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Polimer-metal kuru sürtünmesi ve tutma bırakma titreşimleri

Polimer-metal kuru sürtünmesi ve tutma bırakma titreşimleri

##### Dosyalar

##### Tarih

1991

##### Yazarlar

Demiral, Oğuzhan

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Polimerler, mekanik olarak viskoelastik davranış gös termektedirler. Viskoelastik davranışta gerilme-şekil de ğiştirme ilişkisinin gerilme ve şekil değiştirmenin yalnız ca zamana bağlı türevleri içermesi haline lineer viskoelas tik davranış denilmektedir. Lineer viskoelastik davranış, Hooke ve Newton yasalarına uyan ideal yay ve viskoz sönüm elemanlarının değişik kombinasyonları ile model lenebilmek- tedir. Oluşturulan mekanik bünye modelleri polimerlerin sür tünme özelliklerinin belirlenmesinde de kullanılmaktadır. Polimer rijit karşıt yüzey kuru sürtünmesinin iki bileşe ni (adhezyon ve histerezis) üzerinde de viskoelastik dav ranışın etkileri ortaya çıkmaktadır. Her iki sürtünme bi leşeninde de viskoelastik davranıştan dolayı, sürtünme kat sayısı, düşük kayma nızlarında bir maksimum göstermekte ve toplam sürtünme katsayısının hızla değişimi grafiğinde iki tane tepe noktası ortaya çıkmaktadır. Bu şekilde sürtünme katsayısı düşük kayma hızlarında hız ile azalan bir karakter göstermektedir. Sürtünme kat sayısının düşük kayma hızları bölgesinde artan hız ile azalması, sürtünme uyarılı titreşimlerden olan tutma-bırak- ma titreşimlerinin ortaya çıkmasına neden olmaktadır. Sür tünen malzemelerin iç sönümlerin yeterince büyük olmaması halinde titreşimler ortaya çıkmakta ve sönümlenmemektedir. Değişik bünye modelleri kullanılarak bu titreşimlerin sta- bilitesinin incelenmesinde, yaylanma rijitliğinin büyük olması halinde, sürtünme' katsayısının hızla azalma oranı nın daha büyük değerlerinde de sistemin stabil olduğu gö rülmüştür.

The mechanical properties of polimers (especially elastomers, commonly known as "lastikler" in Turkish) are like neither solid materials nor liquids. However they show the properties of both solids and liquids in different ratios. Therefore Hooke's law which establishes the stress and strain relation ship in solids and Newton's Law which establishes the stress and rate of strain relationship in liquids cannot be used for examining the mechanical proper ties of these polymers. In fact both real liquids and solids don't obey exactly Newton's law and Hooke's law respectively, they show deviations. There are two important deviations: 1) The Strain (in solid) or the rate of strain (in liquids) may not be directly proportional to the stress, but may depend on stress in a more complicated manner. 2) The stress may depend on both strain and rate of strain as well as higher derivatives of strain. In the first case stress and strain ratio depends on the magnitude of the stress and the second case it depends on time only. Both these deviations are classified as viscoelastic but the second case is linear. The chemical structure of polymers is responsible for viscoelastic behavior. The long chain molecules and physical and chemical likages between these molecules create different kind of structures and of course properties. For instance if chemical linkages form a rigid, cross-liked molecular structure, a thermo setting plastic results. Where as if chemical linkages are not so, stronf but from a c,ross-linked structure the result will be an elastomer. The molecules are generally in irregular spiral form. When the elastomer is streched, these molecules behaves like a spring and the friction among the chain molecules act like a dashpot. Linear viscolastic behavior can be represented by various suitable combinations of simple spring elements v which obey Hooke ' s law and viscous dashpots which obey Newton's law. In other words, the mechanical properties of viscoelastic materials can be modelled by sprigs and dashpots in Linear manner. The basic mechanical models which are used in model ling Linear visco elastic behavior are shown in the figure below (Fig 1), where E is the elasticity modulus of spring elements and f) viscousity of dashpot. 1 w Maxell Voigt Modified Maxwell IİJ Modified Voigt Maxwell Voigt Fig 1 Basic Mechanical Models For Modelling Linear Viscoelastic Behavior. When these models are examined, finally it is conclu- ted that all these mechanical models give +h« special cases of generalized Hooke * s Law which is presented below. (Egn. 1) (ao+ax ss ts/sjsssf i - V Fig. 3. Simple Mechanism Of Adhesion vxn During which the body moves a distance and then relase takes place. An associated strain develops in the material causing energy to be stored elastically in the molecule. When the elastic stress exceeds the adhesive force, failure of the adhesive bond takes place and the molecule relaxes. Then it starts a new bond. This mecha nism can be called thermally activated molecular stick- slip. The integration of the force which acts on the mole cules around all actual contacts gives the total adhesive friction. There are many theories £>.n adhesiv friction. SQ.me of them use molecular-kinetic approach to the subject such as Mixed Theory and Unified Theory, some of them use mechanical approach such as Simple Theory. Although these theories start to calculate the adhe sion from different points, they all agree that adhesion can be calculated or stated by the relationship /Uadh = Constant (E/P) tan& (6) Where tan& is tangent modulus of the material, E is the Young Modulus of the material and P is the mean pres sure acts on the sliding surface. Egn.6. Shows that the adhesion depends on the visco- elastic nature of the polymer, because of tan& known to have viscoelastic properties. The Young's Modulus E refers to E' infact it can be E*. However E1 is used for simplifying the eguation. Since E' and tan& are the functions of strain frequency w ( or sliding speed V) and temperature T, jMadh is the function of these parameters. Whereas the proportional constant includes the surface texture affects, therefore /Wadh is a function of surface structure too. Thus Egn.6. is valid for constant sliding speed and temperature. The influence of sliding speed and temperature on adhesive friction is interchangeable. Therefore the expe rimental data obtained under different conditions can be presented in same master curves. The Williams-Landel.Ferry transform allows doing that»by using the transformation, adhesive friction versus sliding speed curve was obtained for Acrylonitrile-Butadiene Rubber from experimental data (Fig. 4) where ay is the shift factor from WLF transform. IX T0-20°C _i__L ??!.. I. J I I I _J I LOG|0(aTV) Fig. 4. Master Curve For Acrylonitrile-Butadiene The curve in Fig. 4 agrees with the theoretical results. According to the theoertical results, adhesive friction has a viscoelastic peak at low values of sliding speed. Hyteresis component of friction is somewhat due to a load and unload process. It can be b«ically described that (according to the Fig. 5) when polymer body slides on the asperities of a rigid body, a deformation occurs on the counter motion side of the asperity, which creates a pressure distribution and the horizontal component of pres sure force,.is hysteresis resistance. his Fig. 5. Pressure Distribution Due To Sliding On Asperities. x There are many theories dealing with hysteresis fric tion. As in the adhesion theories, hysteresis theories agree that hysteresis friction can be stated with /* his = constant ( -) tan& (7) Where the constant depends on the surface texture of rigid body. This relationship (Eqn.7) is valid for again constant sliding speed (or frequency) and temperature. If Eqn.7 is rewritten as /'his,., _P_. = constant ( ) Tan& (8) the lef hand side of new equation (Eqn.8) can be called Generalized Coefficient of Hysteresis Friction. Experimental data obeys very closely this relationship as seen in Fig. 6., In Fig. 6. there exist experimental data for two seperate elastomers which are Natural rubber and Butyl rubber. 0 3 0-2 CYLINDRICAL SLIDER V = 0-067 m/sec T=300°K V^^- ^. NATURAL RUBBER O BUTYL RUBBER J_ I 001 002 0 03 004 005 cy Fig. 6. Generalized Coefficient Of Hysteresis Friction vs. mean pressure. It is remarkable that whereas in all theories of adhesion and hysteresis, the coefficient of friction is proportional to tan&, the adhesion component is generally proportional to the ratio (E/P) and the hysteresis compo nent to its reciprocal. XI Finally, the total coefficient of friction for visco- elastic material sliding on a rigid body without any lubri cant can be expressed n = [Const 1. ( -|-)+ Const 2 (-|-) ] tan& (9) This equation is valid for constant speed and tempe rature. The variation of speed influence as seen in Fig. 7. Since the influence of temperature and sliding speed are interchangeable, temperature effects are almost same with sliding speed effects. LOG V Fig. 7. Total Friction Coefficient vs. Sliding Speed. When the coefficient of friction decreases by increa sing slidin3 velocity at low speeds, the stick-slip vibra-.. tions occour. Stic-slip vibrations are a type -of. friction induced vibrations whereas the others can be classified as vibrations Induced by Random surface irregularities and Quasi-Harmonic vibrations. Stick-slip vibrations are periodical vibrations and seen under dry or boundary lubrication conditions at low sliding speeds. If the decrease of coefficient of fric tion vs. sliding velocity is sharp enough sticking and slipping may start. As the sliding speed is increased, xn there is a critical value of the speed above which stick- slip type of vibrations disappear. When a polymer slides on a rigid surface, the tribo- logical system can be represented by the mechanical models described in previous sections. By using different mechanical models, stick-slip attitude of polymeric fric tion is examined. Decreasing property of friction vs. sliding speed is considered linear for the vibrations with little amplitudes. Ruth-Hurwitz criterion is used for determining the stability of vibrations and it is concluded that the exisfance of vibrations mainly depends on the damping factor of sliding material and the magunitude of the negative slope of friction-velocity curve in both Voigt and Modified Maxwell Models. Representation with Maxwell and Maxwell-Voigt Models don't give satisfactory results, thus they have to be examined in a more complicated (non-linear) manner. The assumption which is to consider the linear friction-velocity relation ship, is not suitable for Maxwell and Maxwell-Voigt models and the real situation of friction-velocity curve should be considered.

The mechanical properties of polimers (especially elastomers, commonly known as "lastikler" in Turkish) are like neither solid materials nor liquids. However they show the properties of both solids and liquids in different ratios. Therefore Hooke's law which establishes the stress and strain relation ship in solids and Newton's Law which establishes the stress and rate of strain relationship in liquids cannot be used for examining the mechanical proper ties of these polymers. In fact both real liquids and solids don't obey exactly Newton's law and Hooke's law respectively, they show deviations. There are two important deviations: 1) The Strain (in solid) or the rate of strain (in liquids) may not be directly proportional to the stress, but may depend on stress in a more complicated manner. 2) The stress may depend on both strain and rate of strain as well as higher derivatives of strain. In the first case stress and strain ratio depends on the magnitude of the stress and the second case it depends on time only. Both these deviations are classified as viscoelastic but the second case is linear. The chemical structure of polymers is responsible for viscoelastic behavior. The long chain molecules and physical and chemical likages between these molecules create different kind of structures and of course properties. For instance if chemical linkages form a rigid, cross-liked molecular structure, a thermo setting plastic results. Where as if chemical linkages are not so, stronf but from a c,ross-linked structure the result will be an elastomer. The molecules are generally in irregular spiral form. When the elastomer is streched, these molecules behaves like a spring and the friction among the chain molecules act like a dashpot. Linear viscolastic behavior can be represented by various suitable combinations of simple spring elements v which obey Hooke ' s law and viscous dashpots which obey Newton's law. In other words, the mechanical properties of viscoelastic materials can be modelled by sprigs and dashpots in Linear manner. The basic mechanical models which are used in model ling Linear visco elastic behavior are shown in the figure below (Fig 1), where E is the elasticity modulus of spring elements and f) viscousity of dashpot. 1 w Maxell Voigt Modified Maxwell IİJ Modified Voigt Maxwell Voigt Fig 1 Basic Mechanical Models For Modelling Linear Viscoelastic Behavior. When these models are examined, finally it is conclu- ted that all these mechanical models give +h« special cases of generalized Hooke * s Law which is presented below. (Egn. 1) (ao+ax ss ts/sjsssf i - V Fig. 3. Simple Mechanism Of Adhesion vxn During which the body moves a distance and then relase takes place. An associated strain develops in the material causing energy to be stored elastically in the molecule. When the elastic stress exceeds the adhesive force, failure of the adhesive bond takes place and the molecule relaxes. Then it starts a new bond. This mecha nism can be called thermally activated molecular stick- slip. The integration of the force which acts on the mole cules around all actual contacts gives the total adhesive friction. There are many theories £>.n adhesiv friction. SQ.me of them use molecular-kinetic approach to the subject such as Mixed Theory and Unified Theory, some of them use mechanical approach such as Simple Theory. Although these theories start to calculate the adhe sion from different points, they all agree that adhesion can be calculated or stated by the relationship /Uadh = Constant (E/P) tan& (6) Where tan& is tangent modulus of the material, E is the Young Modulus of the material and P is the mean pres sure acts on the sliding surface. Egn.6. Shows that the adhesion depends on the visco- elastic nature of the polymer, because of tan& known to have viscoelastic properties. The Young's Modulus E refers to E' infact it can be E*. However E1 is used for simplifying the eguation. Since E' and tan& are the functions of strain frequency w ( or sliding speed V) and temperature T, jMadh is the function of these parameters. Whereas the proportional constant includes the surface texture affects, therefore /Wadh is a function of surface structure too. Thus Egn.6. is valid for constant sliding speed and temperature. The influence of sliding speed and temperature on adhesive friction is interchangeable. Therefore the expe rimental data obtained under different conditions can be presented in same master curves. The Williams-Landel.Ferry transform allows doing that»by using the transformation, adhesive friction versus sliding speed curve was obtained for Acrylonitrile-Butadiene Rubber from experimental data (Fig. 4) where ay is the shift factor from WLF transform. IX T0-20°C _i__L ??!.. I. J I I I _J I LOG|0(aTV) Fig. 4. Master Curve For Acrylonitrile-Butadiene The curve in Fig. 4 agrees with the theoretical results. According to the theoertical results, adhesive friction has a viscoelastic peak at low values of sliding speed. Hyteresis component of friction is somewhat due to a load and unload process. It can be b«ically described that (according to the Fig. 5) when polymer body slides on the asperities of a rigid body, a deformation occurs on the counter motion side of the asperity, which creates a pressure distribution and the horizontal component of pres sure force,.is hysteresis resistance. his Fig. 5. Pressure Distribution Due To Sliding On Asperities. x There are many theories dealing with hysteresis fric tion. As in the adhesion theories, hysteresis theories agree that hysteresis friction can be stated with /* his = constant ( -) tan& (7) Where the constant depends on the surface texture of rigid body. This relationship (Eqn.7) is valid for again constant sliding speed (or frequency) and temperature. If Eqn.7 is rewritten as /'his,., _P_. = constant ( ) Tan& (8) the lef hand side of new equation (Eqn.8) can be called Generalized Coefficient of Hysteresis Friction. Experimental data obeys very closely this relationship as seen in Fig. 6., In Fig. 6. there exist experimental data for two seperate elastomers which are Natural rubber and Butyl rubber. 0 3 0-2 CYLINDRICAL SLIDER V = 0-067 m/sec T=300°K V^^- ^. NATURAL RUBBER O BUTYL RUBBER J_ I 001 002 0 03 004 005 cy Fig. 6. Generalized Coefficient Of Hysteresis Friction vs. mean pressure. It is remarkable that whereas in all theories of adhesion and hysteresis, the coefficient of friction is proportional to tan&, the adhesion component is generally proportional to the ratio (E/P) and the hysteresis compo nent to its reciprocal. XI Finally, the total coefficient of friction for visco- elastic material sliding on a rigid body without any lubri cant can be expressed n = [Const 1. ( -|-)+ Const 2 (-|-) ] tan& (9) This equation is valid for constant speed and tempe rature. The variation of speed influence as seen in Fig. 7. Since the influence of temperature and sliding speed are interchangeable, temperature effects are almost same with sliding speed effects. LOG V Fig. 7. Total Friction Coefficient vs. Sliding Speed. When the coefficient of friction decreases by increa sing slidin3 velocity at low speeds, the stick-slip vibra-.. tions occour. Stic-slip vibrations are a type -of. friction induced vibrations whereas the others can be classified as vibrations Induced by Random surface irregularities and Quasi-Harmonic vibrations. Stick-slip vibrations are periodical vibrations and seen under dry or boundary lubrication conditions at low sliding speeds. If the decrease of coefficient of fric tion vs. sliding velocity is sharp enough sticking and slipping may start. As the sliding speed is increased, xn there is a critical value of the speed above which stick- slip type of vibrations disappear. When a polymer slides on a rigid surface, the tribo- logical system can be represented by the mechanical models described in previous sections. By using different mechanical models, stick-slip attitude of polymeric fric tion is examined. Decreasing property of friction vs. sliding speed is considered linear for the vibrations with little amplitudes. Ruth-Hurwitz criterion is used for determining the stability of vibrations and it is concluded that the exisfance of vibrations mainly depends on the damping factor of sliding material and the magunitude of the negative slope of friction-velocity curve in both Voigt and Modified Maxwell Models. Representation with Maxwell and Maxwell-Voigt Models don't give satisfactory results, thus they have to be examined in a more complicated (non-linear) manner. The assumption which is to consider the linear friction-velocity relation ship, is not suitable for Maxwell and Maxwell-Voigt models and the real situation of friction-velocity curve should be considered.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1991

##### Anahtar kelimeler

Polimerler,
Sürtünme katsayısı,
Tutma-bırakma titreşimleri,
Viskoelastik davranış = Viscoelastic behavior,
Polymers,
Friction coefficient,
Stick-slip vibrations,
Viscoelastic behavior