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Vibroacoustics Analysis of Punching Machine Hydraulic Piping
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 106 (2015) 17 – 26
Dynamics and Vibroacoustics of Machines (DVM2014)
Vibroacoustics Analysis of Punching Machine Hydraulic Piping Georgy M. Makaryants*, Andrey B. Prokofiev, Evgeny V. Shakhmatov Samara State Aerospace University (SSAU), 34, Moskovskoe shosse, Samara, 443086, Russian Federation
Abstract The reduction of elevated dynamic loads, affecting the elements of the hydraulic drive, is an important task in production equipment maintenance. In case of the hydraulic drive with actuators, remotely located from the power source, the piping defines the working capacity of the whole system. Hence the development of piping vibroacoustic analysis methods appears to be the vital task. The said methods would not only help to define the cause of increased loads, but also permit to develop an adequate design solution without prolonged experimental checks. The article proposes the method of pipeline system vibroacoustics analysis through the example of press-forge unit drain piping. The novelty of this method consists in the use of the fluid pulsation and piping vibration spectra analysis in their correlative comparison with account to the calculated modal parameters of a pipeline. The measurements of working fluid pressure pulsation and pipeline vibration in the vicinity of the breakage locations were carried out. The experimental data spectrum analysis indicated an apparition of intense water-hammer process along with the frequency coalescence of fluid pulsation and pipeline vibration. The resonant vibration amplification, caused by the waterhammer effect, was suggested. The pipeline system mathematical model, allowing to calculate its modal parameters, was derived. The comparison of the modal analysis with the vibroacoustic response confirmed the hypothesis of the pipeline resonant breakdown. The article depicts, that the study of the pipeline system vibroacoustic response, based only on Fourier analysis of the working fluid pulsation and pipeline vibration, is prone to fail the reliable causation of elevated dynamic loads. It is suggested to complement the vibroacoustic response analysis with the modal parameters calculation. The mathematical computation of the modal frequencies and shapes was implemented instead of their experimental observation in order to exclude the undesired signal, introduced with attached mechanical equipment. On top of that, the mathematical computation of the pipeline modal parameters allowed to perform the pipeline modal frequency shift from the water-hammer effect frequency range through cautious relocation of additional supports. © 2015 2014The TheAuthors. Authors. Published by Elsevier Ltd. © 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 organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
* Corresponding author. Tel.: +7-927-688-95-05; fax: +7-846-335-19-05. E-mail address: [email protected]
1877-7058 © 2015 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 organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
doi:10.1016/j.proeng.2015.06.004
18
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Keywords: hydraulic piping; pressure pulsation; power fluid; vibration; press-forging industry; finite element method; modal analysis.
1. Introduction The increase of the piping systems efficiency is vital due to its direct connection with the overall facility performance and operation quality. The automatic press line "Erfurt" breakdown, caused by the piping system problems, is an example of production machinery failure. The line outfitted with PTr 2000+1200 SS punching unit is installed on press-forging line in joint-stock company AUTOVAZ (Togliatti, Russia) [1]. The press-forging process of the considered line is represented by the deep-drawing of billet sheet. The construction of punching machine is shown on Figure 1. Half of the stamp which performs reciprocation is attached to a sliding bar 1. A billet sheet 2 is placed on supports 3 which are rigidly held by a bottom plate 4. A fixed counterpart 5 is placed under the billet sheet 2. Downward motion and press-forging are performed with the sliding bar 1 with a die block. This process is counteracted by press forces in the extraction cylinders 6. Extraction cylinders 6 lean on bottom plate 4 via endthrust bearings 7. During the automatic line operation the drain piping of extraction cylinders power hydraulic system and upper piston chamber of the central cylinder periodically broke off and suffered from a total loss of power fluid, which led to the shutdown of the whole press-forging line [1]. The disruption took place x in the junctions of drain line and hydraulic cylinder automatic control device 1 (Fig. 2), x in the drain line and collector, x between left and right collectors (Fig. 2). The crosscut character of breakage indicated that the pipe bending vibrations were the cause of the disruption.
Fig. 1. Erfurt PTR 2000+1200 SS schematic layout 1- sliding bar; 2 - billet sheet; 3 – supports; 4 – bottom plate; 5 – counterpart; 6 – extraction cylinders; 7 – end-thrust bearings; 8 – central cylinder; 9 – rod
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 2. Drain piping [1] 1 - the hydraulic cylinder automatic control device; 2 - pipeline disruption locations; 3 - the fluid storage tank joint flange
2. Analysis of vibroacoustic interaction in the pipeline systems The curvilinear pipeline bending vibration genesis was first described in the article [2]. The pipeline vibration is linked to the apparition of the non-steady unbalanced stresses, caused by the pulsing flow dynamic pressure losses in the knee-shaped elements. The described bending vibration genesis mechanism is typical for pipeline systems with relatively low fluid flow speeds. This model is commonly used to define the cause of vibration increase in the booster stations piping. The articles [3, 4] link the pipeline vibration phenomenon with the hydro-torque of mechanical pipeline subsystem flexible elements. This kind of vibration appears in the high velocity pipelines, specific to the fuel mains of a carrier rocket with liquid-propellant engine or gas-turbine engines fuel systems. Anyway, the pulsating flow energy may cause significant mechanical oscillations of piping, attached equipment and bearing structure due to its interaction with the piping itself. The fluid supply units operation, self-excited oscillations, caused by the actuating of flow regulators and valves, and water-hammer processes are the main causes of the hydraulic mains power fluid pulsations. The pipeline system vibroacoustics analysis methods include experimental methods, based on modal parameters analysis [5, 6], as well as theoretical, using the vibroacoustic interaction models [7-13], transfer function matrix [14, 15] ,differential transformation method [16], dynamic stiffness method [17] and numeric modal analysis [18]. Although, most of existing methods are used to solve more specific tasks, such as computation of a straight pipeline section, booster station piping and steam pipeline. Obviously, the study of a pipeline system with complicated spatial configuration and arbitrary number of supports requires a versatile analysis method, taking into account both experimental statistics and computational parameter analysis. That’s why the measurements of the power fluid pressure oscillation and piping vibration, which appeared during the press-forge equipment operation, were taken first in order to define the cause of the studied pipe main excitation. 3. Experimental study of the press-forge unit hydraulic pipeline dynamics Experimental study data analysis [1] demonstrated the apparition of two intense water-hammer processes in the drain piping (Fig. 3). The first process at the time period is caused by the power fluid draining during the downward motion of the billet sheet. The upward motion of the billet sheet starts at the time period. Therefore the second hydraulic impact, caused by the automation valves actuations which slow down the billet movement, occurs in the end of the motion at the time period. The peak pressure value amounts from 0.6 to 0.8 MPa, the minimum value amounting to 0.2 MPa with mean level of 0.39 MPa.
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 3. Drain piping pressure oscillations [1]
The spectrum analysis of the first hydraulic impact showed the presence of two resonant zones (Fig. 4): the interval of 12 to 60 Hz with maximum at 45 Hz and the interval of 70 to 120 Hz with maximum at 93 Hz. The intensity of the resonant peaks in the second zone is 4.5 times lower than in the first one. Spectrum analysis of the second hydraulic impact (Fig. 5) shows the most intensive resonance in the interval of 15 to 88 Hz with maximum at 45 Hz.
Fig. 4. Pressure oscillations spectrum (downward motion of bottom plate)
The three-dimensional system vibration activity analysis was performed simultaneously with the piping pressure pulsation analysis. The following locations of vibration sensors installation were chosen: x Junction points of the main drain line and drain piping of central cylinder and each of extraction cylinders; x Piping breakdown locations. The figure 6 represents the vibro-acceleration oscillogram of the drain piping under the central cylinder manifold.
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 5. Pressure oscillations spectrum (upward motion of bottom plate)
Fig. 6. Vibratory acceleration oscillogram of the manifold under the central cylinder
The drain line oscillation analysis indicated two intense oscillatory processes, occurring in every vibration monitored point during the press forward stroke. The first one was noticed in the beginning of the press forward stroke and coincided with the moment of fluid displacement from cylinders. The second one is correlated with the stamp lift action. In both cases the spectral density reached maximum at 45 Hz (Figures 7-8). The performed analysis allowed concluding that the system oscillations are caused by the force loads of pressure pulsations resulting from the press control system piping hydraulic impacts. The resonant amplification of the press drain piping oscillatory movement was suggested in this case. The numerical modal analysis was performed in order to verify this presumption. 4. Finite element modal analysis of the pipeline system In accordance to the article [19], the definition of modal frequencies and modes via finite element method is performed through substitution of the distributed masses by equivalent ones, concentrated on the nodes of the finite element grid, representing the studied object. For the oscillating system the bending function can be expressed as follows:
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22
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
^ f x, y, z ` f t
ª¬Ɏ x, y, z º¼ ^D ` sin Znt
(1)
with the displacement function matrix
f x, y , z
ª U x, y , z º « » « V x, y , z » «¬W x, y, z »¼
(2)
f t - Displacement functions vector; D - Coefficient matrix of the approximation polynomial; Zn - Oscillation circular frequency. The equation (1) can be rewritten as follows:
> K @ Z > M @ ^u` 2 n
e
(3)
0
Every system element follows the law (3). Therefore the whole oscillatory system can be described by the following equation system:
> K @ Z > M @ ^u ` 2 n
s
s
(4)
0
where ^us ` is the displacement vector;
^M s `
is the overall system mass matrix.
The modal analysis of the liquid-filled pipeline system should take into consideration the interaction between mechanic and hydraulic subsystems [20]: ª ª >M @ >0@ º ª^u` º «> K @ « »« »« ª fs º ª p º p ¬« ¬ M ¼ ¬ M ¼ ¼» ¬^ `¼ « 0 «¬ > @
ª¬ K fs º¼ º » ª ^u` º »« » » ¬^ p`¼ ª¬ K p º¼ » ¼
0
(5)
where ª¬ M fs º¼ stands for the Vibroacoustics interaction mass matrix; ª¬ K fs º¼ is the Vibroacoustics interaction stiffness matrix. 5. Finite element modal analysis of the pipeline system The ANSYS software package has been used for the system study. The piping system modal analysis has been carried out, and the modal frequencies were defined along with the corresponding modal modes. The calculation results of the modal frequency study are presented in the table 1. According to the analysis results, the 6th modal frequency amounts to 45,3Hz and coincides with the piping system fundamental tone (Fig. 7, 8). The 6th modal mode is presented on Fig. 9. The problem of dynamic loads reduction in the pipelines is usually solved by means of the fluid pressure pulsations dampeners. The obvious advantage of this method is its effectiveness, as it directly influents on the source of elevated Vibroacoustics load on the system. However, this method possesses a number of substantial drawbacks in the studied case.
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26 Table 1 Piping system natural frequencies # modal shape
Frequency, Hz
1
15,9
2
31,2
3
35,9
4
37,8
5
41,6
6
45,3
7
47,2
8
59,7
Fig. 7. Manifold vibration velocity spectrum (downward motion)
Fig. 8. Manifold vibration velocity spectrum (upward motion)
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 9 Sixth modal mode of the drain main pipe (45.3 Hz)
The pulsation damper installation requires the pipeline redesigning, thus rendering the press line inoperable for an inacceptable amount of time. Furthermore, the pulsation dampener can have a negative impact on the forge-press unit dynamics, as its installation can profoundly alter the transient processes in the control line of the automatic press line. Another viable way to reduce the Vibroacoustics loads is the alteration of the pipe-line modal frequencies through implementation of additional supports. Thus it would be possible to drastically decrease the vibration level and avoid breakages by raising the modal frequencies of the construction higher, than the working frequencies band. The pressure oscillations spectral analysis (Fig. 4, 5) shows that the peak amplitude values belong to the frequency band limited to 130Hz. Therefore it is required to alter the pipe-line support system in such a way that the first modal frequencies would surpass the level of 130Hz. The additional pipeline supports design, causing the modal frequencies shift into the frequency range higher than the water-hammer effect, is presented on Figure 10. The minimum modal frequency amounts to 167 Hz, which surpasses the excitation force load by 37 Hz.
Fig. 10. Pipeline system supports design case
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
6. Conclusion The performed study allows drawing the following conclusions. The vibration of the pipeline system, leading to its failure, is caused by the water-hammer effect resulting from the valve actuation of the press unit automatic control system. The excessive vibration is caused by the coalescence of pipeline system modal frequency and power fluid water-hammer frequency. In this case the failures result from the hydraulic system flaws, implemented during the design stage. The following measures can be recommended: x Long pipeline sections should be avoided by means of additional supports installation and overall pipeline system length reduction; x The probability of water-hammer effect occurrence should be pre-calculated; x The approximate computation of modal pipeline frequencies and water-hammer effect fluid pulsation frequencies should be performed. The research was based on vibration velocity spectral analysis of hydraulic system key points and pressure pulsation spectral analysis. This study method is unable to categorically define the cause of elevated vibration. It is worth noticing that this method complicates the formulation of the defect genesis hypothesis. In this case, the hypothesis formulation depended mostly on researcher's experience. The cross-correlation experimental data analysis methods appear to be the most promising. Acknowledgements This work was supported by the Ministry of Education and Science of the Russian Federation through SSAU roadmap 2013-2020 implementation. References [1] Makaryants, G.M., Prokofiev, A.B., Kryuchkov, A.N. (2005), "Analysis of the disruption reasons of punching machine Erfurt 2000+1200 SS piping using numerical modeling", Proceedings of III International scientific and technological conference "Hydraulic machines, hydraulic drives and hydraulics and pneumatics automotive systems" ["Opredelenie prichin razrusheniya truboprovodnoy sistemy pressa Erfurt 2000+1200 SS s ispol'zovaniem chislennogo modelirovaniya", Trudy III Mezhdunarodnoi nauchno-tekhnicheskoy konferentsii "Gidravlicheskie mashiny, gidroprivody i gidropnevmoavtomatica"], Polytechnic University [Politekhnicheskiy universitet], St-Peterburg, pp. 250-254. (in Russian). [2] Gladkikh, P.A, Khachaturyan, S.A (1959), Pipes vibration and its eliminating methods [Vibratsiya v truboprovodakh i metody ikh ustraneniya], Mashgiz, Moscow, 243 p. (in Russian). [3] Arinichev, S.V. (2002), Theory of nonconservative systems oscillation: study guide for technical universities [Teoriya kolebaniy nekonservativnykh sistem: uchebnoe posobie dlya vuzov], MSTU [MGTU im. N.E. Baumana], Moscow, 464 p. (in Russian). [4] Kulikov, Yu.A. (1995), Pipes dynamics of aircrafts: Author's thesis [Dinamica truboprovodov letatel'nykh apparatov: avtoref. dis. … dok. tekhn. nauk], MSTU [MGTU im. N.E. Baumana], Moscow, 32 p. (in Russian). [5] TrebuĖa, F., Šimþák, F., HuĖady, R., Pástor, M. (2013), "Identification of pipes damages on gas compressor stations by modal analysis methods", Engineering Failure Analysis, V. 27, pp. 213–224. [6] Wachel, J.C., Tison, J.D. (1994), "Vibrations in reciprocating machinery and piping systems", Proceedings of 23rd Turbomachinery Symposium, Texas A&M University, College Station (Texas), pp. 243-272. [7] Kondrashov, N.S. (1965), "About parametric oscillation of pipes" ["O parametricheskikh kolebaniyakh truboprovodov"], Vibration strength and reliability of aircraft engines [Vibratsionnaya prochnost' i nadezhnost' aviatsionnykh dvigateley], V. XIX, pp. 173-181. (in Russian). [8] Len'shin, V.V. (1997), Vibroacoustical properties of hydro mechanical systems elements of aircraft engines research: dissertation [Issledovanie vibroakasticheskih kharakteristic elementov gidromekhanicheskih sistem dvigateley letatel'nykh apparatov: dis. … kand. tekhn. nauk], SSAU [SGAU], Samara, 193 p. (in Russian). [9] Prokofiev, A.B. (2001), Processes of vibroacoustical interaction at hydro mechanical systems elements of aircraft engines research: dissertation [Issledovanie protsessov vibroakasticheskogo vzaimodeystviya v elementakh gidromekhanicheskih sistem dvigateley letatel'nykh apparatov: dis. … kand. tekhn. nauk], SSAU [SGAU], Samara, 256 p. (in Russian). [10] Ashly, H., Haviland, G. (1950), "Bending vibration of pipeline containing flowing fluid", Journal of Applied Mechanics, Trans. ASME, V. 72, pp. 229-232. [11] Hounser, G.W. (1952), "Bending vibration of pipeline containing flowing fluid", Journal of Applied Mechanics, V. 19, pp. 205-208. [12] Benjamin, T. (1961), "Dynamics of systems of articulated pipes conveying fluids; Part I theory, Part II Experiment", Proceedings of Royal Society, Ser. A261, pp. 457-486. [13] Al-Maaitah, A., Kardsheh, K. (2002) " Flow-induced vibration of a Y-shaped tube conveying fluid ", Electronic Journal Technical Acoustics, no. 2, pp. 8.1-8.12, available at: http://www.ejta.org/en/maaitah2
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26 [14] Li, Sh., Liu, G., Kong, W. (2014), "Vibration analysis of pipes conveying fluid by transfer matrix method", Nuclear Engineering and Design, V. 266, pp. 78-88. [15] Dai, H.L., Wang, L., Qian, Q., Gan, J. (2012), "Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix", Applied Mathematics and Computation, V. 219, is. 5, pp. 2453-2464. [16] Ni, Q., Zhang, Z.L., Wang, L. (2011), "Application of the differential transformation method to vibration analysis of pipes conveying fluid", Applied Mathematics and Computation, V. 217, is. 16, pp. 7028-7038. [17] Li, B., Gao, H., Zhai, H., Liu, Y., Yue, Z. (2011), "Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method", Nuclear Engineering and Design, V. 241, is. 4, pp. 666–671. [18] Zhou, J., Ta, N., Rao, Z. (2009), "Vibration reduction for stream pipeline by supports optimization", Proceedings of 16th International Congress on Sound and Vibration, ICSV 2009 , Krakow, 5-9 July 2009, pp. 2834-2837. [19] Krylov, O.V. (2002), Finite element method and its application to engineering calculation: study guide for technical universities [Metod konechnykh elementov i ego primenenie v inzhinernykh raschetakh: uchebnoe posobie dlya vuzov], Radio and communication [Radio i svyaz'],Moscow, 104 p. (in Russian). [20] Zienkiewicz, O.C., Newton, R.E. (1969), "Coupled Vibrations of a Structure Submerged in a Compressible Fluid", Proceedings of the Symposium on Finite Element Techniques, University of Stuttgart, Stuttgart.
ScienceDirect Procedia Engineering 106 (2015) 17 – 26
Dynamics and Vibroacoustics of Machines (DVM2014)
Vibroacoustics Analysis of Punching Machine Hydraulic Piping Georgy M. Makaryants*, Andrey B. Prokofiev, Evgeny V. Shakhmatov Samara State Aerospace University (SSAU), 34, Moskovskoe shosse, Samara, 443086, Russian Federation
Abstract The reduction of elevated dynamic loads, affecting the elements of the hydraulic drive, is an important task in production equipment maintenance. In case of the hydraulic drive with actuators, remotely located from the power source, the piping defines the working capacity of the whole system. Hence the development of piping vibroacoustic analysis methods appears to be the vital task. The said methods would not only help to define the cause of increased loads, but also permit to develop an adequate design solution without prolonged experimental checks. The article proposes the method of pipeline system vibroacoustics analysis through the example of press-forge unit drain piping. The novelty of this method consists in the use of the fluid pulsation and piping vibration spectra analysis in their correlative comparison with account to the calculated modal parameters of a pipeline. The measurements of working fluid pressure pulsation and pipeline vibration in the vicinity of the breakage locations were carried out. The experimental data spectrum analysis indicated an apparition of intense water-hammer process along with the frequency coalescence of fluid pulsation and pipeline vibration. The resonant vibration amplification, caused by the waterhammer effect, was suggested. The pipeline system mathematical model, allowing to calculate its modal parameters, was derived. The comparison of the modal analysis with the vibroacoustic response confirmed the hypothesis of the pipeline resonant breakdown. The article depicts, that the study of the pipeline system vibroacoustic response, based only on Fourier analysis of the working fluid pulsation and pipeline vibration, is prone to fail the reliable causation of elevated dynamic loads. It is suggested to complement the vibroacoustic response analysis with the modal parameters calculation. The mathematical computation of the modal frequencies and shapes was implemented instead of their experimental observation in order to exclude the undesired signal, introduced with attached mechanical equipment. On top of that, the mathematical computation of the pipeline modal parameters allowed to perform the pipeline modal frequency shift from the water-hammer effect frequency range through cautious relocation of additional supports. © 2015 2014The TheAuthors. Authors. Published by Elsevier Ltd. © 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 organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
* Corresponding author. Tel.: +7-927-688-95-05; fax: +7-846-335-19-05. E-mail address: [email protected]
1877-7058 © 2015 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 organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
doi:10.1016/j.proeng.2015.06.004
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Keywords: hydraulic piping; pressure pulsation; power fluid; vibration; press-forging industry; finite element method; modal analysis.
1. Introduction The increase of the piping systems efficiency is vital due to its direct connection with the overall facility performance and operation quality. The automatic press line "Erfurt" breakdown, caused by the piping system problems, is an example of production machinery failure. The line outfitted with PTr 2000+1200 SS punching unit is installed on press-forging line in joint-stock company AUTOVAZ (Togliatti, Russia) [1]. The press-forging process of the considered line is represented by the deep-drawing of billet sheet. The construction of punching machine is shown on Figure 1. Half of the stamp which performs reciprocation is attached to a sliding bar 1. A billet sheet 2 is placed on supports 3 which are rigidly held by a bottom plate 4. A fixed counterpart 5 is placed under the billet sheet 2. Downward motion and press-forging are performed with the sliding bar 1 with a die block. This process is counteracted by press forces in the extraction cylinders 6. Extraction cylinders 6 lean on bottom plate 4 via endthrust bearings 7. During the automatic line operation the drain piping of extraction cylinders power hydraulic system and upper piston chamber of the central cylinder periodically broke off and suffered from a total loss of power fluid, which led to the shutdown of the whole press-forging line [1]. The disruption took place x in the junctions of drain line and hydraulic cylinder automatic control device 1 (Fig. 2), x in the drain line and collector, x between left and right collectors (Fig. 2). The crosscut character of breakage indicated that the pipe bending vibrations were the cause of the disruption.
Fig. 1. Erfurt PTR 2000+1200 SS schematic layout 1- sliding bar; 2 - billet sheet; 3 – supports; 4 – bottom plate; 5 – counterpart; 6 – extraction cylinders; 7 – end-thrust bearings; 8 – central cylinder; 9 – rod
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 2. Drain piping [1] 1 - the hydraulic cylinder automatic control device; 2 - pipeline disruption locations; 3 - the fluid storage tank joint flange
2. Analysis of vibroacoustic interaction in the pipeline systems The curvilinear pipeline bending vibration genesis was first described in the article [2]. The pipeline vibration is linked to the apparition of the non-steady unbalanced stresses, caused by the pulsing flow dynamic pressure losses in the knee-shaped elements. The described bending vibration genesis mechanism is typical for pipeline systems with relatively low fluid flow speeds. This model is commonly used to define the cause of vibration increase in the booster stations piping. The articles [3, 4] link the pipeline vibration phenomenon with the hydro-torque of mechanical pipeline subsystem flexible elements. This kind of vibration appears in the high velocity pipelines, specific to the fuel mains of a carrier rocket with liquid-propellant engine or gas-turbine engines fuel systems. Anyway, the pulsating flow energy may cause significant mechanical oscillations of piping, attached equipment and bearing structure due to its interaction with the piping itself. The fluid supply units operation, self-excited oscillations, caused by the actuating of flow regulators and valves, and water-hammer processes are the main causes of the hydraulic mains power fluid pulsations. The pipeline system vibroacoustics analysis methods include experimental methods, based on modal parameters analysis [5, 6], as well as theoretical, using the vibroacoustic interaction models [7-13], transfer function matrix [14, 15] ,differential transformation method [16], dynamic stiffness method [17] and numeric modal analysis [18]. Although, most of existing methods are used to solve more specific tasks, such as computation of a straight pipeline section, booster station piping and steam pipeline. Obviously, the study of a pipeline system with complicated spatial configuration and arbitrary number of supports requires a versatile analysis method, taking into account both experimental statistics and computational parameter analysis. That’s why the measurements of the power fluid pressure oscillation and piping vibration, which appeared during the press-forge equipment operation, were taken first in order to define the cause of the studied pipe main excitation. 3. Experimental study of the press-forge unit hydraulic pipeline dynamics Experimental study data analysis [1] demonstrated the apparition of two intense water-hammer processes in the drain piping (Fig. 3). The first process at the time period is caused by the power fluid draining during the downward motion of the billet sheet. The upward motion of the billet sheet starts at the time period. Therefore the second hydraulic impact, caused by the automation valves actuations which slow down the billet movement, occurs in the end of the motion at the time period. The peak pressure value amounts from 0.6 to 0.8 MPa, the minimum value amounting to 0.2 MPa with mean level of 0.39 MPa.
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 3. Drain piping pressure oscillations [1]
The spectrum analysis of the first hydraulic impact showed the presence of two resonant zones (Fig. 4): the interval of 12 to 60 Hz with maximum at 45 Hz and the interval of 70 to 120 Hz with maximum at 93 Hz. The intensity of the resonant peaks in the second zone is 4.5 times lower than in the first one. Spectrum analysis of the second hydraulic impact (Fig. 5) shows the most intensive resonance in the interval of 15 to 88 Hz with maximum at 45 Hz.
Fig. 4. Pressure oscillations spectrum (downward motion of bottom plate)
The three-dimensional system vibration activity analysis was performed simultaneously with the piping pressure pulsation analysis. The following locations of vibration sensors installation were chosen: x Junction points of the main drain line and drain piping of central cylinder and each of extraction cylinders; x Piping breakdown locations. The figure 6 represents the vibro-acceleration oscillogram of the drain piping under the central cylinder manifold.
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 5. Pressure oscillations spectrum (upward motion of bottom plate)
Fig. 6. Vibratory acceleration oscillogram of the manifold under the central cylinder
The drain line oscillation analysis indicated two intense oscillatory processes, occurring in every vibration monitored point during the press forward stroke. The first one was noticed in the beginning of the press forward stroke and coincided with the moment of fluid displacement from cylinders. The second one is correlated with the stamp lift action. In both cases the spectral density reached maximum at 45 Hz (Figures 7-8). The performed analysis allowed concluding that the system oscillations are caused by the force loads of pressure pulsations resulting from the press control system piping hydraulic impacts. The resonant amplification of the press drain piping oscillatory movement was suggested in this case. The numerical modal analysis was performed in order to verify this presumption. 4. Finite element modal analysis of the pipeline system In accordance to the article [19], the definition of modal frequencies and modes via finite element method is performed through substitution of the distributed masses by equivalent ones, concentrated on the nodes of the finite element grid, representing the studied object. For the oscillating system the bending function can be expressed as follows:
21
22
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
^ f x, y, z ` f t
ª¬Ɏ x, y, z º¼ ^D ` sin Znt
(1)
with the displacement function matrix
f x, y , z
ª U x, y , z º « » « V x, y , z » «¬W x, y, z »¼
(2)
f t - Displacement functions vector; D - Coefficient matrix of the approximation polynomial; Zn - Oscillation circular frequency. The equation (1) can be rewritten as follows:
> K @ Z > M @ ^u` 2 n
e
(3)
0
Every system element follows the law (3). Therefore the whole oscillatory system can be described by the following equation system:
> K @ Z > M @ ^u ` 2 n
s
s
(4)
0
where ^us ` is the displacement vector;
^M s `
is the overall system mass matrix.
The modal analysis of the liquid-filled pipeline system should take into consideration the interaction between mechanic and hydraulic subsystems [20]: ª ª >M @ >0@ º ª^u` º «> K @ « »« »« ª fs º ª p º p ¬« ¬ M ¼ ¬ M ¼ ¼» ¬^ `¼ « 0 «¬ > @
ª¬ K fs º¼ º » ª ^u` º »« » » ¬^ p`¼ ª¬ K p º¼ » ¼
0
(5)
where ª¬ M fs º¼ stands for the Vibroacoustics interaction mass matrix; ª¬ K fs º¼ is the Vibroacoustics interaction stiffness matrix. 5. Finite element modal analysis of the pipeline system The ANSYS software package has been used for the system study. The piping system modal analysis has been carried out, and the modal frequencies were defined along with the corresponding modal modes. The calculation results of the modal frequency study are presented in the table 1. According to the analysis results, the 6th modal frequency amounts to 45,3Hz and coincides with the piping system fundamental tone (Fig. 7, 8). The 6th modal mode is presented on Fig. 9. The problem of dynamic loads reduction in the pipelines is usually solved by means of the fluid pressure pulsations dampeners. The obvious advantage of this method is its effectiveness, as it directly influents on the source of elevated Vibroacoustics load on the system. However, this method possesses a number of substantial drawbacks in the studied case.
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26 Table 1 Piping system natural frequencies # modal shape
Frequency, Hz
1
15,9
2
31,2
3
35,9
4
37,8
5
41,6
6
45,3
7
47,2
8
59,7
Fig. 7. Manifold vibration velocity spectrum (downward motion)
Fig. 8. Manifold vibration velocity spectrum (upward motion)
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Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
Fig. 9 Sixth modal mode of the drain main pipe (45.3 Hz)
The pulsation damper installation requires the pipeline redesigning, thus rendering the press line inoperable for an inacceptable amount of time. Furthermore, the pulsation dampener can have a negative impact on the forge-press unit dynamics, as its installation can profoundly alter the transient processes in the control line of the automatic press line. Another viable way to reduce the Vibroacoustics loads is the alteration of the pipe-line modal frequencies through implementation of additional supports. Thus it would be possible to drastically decrease the vibration level and avoid breakages by raising the modal frequencies of the construction higher, than the working frequencies band. The pressure oscillations spectral analysis (Fig. 4, 5) shows that the peak amplitude values belong to the frequency band limited to 130Hz. Therefore it is required to alter the pipe-line support system in such a way that the first modal frequencies would surpass the level of 130Hz. The additional pipeline supports design, causing the modal frequencies shift into the frequency range higher than the water-hammer effect, is presented on Figure 10. The minimum modal frequency amounts to 167 Hz, which surpasses the excitation force load by 37 Hz.
Fig. 10. Pipeline system supports design case
Georgy M. Makaryants et al. / Procedia Engineering 106 (2015) 17 – 26
6. Conclusion The performed study allows drawing the following conclusions. The vibration of the pipeline system, leading to its failure, is caused by the water-hammer effect resulting from the valve actuation of the press unit automatic control system. The excessive vibration is caused by the coalescence of pipeline system modal frequency and power fluid water-hammer frequency. In this case the failures result from the hydraulic system flaws, implemented during the design stage. The following measures can be recommended: x Long pipeline sections should be avoided by means of additional supports installation and overall pipeline system length reduction; x The probability of water-hammer effect occurrence should be pre-calculated; x The approximate computation of modal pipeline frequencies and water-hammer effect fluid pulsation frequencies should be performed. The research was based on vibration velocity spectral analysis of hydraulic system key points and pressure pulsation spectral analysis. This study method is unable to categorically define the cause of elevated vibration. It is worth noticing that this method complicates the formulation of the defect genesis hypothesis. In this case, the hypothesis formulation depended mostly on researcher's experience. The cross-correlation experimental data analysis methods appear to be the most promising. Acknowledgements This work was supported by the Ministry of Education and Science of the Russian Federation through SSAU roadmap 2013-2020 implementation. References [1] Makaryants, G.M., Prokofiev, A.B., Kryuchkov, A.N. (2005), "Analysis of the disruption reasons of punching machine Erfurt 2000+1200 SS piping using numerical modeling", Proceedings of III International scientific and technological conference "Hydraulic machines, hydraulic drives and hydraulics and pneumatics automotive systems" ["Opredelenie prichin razrusheniya truboprovodnoy sistemy pressa Erfurt 2000+1200 SS s ispol'zovaniem chislennogo modelirovaniya", Trudy III Mezhdunarodnoi nauchno-tekhnicheskoy konferentsii "Gidravlicheskie mashiny, gidroprivody i gidropnevmoavtomatica"], Polytechnic University [Politekhnicheskiy universitet], St-Peterburg, pp. 250-254. (in Russian). [2] Gladkikh, P.A, Khachaturyan, S.A (1959), Pipes vibration and its eliminating methods [Vibratsiya v truboprovodakh i metody ikh ustraneniya], Mashgiz, Moscow, 243 p. (in Russian). [3] Arinichev, S.V. (2002), Theory of nonconservative systems oscillation: study guide for technical universities [Teoriya kolebaniy nekonservativnykh sistem: uchebnoe posobie dlya vuzov], MSTU [MGTU im. N.E. Baumana], Moscow, 464 p. (in Russian). [4] Kulikov, Yu.A. (1995), Pipes dynamics of aircrafts: Author's thesis [Dinamica truboprovodov letatel'nykh apparatov: avtoref. dis. … dok. tekhn. nauk], MSTU [MGTU im. N.E. Baumana], Moscow, 32 p. (in Russian). [5] TrebuĖa, F., Šimþák, F., HuĖady, R., Pástor, M. (2013), "Identification of pipes damages on gas compressor stations by modal analysis methods", Engineering Failure Analysis, V. 27, pp. 213–224. [6] Wachel, J.C., Tison, J.D. (1994), "Vibrations in reciprocating machinery and piping systems", Proceedings of 23rd Turbomachinery Symposium, Texas A&M University, College Station (Texas), pp. 243-272. [7] Kondrashov, N.S. (1965), "About parametric oscillation of pipes" ["O parametricheskikh kolebaniyakh truboprovodov"], Vibration strength and reliability of aircraft engines [Vibratsionnaya prochnost' i nadezhnost' aviatsionnykh dvigateley], V. XIX, pp. 173-181. (in Russian). [8] Len'shin, V.V. (1997), Vibroacoustical properties of hydro mechanical systems elements of aircraft engines research: dissertation [Issledovanie vibroakasticheskih kharakteristic elementov gidromekhanicheskih sistem dvigateley letatel'nykh apparatov: dis. … kand. tekhn. nauk], SSAU [SGAU], Samara, 193 p. (in Russian). [9] Prokofiev, A.B. (2001), Processes of vibroacoustical interaction at hydro mechanical systems elements of aircraft engines research: dissertation [Issledovanie protsessov vibroakasticheskogo vzaimodeystviya v elementakh gidromekhanicheskih sistem dvigateley letatel'nykh apparatov: dis. … kand. tekhn. nauk], SSAU [SGAU], Samara, 256 p. (in Russian). [10] Ashly, H., Haviland, G. (1950), "Bending vibration of pipeline containing flowing fluid", Journal of Applied Mechanics, Trans. ASME, V. 72, pp. 229-232. [11] Hounser, G.W. (1952), "Bending vibration of pipeline containing flowing fluid", Journal of Applied Mechanics, V. 19, pp. 205-208. [12] Benjamin, T. (1961), "Dynamics of systems of articulated pipes conveying fluids; Part I theory, Part II Experiment", Proceedings of Royal Society, Ser. A261, pp. 457-486. [13] Al-Maaitah, A., Kardsheh, K. (2002) " Flow-induced vibration of a Y-shaped tube conveying fluid ", Electronic Journal Technical Acoustics, no. 2, pp. 8.1-8.12, available at: http://www.ejta.org/en/maaitah2
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