes it possible to organize conveniently hypertext

links to various components of the complex together in many different ways. For example, the

developers of the complex took advantage of this opportunity to insert hyperlinks on tests and

simulators directly in the presentation slides, on the pages of the training group in the office of a

teacher on the portal of the University etc. Thus, the MS OneDrive been a part of a resolution of the

main tasks effectively used as a medium for improving the IT competence of developers in the

mode of self-education.

We particularly should note that the usage of this resource is very high, taking into account its

dynamic. For example, recently some instruments were significantly developed. In particular, the

functions of the embedded spreadsheet tool SURVEY. It allows us to design the on-line tests of all

types with automatic collection of the results and their processing in real time. Currently the

possibilities to use the programs for the application in the media complex are under investigation.

Summary. Discussed in the paper results on the development of media complex in physics for

foreign students of the preparatory Department and organization of accommodation and access to

its components based on Internet resource MS OneDrive and experiences of the network elements

of the educational system allows to make a conclusion about the effectiveness of, and prospects for

the selected configuration of its tools and to identify areas for further development.

References

[1] Yefremov A.P., Pevnitskaya E.V., Kutuzov Yu.A. and others. Mechanics. RUDN. 2008.

[2] Gracheva O.A., Elsgolts S.L., Pevnitskaya E.V. Studying Physics in Russian. P.1-3. RUDN.

2011-13.

[3] Rhuzhentseva T.S., Matukhin P.G. Structure and methodical aspects of the use of professionally

- oriented electronic English language Manuals//Bulletin of the PFUR. Series: Russian and foreign

languages and methods of their teaching. 2004. № 1. P. 136-145.

[4] Titova E.P., Matukhin P.G., Provotorova E.A., Zabolotnaya I.M. Development of a complex of

electronic means of distant study of the course «Anatomy» for foreign medical students of pre-

university training period based on the Microsoft SkyDrive cloud technologies // Natural and

technical Sciences. 2013. № 5. P. 299-305



89

[5] Gracheva O.A., Elsgolts S.L., Matukhin P.G. Interdisciplinary IT Projects in The Development

of Electronic Manuals and Test Systems on Russian as a Foreign Language of Physics// Bulletin of

the People Friendship University of Russia. Series: Information Technologies in Education. 2013.

№ 4. P. 27-39.

[6] Gerasimenko T.L., Grubinin I.V., Gulaja T.M., Zhidkov, O., Romanova S.A. Development of

the language competence of students at a non-language University using smart technologies// UMO

Bulletin. Series: Economics, Statistics and Informatics. – M: Publishing house: Moscow state

University of Economics, Statistics and Informatics, no: 1, 2013 - P: 3-6

[7] Gracheva O.A., Elsgolts S.L., Matukhin P.G., Pevnitskaya E.V., Matyash, G.A. Base of

questions, test simulator, generator of tests and set options for the «Mechanics» section of the

introductory physics course for foreign students. EXCEL tables// Moscow, Database of OFERNIO

INIM RAO, 2013. - 9 P.

[8] Gerasimova A.V. Gracheva O.A., Zavadskaya O.A. Kuznetsova YU.V., Matukhin P.G.,

Pevnitskaya E.V. Tkachenko D.I., Elsgolts S.L., Introduction to the course of Physics. Set of tests

on Russian as a foreign language (the language of physics)// Register of algorithms and programs

VNTIC. - M: the Certificate of registration of the electronic resource № 50201350724; Appl.

04.07.2013 ; publ. 09.07.2013.

[9] Hill D. News About Microsoft Skydrive, Windows IT Pro/ RE. 2012. № 8. P. 64.



90

Petrus Peregrinus of Maricourt and the Medieval Magnetism

Amelia Carolina Sparavigna


Keywords: History of Science, History of Magnetism.

ABSTRACT. Petrus Peregrinus of Maricourt, a 13th-century French scholar and engineer, wrote what we can consider

as the first extant treatise on magnetism of Europe. This treatise is in the form of a letter, probably composed during the

siege of Lucera in Italy, in 1269, where Peregrinus worked to fortify the camp and built engines for projecting stones

and fireballs into the besieged town. Peregrinus’ letter consists of two parts. The first is discussing the properties of

magnets, describing also the methods for determining their north and south poles. The second part of the letter

describes some instruments that utilize the properties of magnets, ending with the Peregrinus’ art of making a wheel of

perpetual motion. In this paper, we discuss the first part of the letter and the related medieval knowledge of magnetism.

Introduction: Petrus Peregrinus of Maricourt was a 13th-century French scholar and engineer, that

conducted and reported several experiments on magnetism. His abilities as an experimenter were

well-known in that period and highly praised by one of his contemporaries, the English philosopher

and Franciscan friar Roger Bacon. Peregrinus wrote what we can consider as the first extant treatise

on magnets of Europe. This treatise is in the form of a letter, and it is entitled “Epistola Petri

Peregrini de Maricourt ad Sygerum de Foucaucourt, Militem, de Magnete”, “Letter of Peter

Peregrinus of Maricourt to Sygerus of Foucaucourt, Soldier, on the Magnet”. In one of the surviving

manuscript copies, it is told that the letter was composed during the siege of Lucera in Italy, dated 8

August 1269. Probably, Petrus Peregrinus was in the army of Charles I, duke of Anjou and king of

Sicily, who was besieging Lucera in a “crusade” sanctioned by the pope.

Peregrinus’ Letter on the magnet consists of two parts. The first treats the properties of the

lodestone (magnetite), providing a description of the polarity of magnets and methods for

determining their north and south poles. In the first part, Peregrinus describes also the effects of

attraction and repulsion between poles. The second parts of the Letter describes instruments that

utilize the properties of magnets, in particular the floating compass, and proposes a new pivoted

compass in some detail. The Letter ends with the Peregrinus’ art of making a wheel of perpetual

motion.

As we will see in the following discussion, some observations about magnets were existing in the

medieval cultural environment. However, Peregrinus was able organizing the whole into a text that

formed the basis of the science of magnetism. The Letter is generally considered as one of the great

works of medieval experimental research, and, the methods exposed in it as precursors of modern

scientific methodology [1]. We can find the Letter in the text entitled “Petrus Peregrinus on the

Magnet, A.D. 1269” [2], translated from Latin by Brother Arnold (Joseph Charles Mertens [3]),

Principal of La Salle Institute in Troy. The Letter was introduced by a discussion of Brother

Potamian (Michael Francis O Reilly [4]), professor of Physics at Manhattan College of New York.

Magnetism in classic antiquity and middle ages: In the classic antiquity and in the medieval

period, we can find several descriptions of the attraction which lodestone manifests for iron. In his

introduction to Peregrinus’ Letter [2], Brother Potamian writes that Lucretius (99-55 BC) gave a

poetical dissertation on the magnet in his “De Rerum Natura”, Book VI. Lucretius recognized



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magnetic repulsion, magnetic induction, and, according to Potamian, “to some extent the magnetic

field with its lines of force”. The poet Claudian (365-408 AD) wrote a short idyll on the attractive

virtue of the lodestone and its symbolism; Saint Augustine (354-430 AD), in his work “De Civitate

Dei”, wrote that a lodestone, held under a silver plate, draws after it a scrap of iron lying on the

plate [2,5]. It is also interesting to note that the Augustinian Abbot Alexander of Neckam (1157-

1217) was distinguishing between the properties of the two ends of the lodestone. In his “De

Utensilibus”, Neckam provides what is perhaps the earliest reference to the mariner's compass in

the Western Europe. In the world, it was a Chinese encyclopedist author, Shen Kuo, who gave the

first known account of suspended magnetic compasses, a hundred years earlier, in 1088 AD, in the

book entitled “Meng Xi Bi Tan” (Dream Pool Essays) [6].

The Dominican friar and bishop Albertus Magnus (1193-1280), in his treatise “De Mineralibus”,

describes several kind of magnets and states some of the properties commonly attributed to them

[2]. The minstrel Guyot de Provins, in a satirical poem written about 1208, refers to the directive

quality of the lodestone and its use in navigation [2,7]. We find the magnetic compass also in the

“Historia Orientalis” (1215-1220) by Cardinal Jacques de Vitry, in the “Tresor des Sciences”

(1260) written in Paris by Brunetto Latini, poet and philosopher, in a treatise written by the

‘Enlightened Doctor’ Raymond Lully, and in the famous canzone “Al cor gentil rempaira sempre

amore” (Love always has its home in the noble heart), composed by Guido Guinizelli, the poet-

priest of Bologna [2]. In Ref.1 we find mentioned other scholars too. Bartholomaeus Anglicus

(1220-1250) refers to the magnet in his encyclopedic treatise “De proprietatibus rerum” (On the

properties of things). Henry Bate (1246-1317) included a substantial discussion of magnetism in his

“Speculum divinorum et quorundam naturalium” (Mirror of divine things and of some natural

ones).

Magnets and diamonds: Let us discuss for a while the reference to Guinizelli’s poetry. In his

canzone on love, the poet tells “Amore in gentil cor prende rivera per suo consimel loco

com’adamas del ferro in la minera,” that is “love has home in a gently noble heart, like, in the same

manner, adamas has home in an iron mine.” What is the “adamas”? Some commentators translate it

as “diamond”, others, probably more correctly, as “magnet” [8]. In fact, the word “adamas” is the

medieval word for both lodestone and diamond. In the Guinizelli’s canzone, when we consider

“adamas” as “magnet”, we have a clear example of the medieval similitude between “love” and

“magnet” that was common in troubadour lyrics. For instance: “tira com azimans, la bela”, that is,

“the fair lady draws me toward her like a magnet”, writes Bernart de Ventadorn [9]. The similitude

is reinforced by a phonetic resemblance between the words for “magnet” and “love”. As noted in

[8], for medieval poets the true lover (amans) was like a magnet (azimans, adamas).

In the book of William Gilbert (1544-1603), English physicist and natural philosopher, on

magnetism [10], we find several names for magnets from different countries. Gilbert writes that in

English, the magnet is known as “lodestone” and “adamant stone” (William Shakespeare used

“adamant” too, in the Midsummer Night’s Dream: “You draw me, you hard-hearted adamant, but

yet you draw not iron; for my heart is true as steel”). Adamant is another form of “adamas”. In

various forms (adamas, adamant, aimant, azimans, aymant, yman) and in many languages, we find

the original ancient Greek “adamas”, the “unconquered”. Originally, the word was applied by the

Greeks to the hardest of the metals with which they were acquainted, that is to say, to hard-

tempered iron or steel. Due to its meaning, this word was subsequently applied to diamond for the

same reason. In the writings of the middle ages, and even in Pliny the Elder, we find some

confusion between the two uses of “adamas” to denote the lodestone as well as the diamond [10].

Petrus Peregrinus and the perpetual motion: As told in [2], of the early years of Peregrinus

nothing is known. He studied probably at the University of Paris and graduated with the highest

scholastic honors. His surname is coming from the village of Maricourt, in Picardy, whereas the

appellation Peregrinus, or Pilgrim, is due to the fact that he visited the Holy Land. He was also



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known as ‘Peter Adsiger’, as we can find in a book of 1787, written by Tiberio Cavallo (1749-

1809), entitled “Treatise on Magnetism” (London) [11].

In 1269, we find Peter Peregrinus in the engineering corps of the French army that was besieging

Lucera, in Southern Italy. Peregrinus worked to fortify the camp and lay mines. He also worked to

build engines for projecting stones and fireballs into Lucera. It seems that, during such warlike

preoccupations, an idea occurred to Peregrinus: the idea was of devising a mechanism able of

keeping the astronomical “sphere” of Archimedes in uniform rotation [2].

Of the “spheres” of Archimedes, wrote Cicero, the Roman philosopher and politician, in the first

century BC. Cicero wrote of two spherical objects built by Archimedes, that Marcellus, the Roman

consul who conquered Syracuse in 212 BC, brought to Rome [12]. One was a solid sphere on which

were engraved or painted stars and constellations; the second sphere was much more ingenious and

original. It was a planetarium, a mechanical device showing the motions of sun, moon, and planets

as viewed from Earth. No physical trace of Archimedes' planetarium survives, but we can have

some ideas about it. In 1900, a shipwreck found near the Greek island of Antikythera uncovered an

exceptional object. Amidst the cargo of a ship dated from the first century BC, there was a small

lump of wood and corroded gears of bronze, which revealed itself as an analog computer designed

to predict astronomical positions and eclipses. The device is known as the ‘Antikythera mechanism’

[13,14]. Of course, we cannot attribute this mechanics to Archimedes, but we can imagine he could

had built a similar device too, that the consul Marcellus brought to Rome. And in fact, recently, a

model of Archimedes’ sphere had been reconstructed by Michael Wright, who was a curator at the

Science Museum in London and that spent many years studying the Antikythera mechanism. His

globe, made from copper and brass displays the movements of the sun, moon and planets as they

travel through the night sky [15].

Peregrinus, attracted by the mechanical problems connected with Archimedes’ planetarium, was

gradually led to consider the problem of perpetual motion. The result was that he described, “to his

own evident satisfaction,” [2] how a wheel might be driven round forever by the power of magnetic

attraction. “Elated over his imaginary success,” Peregrinus wrote to inform a friend at home. To

allow his friend comprehending the mechanism of the motor and the functions of its parts, “he

proceeds to set forth in a methodical manner all the properties of the lodestone, most of which he

himself had discovered.” [2]

Fig. 1. Two drawings from the notebook of Villard de Honnecourt, an artist from Picardy,

contemporary of Peter Peregrinus. A drawing is showing how could appear a soldier at the time.

On the right, we can see a wheel of perpetual motion as imagined by Villard de Honnecourt.



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Peter Peregrinus was not the only person from Picardy that studied the problem of perpetual motion.

Another one was his contemporary Villard de Honnecourt. Villard is known to history only through

a surviving notebook of 33 sheets of parchment containing about 250 drawings dating from the

1220s/1240s, which is now in the Bibliothèque Nationale, Paris (MS Fr 19093). The great variety of

subjects (religious and secular figures, architectural plans and mechanical devices), makes it

difficult to determine his profession. Since the discovery of his notebook, it is general opinion that

Villard was an itinerant architect. Among the mechanical devices sketched by Villard, we see the

perpetual-motion machine shown in the Figure 1. The problem of perpetual motions was of great

appeal during the middle ages. This interest was probably stimulated by the books on mechanics

coming from Arabic world, where we can find such wheels. The wheel sketched by Peregrinus is

discussed in a very interesting article [16], which is also showing several layouts of it in different

manuscripts and also wheels from Arabic manuscripts.

Roger Bacon’s opinion: Peregrinus’ Letter was the first landmark among the studies on

magnetism, the next being William Gilbert's De Magnete, in 1600. The Letter was addressed to

Sigerus de Foucaucourt, his "amicorum intimus," the dearest of friends. Another friend was Roger

Bacon, who held Peregrinus in the very highest esteem, as shows by his following words: "There

are but two perfect mathematicians," wrote the English monk, "John of London and Petrus de

Maharne-Curia, a Picard" [2]. Bacon thus writes of Peregrinus [2]: "I know of only one person who

deserves praise for his work in experimental philosophy, for he does not care for the discourses of

men and their wordy warfare, but quietly and diligently pursues the works of wisdom. … he is a

master of experiment. … he knows all natural science whether pertaining to medicine and alchemy,

or to matters celestial and terrestrial. He has worked diligently in the smelting of ores as also in the

working of minerals; he is thoroughly acquainted with all sorts of arms and implements used in

military service and in hunting, besides which he is skilled in agriculture and in the measurement of

lands. It is impossible to write a useful or correct treatise in experimental philosophy without

mentioning this man's name”. Other references and information on Petrus Peregrinus are reported

in [17].

Analysis of the Letter: The analysis proposed in [2] shows that, according to the known

manuscripts: 1) Peter Peregrinus was the first to assign a definite position to the poles of a lodestone

and to provide a method for determining which is north and which south; 2) he proved that unlike

poles attract each other, and that similar ones repel; 3) after experiments, he established every

fragment of a lodestone, however small, has two poles and then it is a complete magnet; 4) he

recognized that a pole of a magnet may neutralize a weaker one of the same name, and even reverse

its polarity; 5) he was the first to describe the use of a pivot for a magnetized needle and surround it

with a graduated circle, creating, in such a manner, a model for the modern magnetic compass; 6)

he determined the position of an object by its magnetic bearing as done in modern compass

surveying; and, at the end of the letter, 7) he described his perpetual motion machine, based on the

idea of a magnetic motor, a clever and new idea for a thirteenth century engineer [2].

The copies of Peregrinus’ Letter for nearly three centuries, remained unnoticed among the libraries

of Europe, until William Gilbert, who makes frequent mention of it, published his “De Magnete” in

1600. After, a Jesuit writer, Niccolò Cabeo, refers to it in his “Philosophia Magnetica”, 1629. And

Athanasius Kirches quotes from the Letter, in his “De Arte Magnetica”, 1641. Kircher also

constructed a magnetic clock, the mechanism of which is described in his book.

In the first part of the Letter: After an introduction, where Peregrinus writes that he wants to

explain to his friend the hidden virtue of the lodestone in a simple style, he poses the “qualifications

of the experimenter”. “Whoever wishes to experiment, should be acquainted with the nature of

things, and should not be ignorant of the motion of the celestial bodies. He must also be skilful in

manipulation in order that, by means of this stone, he may produce these marvelous effects…

Besides, in such occult experimentation, great skill is required, for very frequently without it the



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desired result cannot be obtained, because there are many things in the domain of reason which

demand this manual dexterity” [2].

After the experimenter has found a good lodestone, he can find and distinguish its poles. “I wish to

inform you that this stone bears in itself the likeness of the heavens, as I will now clearly

demonstrate.” That is, we have in the heavens “two points more important than all others, because

on them, as on pivots, the celestial sphere revolves:” these points are the Arctic or north pole and

the Antarctic or south pole. The lodestone has two points which are respectively the north pole and

the south pole. “If you are very careful, you can discover these two points in a general way. One

method for doing so is the following: with an instrument with which crystals and other stones are

rounded, let a lodestone be made into a globe and then polished. A needle or an elongated piece of

iron is then placed on top of the lodestone and a line is drawn in the direction of the needle or iron,

thus dividing the stone into two equal parts. The needle is next placed on another part of the stone

and a second median line drawn. If desired, this operation may be performed on many different

parts, and undoubtedly all these lines will meet in two points just as all meridian or azimuth circles

meet in the two opposite poles of the globe. One of these is the north pole, the other the south pole.”

[2] In fact, Peter Peregrinus is telling that it is possible to create a globe and, on it, finding the poles

by drawing on it a set of meridians, which are following the lines of the magnetic field, detected by

means of a needle (see Figure 2).

Fig. 2. A spherical magnet with poles and meridians, as illustrated in the “Tractatus, sive

Physiologia nova de magnete, magneticisque corporibus & magno magnete tellure” by William

Gilbert, published 1633 by Lochmans.

In the Figure 2, the spherical magnet looks like a “terrella”, Latin of "little earth", a small

magnetised model representing the Earth. Terrella is usually thought to have been invented by

William Gilbert, but based on an idea of Peter Peregrinus.

Peter Peregrinus is describing another method for determining the poles. “Note the place on the

above-mentioned spherical lodestone where the point of the needle clings most frequently and most

strongly; for this will be one of the poles as discovered by the previous method. In order to

determine this point exactly, break off a small piece of the needle or iron so as to obtain a fragment

about the length of two fingernails; then put it on the spot which was found to be the pole by the

former operation (see Figure 2). If the fragment stands perpendicular to the stone, then that is,

unquestionably, the pole sought; if not, then move the iron fragment about until it becomes so; mark

this point carefully; on the opposite end another point may be found in a similar manner. If all this

has been done rightly, and if the stone is homogeneous throughout and a choice specimen, these two

points will be diametrically opposite, like the poles of a sphere” [2].

North and South Poles: After we have found the poles, we have to determine which is north and

which south. We can proceed in the following manner, according to Peregrinus. He is proposing to

use the celestial pole as a reference. Let us take a wooden vessel, made like a dish, and place in it



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the stone in such a way that the two poles will be equidistant from the edge of the vessel. Then, let

us place the dish in another and larger vessel full of water, so that “the stone in the first-mentioned

dish may be like a sailor in a boat”. The second vessel should be of considerable size, in order that

the lodestone may not be impeded by contact of one vessel against the sides of the other. “When the

stone has been thus placed, it will turn the dish round until the north pole lies in the direction of the

north pole of the heavens, and the south pole of the stone points to the south pole of the heavens”.

And then “since the north and south parts of the heavens are known, these same points will then be

easily recognized in the stone because each part of the lodestone will turn to the corresponding one

of the heavens,” Peregrinus explains.

How lodestones attract each other: After we discovered the north and the south pole in the

lodestone, we have to mark them both carefully. If we want to see how one lodestone attracts

another, then, with two lodestones selected and prepared as previously told, we can proceed as

follows. “Place one in its dish that it may float about as a sailor in a skiff, and let its poles which

have already been determined be equidistant from the horizon, i.e., from the edge of the vessel.

Taking the other stone in your hand, approach its north pole to the south pole of the lodestone

floating in the vessel; the latter will follow the stone in your hand as if longing to cling to it. If,

conversely, you bring the south end of the lodestone in your hand toward the north end of the

floating lodestone, the same phenomenon will occur; namely, the floating lodestone will follow the

one in your hand. Know then that this is the law: the north pole of one lodestone attracts the south

pole of another, while the south pole attracts the north. Should you proceed otherwise and bring the

north pole of one near the north pole of another, the one you hold in your hand will seem to put the

floating one to flight. If the south pole of one is brought near the south pole of another, the same

will happen. This is because the north pole of one seeks the south pole of the other, and therefore

repels the north pole” [2].

After the discussion of this experiment, Peregrinus continues remarking that it “is well known to all

who have made the experiment, that when an elongated piece of iron has touched a lodestone and is

then fastened to a light block of wood or to a straw and made float on water, one end will turn to the

star which has been called the Sailor's star because it is near the pole; the truth is, however, that it

does not point to the star but to the pole itself”. Peregrinus is also telling an important fact, that

every fragment of a lodestone has two poles and then it is a complete magnet. “Take a lodestone

which you may call AD, in which A is the north pole and D the south; cut this stone into two parts,

so that you may have two distinct stones; place the stone having the pole A so that it may float on

water and you will observe that A turns towards the north as before; the breaking did not destroy the

properties of the parts of the stone, since it is homogeneous; hence it follows that the part of the

stone at the point of fracture, which may be marked B, must be a south pole; this broken part of

which we are now speaking may be called AB. The other, which contains D, should then be placed

so as to float on water, when you will see D point towards the south because it is a south pole; but

the other end at the point of fracture, lettered C, will be a north pole; this stone may now be named

CD. If we consider the first stone as the active agent, then the second, or CD, will be the passive

subject. You will also notice that the ends of the two stones which before their separation were

together, after breaking will become one a north pole and the other a south pole. If now these same

broken portions are brought near each other, one will attract the other, so that they will again be

joined at the points B and C, where the fracture occurred. Thus, by natural instinct, one single stone

will be formed as before” [2].

The natural virtue of magnets: In the part of the Letter discussing the natural virtue of magnets,

we can find an experimental device, which Peregrinus is proposing for having a magnetic clock. To

Peregrinus, “it is clear that the poles of the lodestone derive their virtue from the poles of the

heavens. As regards the other parts of the stone, the right conclusion is that they obtain their virtue

from the other parts of the heavens. … You may test this in the following manner: A round

lodestone on which the poles are marked is placed on two sharp styles as pivots having one pivot

under each pole so that the lodestone may easily revolve on these pivots. Having done this, make



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sure that it is equally balanced and that it turns smoothly on the pivots. … Then place the stone with

its axis in the meridian, the poles resting on the pivots. Let it be moved after the manner of bracelets

(the bracelets are the circles, “armillae”, of armillary spheres) so that the elevation and depression

of the poles may equal the elevation and depressions of the poles of the heavens of the place in

which you are experimenting. If now the stone be moved according to the motion of the heavens,

you will be delighted in having discovered such a wonderful secret; … With such an instrument you

will need no timepiece, for by it you can know the ascendant at any hour you please, as well as all

other dispositions of the heavens which are sought for by astrologers” [2].

About this experiment, William Gilbert tells in his book [10]: “I omit what Peter Peregrinus

constantly affirms, that a terrella suspended above its poles on a meridian moves circularly, making

an entire revolution in 24 hours: which, however, it has not happened to ourselves as yet to see …”.

A comment in [10] tells us that, besides Gilbert, Galileo too discussed this experiment in the third

of his Dialogues, the book which presents a series of discussions among two philosophers and a

layman: Salviati, who presents some of Galileo's views directly, Sagredo and Simplicio, a follower

of Ptolemy and Aristotle. About Peregrinus’ experiment, Salviati tells “I will speak to one

particular, to which I could have wished, that Gilbert had not lent an ear; I mean that of admitting,

that in case a little Sphere of Loadstone might be exactly librated, it would revolve in itself; because

there is no reason why it should do so; For if the whole Terrestrial Globe hath a natural faculty of

revolving about its own centre in twenty four hours, and that all its parts ought to have the same, I

mean, that faculty of turning round together with their whole, about its centre in twenty four hours;

they already have the same in effect, whilst that, being upon the Earth, they turn round along with

it: And the assigning them a revolution about their particular centres, would be to ascribe unto them

a second motion much different from the first; for so they would have two, namely, the revolving in

twenty four hours about the centre of their whole; and the turning about their own: now this second

is arbitrary, nor is there any reason for the introducing of it” [18].

With the discussion of the pivoted sphere made by Galileo, let us conclude this discussion on the

medieval magnetism as we find in the Peregrinus’ Letter. However, let us stress that the attraction

the Peregrinus had for pivoted magnets, forced him to imagine new devices. In the second part of

the Letter, he discussed three devices: one is an instrument for measuring the azimuth of sun, moon

and stars on the horizon, the second a pivoted compass and the third a wheel of perpetual motion.

The use of a pivoted compass to determine the azimuth of the sun is clearly shown by the Figure 3,

which is obtained adapting images from [2]. The devices described by the Peregrinus will be the

subject of a future paper, on pivoted mechanisms of the Middle Ages.

Fig. 3. The pivoted magnet used for measuring the azimuth of stars.



97

References

[1] T.F. Glick, S. Livesey, F. Wallis (2014). Medieval Science, Technology, and Medicine: An

Encyclopedia, Routledge.

[2] Peter Peregrinus (1904). The Letter of Petrus Peregrinus on the Magnet, A.D. 1269, Translated

by Brother Arnold, with introductory notice by Brother Potamian, New York, McGraw Publishing

Company.

[3] E. Grant (1974). A Source Book in Medieval Science, Volume 1, Harvard University Press.

[4] W.J. Battersby (1953). Brother Potamian: Educator and Scientist, Antic Hay Books.

[5] E. Du Trémolet de Lacheisserie, D. Gignoux, M. Schlenker (2005). Magnetism, Springer

Science & Business Media.

[6] T. Breverton (2012). Breverton's Encyclopedia of Inventions: A Compendium of Technological

Leaps, Groundbreaking Discoveries and Scientific Breakthroughs that Changed the World,

Hachette UK.

[7] J. Block Friedman, K. Mossler Figg (2013). Trade, Travel, and Exploration in the Middle Ages:

An Encyclopedia, Routledge.

[8] L. Spitzer, A.K. Forcione, H.S. Lindenberger, M. Sutherland (1988). Representative Essays,

Stanford University Press.

[9] F. Jensen (1994). Tuscan Poetry of the Duecento: An Anthology, Taylor & Francis.

[10] W. Gilbert (1600). De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, On

the Magnet, edited and with notes by Silvanus P. Thompson. Available on line at:

https://ebooks.adelaide.edu.au/g/gilbert/william/on-the-magnet/complete.html

[11] G.W.F. Hegel (2004). Philosophy of Nature, Volume 2, Psychology Press.

[12] https://www.math.nyu.edu/~crorres/Archimedes/Sphere/SphereSources.html

[13] D. De Solla Price (1975). Gears from the Greeks, The Antikythera Mechanism-A Calendar

Computer from ca. 80 B.C., Science History Publications, New York, 1975,

[14] D. De Solla Price (1974). Gears from the Greeks, The Antikythera Mechanism-A Calendar

Computer from ca. 80 B.C., Transaction of The American Philosophical Society, New Series,

Volume 64, Part 7.

[15] J. Marchant (2015). Archimedes’ Legendary Sphere Brought to Life; Recreation of a 2,000-

year-old Model of the Universe to Appear in Exhibition, Nature 526(19), 01 October 2015.

Available on line at: http://www.nature.com/news/archimedes-legendary-sphere-brought-to-life-

1.18431 DOI: 10.1038/nature.2015.18431

[16] A. Kleinert (2003). Wie funktionierte das Pepertuum Mobile des Petrus Peregrinus?,

International Journal of History & Ethics of Natural Sciences, Technology & Medicine, 11(3):155-

170. DOI: 10.1007/s00048-003-0168-5

[17] T. Bertelli (1868). Pietro Peregrino di Maric e la sua Epistola de Magnete, Roma, Tipografia

della Scienze Matematiche e Fisiche.

[18] Galilæus Galilæus Lyncæus, His System of the World, The Third Dialogue. Available on line

at: http://www.chlt.org/sandbox/lhl/Salusbury/page.376.php?

https://ebooks.adelaide.edu.au/g/gilbert/william/on-the-magnet/complete.html



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Depletion Gilding: An Ancient Method for Surface Enrichment of Gold Alloys

Amelia Carolina Sparavigna


Keywords: Gilding, Depletion Gilding, Gold-Copper Alloys, Tumbaga, Gold-Silver-Copper Alloys, Electrum,

Archaeological Artefacts, Gold-Copper nanoparticles, Nanoporous Gold.

ABSTRACT. Ancient objects made of noble metal alloys, that is, gold with copper and/or silver, can show the

phenomenon of surface enrichment. This phenomenon is regarding the composition of the surface, which has a

percentage of gold higher than that of the bulk. This enrichment is obtained by a depletion of the other elements of the

alloy, which are, in some manner, removed. This depletion gilding process was used by pre-Columbian populations for

their “tumbaga”, a gold-copper alloy, to give it the luster of gold.

Introduction: A phenomenon often encountered when ancient objects made of noble metal alloys

are analyzed is that of their surface enrichment. Let us consider, for instance, a statuette made of an

alloy of gold with copper and/or silver; it can occur that its surface has a percentage of gold higher

than that of the bulk. This enrichment can be due to an addition of gold on the surface, or to a

depletion process during which the less chemically stable elements leach out causing the surface

composition to change. In both cases, the local percentage of gold is increased consequently.

Therefore, both processes are gilding processes, the second being known as “depletion gilding”. It

happens because a specific depletion process had been applied to the surface of the object or

because it had been buried for a rather long time [1] (of course, besides such a slow gilding process,

time is causing a long series of damaging and corrosive effects [2]). Masters of the depletion gilding

were the pre-Columbian populations of America that used it for their “tumbaga”, an alloy of gold

and copper, to give the luster of gold to the objects made of it. In this paper, we will discuss some

aspects of tumbaga and depletion gilding.

Gilding: The term “gilding” covers several techniques for applying a gold leaf or a gold powder to

solid surfaces, in order to have a thin coating of this metal on objects. Several methods of gilding

exist, including hand application, chemical gilding and electroplating. These are additive methods,

which act by depositing gold onto the surface of objects usually made of a less precious material.

Among the techniques of gilding, some are quite old. Fire-gilding of metals for instance goes back

at least to the 4th century BC, and was known to Pliny the Elder and Vitruvius. Fire-gilding is a

process by which an amalgam of gold is applied to metallic surfaces. Objects are set on fire and

mercury volatilizes, leaving a film of gold or a gold-rich amalgam on the surface. About the coating

with gold leaf, Pliny is also telling the following. “When copper has to be gilded, a coat of

quicksilver is laid beneath the gold leaf, which it retains in its place with the greatest tenacity: in

cases, however, where the leaf is single, or very thin, the presence of the quicksilver is detected by

the paleness of the colour” [3].

As previously told, besides the gilding obtained by the abovementioned techniques, we have also

the subtractive process of depletion gilding. In this gilding, some material is removed to increase

the purity of the gold. Of course, gold must be already present on the surface of the object. For this

reason, this gilding procedure can be applied only to objects composed by gold alloys, usually gold

with copper and/or silver. The gilding is performed by removing the metals, which are not gold.

These metals are etched away from the surface by means of the use of some acids or salts, often



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combined with the action of heat. Of course, there is no gold addition, because the object already

contains gold.

Depletion gilding: Depletion gilding is based on the property of gold of being resistant to oxidation

or corrosion by most chemicals, whereas many other metals, such as copper and silver, are not so.

Therefore an object, cast for instance by an alloy of gold with copper and silver, can be immersed in

a suitable acid or packed in a salt, which attacks the copper and silver in the object's surface. The

action of acid or salt is transforming these elements to some copper/silver compounds that can be

removed from the object's surface by washing or heating, or by using a brick dust [4, 5]. The result

is a thin layer of nearly pure gold on the surface of the object. Often it is necessary to repeat this

procedure several times, making the resulting surface soft and spongy with a dull appearance. For

this reason, most depletion-gilded objects are burnished to make their surfaces more durable and

give them a more attractive polished finish.

Depletion gilding was widely used in antiquity. A historical and technical introduction of this gold

surface enrichment is given in [6], which discusses how goldsmiths have used the depletion gilding

technique for “coloring the gold”. The process requires some skill to execute it properly, but it is

technologically simple. Moreover, it is requiring materials that were available to most ancient

civilizations, those that were able of making alloys.

For what concerns the color of gold, let us note that pure gold is slightly reddish yellow in color.

Other colors can be produced making alloys with silver, copper, nickel and zinc in various

proportions, producing white, yellow, green and red golds [7] (see Appendix for some data). In the

case of an alloy of gold and copper, the result is a red or yellow-red color. These alloys were used

especially in the pre-Columbian Meso- and South America. Known as “tumbaga”, this material was

used widely both for castings and for hammered metal works. A further depletion gilding was

giving to these objects the color and luster of pure gold.

Today, gold alloys have many applications in dentistry, jewelry and industrial areas too (let us note

that gold is used for corrosion protection of electrically conductive surfaces [8]). For economic

reasons then, much effort has been made to lower the gold content in the bulk of such alloys. As a

consequence, the surface enrichment of low gold alloys became an interesting subject of researches

[9]: in this reference, we find the modern methods for the creation of a gold-enriched surface on a

gold alloy by depletion processes. Experiments tell that the additions of sodium chloride to pure

water speed up the oxidation of copper to copper chloride, which is dissolved at the metal-solution

interface. Additions of sodium sulfide to pure water should also speed up the oxidation of copper to

cuprous or cupric sulfide, but these compounds are insoluble in water, and then they are tarnishing

the alloy [9]. Let us remember that, in pure water, copper dissolves regardless of being in a gold

alloy or as metal [9].

American goldsmiths: However, how did the pre-Columbian populations of Meso- and South

America a depletion gilding? This question was the subject of several researches made by

archaeologists. In [4], we can find a description of techniques. It is also told that was Gonzalo

Fernandez de Oviedo (1478-1557), to give a hint on pre-Columbian depletion gilding, writing that

the pre-Columbian goldsmiths knew how to use a certain herb for gilding objects made of debased

gold. The alloys used were generally of two types [4]. One type is composed by the tumbaga

copper-gold alloys produced with differing gold contents, the other was that of pale greenish-white

ternary silver-gold-copper alloys, containing a high proportion of silver, similar to the

Mediterranean electrum and widely used in Peru.

For tumbaga, a depletion gilding technique was the following: the object made of tumbaga was

rubbed with the juice of a plant and then heated so that it assumed a gold coloration. This process

was repeated many times to improve the colour and increase the superficial gold contain. It is

believed that the plant was a species of oxalis and that the juice contained oxalic acid [4]. For

objects made of alloys of electrum type, they were probably gilded using a cementation process or

by using some aqueous pastes [4]. In the first process, the object was placed in a crucible and



100

surrounded with a powdered mixture containing alum, common salt and brick dust [4]. The crucible

and its contents were heated. The mixture reacted with the surface of the object, forming chlorides

of silver, copper and other impurity metals. The chlorides were absorbed by the brick dust [4].

Probably, additional ingredients may have been used too. After cooling, and subsequently washing

the object, the brilliance of the surface was increased by burnishing [4]. The second method was

that of immersing the object in an aqueous paste or solution of alum, iron sulfate and salt at room

temperature. After about ten days [4], the object was washed in a strong salt solution and then

heated to convert the spongy, gold-enriched surface to a smooth and compact surface. Both

cementation and aqueous methods work equally well on electrum and tumbaga [4].

Phase diagram of gold and copper: Tumbaga is an alloy of gold and copper then. However, we

can tell more about these two metals together. A study of the phase diagram of copper and gold

shows that they are completely soluble in each other with eutectic type low melting point, occurring

at a composition of 80.1% gold at 911 °C. In the Figure 1, the phase diagram is shown, adapted

from [10]. Phase diagrams of gold with other elements, such as platinum, silver, nickel and cobalt

are given in Ref.11. Let us remember that a naturally occurring alloy of gold and silver exists, the

electrum.

Fig. 1. Phase diagram Au/Cu

In the Figure 1, it is easy to see the eutectic composition. The word “eutectic” comes from the

Greek word “eutektos”, that is, “easily melted”. At the eutectic-composition, an alloy of two or

more metals, when heated to its melting point, completely changes from solid to liquid at the same

temperature [12]. Thus, the eutectic-composition is characterized by being the first alloy-

composition to melt during heating [12], such as the last to freeze during cooling.

The rounded shapes at the bottom of the diagram in Fig.1 show the regions where ordered phases

exist. According to [10], these ordered phases are usually harder than the disordered alloy of the

same composition, and they may make the process of working and annealing to shape more

difficult. Moreover, the quenched alloys between about 85% gold and 50% gold are softer than the

alloys that are allowed to cool slowly in air (quenching is the rapid cooling of a work piece). This is

the opposite of what happens in alloys such as iron and carbon, where the material is hardened by

quenching because of the formation of martensitic phase [10]. For the gold-copper alloys, the

softening by quenching process happens because it is suppressing the formation of the ordered

phases, which need some time to form. As told in [10], South American populations used water

quenching after annealing in order to make their alloys easier to work to shape and to avoid

embrittlement.



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The raft of El Dorado: The alloys of gold with copper or silver were produced by the pre-

Columbian people to create wonderful statues and ornaments. In the Figure 2, it is shown one of

such objects. It is the Muisca Raft, obtained in a lost-wax casting by the Muisca culture in a region

which currently corresponds to the center of Colombia. A recent study on Muisca metallurgy shows

that gold alloys were especially composed for votive metalwork [13], and in fact, the Raft is a

votive object. Today, it is exhibited at the Gold Museum in Bogota. The Raft refers to the ceremony

of El Dorado, during which Muisca chief, after covering his body with gold powder, dove into the

Guatavita Lake. Then, El Dorado was El Hombre Dorado, the Golden Man.

Fig. 2. The Muisca Raft (Courtesy: Wikipedia). It is a representation of the legend of El Dorado.

The cacique at the center of the raft is surrounded by attendants and oarsmen

The legends surrounding El Dorado changed over time, so that it became a golden city or a lost

kingdom full of gold. Many expeditions were made in the search for El Dorado: among the most

famous there was that led by Sir Walter Raleigh [14, 15]. All the expeditions did not find El Dorado

but mapped a large part of South America.

After failing in discovering El Dorado and its gold mines, the Spaniard conquistadores that had

promised their king a mass of gold in return for investing in the transatlantic voyage, resorted to

looting the treasuries of the local chiefs and the grave goods of cemeteries [16]. However, as

Shakespeare writes in his play “The Merchant of Venice”, “all that glitters is not gold”: when

Spaniard soldiers began to melt down the mass of the glittering ornaments, they discovered that

they had not pure gold, but an alloy debased with large amounts of copper. The result was that a

large part of beautiful objects, such as those held in the Gold Museum, were plundered by the

Spaniards and melted into “tumbaga” bars for transport across the Atlantic. Hernan Cortes and his

men for instance improvised a manufacture of such metallic bars [17].

Because all the metals that reached Europe were melted back into their constituent metals in Spain,

there is only an example of such a load, a group of over 200 tumbaga bars, discovered in the

remains of an unidentified shipwreck (around 1528), off Grand Bahama Island. This shipwreck was

found in 1993 [17]. Since we have mentioned Hernan Cortes, the conquistador who caused the fall

of Aztec Empire and brought Mexico under the rule of the King of Castile, let us mention an

interesting article on the metallurgy of Aztecs [18]. In it, is mentioned the pioneering research work

of Dora M.K. de Grinberg and others on the metallurgical skills of the pre-Columbian population

[19]. De Grinberg, an Argentinian archeologist working in Mexico, uncovered ample evidence that

the ancient American metalworkers were far more skilled than had previously been supposed [18].

Tumbaga: The word “tumbaga” is not native to any language of the area of Meso- or South

America. But it is not a Spanish word too. It is coming from Malay and means copper [20]. The



102

historical documentation on ancient American gold alloys begins with Columbus, who reported that

the word "guanin" was employed to express these alloys. Washington Irving, in his “Life of

Columbus”, wrote that in 1503 Columbus was on the Mosquito Coast. “There was no pure gold to

be met with here, all their ornaments were of guanine; but the natives assured the Adelantado that in

proceeding along the coast, the ships would soon arrive at a country where gold was in abundance”

[21]. In the reports of Columbus, it is evident his quest for gold. The same happens for other

explorers. In a 1546 communication to his king, Juan Perez de Tolosa reported on a population of

the Northwestern Venezuela that, in addition to possessing gold and other precious metals, had

ornaments of a copper-gold alloy called “carcuri”. Similar reports appear in the writing of Pedro de

Cieza de Leon, who explored the Cuca Valley of Northern Colombia during 1532-1550.

In a book of 1760 [22], written by Antonio de Ulloa (1716-1795), Spanish general and explorer, we

find other information about gold: “In the district of Choco are many mines of Lavadero, or wash

gold … There are also some, where mercury must be used, the gold being enveloped in other

metallic bodies, stones and bitumens. Several of the mines have been abandoned on account of the

platina; a substance of such resistance, that, when struck on an anvil of steel, it is not easy to

separate … In some of these mines the gold is found mixed with the metal called tumbaga, or

copper, and equal to that of the east”. Antonio de Ulloa uses the word “tumbaga” for copper then.

He continues telling that “its most remarkable quality is that it produces no verdigrease (verdigris),

nor is corroded by any acids, as common copper is well known to be” [22]. In fact, if we treat

tumbaga with an acid, copper is dissolved off the surface. On the surface, it remains a shiny layer of

nearly pure gold. As previously discussed, the use of an acid produces a process of depletion

gilding, not the verdigris. Note that, in the description made by Antonio de Ulloa, there is also

mentioned another material, the platina, that is, the platinum.

Among the first modern reports about tumbaga, there is that by G. Créqui-Montfort and P. Rivet,

published in 1919 [23], who described the tumbaga in Colombia. The documentation of a similar

pre-Columbian alloy with depletion gilding to produce a golden surface is given in the Ref.24. In a

report of 1949, W. Root is comparing the physical properties of tumbaga with those of unalloyed

gold and copper. In his review [25], Root tells that tumbaga seems to have originated in Colombia

or Venezuela before AD 1000 and spread to Ecuador and Peru. But, in a discussion about gilding

[26], Heather Lechtman et al. tell that the depletion gilding was first developed by the Moche

culture of Peru, about AD 100-800. Therefore, depletion methods of gilding used in Peru, from this

center of origin, spread north into Ecuador, Columbia, Venezuela, Panama till Mexico [26].

In nanotechnologies: Today, tumbaga has an important role in nanotechnology. In fact, the gold-

copper alloys are emerging as an important catalyst. In [27], the authors investigated the phase

diagrams of various polyhedral nanoparticles, made of gold-copper alloy. In these particles, the

researchers revealed a gold enrichment at the surface, like in tumbaga, leading to a kind of core-

shell structure, analogous to the surface enrichment of archaeological artifacts. The most stable

structures of the nanoparticles were determined to be the dodecahedron, truncated octahedron, and

icosahedron with a Cu-rich core/Au-rich surface. In [28], nanorods of AuCu3 had been investigates,

in particular to determine the catalytic activity of them, when different surface ligands are used.

Besides nanoparticles, in catalysis, sensing, and other areas, porous gold is used [29-32]. This

material is made by dealloying gold alloys [29]. In fact, this relatively new material is like the

surface of tumbaga, the spongy gold which is produces by dealloying the surface layer with gilding

depletion. For what concerns porous gold, let us conclude with an interesting feature of the layer of

gold on tumbaga, discussed by Stuart J. Fleming in Ref.16. Fleming tells that tumbaga has a “self-

healing” property. When corrosion happens, some gold atoms are set free by it. These atoms can

migrate and seal the minute channels, which are originated by the corrosive attack. For this reason,

objects made of a relatively gold-rich tumbaga can retain for a long time their original luster. This

property of self-healing of gold alloys could be interesting for nanotechnologies too, where surfaces

have a relevant role, due to the reduced dimensions of involved materials.



103

Appendix on colors of gold-copper alloys: Here a table on the color and chemical composition of

some alloys with karat number 18 [7]. Let us remember that 24 kt gold is pure gold. The

designations 18 kt, 14 kt, or 10 kt indicate how much pure gold is present in the mix: 18 kt gold

(75% gold) has 18 parts gold and 6 parts of another metal(s), 14 kt gold (58.3% gold) has 14 parts

gold and 10 parts of another metal(s), and so on for 12 kt and 10 kt gold. 10 kt gold is the minimum

karat designation that can still be called gold in the US [7].

Table 1

Color of Gold Alloy Compositions Containing Copper

Yellow Gold (22 kt) Gold 91.67%, Silver 5%, Copper 2%, Zinc 1,33%

Red Gold (18 kt) Gold 75%, Copper 25%

Rose Gold (18 kt) Gold 75%, Copper 22.25% Silver 2.75%

Pink Gold (18 kt) Gold 75%, Copper 20%, Silver 5%

Gray-White Gold (18 kt) Gold 75%, Iron 17%, Copper 8%

Light Green Gold (18 kt) Gold 75%, Copper 23%, Cadmium 2%

Green Gold (18 kt) Gold 75%, Silver 20%, Copper 5%

Deep Green Gold (18 kt) Gold 75%, Silver 15%, Copper 6%, Cadmium 4%

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