UDK 621.892:621.771:621.778 Pregledni znanstveni članek
ISSN 1580-2949 MTAEC9, 39(3)61(2005)
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
LUBRICANTS FOR THE ROLLING AND DRAWING OF
METALS
MAZIVA ZA VALJANJE IN VLEČENJE KOVIN
Dušan ]určija1, Ilija Mamuzi}2
1 Kneza Branimira 7, 44103 Sisak, Croatia 2 Metallurgical faculty, University of Zagreb, Aleja narodnih heroja 3, 44103 Sisak, Croatia
Prejem rokopisa – received: 2004-01-19; sprejem za objavo – accepted for publication: 2005-03-24
A survey is given over lubricants for rolling and drawing of metals. Emulsions, suspensions, natural fats and oils and synthetic lubricants are presented. Fluid mechanics Reynolds equations are used for the calculation of the lubricant layer in the entering section of the metals deformation zone. Colloide chemistry is used for the analysis of surface active additions on lubricant properties, lubricant layer thickness and the wetting angle. Lubricants for hot rolling based on suspensions and glass are presented also. Special attention is given to the removing of lubricant from the surface after processing, to measures for the protection of workers and to ecological problems of used lubricants.
Key words: lubricants, emulsions, suspensions, Reynolds equations, lubricants toxicity, surface roughness
Dan je pregled maziv, ki se uporabljajo pri valjanju in vlečenju kovin. Opisane so emulzije, suspenzije, naravna olja in masti ter sintetična maziva. Reynoldssove enačbe iz mehanike tekočin so uporabljene za izračun debeline sloja maziva na prerezu kovine na začetku deformacijske zone. Koloidna kemija je uporabljena za opis vpliva površinsko aktivnih snovi na lastnosti maziva, na debelino sloja maziva in na kot omočljivosti. Opisana so maziva za vroče valjanje na osnovi suspenzij in stekel. Posebna pozornost je namenjena odstranitvi sloja maziva s površine kovine po procesiranju, ukrepom za zavarovanje delavcev pri delu in okolju.
Ključne besede: maziva, emulzije, suspenzije, Reynoldsove enačbe, toksičnost maziv, hrapavost površine
1 INTRODUCTION
The basic tribological principles presented in ref. 1 for the manufacturing of steel ropes and metal extrusion are enlarged to the use of lubricants for the rolling and drawing of metals. The methods for the deposition of lubricant in the processs of working of metals were developped gradually. In Figure 1 a modern system for lubricant deposition is shown shematically.
Water, water steam and air temperarure are adjusted to the the type of lubricant by means of thermoregu-lators. The system is equipped with contact manometers,
Figure 1: Functional lubrication system. A – Entering collector, B – Preparation of the mixture, C – Mixing of components, D – Feeding, E – Rollls, M – Lubricant, VMS – Water rich mixture, MS – Lubricabnt mixture, V – Water, Z – Air, REC – Lubricant recirculation Slika 1: Funkcionalni sistem za mazanje. A – Vhodni kolektor, B – Priprava zmesi, C – Mešanje komponent, D – Dodajanje, E – Valji, M – Mazivo, VMS – Zmes, bogata z vodo, MS – Zmes maziva, V – Voda, Z – Zrak, REC – Recirkulacija maziva
devices for condensation, flow regulators, devices for authomatic feeding of lubricant and for the recycling and regeneration of lubricant returned in the processing. Pioner works in these topics are of Troost A., Roberts W.L., Billigman Y. and Stone M. The hydraulic resistance of emulsions at flowing through the feeding tubes and devices is specific by relation to other liquids. The hydrodynamic findings related to these topics were established by Dans and Rosii, while Darsi and Vejsbah developped the theoretical base.
2 LUBRICANTS FOR DRAWING AND ROLLING
2.1 Emulsions for cold working
Emulsions are of the greatest importance for the cold working of metals. The viscosity of the systen can be calculated using Einstein’s and the Taylor’s equation1
ß = ßd
1 + 2,5<p
ß
+ 2ß
ße  +ßd
¦])
(1)
This equation describes well the viscosity of dispersion systems up to the content of 15-20 %. For greater concentrations emulsions of the type water in oil consist of colloide systems with more phases. Equation (1) can’t be applied for boundary conditions where the viscosity changes rapidly and also using optical microscopy reliable informations on the colloide systems can not be obtained. These areas of colloide systems limit the technological use of emulsions, since, the
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
friction force does not depend on emulsion concentration due to possible inversions of phases in the emulsion. These problems were approached with investigations of sedimental characteristics of half dispersed concentrated emulsions and modelling of their layering2. The simulation is performed on the base of electrostatic fields.
The layering rate is defined as
dt
k1 (H
H)
and calculated using the following solution
b  \ U=\a+-----(H-Hdf)
(2)
(3)
With constants a and b independent of the quatity of dispersed phase in the initial emulsion and on it concentration and k1-reaction rate constant. The rate coarsening of emulsion particles (droplets) is calculated using the equations3.
64 sDCv
d3 =a0 +b0t   andb0
9    kT
(4)
The decrease of the solubility of soap in emulsions deteriorates their technological properties. For lowering the effect of impurities 0.4 g/L sodium polyphophate (NaPO3)x with x = 20–200 is added without effect on the layering, on the viskosity and pH. In place of sodium polyphosphate, stearate and the expensive olein acid also cotton oil can be added to the emulsion, however, this addition decreases the emulsion properties.With change of temperature, also physical properties of emulsions, such as density, adhesion and cooling capacity are modified. The proper use of emulsion can lower down to 10 % the rolling energy used, while the rejection is diminished up to 20 %9,10. The stability of the emulsion is of very great practical importance11, while it inversion causes serious problems for the emulsion treatment. The problem is mostly investigated with the determinatiomn of the coalescence of emulsion particles (droplets) in the dispersed medium or determining the life time of a particle on the boundary of two liquids12.
C/(g/L)
Figure 2: Influence of Ca2+ and Fe2+ ions c/(g/L) on the destabilisation of the emulsion composition we/%.1,3 - content of Ca2+; 2,4 -content of Fe2+; 1,2-emulsion with 4 % of additions; 3,4 emusions with 2 % of additions
Slika 2: Vpliv Ca2+in Fe2+ ionov c/(g/L) na destabiliziranje sestave emulzije we/%: 1,3 - vsebnost Ca2+; 2,4 - vsebnost Fe2+; 1,2 - emulzije s 4 % dodatkov; 3,4 emulzije z 2 % dodatkov
600
_ 500 E 400
E 300
S 200 a 100
			
iF=-Č			
			
			
			
			
200
400 d /(mm)
600
800
Figure 3: Distribution of the oil quantity pon/(mg/m2) over the sheet width d/mm for the cooling of rolls with emulsions; - emulsion based on water, A - emulsion based on water and lubricant Slika 3: Porazdelitev količine olja pon/(mg/m2) na površini traka po širini d/mm pri hlajenju valjev z vodnimi emulzijami; - emulzije na osnovi vode, A - emulzije na osnovi vode in maziva
Microflore contamination has a deleterious effect on emulsions and their cooling capacity, it causes also the demulsion and decreases the emulsion concentration. Such emulsions are faster saturated with mechanical particles and require more addition of fresh emulsion. For this reason, to emulsions 0.1–0.15 % of stabilising antimicrobic substances are added. This addition lowers the consumption of emulsoil, diminishes the sheet contamination, it can however, due to the change of pH, increase the corrosivity. The stability of emulsions is decreased with increased content of ions, f.i. Ca2+, Fe2+ and Cl–. The origin of calcium ions is the used water, while, the sheet surface is the source of iron and chlorine ions. On Figure 2 the destabilisation of emulsuons is shown in dependence of some ions concentration.
The destabilisation of the emusion can be prevented with addition non ionic emulgators, with use of pure water and with clean sheet surface. The addition of 10 % of palm oil has a beneficial effect on cooling emulsions and improve the cleannless of the sheet14, as shown in Figure 3.
Applying the proper droplets size and thickness of the filtering layer, the properties of emulsions are improved and the quantity of mechanical impurities, oxydation products and polymerisation products is diminished. With active additions and fillings, the properties of emulsions can be modified. It is important that surface active additions are stable in the range of temperature of the processing and play a role of plasticators15 thickening the emulsion16.
Microemulsions16 with droplet size below 0.1E-6 were not investigated sufficiently for eventual use for plastic deformation of metals. Three types of stable properties are required from these emulsions: sedimentation, floculation and coalescence. According to russian standards for microemulsions, the surface active additions Span-80, T-2, Sorbitan-O, Pentol and Stearoks 6 are used, especially in case of greater cooling efficiency.

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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
2.2 Emulsoils
Emulsoils are colloidal solutions of soap and free high molecular acids in mineral oil of average viscosity (20–40) E-6 m2/s stabilised with water or alcohol and with a content of organic acids of 8–12 % and are widely used in metallurgy17. Their effect on the lubricant layer in the deformation zone can be opposite to that expected from solutions of theoretical equations developped for standard emulsions. Up to now, no explanation was proposed for their effect and the theory was advanced that they represent a special form of the Rebunder effect. Emulsoils based are some alloyed lubricants with the viscosity of 4.19 mm2/s, density of 845 kg/m3 at 20 °C, surface tension of 0.03 N/m2 and flash point of 138 °C.
2.3 Graphite lubricants and emulsions
Graphite lubricants combined with emulsoils are frequently used for plastic deformation of metals18, as shown in Figure 4.
On the base of experimental results the following equation was deduced for the wetting angle:
\RT J
With: T- temperature, E - activation energy, R - gas constsnt and 00 - wetting angle for the null concentration of the active substance. The wetting angle is decreased with increasing the content of surface active additions and of electrolyte.
The stabilising additions should be adapted to the emulsion type19. In dependence of pH of the emulsion, cation or anion type emulgators should be used with the hydrofilic-liofilic number known. The efficiency of the lubricant is increased also using ultrasound in the preparation of the emulsion. Unstable emulsions for plastic working of metals are of the water - oil type and are manufactured by mixing at the rate of 100-200 r /min. Without addition of emulgator, these emulsions are kept at the temperature aronund 70 °C. According to I.A. Buchbinder, the turbulent flow occurrs in emulsions with fat oils in content of 20 % for a Reynold’s number of
150 i------
145      \Č
©   14°        Č\-
135                   Čv
130 I                                "-
0         0,05        0,1        0,15        0,2        0,25
CNaci /(mol/L)
Figure 4: Wetting angle 9 / ° of emulsions on graphite in dependence of the concentration of NaCl (mol/L)
Slika 4: Kot omočljivosti 9 / ° na grafitu v odvisnosti od vsebnosti NaCl (mol/L)
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
1400-1600, thus earlier than for pure water. The Reynold’s number is generally determined using potential functions frequently called also as "catastrophe theory". Synthetic oil emulsions are stable due to the presence of glycol monoether and more atomic alcohols acting as emulgators. By mixing, it is necessary to consider the product n1/2d0.8m which value should be between 0.7 and 10 and the Weber number: We = pn2 dm3/a. In the gravity field this number is deduced as: d/dm « We-0,6 with p -emulsion density, n - frequency of rotation and dm -mixer diameter and d - the average size of emulsion droplets: d = XNidi3 / XNidi2; o - surface tension on the boundary of both phases solid (T) and liquid (P), Ni -number of droplets of diameter d. The surface tension can be deduced using the Džirifalc relation: cos 6 = 1 - 2 JôT /ôP - m / op, with m as correction4 because of the
absorbtion of liquid vapour on the solid surface.
The distribution of particles of dispersed phase follows the law of normal distribution in emulsion of the type "oil in water" and "water in oil". However, the normal distribution is not met always23 and other types of distribution occurr also, f.i. Rosin-Rammler, normal-logarihtmic and Pearson distribution. In Figure 5 the Pearson distribution is shown23.
Also the size decreasing of droplets in turbulent field using mechanical, ultrasound and vibrational mixer is modelled mathematically. For the size decrease of droplets a determined time is required which can be evaluated using the Navier-Stokes equation: t « pvd / o considering fluid density, kinematical viscosity, droplets size and surface tension. The proces was investigated
0        1         2        3        4$
Figure 5: Pearsons diagram. ß1 - index of normal square of asimetry, ß2* - index of of the normal square of peaked distribution, A - crytical area, B - U area of beta distribution, C - area of J distribution, E -gama distribution and F- normal logaritmic distribution. Slika 5: Pearsonov diagram. ß1 - indeks kvadratov normalne simetrije, ß2* - indeks normalnih kvadratov žagaste distribucije, A -kritična površina, B - U površina ß distribucije, C - površine J distribucije, E - gama distribucija, N - normalna logaritmična distribucija
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
little and several theoretical and empirical relations have ben proposed for its generalisation.
2.4 Natural oils and fats
For the plastic working of metals natural and synthetical oils and fats are used23. Of natural oils the ricinus oil consisting of hydro acids is mostly used (it is used the most for lubrication of aircrafts engines). Also palm and cocos oil are widely used. Natural oils have an agreable scent, are oxydation resistant, dry slowly in air and are classified according their yodine number, which is indicator the drying and polymerisation rate. For use in plastic working these oils are hydrogenised and their yodine number is diminished to below 80. The palm oil consists of groups of oleine and linoline acids.
Cattle and sheep tallow and whale oil are the most used of animal products. Fats of animal origin are more propensive to bacterial activity than plant oils and are easier oxydised and contaminated. The addition of whale oil increases the emulsion viscosity by thre times. Fat oils should be used only in a very thin layer, since, thanks to the polarity of fat molecules, form a layer of molecular thickness26. Sulphurised fat oils are added to cutting oils to increase their stability to a higher temperature, as the formed iron sulphide prevents the direct contact of two clean metal surfaces. Technical fats of soaps origin are classified by the length of soap thread 1–100 µm and are used for the lubrication of reductors and rolling stands. Oils decay with formation of CO2 by atmospheric oxydation and are carbonised if the working temperature is increased above a limit characteristic for the oil. All degeneration processes are inhibited by keeping the lubricant in vacuum or in nitrogen.
2.5 Soaps
Soaps are widely used as lubricants for the drawing of metals. The first informations on the nature of soaps and water-soap emulsion of MacLennon date from 1923. Soaps don’t have a crystal structure and exist in different phases: izotropic solutions, soaps kernels and threads. Mc Bain and Langdon discovered the half soaps, which according to Voldo, do not contain liquid crystals but soap mycelia and are called also "boiler soap". After McMahon discovery that the Gibbs rules apply also for soap phases, the treatment of soaps changed from empirical to scientific. More informations on soap phases are obtained with calorimetric and dilatometric investigations than with X ray diffraction. The Kraft point defines the boundary between the isotropic solution and the thread. The phase behaviour of soaps was relatively little investigated up today. Harkins and Langmuir investigated the orientation of soaps molecules on free surfaces and Rayleigh showed that the orientation depends on static and dynamic tension. Christo-person and Naylor27 were the first to investigate the use of soaps in metallurgy, while Perlin28 applied as first the fluid mechanics to soap emulsions.
64
2.6 Synthetic fats and oils
The use of synthetic fats and oils dates from the end of the second world war and actually are used for the range of temperature from -60 °C to 300 °C. With antifriction additions the rheology and colloidal stability of fats are improved. As additions, graphite and molybdenum disulphide are used, mostly. The addition of polymers increases the resistance to mechanical and thermal loading. More frequently used polymer additions are polyisobutilene, poymetacrilate, plaxol and lubtisol. Also powder lubricants are a useful addition, f.i. poly-etilene with high and low density, polytetrafluoretilene, polyvinyl chloride etc. With appropriate thermal treatment at the temperature of 150 °C the fat resistance is increased up to four times. Fat lubricants are able to support heavy loading in hard working conditions. They decrease the contact friction due to the absorption of molecules on the metal surface. The absorbtion strength is determined by measuring the exit work for electrons applying the method of contact potential difference KRP. The absorption of radicals and molecules on the metal surface can decrease or increase KRP. With longer metal immersion in oil also the absortion is increased and the friction is diminished. The absorbtion is affected by pitch products containing oxygen, sulphur, nitrogen and polycyclic aromatic hydrocarbons.The absorbtion rate is defined as: AKRP/Ar = d<p/dr with the exit work inversely proportional to the immersion time. The rate of the exit process depends on the donor and acceptor mechanisms32.
Also surface active substances, mostly oleine acid, are added to fats. According to Rebinder, surface active additions inhibit in absorbtion time the formation of a structural skeleton and increase, in this way, the fat fluidity. The origin on the anomaly of litium soap is in the formation of eutectic mixtures by crystallisation. The hermetic capacity of fats depends on the type and the dispersion of the filler.
Fat lubricants for steel ropes are controlled also for the resistance to cold. The rope is covered with lubricant, loaded and cooled to -40 °C. The adhesion work is than determined measuring the electrical resistance33 of the lubricant layer, which increases with increasing pelling.
Figure 6: Device for the pressure impregnation of steel rope Slika 6: Naprava za impregnacijo jeklene vrvi pod pritiskom
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
e?—?	¦          n          rn   -----n-------c	
	3-------t-l          L	Č450
f	Či	Č
/_AČČ	ČČ	120
iiČ*     ;		90 -
2000
?6 Ě4
C- 2 0
C/%
Figure 7: Dependence of kinematical viskosity (A) r\/ (mm s ) and of the viscoosity index (D) for a synthetic oil on the content of copolymer c/%.
Slika 7: Vpliv vsebnosti kopolimera c/% v sintetičnem olju na kine-matično viskoznost(A) r\/ (mm2 s-1) in na indeks viskoznosti (D).
The surface cleaning can also be included in the finishing operation of the manufacturing process, as shown in Figure 6, where the sheme of pressure impregnation of steel wire with a hydromechanical gate is shown.
The steel rope (1) is covered with a protective layer from the vat (2), it is than lead over the toothed pump with a pressure gauge (4), through the pressure tube (3) and through the switch point (5). Fats for steel ropes are improved with addition of zinc34 up to the mass fraction (1-7)E-2 %.
Catalisators and additions increasing the viscosity are important also for the properties of synthetic oils. Figure 7 shows the influence of the copolymers35 vinipol+stirol on kinematical viscosity at the temperature of 100 °C. The lubricansts are checked for the crytical loading36 in dependence of the gliding rate and for the load capacity37 in dependence of the friction coefficient.
Polyphenilethers are aromatic compounds particularly resistant to higher temperature. The lubricant properties of these compounds in temperature range 200 °C to 300 °C are similar to those of mineral oils and better than those of silicon oils and aromatic hydrocarbons, they have, however, a lower load supporting capacity than mineral oils. Perfluorinepolyethers developped in 1968 as lubricant for space technology38 are resistant also to thermal and oxidation loading above 260 °C.
2.7 Clay suspensions
For the seamless tube technology the proper selections of lubricants39 for tools and accessories is of the greatest importance. The best performances are obtained using powdered slags and graphite as oil suspensions40 which could be used also for the drilling of tubes. Clay suspensions are used in petrol drilling technology41. Figure 8 shows the effect of additions on the stability of the montmorillonite in water suspensions.
For the content above 0.2 g-eq./L of KCl in suspension the clay is less stable than for suspensions
E
g
ige
Figure 8: Stability of montmorillonite as rate of clay decomposition (in v mg for 30 min) in dependence of the log. value of the content of salts D - KCl, A - CaCl2 and O - NaCl in water suspension Slika 8: Stabilnost montmorillonita kot hitrost razgradnje gline (v mg na 30 min) v odvisnosti od logaritma vsebnosti soli D - KCl, A -CaCl2 in O - NaCl v vodi.
with other salts. By increasing the content of salt up to 0.5-0.8 g-eq./L the stability is increased. This is explained in terms osmotic pressure preventing the capillary absorbtion of water in clay.
2.8 Glas as lubricant
Glas lubricants form by hot working a protective layer42 which prevents the surface oxydation, as shown in Figure 9.
By metal plastic deformation the scale can have also a lubricant action91. At high temperature a three layer scale is formed, an internal layer of FeO, an intermediate layer of magnetite and a layer of hematite in contact with the atmosphere. By air cooling FeO is decomposed to iron and magnetite. By low temperature the scale consists of two layers, a layer of magnetite in contact with the metal and a layer of hematite.
Experimental data show that the average oxydation rate of steel in an atmosphere containing oxygen and water vapour (pH2O « 40 kPa, T = 1273 K) is of 270 mg/cm2 h. If the steel surface is covered with a 0.2 mm thick layer of 0,33 Na2O 0,67 SiO2 glas the oxydation rate is diminished by 5 times and for a layer thickness of 2.5 mm by 55 times. The bare metal surface is oxydised according to the reactions:
2Fe + O,->2FeO and Fe + H,OČFeO + H,
(6)
				
	,			
5  9nn	\			
Ž* iČn				
sr' mn	v			
Ł"    50	V			
0		č"""--------------		
0.E+00         1.E-03
2.E-03 dim
3.E-03         4.E-03
Figure 9: Influence of the thickness d/mm of the glas layer on the surface on the oxydation rate vT/(mg/cm  h) of a steel Slika 9: Vpliv debeline sloja stekla na površini d/mm na hitrost oksidacije vT/(mg/cm2 h) površine jekla
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
By surface oxydations blistering may occur. The crushing of blisters shell lays the metal surface bare and accelerates the oxydation rate. The crytical radius of the blister in the scale layer is calculated using the equation:
2o   sino
2pg 3o
1/3(pg(6+3cosö-cos3ö))
(7)
Using appropriate data a radius of 0.52 mm is calculated. Soda water with the SiO2 : Na2O2 ratio of 2 -2,5 was used as lubricant in the past.
3 FUID MECHANICS BY WORKING OF METALS
For the simple die design43 in Figure 10 the process of cold drawing can be described with the Reynold’s equation
dp    6nv0(h0-h(x))
dx
h 3 (x)
with
µ = µ0 exp (yp), h(x) = h0-xtana            (8)
The solution of this differential equation allows to calculate the pressure in the lubricant layer in the matrix;
3fi0yv0
p
 1
ln
y
1
hm
(9)
Introducing p = equation is obtained
h
h(x)tana\       h pm; h = hm the Mizun-Grudev
3ju0yv0
(10)
Š1-exp(-ypm)tana]
A die of more complex design44 is shown in Figure 11.
The proces is divided in two phases and for each of them the Reynold’s equation is applied separately. The connection of the lubricant layer between the areas of thickness Ł2 and Ł1 is given by the following relation:
2
Łl(1-exp(-yp0))
12ju0yv0lk
(11)
By increased drawing rate in the Reynold’e equation also the effect of inertia45 is considered in the following way:
Die
lubricants
Figure 10: Sheme of die drawing with lubricant Slika 10: Shema vlečenja z votlico z mazivom
T hi
Figure 11: Sheme of drawing with a more complex die Slika 11: Shema vlečenja z bolj kompleksno votlico
dp    6ß.v0      C1!x
tanap
dx    h2(x)    h3(x)   120h3(x) withC   = —
(16v20h2 -C1
- + 2vh(8vh + 3k); k
2   (12) 120u
tana
For an actual technological processing, the calculations according to equation (12) gives an increase of the pressure gradient in the lubricant layer on the die entering section for a few %. In the lubrication equations also the effect of diffusion forces can be introduced46 as result of the interaction between the lubricant and the solid metal surface: Ž(x,y) « Ł (tan2ö - 62)/e3 with: Ł « 10–20 J, O - equilibrium vetting angle and Ł - lubricant layer thickness.
An analogous treatment can be evolved also for the rolling of metal, only the linear projection of the rolls vector is to be added to the rolling rate, as shown in Figure 12.
The proces is described with the simplified version of the Reynold’s equation47:
dx
jU
d2vx   dp
0;
dv     dvy
y 2     Č         dx      dy
0
(13)
The solutions of this equation are different and for the case of calculation the roll jump48 and the lubricant back rate before the rolling gap the following solution is used:
Figure 12: Sheme of rolling with lubrication Slika 12: Shema valjanja z mazanjem
r   =


Ł
2
66
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
dp _    2>uw(R-4r dx
yv
(y0
= Ł„ + R-4r
H)2-(y0-yv)2
(14)
With: m - rolls angular velocity, AH - decrese of sheet thickness, R - roll radius, µ - lubricant dynamical viscosity, y0 - lubricant layer thickness in the gap section with the maximal rate of back flow of metal, Ł0 -lubricant thickness in the entering section of the deformation zone, vx ; vy - lubricant rate in Descartes coordinates.
A more used form of the equation49 is:
dp dx
: 6fi(v0 + vR )
e0-e(x) e(x)
; e(x) = Rcosa-Rcos<p0 + e0
Ux2 -R(AH-2e0)]
2R
(15)
If in equation (13) also the sheet and rolls surface roughness are considered50 the solution for the case of an average roughness is:
'dp) \dxl
--6/u(v0+vRx)
	I1)	
1 \	w	V3(x)/
Ł2(x)/	/1\	
	Vol	
(16)
With e(x) = Ł(xsmooth) + ŠôV(x) + ôT(x)]. For the solution for a smooth surface the lubricant layer thickness related to the roughness of the rolls and sheet surface is added. The influence of the roughness was carefully checked empirically. It was established that the longitudinal roughness decreases the layer thickness in the entering section of metal deformation, while the transverse roughness increases the lubricant layer thickness in the deformation zone and it is, therefore, usefull. The lubricant layer thickness at the initial section of the plastic deformation zone depends on the thickness on the sheet and it was established that the thickness of 1 mm is sufficient. It is, however, in surplus and necessary only as boundary condition x = °° required for the solution of the equation (16).
The physics of the proces can be explained considering tangential stresses52. In this case the equations are written as follows:
dp dx
1 d(2kh)    2n; dp h    dx        h   dx
6ju(v0 +vR)   12fiQ
Ł2(x)
Ł3(x)
.ß(vR
-v0)
e(x)
e(x) dp 2   dx
(17)
The equation taking in account also the longitudinal surface roughness is written as:
Ł(x)-Ł0
1
dp
6ju(v0+vR)\dx/     (Ł3(x)Y
(Ł3(x))«Ł3(x) + 3(52Ł(x)
(18)
y
Q
A		AFA		,Čo    Č
				45   /
L L L LCäüK				
LLLLLLLL				
LLLLL L.L>-				feilWČČ  RMS
LLLLUČ >->->-Jr       t—,				
Y      fe/				XllllC.
				X   \l_Ll_Lt,
ČAO     /				1 _---""\ L L L 11 VlllJ
				lllI
*A	0			ČA9o \f
i   *o
X
Figure 13: Graphic determination of the average roughness Ras Slika 13: Grafična določitev povprečne hrapavosti Ras
The surface roughness is of very great practical importance53. Its anisotrophy54 on the cold rolled sheet depends on the rolling rate, the reduction and the lubricant quality. In Figure 13 the method of determination of the roughness of the cold rolled sheet is shown.
The surface of an specific roughness area can be calculated considering the coordinates of it center (x0 ; y0) and radius (r) using the equation:
R                 R2
R„nr,   —R„a<   H-----a 4=(R„
42
R
-)
2R„
R
-V2Ra45 (1+a 90-)
R,
R2
"Ra 90  + 2 x0Ra90
2Rn
(19)
r = Čy0+(Ra90-x0)2
considering the following relations:
(0 : Ra0); (Ra45 / 42 : Ra45 / 42); (Ra90 : 0) The specific area of the roughness shape is:
y,               x
i—
x
R a0-y0
F          R a90 y 0 + R a0 x 0    ,    r2 t',   — ------------------+---
2               2
y0
.     -*a90     x 0 arctan--------------- arctan -
y0                         x0
The center of the isotropic roughness is then:
V    71
(20)
On Figure 14 the roughness56 of the cold rolled sheet in dependence of its initial roughness and on Figure 15 the solutions of the equation (17)57 are shown. The roughness decreases with the increasing number of rolling passes. The rough surface of rolls can be obtained either mechanically58 or, as it is presently achieved, with electropolishing. For the case of boundary lubrication, the roughness of the sheet could be greater than that of the rolls. In this case, the rolls require a suitable surface
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
67
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
1,5
1
0,5
			
1________			
		 2	3
		4	
Figure 14: Influence of the sheet roughness RZ / µm on the lubricant layer after e /µm cold rolling. The numbers designate the pass number Slika 14: Vpliv hrapavosti RZ / µm pločevine na sloj maziva e /µm po hladnem valjanju. Številke so oznake za valjalniške prehode
treatment. Small sheet roughness smaller than 1,0E-6 m is not recommemded, since it related to sheet micro welds by the annealing of coils. The use of unproper lubricants, especially those containing graphite, can produce sooth stains which, according to Howkins and Mecallan, contain carbon, iron, oxygen or iron carbide. The coefficient of roughness transmitted from the rolls to the sheet is in case of lubrication of 0.6-0.7 and by dressing it is of 0.5. Inaccuracies of solutions of the equation (17) can result from the slippage of lubricant between the rolls and the sheet because of the to small adhesion work.The forced slippage decreases the pressure gradient in the lubricant in relation to its complete adhesion to the rolls and sheet surface(*) of: grad p / grad p* = 1/(1 + 6fißC / e02) with ßC as coefficient of forced slippage. This relation was not yet experimentally confirmed.
4 LUBRICANTS FOR HOT ROLLING
The metal resistance to deformation is smaller by hot59 than by cold working and other lubricants are used, also, for hot rolling. Earlier, lubricants were used resistant to oxidation and producing smoke60, f.i. glass,
Figure 15: Change of contact stresses PC/MPa, CS/MPa, lubricant layer ec/µm and wear coefficient CA along the deformation zone Lc. 1-pressure, 2-lubricant layer, 3-tangential stress, 4-wear coefficient Slika 15: Sprememba kontaktnih napetosti PC/MPa, CS/MPa sloja maziva ec/µm in koeficienta obrabe CA vdolž zone deformacije Lc. 1-pritisk, 2-sloj maziva, 3-tangencialna napetost, 4-koeficient obrabe.
graphite and eutectic salts. The use of colloidal graphite was investigated in Russia allready by the 1930-thies and it is investigated also presently due to the great importance of graphite as lubricant for mechanical, metallurgical and electrical industry.
The use of appropriate lubricant for hot rolling has prolonged the working life of rolls from 2600 t to 3200 t.62 The use of synthetic lubricant decreased the pressure of metal on rolls by 17 % and the coefficient of contact friction by 35 % when compared to the rolling using cooling water only63. A greater decrease of contact friction is obtained using64 synthetic lubricants than with castro oil and masut. The fat addition65 to the lubricant is by hot working greater than by cold working and it does not exceed 8 %. Also surface active subtances66 are added, such as IS-20 and P-20, both increasing the adhesion in the range of boundary friction67 by a surface roughness of (0.04–0.06) E-6. The perspective for hot rolling67 seems to be the use of solid fats, mixtures of fats and synthetic additions and of lubricant in form of air suspension.
At high temperature fat and oils are not stable, f.e. palm oil is decomposed in several products which, mixed with wear products and oxide particles, contaminate the sheet surface. The process of decomposition is slowed by proper aditions and in Figure 16 the effect of sodium polyphosphate on the layering of palm oil is shown69.
The maximum is by the addition of 0.15 % of sodium polyphosphate for the water emulsion with 1/7 of palm oil and for the temperature of 70 °C. As lubricant and cooling agent for hot working70, it is possible to use also water with soap addition, even sea water with soap addition.
Lubricant emulsions used for hot working are rapidly degraded because of the effect of microorganisms, such as aerobic and aneorobic bacteria and mildew spores all causing earlier ageing and lowering of chemo-physical, technological and hygienic properties. The degradation can be slowed with bactericide additions. A strong antimicrobic effect is obtained by addition of thriso-diumphophate and soda in the content of 30-60 g/L of
ß/s
150		¦ -č	«*.	Č Č	
100					N \
50					
0.2
0.6
CpFN''
PFN'%
Figure 16: Layering time for the emulsion ß/s in dependence of the content of sodium polyphosphate CPFN/%
Slika 16: Čas za razslojenje emulzije ß/s v odvisnosti od vsebnosti natrijevega polifosfataCPFN/%
68
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
emulsion and of 0.4-0.5 % of phormacide. The exploitation time can be increased up to 4-6 times and the quantity of used additions significantly lowered.
The dilatation of emulsion lubricant because of the increased temperature is calculated using the equation:
V1 = V0Š1-Cln(1 + p/D)];V1 = V0Š1 + C(t-t0)]      (21)
With: V0 as initial lubricant volume by the pressure p0 and C and D empirical constants, the volume expansion
coefficient: C0 = 0,0006 - 0,0008 —, -t,t0 rolling
temperature and temperature of softening of the solid lubricant. From equation (21) it is possible to develop the Barussa's equation, which gives the dependence of viscosity on temperature.
 /u0 expyD
exp
— (t-t0)ď C            )
(22)
Very good effects are obtained by hot working using suspensions, which differ from colloide solutions being more finely dispersed. If resistant to coarsening and sticking, suspensions are stable agregates. The stability is affected73 by absorption of electrically charged particles, which promote the hydratising of their surface. The measure of hydratising is the electrokinetic potential \p, which is shown in Table 1 for some compounds.
Table 1: Effects of the electrokinetic potential of some elements on clay suspensions
Tabela 1: Vpliv elektrokinetičnega potenciala nekaterih elementov na suspenzije gline
Absorbed ion	t/)/(mV)	Coagulation threshold KCl eqvi./(mg/L)
Li+	-58,8	21,6
Na+	-57,6	11,2
K+	-56,4	7,8
NH4+	-56,0	5,4
Ca+2	-52,6	3,0
Sr+2	-51,8	2,6
Ba+2	-50,8	2,3
La+3	-45,5	0,86
The clay electrokinetic potential74 and the clay suspension stability decrease with the increase of the valence of the compensating ion and a greater stability is found f.e. for lithium clay and a smaller for the lantan clay. The suspension is stabilised also with addition of isopolychromate, K2CrO4 and polyakrilamide. The montmorillonite and caolinite clays are stabilised and their properties improved with addition of lime.
The heat conductivity of suspensions increases linerly with the clay content and the heat capacity is, in the range of working temperature, independent of the mineral type. The viscosity of suspensions75 in homo-geneus field of gradient G and by gliding flowing for an elipsoide shape of suspension particles is:
Ši* = ŠiŠ1 + <pV(VF -SFG2 /D2)j;D = ňFkT/fiV0   (23)
With: F - shape index, V0 - the specific volume of the suspended particle, <pV - the volume content of particles, D - coefficient of diffusion by rotational mixing, k - Stefan-Boltzmann constant, T - temperature in K, µ*; µ - the effective suspension viscosity and the viscosity of the medium (solvent). The flowing of the suspension is described with the Fokker-Planck equation. However, the analytic solution are far from experimental findings and acceptable agreemenst was found only for diluted suspensions.
For the cleaning of suspensions with filtering76 the following equation was derived:
W
dr
	Wp	
l_(1	1 --------+ K2 -K1q)	q
(24)
With: W and WP - momentary and initial filtering rate (m/s), q - specific volume of the filter, r - filtering time and K1 and K2 - constants characteristic for the filtering process, first of all plugging and deposits.
Good properties, as f.e. low friction coefficient and longer layer stability at all temperatures are characteristic also for the flouorocarbon (CF)n. By reaction of fluorine with graphite or carbon at determined temperature the componud (C2F)n is obtained77. The fluorinating time is of 60 h and in graphite up to 14,4 % of fluorine is dissolved without effect on particle integrity although the specific volume is increased.
For the hot working of metals also glas based lubricants can be used. A very important property of glas used for hot working lubrication is the viscosity for which the following equation was derived:
fi = Aexp(H„ /RT) = AT exp(EČ /RT)       (25)
In the left relation the activation enthalpy is included and in the right the activation energy. AT depends on a number of factors, first of all the temperature range79. Eyring connected AT theoretically with the molar volume. The activation energy is than deduced from the equation:
EČ = 2,303RT (lg n - lg AT )                (26)
The driving force for the flowing of a drop of molten glas on a hard and flat surface is calculated using the Truton equation:
f S =3-"
dv dx
(27)
The driving force is proportional to the dynamic viscosity and to the gradient of flowing rate in the direction of the force. The wetting of the metal surface by hot working is not in thermodynamical equilibrium, since by high temperature also oxydes are formed and decomposed and films of water steam and oxyde vapour are chimisorbed on the metal surface. On more impure areas, the kinetics of the process can cause greater
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
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D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
equilibrium differences. Investigations have shown that in temperature range 550–600 °C the equilibrium wetting angle is achieved only after 10 min when the adhesion force is increased sufficiently. By lower temperature the equilibrium wetting angle is not achieved even after one hour. This is however without theoretical and practical interest80.
5 CLEANING OF METAL SURFACE AND LUBRICANT TOXICITY
Before further processing or use the, surface of cold worked products has to be cleaned81 of lubricant residues and impurities82. The cleaning could be also included in the finishing operation of the manufacturing process. The quality of the cleaned surface83 depends on the quality and type of the lubricant used. Specific problems are met in case of graphite containing lubricant84, since, and especially on the internal surface of tubes, residual sooth bands are found as residues of non removed lubricant. Electrochemical cleaning is frequently used for cold rolled sheet85. The removing of fat lubricant is improved applying ultrasound, which may, however, cause cavitation. For a better lustre, surface active compounds are added to the electropolishing solution87. The optimal lustre is obtained by a current density of 140–150 A/dm2 and the temperature 60–70 °C. Concentrated emulsions leave more impurities on the metal surface88, while emulsions with less than 1 % of addition may have even a corrosive effect for the metal surface. Mechanical particles with a diameter below 5.0 E-6 do not leave surface stains if their content is below appr. 5 g/L of emulsion. On Figure 17 a sheme of the installation for the efficient dry cleaning of sheets is shown.
The steel sheet (2) passes through the storage bin (1), over the guiding wheels (3) and through the powder
Figure 17: Sheme of the installation for the dry cleaning of lubricant
for sheets
Slika 17: Shema naprave za suho čiščenje maziva s površine trakov
70
store (4). With the belt (5) and the guiding rolls (6) the cleaning intensity is regulated. At the storage bin entry the rough cleaner and at the exit the fine cleaner are set. The circular brushes (8) remove the powder from the sheet.
Dry cleaning has a number of advantages over electropolishing: no evolution of hydrogen, no sheet surface oxydation, no additional treatment with chemicals, no scrap water, no nocive vapour and a smaller use of energy. Circular brushes are manufactured from technical felt. Sheets with thickness 0.15 mm to 1 mm can be cleaned with a sheet motion rate of up to 800 m/min. The relation of the sheet and the belt velocity is 2.5–3 and f.e. by a sheet velocity of 200 m/min the belt rate is of 500–700 m/min. The cleaned sheet has les than 0.2g/m2 of impurities. Approximately 20 kg of marble powder is used per t. of sheet and the cleaning capacity is of 3 t/min or more, depending on the sheet thickness.
To decrease the corrosive effect inhibitors are added to lubricants92. A direct relation was established between the inhibitor concentration, the stationary potential and the steel corrosion rate. The lubricant MT-16p has no protective capacity and the corrosion current increases from cyclus to cyclus. If 20 % of inhibitor is added the current is strongly diminished and after 1.5 h a constant value is achieved.
Efficient cleaning of fats from the steel surface is achieved using surface active componds93. The change of surface free energy ?G due to the removal of fat is:
?G = dMP e + dMP - dMM e                     (28)
The first term in the equation represents the change of specific free energy of the interface metal-liquid, the second the interphase tension and the third the specific energy of the interface metal – oil. In Table 2 some data on surface active compounds used for the removal of fat from steel surface are given.
Table 2: Effect of some surface active compounds, as wetting angle on the phase boundary, on the removal of fat from steel surface. Tabela 2: Vpliv nekaterih površinsko aktivnih snovi, kot je kot omočenja na fazni meji, na odstranitev masti s površine jekla
Surface active compound (PAT)	Degree of steel cleanliness	Wetting angle 0 degrees	remark
In absence of PAT	0,1	66,6	High efficient PAT
DS-10	0,91	67,5	
NF	0,78	66,7	
TBA	0,4	69,2	
NP-3	0,02	112	Low efficient PAT
Pentadecilovium Spirit	-	115	
Pentadekanovium acid	-	131,9	
The low fat removing capacity of the solution NP3 is explained assuming that the adhesion is due to the low interface metal-solution and oil-solution activities, it partial solution in oil and to the absorbtion on the
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
interface oil-metal. For such a case: ? = 90°; dMP e = dMM e . On the other side, DS-10 gives a very clean surface because the surface active compound is adsorbed at the interface metal-solution and oil-solution and does not affect the surface condition at the interface metal-oil.
The property for absorption on metallic surfaces is due to the ionisation potential of surface active com-pounds94. The adsorption is explained in terms of resonant potential95. When for an organic compound the resonant potential is achieved, also the maximal adsorbtion on the metal surface is achieved. The adsorbtion intensity depends on the length and electronic structure of molecules. The standard free adsorbtion energy shows a maximum at a determined potential of the surface active compound.
By working with lubricants special attention should be given to fire danger and to hygienic protection of working personal. If systems with oil fog are used, the ventilation system must ensure that the content of oil droplets and vapour in the working place is below 5 mg/m3. Serious harm maybe due to contact with unclean lubricants and polycyclic aromates. Of low toxicity are lubricants containing compouds with low vapour pressure, like white spirit, kerosene and solvents with mucous membrane. By using chlorinised hydrocarbons smoking is dangerous, since, the vapour is oxydised on the burning cigarette and aspired. The maximal toxicity is found by synthetic lubricants, especially triarylphosphates96, these having a neurotoxic effect and requiring the use of appropriate protective equipment. Lubricants and additives contain toxic compounds with Zn, Ba, Pb, S and P, for this reason, filters are required for furnaces and chimneys. Emulsion coolants can be treated with vacuum distillation, water dilution and ultra filtering.
According to their cancerogeneity, lubricants97 are classified in specific groups. The oils cancerogenity increases with the temperature. Plant oils and fats are not cancerogeneus and do not affect the skin98. The permitted concentration of hydrocarbon vapour is of 300 mg/m3, however, if hydrocarbons are found in air suspesion, the permitted concentration is of only 10 mg/m3. The toxicity of spirits increases with the increasing number of carbon atoms in the molecule. Emulsoils are very toxic and allready by the concetration of 400 mg/m3 can provoke pathologic changes on internal organs.
Fats are decomposed at high temperature99 in complex chemical reactions, which may produce a noisome or even poisonous scent, which may cause eyes burning, dry coughing and headache. The concentration of acroleine, which may form also by the burning of mineral oils, is especially limited. Surface active compounds diminish the human reflexes also by low concentration and are life dangerous by greater concentrations. Non ionised compounds are not dangerous. In
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
Table  3  the  permitted  concentration  of  harmfull compounds in air and water is given100.
Table 3: Allowed limit concentration of harmfull compounds in water
and air
Tabela 3: Dovoljena mejna koncentracija škodljivih snovi v vodi in v
zraku
Compound	Allowed concentration	
	PAir/(mg/m3)	PWater/(mg/L)
Acetone	200	4
Petrol	300	0,1
Kerosene	300	0,3
Hydrocarbons	300	0,3
Petrol acids	200	0,3
Mineral oils	300	0,4
Spirits	2	-
Etylene	1	-
Petrolether	300	-
Ammonia	20	-
Synthetic fat acids	4	
C5-C20	4	
OP-7	-	0,4
OP-10	-	1,5
The content of bacteria in emulsions should be below of 5,0 E5 /mL. In half synthetic amulsions for working of metals the content of microorganisms after 11 h of use my be of 1,0 E9101. In emulsions coolants the formation of N-nitrozodietanolamine (NNDEA) could occurr by reaction between NaNO2 an DEA (alcanolamine) which are cancerogeneus. Also toxic formaldehide vapours can be formed especially in presence of aerosole and glycole. The most used test for the determination of the biological stability of emulsions is the method CEC-L-33-A-93102 and the biological decomposition with the CO2 modified Sturm test.
The properties of lubricants are checked using trybo devices103 like that shown in Figure 18104. Also variations with four balls are used105.
The steel cylinder (8) with the internal ring (7) is placed in the thermostate (6) at the temperature of 180 °C and filled with oil. With the electrical motor (1) the frixion between the metal plate (9) and the ring (7) is achieved. The contact pressure is controlled with the centrifugal regulator (10).The toothed pump (5), driven by the motor (2), pumps the oils through the tubes (4) in contact with the solid inhibitor (3) in the upper part of the device (11). Sprayed with the centrifugal regulator (10) oil falls on the bottom of the steel cylinder to be pumped again in the circular flow (5).
It was demonstrated that the oil corrosivity and the frixion of the metal surfaces (7) and (9) depend on the type of the inhibitor (3). The device can stay in operation for 20 h with a linear flow rate of 20 m/s and by the oil pressure of 400 N/cm2.
The tribological efficiency of oils is very different, also between oils of the same type, as defined in european specifications. All lubricants must be ecolo-71
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
Figure 18: Device for the determination of wear of metal surfaces Slika 18: Naprava za določanje obrabe kovinskih površin
gically friendly106. Improvements of oil properties are mostly found with new additives and are used if confirmed as ecologically acceptable107.
The properties of lubricants of ecological significance are108: biological stability, low water pollution, low water solubility, low toxicity, absence of heavy metals, high ignition point, low wapour pressure and natural origine like ether, rape, soya and animal oils.
In use and development of lubricants care must be taken for the hygienic protection of workers and for the microclimate in the working location. This warning is confirmed in Figure 19109, which shows that the addition of polymer to an indutrial oil affects the formation of oil aerosol in the atmosphere and that allready by a small change in polymer content the formation of aerosol is greatly changed.
By hot rolling the lubricants are even more dangerous for the ambient because of the high processing temperature. On Figure 20 the DTA curve for palm oil and emulsoils OM110 are shown. Emulsoil is less prone to thermal decomposition and to air oxydation and it is also less prone to exo and endothermic reactions, however, it is less stable in temperature range 350 °C to 400 °C. For this reason, natural oils can not be used as lubricants for hot working.
30 25
Ç   15        f                 \    Č----------
°" 10   -/                       Č—
5 -Č-
0  I--------------------------------------------1-----------1-----------
0            2           4            6            8           10          12
C/%
Figure 19: Influence of the content of polyisobuthilene c/% on the loss of aerosol of industrial oil in atmosphere q/% Slika 19: Vpliv vsebnosti poliizobutilena c/% na izgubo aerosola industrijskega olja v atmosfero q/%
72
Figure 20: DTA curves T/°C for emulsol-OM, palm oil-PU. First range 90–280 °C, second range 280–350 °C, third range 350–400 °C and fourth range 400–500 °C, time t/min
Slika 20: DTA krivulje T/°C za emulzijsko olje – OM in za palmovo olje-PU. Prvo območje 90–280 °C, drugo 280–350 °C, tretje 350–400 °C in četrto 400–500 °C, čas t/min
6 CONCLUSION
Inspite of the great importamce of tribology for the plastic working of metals, survey articles are very rare. This article is an attempt to present the more important knowledge on the tribology of use of lubricants for the plastic working of metals. The lubrication and lubricant topics are very wide and include:
1.   theory of plastic working of metals
2.   fluids mechanics
3.   metal corrosion
4.   colloide chemistry
5.   manufacturing and regeneration of lubricants
6.   lubricant devices
7.   ecology and hygienic protection. The author included in this work only some essential
of the enumerated topics. From the first paper of Mizumo on fluid mechanics calculation related to the lubricant layer in the rolling deformation zone, through it confirmation by A.P. Grudev in 1966, the volume of investigations has grown very much. In Reynolds equations the following parameters are considered:
1.   logintudinal and transversal surface roughness,
2.   effect of inertial forces for great drawing rate,
3.   potential of diffusion forces as results of the interaction of lubricant molecules with the solid metal surface, The analytical solutions of equations are complex
also in case when they can be obtained, for this reason, numerical solutions are used, especially the Monte-Carlo method.
Colloide chemistry was introduced through equations for the spreading of lubricants on solid surface involving the wetting angle, adhesion work and surface tension. Since a few years, the ionisation potential of organic compounds, surface active compounds and the index of the resonant potential are involved, also, in topics of lubrication.
MATERIALI IN TEHNOLOGIJE 39 (2005) 3
D. ]URČIJA, I. MAMUZI]: LUBRICANTS FOR THE ROLLING AND DRAWING OF METALS
Authomatic lubrication devices were developped with inclusion of processing technology for the deposition and the regeneration of lubricants. Synthetic lubricants of high quality based on animal and plants oils and fats were developped. Systematic investigations on the use of microemulsions were started also with the main aim to improve the cooling efficiency. The use of lubricant shows a number of positive effects and it is estimated that the use of energy in industrial countries can be lowered up to 20 % using lubricants with the best tribological properties and the application of tribological principles
The authors are indebted to prof A. Markoti}, prof. A. Preloščan, dr. B. Iharoš, ms. Lj. Vukovi}, mr. A. Paulin, mr.V. Begovi} and mr. J. ]určija.
Translation from Croatian: F. Vodopivec
SYMBOLS EV. NOT EXPLAINED IN THE TEXT
Symbol
Meaning
a_____Drawing angle and grippping rolling angle_____
y______Piesocoefficiant of lubricant viskcosity_________
ň          Eventual lubricant layer thickness determinated
________by the surface roughness______________________
_Ł______Height layer lubricant on the sheet (1 E-6 m)
Łc         Height lubricants layer (1 E-6 m = 1 µm) ________(Figure 15)
Equilibrium wetting angle
ß______Dynamical viscosity of the lubricant________
HA         1 E-6 A Figure 18._______________________
Čd         Viscozity of the dispersed phase in form of
________sphere____________________________________
IUe_Effective viscosity of the dispersed phase v          Kinematical viscosity
Kinematics viskosity copolymers
p______Fluid density________________
a_____Interphase or surface tension
jr______Time_________________________________________
Ts_____Tangential stress in differential equations_______
(p          Volume concentration of the dispersed phase in
_______equ. (1)______________________________________
(p0
Auxiliary reduction angle in equation (15)
d(p/dr Exits angle of electrons in dependence on the time (t) of immersion of the metallic plate in oil.
Q	Consumption of lubricant on the sheet surface
C	Volume solublity in the dispersed phase
cs	Contact strains (MPa) : Cs = Cs(Lc)
Ca	Coefficient abrasion
D	Diffusion coefficient
D	Diameter of the droplet in the coarsening emulsion
exp	Natural log. base
#	Free fall accelaration
h0         Lubricant layer thickness in the entering section ________of the deformation zone by metal drawing_______
H         Distance of the accumulation of the dispersed
phase from the boundary emulsion/clear
_________dispersed medium at the timen t______________
Hdf        Initial quantity of dispersed phase____________
h(x)       Fluid height________________________________
< i >       Mark for mathematical hope
K_____Stefan-Boltzmann constant___________________
k1_____Parameter of the kinematical inertial effect
h          Matrix deformation zone length according to
_________Figure 10
Lc_____Scale length of deformation Š-1.0 to 0]_______
P______Pressure in lubricant layer___________________
Pc        Pressure ( MPa): Pc= Pc(Lc)__________________
Rz        Initial roughness (1 E-6 m = 1 µm)___________
T_____Temperature in K___________________________
T_____Time_______________________________________
U          Layering rate rate for the regimes of
_________compression and coalescence________________
v0, vr      Sheet rate and circumferential rolling rate
VRx
VT
Projection of the roll rate vector on the ordinate
_x_____________________________________________
Speed temperature corrosion___________________
Loose aerosol (weight %)
Mark for infinite
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