Constants of Metal Rubber Material

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1 Constants of Metal Rubber Material Modern Applied Science; Vol. 8, No. 5; 014 ISSN E-ISSN Published b Canadian Center of Science and Education Aleander Mikhailovich Ulanov 1 1 Samara State Aerospace Universit (SSAU), 34, Moskovskoe shosse, Samara, , Russia Correspondence: Aleander Mikhailovich Ulanov, Samara State Aerospace Universit (SSAU), 34, Moskovskoe shosse, Samara, , Russia. aleulanov@mail.ru Received: Jul 3, 014 Accepted: August 4, 014 Online Published: September 6, 014 doi: /mas.v8n5p16 URL: Abstract Damping materials made of pressing ire, such as Metal Rubber (MR material), metal-fle, spring cushion etc. are used idel in vibration protection sstems. The have high strength and damping, hoever the are non-linear and anisotropic. To use contemporar finite element softare for calculation of vibration insulators made of ire damping material one should kno constants of this material. Till this time this problem almost isn t researched, there is onl a fe data in linear approimation. A Young modulus for pressure and bending, shear modulus, Poisson ratio, friction force for pressure and for shear, friction coefficient beteen ire material and steel plate are obtained for MR material made of stainless steel ire for different load directions b static eperiment in the present research. An influence of deformation, relative densit, ire diameter, pressing force, deformation in other direction on these constants is considered. Peculiarities of pressing ire material deformation process are discussed: a difference of Young modulus for pressure and bending, a stabilization of hsteretic loop for one direction during load in another direction, an energ dissipation coefficient for different load directions. Results of the present research not onl allo calculation of vibration isolator made of MR material b finite element softare, but give a method for research of other pressing ire damping materials. Keords: MR material, Young modulus, shear modulus, friction force, Poisson ratio 1. Introduction MR material (MR Metal Rubber is manufactured b cold pressure of ire spiral) are used idel for elastic-damping elements of vibration insulators (Ao et al, 005; Jiang et al, 008; Xia et al, 009). It has high strength, high energ dissipation coefficient, abilit to ork under hugh and lo temperature, in agressive media, in vacuum etc. Analogous ire materials are metal-fle, spring cushion, ire mesh damper (Gildas, 1989; Kozian and Schmoll, 1998; Al-Khateeb, 00). These ire damping materials ma be used in combination ith squeeze film damper (Jiang et al, 005). Hoever these materials have large non-linearit and anisotrop (Ao et al, 003). The onl a to calculate elastic-damping element made of ire material b contemporar finite element softare is to consider this material as anisotropic continuous media (Ulanov and Ponomarev, 009) and to kno constants of this material for different ais direction and dependencies of these constants on parameters of ire material and load. A present paper continues orks (Yan et al, 010a) and (Yan et al, 010b) and contains a number of constant hich is maimall possible in the present time.. Method To obtain constants of MR material a static load eperiment as used in the present research. Elastic-damping element ith size mm as used. To research deformation of shear and tension this element as glued to plane surface. X ais is a direction of pressing during MR elastic-damping element manufacturing. Y and Z ais are perpendicular to direction of pressing. Compression direction is positive. Parameters of ire material are diameter of ire d and relative densit of material. The relative densit is ratio of densit of manufactured elastic-damping element to densit of material of ire (for MR it is stainless steel usuall). Pressure of manufacturing of elastic-damping element depends on its relative densit: press (1) Hsteretic loop of damping elements made of MR material is significantl nonlinear (Fig. 1). To make results more common it is better to use relative coordinates such as stress and relative deformation. 16

2 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; 014 Fig. 1. Hsteretic loop of elastic-damping element used in the present research for X ais direction. =0.18, d =0.1 mm Full stress consists from elastic stress and friction stress L L. H H () Here + is for load process ith stress 1 and - is for unload process ith stress. Elastic stress is a middle line of hsteretic loop described b equation L ( 1 )/ (3) Friction stress is difference beteen load (or unload) process and the middle line, thus H ( 1 )/ (4) Equations (3) and (4) are correct if all ire contacts slip. For the beginning of unloading process it is not so. (Ulanov and Lazutkin, 1997) gives a range for correctness of (3) and (4) as [0.7 Amin ;0.7 A ma ] (here A ma and A min are maimal and minimal amplitude of deformation respectivel). For one time loading in eperiment A ma and A min ma be much more than usual orking amplitude of vibration isolator, so range [0.7 Amin ;0.7 A ma ] is sufficient for practice. For Х ais a researched range of strain is [ 0.06;0.4], for Y and Z ais [ 0.06;0.16]. Usual orking strain of MR material is less (Yan et al, 013). Range of relative densit is [0.18;0.3]. Range of ire diameter is mm. 3. Results 3.1 Young Modulus and Friction Stress for Pressure and Tension The elastic stress and friction stress for 0.18 and d = 0.1 mm for Х and Y ais direction are presented at Fig (Yan et al, 010a). Equations (5) (8) describe dependencies of stress on strain and relative densit ith an error about 5%. 17

3 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; 014 Fig.. Elastic stress and friction stress for 0.18, d = 0.1 mm for Х and Y ais directions H ( ), MPa; (5) H ( ), MPa. (6) L ( ), MPa; (7) L ( ) MPa. (8) First efficient in equations (7) and (8) is analogous to Young modulus E. Because Z ais is similar to Y ais, it is possible to find stress Hz as H and stress Lz as L. To obtain dependenc of Young modulus on ire diameter the elastic force and friction force for ire diameters mm ere divided b force for d = 0.1 mm. These ratios are required coefficients of influence. The are described b functions f d d (9) H H f d d (10) L fl 7.1d 1, 90d f d d (11) (1) Thus to take into account an influence of ire diameter it is enough to multipl the function (5) b coefficient (9), function (6) b coefficient (10) etc. 3. Young Modulus for Bending To obtain Young modulus for bending a process of deformation of ring-shape elastic-damping element as considered (Xia et al, 005). For a deformation of ring made of linear material under load P is knon (Timoshenko S. and J.N. Goodier, 1951): 3 3 P R R Eb Cp J J (13) here is deformation, R is radius of ring middle line, J is ring section inertia moment, C p is ring stiffness. For little deformation Cp ( T1 T )/( a1 a ). It is possible to obtain segmentst 1, T, a1 and a eperimentall b a hsteretic loop (Fig 3). 18

4 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; P, N 1.5 a T a 1 T 1 X, mm Fig. 3. Obtaining oft 1, T, a1 and a from hsteretic loop Dependenc of Young modulus on and d is E 10.5 d ( ) (MPa) (14) 3.3 Shear Modulus and Friction Stress for Shear In a case of shear the hsteretic loop (if to eclude its ends) is more near to linear (Fig. 4), thus it is possible to use a linear dependenc for its description. G H (15) here H is friction stress for shear. Fig. 4. Hsteretic loop of researched elastic-damping element for shear ( =0.18, d =0.1 mm) and its dependenc of shear in XY ais direction on strain in X ais direction. 1 - =0; - =0.08; =0. Dependencies on relative densit (for d = 0.1 mm and the range of deformation [ 0,1;0,1], hich ecludes ends of the loop) for shear direction XY are For shear direction YZ Gz G MPa, 1,7 18,3, MPa, H Hz 1,3 0,151 MPa. (16) 1,3 0,301, MPa. (17) Shear modulus and shear friction stress are independent on ire diameter. It is shon in (Yan et al, 010b) that it is possible if during shear most of ires in MR material ork on shear but not on bending. 3.4 Dependenc of Constants on Load in Other Direction Pressure in one ais direction increases force in each ire contact. Of this reason a stiffness and friction should increases in other ais direction. Dependenc of shear in XY ais direction on strain in X ais direction is presented on Fig

5 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; 014 In this case if strain 1.4 (1 ). >0, it is necessar to multipl shear modulus G and shear friction stress H on Influence of pressure in X ais direction on elastic and friction properties in Y direction is researched for analogous ire material in (Choudhr, 004). Because shear changes force in ire contacts insignificantl, there is no influence of shear deformation in Y direction on friction stress in Х direction. An elastic stress in this case should be multiplied on (1 1.5 ). 3.5 Poisson Ratio For load in X ais direction the Poisson ratio is z Usuall it isn t necessar to take into account so little value, thus it is possible to assume that element made of MR material during its deformation in manufacturing pressing direction has no an pressure on its sides. If a deformation is in Y direction, one should differ to cases: initial load and multi-time deformation. For initial load there are hsteretic loops in X and Z directions too (Fig. 5). Fig. 5. Hsteretic loops in X and Z ais direction for initial load in Y ais direction It is possible to recalculate these loops in coordinates (or z respectivel). Recalculated loops are described b equations 1 1 ; z z1 z1, (18) (here part ith "+" is taken into account onl for unloading process). In these equations coefficients are analogous to Poisson ratio, coefficients are residual deformation. For free surfaces of specimens equations (18) transforms into 0, 67 (0, 3 0,83 ) ; ma z 0, 33 (0,16 0, 41 ) ma (19) If MR is glued to the load surfaces, coefficients of equations (15) are a little bit different: 0,67 (0, 8 0,7 ) ; ma 0, 33 (0,14 0, 36 ). (0) z ma For multi-time compression in Y direction the structure of MR material becomes stabile. After deformation ccles residual deformation stabilize near values (0,9,3 ) ; ma zma (0,45 1,17 ) ma. (1) Hsteretic loops for X and Z direction in this case are absent, dependencies (15) transform to 0, 49 ; z 0,31 () Thus Poisson ratio for multi-time compression are 0, 49 and z 0, 31. Poisson ratio for tension in a range of possible strain (if tension is more, structure of MR material ill be destructed) is equal to 0. 0 ma

6 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; Friction Coefficient Beside elastic-damping elements made of MR material, vibration insulator has man other steel details (cups for elastic-damping elements, unload springs, bolts for connection etc). Some energ of vibration dissipates on friction beteen these details and elastic-damping element. This process depends on friction coefficient f. This coefficient as obtained as a ratio beteen a force hich moves an elastic-damping element along plane steel surface and a force hich presses the element to this surface. The coefficient is independent on densit and force direction (X ais or Y ais). If pressing stress is less than 0.5 MPa) the value of coefficient is 0.1, its maimal value is 0.15 for pressing stress 0.75 MPa. If pressing stress is higher, the friction coefficient continue to be constant. 4. Discussion To eplain obtained results one need to consider a structure of ire material (Zhu et al, 011). A reason of increasing of Young modulus and friction stress for pressure is increasing of number of ire contacts during pressing. There are to processes hich form the dependenc of Young modulus and friction stress for pressure on ire diameter. When the ire diameter increases, inertia moment of each ire increases too, stiffness of each ire and sum of elastic force increases of this reason. Hoever from another side, if the ire diameter increases for the same densit of MR, number of ire becomes less in a unit of volume. It means that number of ire contacts decreases too. Length of parts of ire (curve beams) beteen contacts becomes more and stiffness of these curve beams decreases. To these processes together provides maimum for f L coefficient. To different processes eist for friction force too. From one side, hen the number of contacts decreases, sum of friction force in all contacts decreases too. From another side, hen the number of contacts decreases, contact force in each contact increases, and friction force in each contact increases too. To these processes together provides maimum for f H coefficient. For MR material the Young modulus for bending is more than for pressure or tension, and friction stress is significantl less. During the bending a detail has neutral ais near hich a strain is near to zero. In these conditions the ires in MR material almost have no sleep. It makes stiffness of elastic-damping element more and energ dissipation in it less. For eample, for the same 0.18 and d = 0.1 mm and deformation in Y ais direction (it takes place for ring-shape elastic-damping element, because during its manufacturing the ring is pressed in the direction of the ring ais) initial value of elastic stress near =0 for pressure is.69 MPa, for bending it is 8.7 MPa, friction stress for pressure is 0.06 MPa, for bending is MPa (Yan et al. 010a). Equation for friction stress for bending (in contrast to Young modulus) isn t obtained in the present research. This stress depends not onl on densit and ire diameter but on thickness of MR element and amplitude of bend. Perhaps it is possible to solve this problem theoreticall: to consider the bending element as a sum of man laers ith compression or tension in each of them ith different amplitude. Thus this problem needs future research. Equations (5) (1) and (16) (17) allos approimate calculation of area of hsteretic loop (an mistake ill be in the ends of loop, because man ire contacts still didn t sleep there) and area under a line of elastic force. A first value is an energ dissipated during one ccle of loading, second one is potential energ of deformation, their ratio is energ dissipation coefficient. Thus it is possible to compare this coefficient for different load directions. If to take onl first parts in equations (5) (8) (let e suppose that and d are the same and strain is little), ratio of elastic stress for Y and X ais directions is about 49.6:11=4.5, ratio of friction forces is about 0.56:0.167=3.35, therefore ratio : 1/(3.35 : 4.5) Thus the energ dissipation coefficient is more in direction of X ais. Because the hsteretic loop for shear is near to linear, its area (ith an mistake for the ends of loop) is about H, and potential energ of deformation is G /. Thus its ratio is / H G. For the same shear angle from equations (16) and (17) : z It is follo from equations (16) and (17) that for shear is proportional to Values of and are comparable. ( )

7 .ccsenet.org/mas Modern Applied Science Vol. 8, No. 5; 014 For 0.1 ratio : 1.1. For 0.15 ratio : 0.8. Unfortunatel till this time that fe researchers ho ork on ire damping materials (Andrés and Chirathadam, 011; Li et al, 010; Tian et al, 008) obtained for researched materials the linear stiffness and energ dissipation coefficient onl, and for one-dimensional load process. It isn t enough to describe a behavior of material in contemporar vibration protection sstems. 5. Conclusions Results of the present research give constants for calculation of vibration isolators made of MR material b finite element softare. It gives a method for research of other pressing ire damping materials (such as metal-fle, spring cushion, ire mesh damper etc). All these results are presented for MR material made of stainless steel ire. Hoever sometimes another materials are used in MR (for eample, copper ire to increase heat conductivit). Thus the constants ill depend on properties of ire material and on part of materials in a ire bod. This problem needs future research. If MR material is used in squeeze film damper, it is necessar to research ho its constants ill change in other media (such as oil). If MR material is too thin, during its deformation some ires don t meet other ire, and increasing of number of contacts doesn t take place. All results above are correct if H/ d ratio is more than 100 (here H if thickness of element in load direction). Elastic-damping elements for pipeline supports have H/ d ratio about 10 30, it is necessar an additional research of its properties. All results above are for ne MR material. An important problem is a life-time of vibration insulators made of MR material. Constants of material ill change during its earing. It depends (Ao et al, 006) on number of load ccles, vibration stress, static preload stress, densit of material, ire diameter, orking temperature of vibration insulator. The present paper gives a method for future researches of these influences. 6. Support This ork as supported b the Ministr of education and science of the Russian Federation in the frameork of the implementation of the Program of increasing the competitiveness of SSAU among the orld s leading scientific and educational centers for ears. References Al-Khateeb, E. M. (00). Design, Modelling and Eperimental Investigation of Wire Mesh Vibration Dampers. Department of Mechanical Engineering, Teas A &M Universit, pp. 15. Andrés, L. S., & Chirathadam, T. A. (011). Metal mesh foil bearing: Effect of motion amplitude, rotor speed, static load, and ecitation frequenc on force coefficients. Proceedings of the ASME Turbo Epo 6 (Parts A and B): Ao, H. R., Jiang, H. Y., Wang, S. G., Xia, Y. H., Jia, C. H., & Ulanov, A. M. (003). Eperimental research on anisotropic characteristics of elastic damping elements of metal rubber. Journal of Materials Engineering, (9), Ao, H., Jiang, H., & Ulanov, A. M. (005). Dr friction damping characteristics of a metallic rubber isolator under to-dimensional loading processes. Modelling and Simulation in Materials Science and Engineering, 13(4), Ao, H., Jiang, H., & Ulanov, A. M. (006). Estimation of the fatigue lifetime of metal rubber isolator ith dr friction damping. Ke Engineering Materials, II: Choudhr, V. V. (004). Eperimental Evaluation of Wire Mesh for Design as a Bearing Damper. Department of Mechanical Engineering, Teas A&M Universit, pp. 86. Gildas, P. (1989). Pat. FR630755, France, B3P17/06; B3P17/00; (IPC1-7): D03D3/0; D04B1/14; D04H3/00; F16F7/00. Spring-tpe cushion material, spring-tpe cushion made thereof and sstem for producing the spring-tpe cushion material. Jiang, H. Y., Hao, D. G., Xia, Y. H., Ulanov, A. M., & Ponomarev, Y. K. (008). Damping characteristics calculation method of metal dr friction isolators. Journal of Beijing Institute of Technolog (English Edition),

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