Calculation of Vibration of Pipeline Bundle with Damping Support Made of MR Material Procedia Engineering 176 ( 2017 ) 169 – 174 Available online at www sciencedirect com 1877 7058 © 2017 The Authors[.]
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 176 (2017) 169 – 174 Dynamics and Vibroacoustics of Machines (DVM2016) Calculation of vibration of pipeline bundle with damping support made of MR material S.A Bezborodov, A.M Ulanov* Samara National Research University, 34 Moskovskoye shosse, Samara, 443086, Russia Abstract Wire damping materials (such as Metal Rubber, MR) are used widely for protection of pipelines against vibration A calculation method for bundle of arbitrary shape pipelines with damping supports made of MR material by finite element method ANSYS software is developed The method takes into account complexity of pipelines shape, interaction of pipelines vibration in the bundle, multi-axial linear and torsion stiffness and damping of nipple supports A constant damping coefficient is obtained by calculation-experimental method from vibration of one pipeline The method allows obtaining amplitude of pipelines vibration and stress in them Calculation results are proved by experiment Errors of natural frequencies are less than %, thus it is possible to use this method for practical application: placement of pipeline supports and design of these supports parameters It allows reducing a large experimental work of measurement a stress in pipelines during pipeline systems design 2017The The Authors Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license ©©2017 Authors Published by Elsevier Ltd This Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of (http://creativecommons.org/licenses/by-nc-nd/4.0/) Machines under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines Peer-review Keywords: Pipeline, bundle, vibration, damping, support, MR material, Finite Element Method Introduction Contemporary engines and machines include a large number of pipelines Group damping of pipeline bundles allows simplifying of structure and reduction of support mass Damping dry friction supports are used widely for protection of pipelines against vibration These supports often use a damping material made of pressed wire, such as MR (Metal Rubber) [1, 2] MR material is manufactured by cold pressing of wire spiral It has high damping, large strength, and high ability to work in aggressive media Analogous wire damping materials are “metal-flex”, “spring * Corresponding author: tel +79171417335, e-mail: alexulanov@mail.ru 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines doi:10.1016/j.proeng.2017.02.285 170 S.A Bezborodov and A.M Ulanov / Procedia Engineering 176 (2017) 169 – 174 cushion” [3, 4], “wire mesh damper” [5] However MR material (as all other materials made of pressed wire) has non-linear properties [6], its stiffness and energy dissipation coefficient depend on deformation amplitude and preliminary static deformation Q However calculation methods for pipeline vibration in a present time are linear previously, they don’t take into account a complexity of pipeline shape, consider a pipeline as straight or bended beam They don’t take into account a joint vibration of some pipelines in the bundle too [7 – 10] A maximal complexity of calculation method in present time is a pipeline as some branches [11] The calculation methods in present time take into account a damping in liquid into the pipeline but not a damping in supports On this reason these methods allow obtaining of pipeline resonance frequencies but don’t allow obtaining of stress in the pipeline, or they give only relative distribution of stress in the pipeline instead its absolute value [12] The aim of the present research is developing of calculation model for pipeline bundle which allows calculation of own frequencies and displacements of pipelines connected by group support with damping elements made of MR material It would be possible to find a placement and characteristics of damping supports by calculation on a base of this model It allows to reduce significantly a time and expenditure for design of pipeline systems Researched object and calculation model As researched object two pipelines made of titanium alloy was chosen They have outer diameter 6.2·10-3 m, inner diameter 4·10-3 m and complex 3D shape Both ends of pipelines have nipple supports as a model of pipeline connection with engine units In a middle part of pipelines the support with a wideness 11·10-3 m is installed Two damping elements made of MR material are placer in this support Nipple supports are connected with angles and vibration stand (Figure 1) Fig Pipeline bundle with damping support on vibration stand TIRA The calculation model is obtained in ANSYS software (Figure 2) A software was developed for modal and harmonic calculation of two pipelines with nipple supports on its ends and group support with damping elements in the middle part Pipelines are modeled by elastic two-node finite element Pipe16 Nipple supports and damping support are modeled by finite element Combin14, mass of group support is modeled by finite element Mass 21 Characteristics of MR material (stiffness С and energy dissipation coefficient Ψ) are calculated by equations obtained from static experiment with thin plates made of MR material The plates have different thickness Н (from 1.15·10-3 to 3.45·10-3 m), density ρ (from 1115 to 2028 kg/m3), relative preliminary static deformation εQ=Q/H (from 0.087 to 0.268), wire diameter dW (from 0.09·10-3 to 0.12·10-3 m) [13] Stiffness of damping elements made of MR material in the present experiment was 181000 N/m, energy dissipation coefficient Ψ = 1.3 Parameters of MR material for this element are presented in Table 171 S.A Bezborodov and A.M Ulanov / Procedia Engineering 176 (2017) 169 – 174 Fig Finite element model of pipeline bundle Table Parameters of damping element made of MR material Wire diameter dW, 10-3 m Thickness, 10-3 m 0.09 2.3 Free outer diameter of system, 10-3 m 10.8 Diameter of hole in the support, 10-3 m 9.8 Pipeline diameter, 10-3 m 6.2 Relative static preliminary deformation εQ 0.22 Density of MR material ρ, kg/m3 1217 Fequency and amplitude of pipeline vibration depend significantly on stiffness and energy dissipation coefficient not only in damping support but in nipple supports too Characteristics of nipple supports are included in the model as stiffness for displacement, stiffness for rotation and energy dissipation coefficient Stiffness for displacement was obtained experimentally for nipple support by applying of force to place of connection of pipeline and nipple support Its value is С0 = 1111000 N/m Stiffness of nipple support for rotation obtained from research [14] as 1000 N/radian around axis in a plane perpendicular to pipeline axis and 150 N/radian around the pipeline axis Energy dissipation coefficient for nipple support Ψ = 0.14 was obtained experimentally by vibration amplification coefficient of resonance for a pipeline without damping support Because deformation of Mr element with little thickness has little influence on frequencies and amplitudes of pipeline vibration, the stiffness and energy dissipation coefficient of damping support were assumed as constant for harmonic analysis Because finite element Combin14 uses viscous friction, a transformation from dry friction energy dissipation coefficient Ψ to equivalent viscous damping coefficient Cv is obtained by equality of hysteretic loops area by equation Cv C 2 (here ω is frequency of vibration) [15] To obtain in harmonic analysis the real amplitudes of vibration it is necessary to assign a correct constant damping coefficient To find it a calculation-experimental method is proposed Experimental part of this method is obtaining of vibration amplitude in specific point of reference during vibration of one pipeline only A sensor of vibration is placed on the pipeline and modeled as a concentrated mass Pipeline supports have stiff connection with a table of vibration stand During experiment a resonance vibration of pipeline for first mode is obtained Vertical displacement of the point of reference of the pipeline for amplitude of table of vibration stand equal 0.012·10-3 m is presented on Figure Vertical amplitude of pipeline vibration in the point of reference is 0.385·10-3 m To find the damping coefficient the calculation research was used The aim of this calculation is obtaining of value of damping coefficient for which the calculated vibration amplitude and experimental vibration amplitude coincide An influence of constant damping coefficient value on vibration amplitude on the point of reference of the pipeline is presented in Table 172 S.A Bezborodov and A.M Ulanov / Procedia Engineering 176 (2017) 169 – 174 Fig Vertical (direction of Z axis) displacement of pipeline on vibration stand Table Influence of constant damping coefficient on vibration amplitude on the point of reference of pipeline Value of constant damping coefficient DMPRAT -3 Calculated amplitude, 10 m 0.001 0.0075 0.01 0.1 11.2 2.33 0.383 0.291 0.037 It is seen from Table that experimental and calculated amplitudes are near to each other for damping coefficient value 0.0075 This value was used in the model for harmonic calculation of pipeline bundle Experimental research Vibration stand TIRA was used for experimental research of pipeline bundle vibration (Figure 1) To obtain a displacement of pipelines near resonance a range of excited frequencies ±5 Hz near resonance frequency was set on vibration stand control system Acceleration of table of vibration stand was 40 m/s2 Non-contact system ARAMIS was used for measurement of pipeline bundle vibration This system has two highspeed cameras which obtain simultaneous pictures of object Comparison of sequency of pictures allows to find 3D shape of obgect and its deformation and displacement To obtain amplitude of table of vibration stand a bold was installed on the table For ARAMIS measurement a coordinate system was placed on a head of bolt in its motionless position Thus during work of vibration stand an amplitude of bolt head displacement (equal to amplitude of movement of table of vibration stand) on resonance frequency was 0.036·10-3 m This value was used in harmonic analysis by ANSYS software as amplitude of excited load Amplitudes of vibration of pipeline bundle measured near damping support by ARAMIS and calculated by ANSYS are presented in Table Table Displacements of pipeline bundle measured by ARAMIS and calculated by ANSYS for different directions Amplitude of support vibration, 10-3 m Amplitude of No pipeline vibration near support, 10-3 m Amplitude of No pipeline vibration near support, 10-3 m Vertical ANSYS ARAMIS ∆,% Horizontal ANSYS ∆,% 1.01 0.94 1.25 1.17 19.2 19.7 0.37 0.31 0.774 0.675 52.2 54 1.02 1.225 16.7 0.4 0.725 44.8 ARAMIS For example, displacement of No pipeline in vertical direction (Z axis) near support is presented on Figure S.A Bezborodov and A.M Ulanov / Procedia Engineering 176 (2017) 169 – 174 Fig Displacement of No pipeline for Z axis direction near the damping support Difference of amplitudes is 17-20 % for vertical direction and 45-54 % for horizontal one It is possible to explain this difference by different nut tightening for nipple connection of one pipeline and pipeline bundle, different stress of assembling in the pipelines Mass of vibration sensor during experiment with one pipeline may be source of any mistake too However in the present time there are no any calculated results about displacement of pipelines with complex shape and pipeline bundles at all Information about it and about stress in pipelines is obtained by large experimental work Thus it is possible to consider the model developed in the present paper as practically useful for preliminary calculation of displacement of pipelines and calculation of stress in pipelines by ANSYS software Error for frequencies is significantly less Comparison of experimentally obtained (by laser vibrometer) and calculated own frequencies of pipeline bundle with damping support is presented in Table Table Comparison of experimentally obtained and calculated own frequencies of pipeline bundle Own frequencies, Hz Laser vibrometer ANSYS Error, % 176.6 221.9 369 187.2 237.4 351 6.0 7.0 4.9 It is seen from Table 4, that error of own frequencies calculation is less than %, it is enough for practice Because the model takes into account characteristics of MR damping elements, the developed model is useful for design of pipeline systems, for obtaining of placement and characteristics of supports by calculation For an improvement of the developed model a future detail research of stiffness and damping in nipple supports and influence of assembling stress is necessary Conclusions Thus a calculation method for bundle of arbitrary shape pipelines with damping supports by finite element software is developed The method takes into account complexity of pipelines shape, interaction of pipelines vibration in the bundle, multi-axial linear and torsion stiffness and damping of nipple supports Calculation results are proved by experiment Errors of natural frequencies are less than %, thus it is possible to use this method for practical application: placement of pipeline supports and design of these supports parameters The method allows 173 174 S.A Bezborodov and A.M Ulanov / Procedia Engineering 176 (2017) 169 – 174 obtaining amplitude of pipelines vibration and stress in them However a future research of damping coefficient for the bundle of pipelines and stress in pipelines is necessary Acknowledgements This work was supported by the Ministry of education and science of the Russian Federation in the framework of the implementation of the Program of increasing the competitiveness of SSAU among the world’s leading scientific and educational centers for 2013-2020 years References [1] H Yan, H Jiang, G Li, A.M Ulanov, Research on the performance of metal isolator used in the pipeline support of aeroengine China Mechanical Engineering, 18 (12) (2007): 1443 – 1447 [2] Y.-H Xia, H.-Y Jiang, H.-D Wei, H Yan, A.M Ulanov, Shock protection characteristics of metal rubber isolators Journal of Vibration and Shock, 28 (1) (2009): 72–75 [3] P Gildas, Pat FR2630755, France, B23P17/06; B23P17/00; (IPC1-7): D03D3/02; D04B1/14; D04H3/00; F16F7/00 Spring-type cushion material, spring-type cushion made thereof and system for producing the spring-type cushion material 1989 [4] R Kozian and E Schmoll, Pat DE19629783, Germany, F16F1/373; F16F1/36; (IPC1-7): F16F1/38 Vibration absorber with spring cushion and two end parts 1998 [5] E.M Al-Khateeb, Design, Modelling and Experimental Investigation of Wire Mesh Vibration Dampers Department of Mechanical Engineering, Texas A&M University, 2002, 215 pp [6] H Yan, H.-Y Jiang, W.-J Liu, A.M Ulanov, Identification of parameters for metal rubber isolator with hysteretic nonlinearity characteristics Acta Physica Sinica, 58 (8) (2009): 5238 – 5243 [7] Veklich, N.A., Equation of small transverse vibrations of an elastic pipeline filled with a transported fluid Mechanics of Solids, 48(6) (2013): 673-681 [8] K Zhang, Y Li, B Han, Z Wang, Numerical Simulation on Spanning Pipeline's Vibration Characteristics and Safety in Flood International Conference on Pipelines and Trenchless Technology (2013): 986-996 [9] Seong-Hyeon Lee, Sang-Mo Ryu, Weui-Bong Jeong, Vibration analysis of compressor piping system with fluid pulsation Journal of Mechanic Science and Technology, 26 (12) (2012): 3903-3909 [10] Y Yesilce, Free and forced vibrations of an axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements Shock and Vibration, 19(4) (2012): 735-752 [11] Gongmin Liu, Shuaijun Li, Yanhua Li, Hao Chen, Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method Journal of Sound and Vibration, 332 (24) (2013): 6519–6536 [12] X.P Ouyang, F Gao, H.Y Yang, H.X Wang, Two-dimensional stress analysis of the aircraft hydraulic system pipeline Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 226(5) (2012): 532-539 [13] A.M Ulanov, A.V Shvetsov, Mechanical characteristics of supports vibration isolator of pipelines made of metal rubber, Proceedings of the SSAU, v.3(27) (2011): 94–99 [14] S.A Bezborodov, A.M Ulanov, Determination of nipple joint torsion stiffness for calculation of pipeline natural frequencies, Proceedings of the SSAU, v.14(3), part (2015): 448–453 [15] S.A Bezborodov, A.M Ulanov, Method of calculation for vibration of pipeline with damping supports made of MR material, Proceedings of the Samara State Aerospace University, v.1 (43) (2014): 159-165 ... displacements of pipelines connected by group support with damping elements made of MR material It would be possible to find a placement and characteristics of damping supports by calculation on a base of. .. made of MR material are placer in this support Nipple supports are connected with angles and vibration stand (Figure 1) Fig Pipeline bundle with damping support on vibration stand TIRA The calculation. .. ends of pipelines have nipple supports as a model of pipeline connection with engine units In a middle part of pipelines the support with a wideness 11·10-3 m is installed Two damping elements made