The metal-tool contact friction at the ultrasonic vibration drawing of ball-bearing steel wires

The friction reversión mechanism during the ultrasonic vibration drawing (UVD) of wires has been detailed for the case when the die is located at the oscillation máxima of the waves and actuated parallel to the friction forcé direction. The decrease of the drawing forcé for the UVD technology as compared to classical drawing has been explained by means of the intermittent contact in the metal-die forming área. A relationship has been derived for the UVD friction coefficient, u u s that allowed the analytical determination of the drawing forcé. In the case of the Romanian RUL IV (AISI 52100) ball bearing steel wires, a good agreement has been found between the analytical and the experimental valúes of the drawing forces that have decreased, as compared to classical drawing, by more than 5 % for drawing rates lower than 0.66 m/s.


INTRODUCTION
The ultrasonic vibration drawing (UVD) of wires consists in the transformation of high frequency electric oscillations, by means of piezoelectric or magnetostrictive transducers, into mechanical oscillations that are transmitted by the tool to the metahforming area^\ The stress state and the kinetics of plástic deformation process depend both on the type of ultrasonic oscillations and on the location of the die within the oscillating system, namely at the oscillation máxima or at the displacement nodes of the waves^ . It is considered that, when the die is located at the oscillation máxima of the waves and actuated parallel to the die's cone generator direction (the friction forcé direction), a significant reduction of the friction forcé can be obtained. This reduction has been ascribed to the "surface effect" of ultrasonics, by means of the socalled "mechanism of friction-reversion" .
The paper aims: (i) to analyse the development of the mechanism of friction-reversion with the assumption that friction is produced according to a Coulomb-type law and (ii) to evalúate the effects of applying the UVD technology in the case of ball-bearing steel wires.

EXPERIMENTAL PROCEDURE
The experiments have been performed by single stage drawing of the wires made from the Romanian steel RUL IV (AISI-52100). The chemical composition of raw wires was: 1.2 % C, 0.4 % Mn, 0.3 % Si, 1.5 % Cr, 0.02 % S, 0.02 % P, 0.08 % Mo, 0.2 % Ni and 0.2 % Cu (wt.%). The wires, with an initial diameter D 0 = 3.8 mm, have been annealed and subsequently prepared for UVD Metallic carbide (WC) dies, with convergent conical geometry (a = 8 ) have been used. As lubricant, a mixture of soap powder with 10-15% fine lime powder and 12-15 % tale powder has been used.
The laboratory installation allows the measurement of both technological and ultraacoustic specific parameters. It comprises three main parts: (i) the drawing equipment with electric actuation and step-variation of speed; (ii) the ultrasonic generator, type U.Z.G. 2-4M and (iii) the oscillating system including the magnetostrictive transducer, type RM.S. 15A-18, with resonance frequencyf= 17.510 3 Hz.
The oscillating system is illustrated in figure 1. Its length is calculated, according to the principie of resonance frequeney, as a múltiple of X/2 as illustrated in figure l(a). X is the ultrasonics wavelength, X = c/f, where c is the ultrasonics propagation speed through the material under study.
The ultra-acoustic energy reflectors enable the formation, along a precise distance within the wire, of a stable system of stationary waves. The stability of the stationary waves system has been monitored by means of a X-Y recorder. The oscillating system is fastened on the stand of the drawing equipment by means of the nodal flange.
The oscillation amplitude (A) can be modified either by tuning the pre-magnetization current in the magnetostrictive transducer or by changing the geometry of the cylindrical step-concentrator. Thus, an amplitude A = 25-10 m could be obtained by setting the amplification factor of the cylindrical step-concentrator, N = (D/d) 2 , at the valué N = 3.2. The cylindrical step-concentrator is made from titanium alloy (Ti-6% Al-4% V). This alloy has a density p = 4.42 Kg/dm , an ultrasonics propagation speed c = 4,900 m/s and a high ultrasonic fatigue Ufe.   The drawing forcé was determined by means of the D.T 106.000-type gauge and a N 2314 tensiometric bridge, both for classical drawing (with nonactive die) and for the UVD technology.
The displacement rate of the drawn wire (V tr ) has been determined by means of a tachometer while the die's oscillation amplitude has been measured by means of a special device that has, as an active element, an "electret"-type block with capacitive functions^ \ For the drawing rate (V tr ) the following valúes have been used: 0.33; 0.5; 0.66; 0.83 and 1.0 m/s. The feed rate (V a ) has been determined as a function of the initial and final wire diameters in the metal-forming área (D 0 and Dj, respectively) as well as of the geometry of the die:

DEVELOPMENT OFTHE FRICTION REVERSIÓN MECHANISM
The principie scheme of the UVD technology, with the die located at the oscillation máxima of the waves and actuated parallel to the drawing direction, has been determined by developing the approach found in™ and is illustrated in figure 2. It is assumed that, within the deformation área, the metal is subjected to two motions with different rates: an oscillation motion, determined by the ultraacoustically actuated tool and a slip motion, determined by the drawing process. According to the above assumption any point M, arbitrarilychosen within the deformation área in figure 2, takes part in two motions: a feed motion (with the rate V a ) and a vibratory motion of the tool (with the rate V v ).
In the case of the classical drawing (without ultraacoustic actuation of the die) the friction forcé vector (Ff) opposes the direction of the metal displacement (V a ), while in the case of the UVD it opposes the direction of the resulting rate vector (determined by the composition of the rates V v and V a ).
Under these circumstances, the resulting vector of the relative rate will influence the motion direction of the point M as a function of both the direction of the two rates (V v and V a ) and the magnitude of the projections of these vectors on the friction direction, B-B^ as illustrated in figure 3(c). Thus, during the interval T/2 -2ti of the oscillation period, its displacement direction will coincide with that of the metal and during the interval T/2 + 2t\ it will move in the opposite direction, as the projection of the V v vector along the direction B-Bj will be larger and smaller, respectively, than the V a vector. Based on the above considerations, it is evident from figure 3(c) that during the interval T/2 -lX\ the friction forcé (Ff) becomes positive and during T/2 + 2t\ it becomes negative. The dashed Une illustrates the variation of the average friction forcé according to the model introduced by Severdenko™, while the solid line represents the theoretical variation. In the metal-tool contact área, the normal stress (a n ) or the pressure induced by the die, gradually-decreases to zero during the interval T/2 -2t\ y when V v >V a , until the metal becomes fully detached from the tool. Under these circumstances, the deformation process is interrupted in such a way that the metal just slips

Figura 3. La cinética de deformación del metal conforme a la tecnología EVU: (a) la onda de desplazamento; (b) variación de la velocidad de vibración de la herramienta (V v ) y de la velocidad de desplazamento del metal (V a ); (c) variación de la fuerza de fricción (Ff).
relative to the die, the friction forcé being considered as positive (Ff) with relatively low valúes. During T/2 + 2t h when V v <V a , since the metal-tool contact is resumed the deformation process is restored and the pressure created by the die gradually-increases to the máximum valué, characteristic of the drawing process. Consequently, the friction forcé is considered negative (Ff) and reaches a máximum valué as the wire deforms. In other words, within the UVD technology, plástic deformation occurs, by impulses, the metal-tool contact being periodically resumed, as a function of the resonance frequency of the oscillating system. Therefore, a reduction of the friction forcé results, based on the "reversión of the friction forcé vector", w henV v >V.

DETERMINATION OF THE UVD FRICTION
COEFFICIENT V" (9) In the case of Coulomb-type friction, the friction coefficient ix is generally expressed as: where T is the shear stress induced by friction and G n is the normal stress on the tool surface, Le. the pressure produced by the tool in any point of the contact área. From figure 3 it is noticeable that the influence of ultrasonics is directly proportional to the time interval 2t x and inversely proportional to the period T/2, which agrees well with the results found rrr . Consequently, the UVD friction coefficient (|I US ) is correspondingly lower as compared to the friction coefficient for classical drawing: By designating the effective influence factor of the ultraacoustical oscillations on the metal-too! contact friction as £, = 4tj/T, equation (3)  Considering the displacement wave shown in figure 3(a), at the moment t¡ its equation will be: where A is the amplitude of the tool's oscillations and CO = 27if is the angular speed. The vibratory rate of the tool is the derivative of the displacement wave: The máximum valué of the vibratory rate is obtained for eos cotí = 1 as: From equations (6) and (7) the vibratory rate becomes: When the feed and the vibratory rates are equal, t\ becomes:

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With this valué of ti, the effective influence factor of the ultraacoustical oscillations on the metal-tool contact friction becomes: Based on equations (4) and (10), the UVD friction coefficient JLX US is expressed as:

EXPERIMENTAL RESULTS AND DISCUSSION
The determination of the friction coefficient at RUL IV steel wire drawing, either with nonactive die (¡a) either with the die ultraacoustically activated (flus) i s based on Sachs'relationship of the drawing forcé^ . The effectiveness of ultrasonics regarding the metal-tool contact friction, as compared to classical drawing, can be expressed as the relative reduction of the friction coefficient^ *: Similarly, the relative reduction of the drawing rate, as an effect of ultrasonics, is 1 .  The experimental results are summarized in table L The valúes F t and F t u| are experimentally determined and F t us is analytically determined by means of equation (12). The relative decreases of the friction coefficient as an effect of ultrasonics range between 28 and 33 %. As a matter of fact, the lower the ratio V a /V v the larger the ultrasonics effectiveness.
The difference obtained between the experimental and the analytical valúes of the drawing forcé, F t {)s and F t Qs , respectively, might be caused by a much more complex influence of ultrasonics upon the plástic deformation processes. For instance, a more uniform distribution of the deformation on the cross-section of the drawn product occurs due to the intermittent metal forming that causes a decrease of the work hardening degree and an increase of the lubricant's effectiveness within the oscillation knots of the waves.

CONCLUSIONS
In case of the UVD technology, the friction reversión mechanism has been explained by means of the intermittent metal-tool contact in the metal-forming área. Considering the effect of ultrasonics, an analytical relationship has been derived for the friction coefficient. |Ltys-The experiments performed on ball-bearing steel wires proved the effectiveness of the UVD technology that has caused relative decreases above 30 % and 5 % for the friction coefficients and the drawing forces, respectively, providing the ratio V a /V v was lower than 0.21. Therefore the UVD technology improves the plástic deformation process and is especially recommended for the cold-working by classical drawing of high strength wires characterized by intense friction as well as by low drawing rates and cross-section reductions.