THEORETICAL AND EXPERIMENTAL RESEARCH ON THE EVOLUTION OF THE FRICTION COEFFICIENT IN DIFFERENT LUBRICATION CONDITIONS IN THE CASE OF FRICTION COUPLES WITH SLIDING MOTION

: In recent decades, the interest of researchers and engineers in obtaining competitive materials is increasing. The effects of friction on materials are quite difficult to explain due to the micro and macroscopic interactions of the surfaces of the friction couple, which slide over each other. The friction and wear behavior of sliding surfaces can be considered important design criteria. The fact that for a kinematic coupling with sliding motion, a material with a higher hardness is used in most cases in combination with a material with a lower hardness, there is the possibility of abrasion wear and local plastic deformations. The paper proposes in analytical model for calculating the coefficient of friction when a rigid conical penetrator passes over a flat surface with a lower hardness and establishing the response mode of the material of the flat surface. The penetration method corresponds to the deformation produced by asperities in practice. The proposed theoretical model will be experimentally validated on a tribological stand made in this sense. Comparing the experimental results with the theoretical ones confirms the veracity of the model and also corresponds to many of the experimental results obtained in specialized works.


INTRODUCTION
Under the external load action, the roughness of the surfaces in contact, belonging to any friction couples, is deformed.This deformation persists until a mechanical equilibrium between the areas of the surfaces is achieved and it depends on a great number of contact variables (the shape and the dimensions of the asperities, the normal load, the sliding velocity, temperature, etc.) [1][2][3][4][5][6][7][8].
The friction of the involved materials are controlled by the nature and the consequences of the interactions generated at the interface of two contact surfaces belonging to any friction couple.Researchers, differently treat the understanding of the phenomena that occur during the relative motion between two surfaces, each of them trying to explain the wear phenomena by using particular models.
In this work, an analysis will be made of the wear behavior of two materials with essentially different hardness (frequently used in couplings with sliding motion) by evaluating the coefficient of friction.

THEORETICAL CONSIDERATIONS
The working conditions of the couples with sliding motion (e.g. the guideways of machine tools) lead to various types of wear.Because the roughness of the fixed guideway has much more hardness than that of the movable guideway, there is the possibility as wear by abrasion and the local plastic deformations to be occurred.Also, it was found that the reaction of the materials with smaller hardness when some conical or pyramidal bodies with much more hardness are sliding on them, depends on the cone or pyramid angle and the normal delivered force [4][5][6][7].
For the quantitative wear process analysis related to some known materials, it is considered the case of the plastic deformations with the separation of the wear particles after a number of cycles typical to the oligocyclic criterion Manson -Coffin.Depending on the value of this angle against a certain critical value (cr), the material reaction can be deformation or microcutting [8,9].
In the theoretical model proposed, the plastic deformation theory is considered as applicable one, such that the specific differential equations are solved for the slip lines [10].
It is considered a stiff roughness with a certain slope angle (tool test bar of the stand), moving with a constant velocity va, on a plane, which can be plastically deformed (the fixed test bar of the stand, being from material for analysis), featured by the shear strength f .

For the description of the friction between the roughness
The Scientific Bulletin of VALAHIA University-MATERIALS and MECHANICS -Vol.19, No. 20 and the deformed material, the adhesion coefficient f is considered as a measure of the lubrication state between roughness and material.For the "thoroughly clean" materials, without lubricant, f = 1 and for the rich lubricated materials, f  0.
Taking into account these considerations, the friction coefficient, in its classic definition, will be [10][11][12][13]: (1) where: Ft = tangential force on the roughness width unit Fn = normal force on the width unit (assumed as known) Figure 1 shows the variation of the friction coefficient depending on the angle of inclination of the roughness and lubrication (expressed by the adhesion coefficient f), For the friction coefficient values higher than one, it is considered that the deformation regime is a plastic one and the deformed material is moved under wave shape and is removed after a certain number of cycles, only, in accordance with the Manson -Coffin model.When the slope angle of the roughness exceeds a critical value, according to the micro-cutting model [5,6,9,12,13], the friction coefficient has the following form: where: The variation of the friction coefficient at micro-cutting for a value of the roughness slope angle () higher than a critical value (cr), is shown in Fig. 2. The materials used in the experimental part are: -non-ferrous material used in machine parts subject to wear (bearings, joint parts, et.all) CuSn14, according to DIN1705 is a copper-tin alloy that has a concentration of 85-87% Cu and 13 -15% Sn; -metal material is a general purpose rolled steel S 235.
The mechanical characteristics of the selected materials are shown in table 1[14].

Tribometric device
In this case, a specially calibrated stand of tribological tests (Fig. 1) will be used.
For the measurement of the frictional force as well as of the coefficients of friction, mainly the method with a resistive tensiometric transducer is used.This method is based on the fact that the frictional force produces the displacement or tendency to move one of the parts of the friction coupler, which can be taken over by a resistive tensiometric transducer, the resistance variation being measurable.
The principle diagram is shown in figure 3. The movable disk on which the non-ferrous material is placed can rotate with a variable speed.

EXPERIMENTAL RESULTS
For the experimental determination of the coefficient of friction, the pin is loaded with the normal force of and the tangential (friction) force is measured, under different lubrication conditions.
Because the lubrication state influences the processes of friction and wear, three cases are taken into consideration: -good lubrication -enough lubricant in the contact area between surfaces; -limit lubrication -some lubricant drops; -without lubrication -the test bars are firstly cleaned with alcohol and operate in conditions of normal moisture and temperature (moisture about 60...70 % and temperature about 18...22C), technically dry friction.
It is theoretically known and experimentally tested, when angular penetrators make the plastic deformation, the friction coefficient depends on their slope angles and the adhesion conditions of the material being deformed by the stiff material.
The experimental values of the coefficient of friction for the material couple under analysis in those three lubrication conditions (good "f", limit "l", dry "u"), depending on the pin cone angle and loading are shown in figures 4 and 5 .Values plotted are mean values of five identical tests.The statistical variation of the experimental results is estimated through the variation coefficient cv (the ratio between the quadratic mean error and the arithmetic average), which for brass is cvAf = 0,507, cvAl = 0,077, cvAu = 0,0082 and for cast iron is cvFf = 0,26, cvFl = 0,031, cvFu = 0,0058.

CONCLUSION
Following the analysis of the module of the theoretical friction coefficient, the following aspects result: The Scientific Bulletin of VALAHIA University-MATERIALS and MECHANICS -Vol.19, No. 20 -the friction coefficient values at deformation increase along with the roughness angle () increase; -the friction coefficient values at micro-cutting increase along with the roughness angle () increase.
Following the analysis of the module of the theoretical friction coefficient, the following aspects result: -the friction coefficient values increase along with the roughness slope angle increase and the lubrication state; -for a certain roughness slope angle, the friction coefficient is higher the more the surfaces are lubricated; -there is an angle with a critical value (cr) up to which the deformations of the material are in the elastic range of deformation, after the value of this angle the deformations of the material become elasto-plastic or plastic, when the coefficient of friction is very high; -excessive lubrication of the surfaces under a certain angle of the penetrator (cr) can lead to a rapid increase in the coefficient of friction.
Any discrepancies between the theoretical values of the friction coefficient and the theoretical ones are due to the fact that: -in the experimental part, the loading force of the pin was taken into account; -the theoretical expression of the coefficient of friction takes into account only the processing method of the pine.

Figure 1 .
Figure 1.Theoretical dependence of the friction coefficients depending on the angle of inclination of the rigid roughness and lubrication

Figure 2 .
Figure 2. The evolution of the micro chipping friction coefficient depending on the angle of inclination of the rigid roughness and lubrication materials are purchased from the trade and are processed by the technological turning operation.The Scientific Bulletin of VALAHIA University-MATERIALS and MECHANICS -Vol.19, No. 20

Figure 3 .
Figure 3. Pin on disc stand operation scheme

Figure 4 .Figure 5 :
Figure 4. Evolution of the experimental friction coefficient for N 1 F 1 n 