ASPECTS OF ANALYSIS OF REVERSE FRICTION - CAUSED CONTACT PHENOMENA

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1 ASPECTS OF ANALYSIS OF REVERSE FRICTION - CAUSED CONTACT PHENOMENA Paweł PIEC, Cracow Univerity of Technology, Cracow, Poland Staniław PYTKO, Univerity of Mining and Metallurgy, Cracow, Poland S u m m a r y In the paper the contact phenomena caued by revere friction tick-lip are dicued. To olve thi complex problem, the author have done the tatitic, numerical computer imulation, bench tet a well a in-ervice tet on a real object. The paper preent the reult of the numerical computer imulation. The effect of friction coefficient characteritic on how the wavy wear originate ha been included. Keyword: numerical analyi, contact effect, revere friction. Keyword: friction, tick-lip АСПЕКТЫ АНАЛИЗЫ КОНТАКТНЫХ ЭФФЕКТОВ ВОЗБУЖДЕННЫХ ПОВОРОТНЫМ ТРЕНИЕМ Резюме Работа относиться до проблема контактных эффектов возбужденных поворотным трением стик-слип. Афторы в своих исследованиях, которые относиться до развязания этого сложного проблема, проводили статистические исследования, нумеричной симуляцию компютеровой, стендовые исследования и эксплуатационные исследования действительного объекта. В работе представлено результаты нумеричной симуляции компютеровой. В исследованиях учитывают вляние характеристик коэффицента трения на развите волнообразного износа. 1. INTRODUCTION In the paper an aumption wa made that during braking the friction procee between the wheel and brake inert are the main procee in the formation of wear in the contact area of thee element Fig.1). The numerical analyi and experiment were done for wheel-brake hoe unit. The reult were verified during in-ervice tet of rail-wheelbrake hoe unit on a real object. 2. NUMERICAL ANALYSIS OF BRAKE SHOE MOTION Brake hoe motion ha been imulated for a mechanical ytem hown in Fig. 2. In the invetigation it wa aumed that in the analyi of the motion of the invetigated ytem the tranlatory movement of the hoe i a baic motion, decribed by equation (6). The hoe rotational motion i aumed not to affect the motion of the invetigated ytem and i thu diregarded in the preent analyi. From the analyi of the hoe motion hown in Fig. 2 it follow that a hoe of ma m upported by pring of pringing rate c can move relative to the wheel rotating at the peripheral peed of v. In teady tate, with no vibration (Fig. 2b), the pring i extended by friction force FN µ( v) correponding to peed v. Thi peed i then equal to relative peed of ( ( v x ) ). 8 th International Tribology Conference, Oktober 2003., Belgrade, Serbia 39

2 Fig. 1. The wear area of the contact effect analyed by the author When the wheel drive i engaged or the pring i extra extended there appear vibration - hoe motion relative to wheel (Fig. 2c). In the condition of tability thee vibration are damped and diappear. Thu the tate hown in Fig. 2b become table. However, elf-excited vibration can appear, due to the characteritic of friction between the hoe and wheel. In cae vibration of the hoe appear, when it velocity at the given moment i x (Fig. 2c), the relative velocity vr = v x, (1) will change in the neighbourhood of velocity v. In the teady tate (Fig. 2.b) the friction force (2) T( v) = FN µ ( v), (2) i equilibrated with force F of the pring (3) F = c x. (3) So the hoe vibration are affected by the difference of friction force (4) T = T( v) = T( vr ) T( v). (4) During braking three variou form of hoewheel contact can be ditinguihed: a) x = 0, v > 0 - hoe lip with no vibration, b) x v, v >0 hoe lip following vibration, c) x = v, v > 0 tick phae following tick-lip vibration. Fig. 2. A diagram of the mechanical ytem under analyi: m ma of brake hoe, c elaticity contant, d dumping coefficient The coure of hoe-wheel interaction in which the tick and lip phae can be ditinguihed i called a boundary cycle. Fig. 3 how the boundary cycle of R CG radiu. The hoe remain in the tick phae until the pring force i equal to the maximum friction force tranferred. In thi ytem the point of eparation X A can be calculated: XA= FN µ / c, (5) at which the hoe tick phae change into lip phae. To decribe the hoe motion ma m (Fig.2) differential equation of the econd order i adopted (6): m x + d x + c x = µ FN gn( x v), (6) where: m concentrated ma, d damping coefficient, c pring contant, F N - normal force th International Tribology Conference, Oktober 2003., Belgrade, Serbia

3 Fig. 3. Diagram of boundary cycle of the invetigated mechanical ytem The wheel linear velocity ν at the contact ite with the hoe in thi equation i dicrete; it i hidden in the formula for friction coefficient. It i convenient to run the analyi uing dimenionle co-ordinate, which reduce the number of the ytem parameter. Hence (7) ω o = c m (7) wa introduced and a power unit wa choen. The choice help to make the friction model uniform. Introducing in equ. (6) the following: non-dimenionle time τ = ω o (8) non-dimenionle dilocation cx X = F N (9) non-dimenionle damping coefficient γ = d 2 cm 12 ( ) / (10) non-dimenionle velocity v c V = ( ) FN (11) and coefficient F ω δ = N o c that i V = v δ (12) non-dimenionle friction coefficient µ δ ( X' V) = µ δ ( x v)/ F N (13) we get: X " + 2 γ X ' + X = µ δ ( X ' V ) gn( X ' V ) (14) The parameter of equation (14) are: µ( V r ) - friction model, γ - non-dimenional damping, V - wheel non-dimenional velocity. The programme for numerical imulation of tick-lip contact effect, i.e. hoe elf-excited vibration ha been written in PASCAL. The numerical program preented define an approximate olution of differential equation (6) which decribe the hoe-wheel motion during braking at given initial condition. The input data for computer calculation program cover: I. Characteritic of friction coefficient for the analyed material of brake inert repreenting the adopted friction model written a equation (15) and( 16) for brake inert material W 1 (Fig.4) and equation (17) and (18) for brake inert material W, (Fig.5): a). Friction model for brake inert material W 1 : " µ > µ k; µ k = f( v)" (15) µ = 0, µ ( vr ) = µ µ * 2 + µ + for 0, 1 v o β vr v α r r for: µ = 0,4, µ * = 0,1, α = 0,2 [ m -1 ], β = 0.0 [ 2 m -1 ], (Fig.4) Fig. 4. Model of friction -" µ > µ k ; µ ( v )", for brake inert material W 1 k = f (16) 8 th International Tribology Conference, Oktober 2003., Belgrade, Serbia 41

4 b). Friction model for brake inert material W : " µ = µ ; µ cont" (17) k k = µ = 0, µ ( vr ) = (18) µ 0, for: µ = 0,4, (Fig.5). inert material W 1 ) doe not caue the boundary cycle (ee Fig.3). Fig. 5. Friction model - " µ = µ k; µ k = cont", for W brake inert material The characteritic in I can be modified accordingly by the choice of kinetic friction coefficient µ k and tatic coefficient µ a well a parameter µ α β *,,, v r. II. Parameter of the invetigated mechanical ytem, Fig. 2. The parameter of the invetigated mechanical ytem can be fed into calculation according to a given methodology of reearch a: - value in dimenionle or dimenional coordinate and - declared a value contant or variable in a given range, with calculation tep defined. 3. RESULTS OF COMPUTER ANALYSIS The friction model " µ > µ k ; µ k = f ( v )", for brake inert material W 1, how how the boundary cycle i formed (ee Fig. 3). At lower wheel velocitie, for hoe initial peed X ' o = 0, the unit approache the boundary cycle (Fig. 6). At higher velocitie there are oberved only periodical vibration with no boundary cycle; at further velocity increae a table lip with no vibration i oberved. The friction model " µ = µ k ; µ k =cont" for brake inert material W, unlike friction model " µ > µ k ; µ k = f( v)" (brake Fig. 6. Phae diagram howing the behaviour of the unit during friction, for friction model " µ > µ k ; µ k = f( v)" (inert material W 1 ): V = 1, X o = 0, γ = 0, δ = 1 Irregardle of the initial condition, the unit how only periodical vibration without the boundary cycle, Fig.7. Fig. 7. Phae diagram of the behaviour of the teted unit during friction, for friction model adopted " µ = µ k ; µ k = cont" (inert material W): V = 0,5; 1; 1,5 X o = 0, γ = 0, δ = th International Tribology Conference, Oktober 2003., Belgrade, Serbia

5 4. CONCLUSIONS On the bai of the analyi of the reult obtained in imulation of the effect of friction model " µ > µ k ; µ k = f( v)" (inert material W 1 ) on the behaviour of the mechanical ytem it wa found that: - at wheel lower velocitie there occur tick-lip vibration in the ytem; - at higher velocitie of the ytem there occur periodical with no boundary cycle. On the bai of the analyi of imulation of the effect of friction model " µ = µ k; µ k = cont" (inert material W ) on the behaviour of the analyed mechanical ytem it wa found that: - irregardle of the initial condition, there i no boundary cycle oberved in the ytem. REFERNCES [1] Piec P.: Zjawika kontaktowe w elementach pojazdów zynowych. Wyd. ITE Radom, [2] Pytko S.: Problemy wytrzymałości kontaktowej. PWN, Warzawa [3] Uetz H.: Tribologie - Verchleikunde. Vorleungmanukript. Univeritaet Stuttgart, 1980, Kpt.6,.10 8 th International Tribology Conference, Oktober 2003., Belgrade, Serbia 43