Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 176 (2017 ) 118 127 Dynamics and Vibroacoustics of Machines (DVM2016) The application of passive vibroprotective systems having power characteristics with hysteresis loops of rectangular shape for the main pumping units Artem Tokarev*, Alexey Zotov, Anvar Valeev Ufa State Petroleum Technological University, 1 Kosmonavtov st., Ufa, 450062, Russian Federation Abstract The causes of large vibrations of main pump units piping and its influence to the level of the pump unit oscillations are analyzed. The source of increased vibration exposure in the "pump - pipe" system is often not only the pump unit, but pump piping also. Piping of the pumping unit in case of its operating parameters changing can be entered to resonance. It is considered the reasons and oscillation magnitude of the booster pump NMP 5000-90 and its piping. Application of different types of vibration isolators is analyzed in terms of their effectiveness and the amount of force transmitted to the foundation. Special attention is paid for vibration isolators having force characteristics with hysteresis loops of rectangular shape that have high efficiency. 2017 2017 The The Authors. Authors. Published Published by Elsevier by Elsevier Ltd. This Ltd. 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 international conference on Dynamics and Vibroacoustics of Peer-review Machines. under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines Keywords: vibration reduction (vibration isolation or protection); pump piping; systems with quasi-zero stiffness; damping 1. Introduction Nomenclature m x mass of the object that is protected from vibration; coordinate of the protecting object; * Corresponding author: Tel.: +7-917-778-3066; fax: +7-347-243-1916. E-mail address: art-tokarev@yandex.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.2017.02.279
Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 119 μ coefficient of damper s resistance; F 0 the amplitude of the disturbing force; p the frequency of the disturbing force; c eq = c +с 2 the equivalent stiffness coefficient, c stiffness coefficient that is determined by the pipeline; c 2 the stiffness coefficient of elastic element of the "classic" vibration isolator; F * restoring force with ignored friction forces; q coefficient that determines the height of the hysteresis loop (0 q 1). Effective operation of the main pumping units one of the most important tasks of oil and oil products transportation. Error-free running time of the pumping unit must be at least 6-8 thousand hours [1, 2]. A number of factors, including, operating conditions and the ability to adapt to their changing, must be taken into account in assessing the effectiveness of the main pumping unit [1, 3, 4]. The increased vibration is among factors that has most adversely effect to the reliability of pumping units. It has negative influence on the state of the main pumping unit, its drive and pump piping, causing their rapid deterioration and, in the future, its breakage. The maintenance of efficient and reliable operation of pumping units requires the development of vibration protective systems. It should be borne in mind that anti-vibration systems must be designed for high load and have a rather low natural frequency, in order to effectively compensate various vibration effects. The development of a reliable, simple and, most importantly, effective vibration isolators is an urgent task of the main oil and its products transport system [5]. The source of increased vibration exposure in the "pump - pipe" system is often not only the pump unit, but pump piping also [5-7]. The vibration effect of the pump piping to the state of pump unit is neglected at the design stage of pumping stations in most cases. In some cases [5-9], one of the main reasons for the increased vibration activity of the main pumps is the large oscillation amplitude of pump piping. Vibrations of pipelines are determined by: the ratio of the major disturbance harmonics of the pump unit and the spectrum of the natural frequencies of the pipeline (the coincidence of spectral components (load with natural frequencies) produces resonance vibration of pipes); values of disturbances which directly determines the vibration amplitude and forces in the pipeline, and other factors [6, 10]. Turbulent fluid pressure fluctuations and vortex formation in the suction and discharge lines, the impeller zone are among the main sources of hydrodynamic disturbances in the pump, that are determines its vibration level. Constructional features of the pump, piping system and of the flow rate determine the intensity of the fluid pressure pulsation. Pipelines are the most abundant element at the oil transport facilities. Such pipelines, which are related to highpressure units, turbine units and elements that have large unstable flow of operating environment, are subjected to high vibration loads. The interaction of turbulent flow with valves, elements of technological pipelines (taps, inserts, etc.) calls vortex formation processes that increases the intensity of the pressure fluctuations in the flow and vibration of piping systems, which is transferred to the pump housing. The described processes (especially in the suction line) has large influence to the vibration of the pump unit [5, 7, 8]. Under these conditions the reducing of the pipeline vibration and, ipso facto, the pump unit vibration, becomes an important practical task. 2. The results of vibration diagnostics of the pump unit NMP 5000-90 and its manifolds Suction line of the pumping unit in case of its operating parameters changing can be entered to resonance. In a number of cases [5, 6, 9] this problem is very actual for booster pumps. In particular, the vibration diagnostic results of the state of three horizontal booster pumps NMP 5000-90 (fig. 1) with a rotor on the head of 120 m and speed of 1000 r/min indicated an increased value of vibration for a long period of observation. Vibrations were measured on the front and rear supports of the bearings of the pump in a vertical, horizontal and axial directions (fig. 2), as well as on the suction and discharge lines in vertical and horizontal position.
120 Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 Fig. 1. The pump NMP 5000-90 Fig. 2. The points of measurement of vibration on the bearing supports of the horizontal pump unit [2] Large levels of the vibration velocity are observed on the front and rear bearings of the pump in the vertical and axial directions (fig. 3, a). The vibration velocity on the rear bearing of the pump reaches 18 mm/s with a normal rate of 7.1 mm/s [2]. Vibrations of bearings in the horizontal direction are within the permissible norm. The sharp decline in the vibration level of the pump in the fourth and seventeenth metering associated with debugging of the pump working modes carried out at these times. The largest values of the vibration velocity are observed on the suction line in the horizontal and vertical directions and reach 13 mm/s and 12 mm/s, respectively (fig. 3, b). The suction line is horizontally disposed pipe 1020 mm in diameter with a 90 branch and two 4 m long spans. Its natural frequency (f 0 = 34.5 Hz) approaches to the second harmonic of the rotor frequency of the pump (f p = 33.3 Hz). The ratio of natural and disturbing frequency is f 0 / f p = 1.04 1 that is a reason of resonance. According to the requirements of the state standard specification the ratio of frequencies must be [10]: f / f 0,75 and f / f 1,3. (1) 0 p 0 p
Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 121 a b Fig. 3. The results of vibration measurements of the pump unit NMP 5000-90 at: (a) bearings; (b) pump piping V vertical direction; H horizontal direction; A axial direction. Thus, resonance between the natural frequency of the suction line and disturbing frequency of the pump oscillation causes large vibration of the pump pipe system. 3. Methods of vibration damping of considered part of the pipeline 3.1. Classic vibration isolator One of the most common methods of vibroprotection is the use of classic vibration isolator: spring that obeys Hooke's law and the damper in which the resistance force is proportional to velocity [11]. Vibrations of the considered section of the suction line under the influence of harmonic disturbing force are described by the following differential equation: m && x x& c x F cos( p t) (2) eq 0 The section of the suction line that was entered to resonance is simulated by mass (m) on the spring (fig. 4), which coefficient of stiffness (c) is determined by the suction line. The suction line is fixed on its ends (fig. 1), and a shock absorber with stiffness coefficient с 2 and the damper resistance factor μ - at the site of the largest vibration values. The pump unit and the suction line with characteristics that are given in the part 2 can be entered to resonance in case of damping system absence (fig. 5). Suppression of vibrations without damping element occurs during the installation of the springing element of the classic vibration isolator with stiffness coefficient с 2 = 5000000 N/m (fig. 6, a). Force transmission coefficient that is a ratio of the maximum force, transmitted to the foundation, to the amplitude of the disturbing force while ensuring the condition (1), for example f 0 / f p 1, 32, reaches 4 that is unacceptable [6, 11]. The amplitude of the pipeline oscillations in case of addition of the damper resistance factor μ = 200 kg/s to the damping system is shown in Figure 6, b. To obtain the oscillation amplitude limits the stiffness coefficient of elastic element must be с 2 = 4500000 N/m. Force transmission coefficient determines analytically at level of 3.6 at the start of pump unit operation and 2.27 for further work. The use of classic vibration isolator in such cases is not reasonable, because the force that is transferred to foundation can be several times more than the force, disturbing the pipeline vibrations. In turn, this leads to large vibrations of the foundation and its destruction.
122 Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 Fig. 4. Diagram of the simulated pipeline with "classic" vibration isolator x, m 0.10 0.05 0.05 10 20 30 40 50 60 t, s 0.10 x, m Fig. 5. The amplitude of the vibrations of the suction line in case of damping system absence x, m 10 20 30 40 50 60 10 20 30 40 50 60 t, s t, s a b Fig. 6. The vibration amplitude of the pipeline with the "classic" vibration isolator: (a) without a damping element, с 2 = 5000000 N/m; (b) with a damping element, μ = 200 kg/s, с 2 = 4500000 N/m. Straight lines are indicate maximum permissible amplitude of vibration, m [2]
Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 123 3.2. Passive vibroprotective systems with force characteristics with hysteresis loops of rectangular shape To reduce the force transmission coefficient it is suggested to use passive vibroprotective systems having force characteristics with hysteresis loops of rectangular shape [13, 14]. Vibrations of the suction line are described by the following differential equation: m & x q F ) sign( x& ) F sign( x) c x F cos( p ) (3) ( * * 0 t The force characteristic of such system is shown in Figure 7. In the first section (I) object will move from the neutral position to the right until stop. In the second section (II) - from the last right position to the left to the neutral position. In the third section (III) object will move from the neutral position to the left until stop. On the fourth section (IV) from the last left position to the right to the neutral position [11]. The maximum force transmitted by the vibration isolator to the foundation vibrations will be equal to F F q). max *(1 Fig. 7. Force characteristics with hysteresis loops of rectangular shape The vibration amplitude is sharply decreases in certain values of F * and q. Thus, when there is no dry friction force, q F*, (q = 0), it s needed an action of restoring force F* 585Н to compensate the driving force F 0 = 700 N. Nevertheless, fluctuations are unstable in this case (Figure 8), and force transmission coefficient is K = 0.84. At low values of the coefficient, that determines the height of the hysteresis loop, it is needed a slight change of the restoring force for locking fluctuations within acceptable values (fig. 9, а, b). Thus, when q = 0,1 and F 0 = 700 N, the restoring force that is sufficient to lock the vibrations is F * = 549 N. The vibration amplitude becomes constant, and force transmission coefficient K = 0.86.
124 Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 x, m 10 20 30 40 50 60 t, s Fig. 8. The vibrations of the pipeline in case of using passive vibroprotective system having force characteristics with hysteresis loops of rectangular shape: q=0, F 0=700 N, F *=585 N Straight lines are indicate maximum permissible amplitude of vibration, m [2] x, m x, m t, s t, s Fig. 9. The vibrations of the pipeline in case of using passive vibroprotective system having force characteristics with hysteresis loops of rectangular shape: a) q=0,1 and F *=547 N; b) q=0,1 and F *=549 N. Straight lines are indicate maximum permissible amplitude of vibration, m [2] While assessing the force transmission coefficient for different values of restoring force and the coefficient that determines the height of the hysteresis loop (fig. 10), we can conclude that, from the viewpoint of damping of suction line oscillations and the minimum level of the force transmitted to the foundation, most profitable to use a small interval of the dry friction force (q=0.1 0.2). Force transmission coefficient in this case K < 1. 4. Layout drawing of the device, allowing obtaining force characteristics of hysteresis loops with given shape Passive vibroprotective systems having force characteristics with hysteresis loops of rectangular shape should provide the following working conditions of the protected object: the force acting to the protecting object should be not greater than a predetermined level with a predetermined level of vibrations; the force transmitted to the foundation should be minimal;
Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 125 if the object goes out of the equilibrium position the vibration limits should be restored for the smallest possible number of "fluctuations" and as soon as possible. Figure 10 The force transmission coefficient for different values of recovery force and the coefficient that determines the height of the hysteresis loop Vibration isolator with the above characteristics will protect the pump piping and pump unit from vibrations and shocks. Systems with stiffness that is as low as possible are effective against vibrations. Shock protective systems should damp it quickly and safely (the restoring force should be significant) [13, 14]. Hysteresis loops with given shape can be obtained by the instrumentality of dry friction force. The layout drawing of the device, allowing obtaining such force characteristics is shown in figure 11. The elastic element 2 is the compression spring, which moves perpendicularly to the axis of the special form guides 1. The compression spring through a rigid connection 5 is fixedly connected to friction discs 8. The movable friction discs 8, pressed to the stationary element 11 by springs 12 provide the necessary strength of dry friction force.
126 Artem Tokarev et al. / Procedia Engineering 176 ( 2017 ) 118 127 1 guides of the special form; 2 compression spring; 3 roller bearing; 4 guiding cartridge; 5 rigid connection; 6 pipeline; 7 collars; 8 friction discs; 9 rollers; 10 guides; 11 stationary element; 12 springs. Figure 11 Layout drawing of the device, allowing obtaining force characteristics of hysteresis loops with given shape by the dry friction force Vibration isolators with force characteristics (fig. 7) appear to be effective at the same time to protect against shock and vibration [15, 16]. The protected object is subjected to a permanent restoring force F* (1 q). Systems [15-18] having a principle similar to those described in this paper, it is widely used in practice. They are used in vibration isolation chairs, protection from vibration mechanism and a number of other areas of application technology. Many years of experience of the authors on the study of vibration isolation passive type systems shows that they have great potential in vibration isolation. A number of studies [15, 16, 17] the possibility of developing a vibration isolation systems with displacement ranges in which the force transmitted to the protected object is no longer a given. Thus, passive vibroprotective systems having force characteristics with hysteresis loops of rectangular shape can be very effective to dump vibrations of pump piping and thereby to reduce pump unit oscillations. References [1] A.G. Gumerov, R.S. Gumerov, A.M. Akberdin, Operation of pumping stations equipment. Moscow, 2001. 475p. [2] RD-75.000.00-KTH-079-10. Guidelines for maintenance and repair of equipment and facilities of pumping stations. - Moscow: OJSC "AK" Transneft ", 2009. - 121 p.
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