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The cyclic operation of the pump s displacement components 1 or theself-excitation of the control components in hydraulic valves 2 due to the action of theflowing liquid 4 or to external mechanical vibrations 3, 5, 6 are among the causes ofpressure fluctuations. Pressure fluctuations cause the individual system components tovibrate. This has an adverse effect, particularly on the precision of positioning of, for ex-ample, the cutting tool in a machine tool. This also applies (although to a smaller degree)to mobile machines which are the source of vibrations affecting the rigidly fixed hydraulicvalves. Generally, the complex problem of the transmission of vibrations by a machine ora piece of equipment can be divided into three interconnected categories:? vibration sources,? vibration transmission paths,? effects.The most frequent cause of vibrations are disturbances connected with the motionor operation of the machine, for example when a mobile machine moves on an unevensurface or when the rotating parts are unbalanced during material machining. Anothermajor vibration source are drive units, for example a combustion engine performinga periodic variable-characteristic work cycle 7, 8. An operating hydraulic system isalso a source of mechanical vibrations caused mainly by pressure surges and the peri-odic operation of the displacement pump. Since the generated vibrations have differentfrequencies the paths of their transmission are also different. The irregularities of thesurface on which a mobile machine moves cause excitations in a frequency range of0.5 250 Hz 9 11. The latter includes excitations generated by the driving (combus-tion) engine and the displacement pump kinematics, manifesting themselves in pres-M. STOSIAK238sure fluctuations in the machine s hydraulic system. The vibrations due to the resis-tance of flowing air are in a frequency range of 250 16 000 Hz and they are caused byairflow separation from the machine s components. Also the flow of the working me-dium in the hydraulic system causes vibration and noise. Sometimes cavitation occurs,generating high-frequency noise. The vibrations generated and transmitted by a ma-chine produce various effects. Mechanical vibrations affect the machine operator. Thecomponents of the systems with which the machine is equipped, particularly hydrauliccomponents and systems are also subject to mechanical vibrations. Such componentsare required to have good dynamic properties and to be characterized by stability,positioning precision, operating reliability and certainty and little noisiness. Modernproportional hydraulic valves or hydraulic microvalves are particularly exposed toexternal mechanical vibrations since the disturbing forces in them can amount to thecontrolling forces, which may lead to many adverse effects, such as stability loss, po-sitioning inaccuracy, damage to seals and increased noisiness 12.2. Flexible fixing of hydraulic valveAs mentioned above, in order to minimize the vibration of the hydraulic valve scontrol element it seems sensible to isolate the valve housing from the external me-chanical vibrations of the base (for example the vibrating frame of a mobile machineor a machine tool). For the analysis of the effect of the flexible fixing of a hydraulicvalve on the vibration of its housing a special clamping holder for the hydraulic dis-tributor was designed. The latter is on its two sides supported by a system of springswith a known linear characteristic and a known pre-deflection (Figure 1).Fig. 1. Valve holder: 1 hydraulic valve (distributor), 2 holder base,3 spring pre-deflection bolts, 4 springs, 5 securing catchesThe design of the holder is such that the valve mounted in it is constrained bysprings (with an equivalent stiffness) and it moves on the holder base (2 in Figure 1)rubbing against it in accordance with the dry friction model. On its two sides the valveVibration insulation of hydraulic system control components239is supported by springs. A scheme of the hydraulic system in which the proportionaldistributor type 4WRE 6 E08-12/24Z4/M operates is shown in Figure 2.TPAB413w = w0 sin(2 ? f t)Fig. 2. Scheme of hydraulic system incorporating investigated component: 1 feed pump,2 relief valve, 3 investigated component, 4 adjustable throttle valveFor a two-mass system the model of the proportional distributor operating in thehydraulic system shown in Figure 2 can be represented by the following system offour equations:?. 01, 02, 025 . 1,2172. 02222022212112122212211111111212121121212111gimwXsingwXsingwXlHgmwXcXXkXXcXmpACpcpcpaQpcpappxxXsQFXXcppxxXsXXhldXmzaqkkppkpmpspMmpst? ? ? (1)M. STOSIAK240The fourth equation describes the forces acting on the valve housing in the consid-ered case. Further on this equation will be modified to describe the characteristics ofthe proposed vibration insulation elements. Some simplifying assumptions to Equa-tions (1):? working liquid does not change its properties,? Coulomb friction is neglected in pair: spool-muff inside directional control valve,? Coulomb friction represents cooperation between valve body and valve holder,? after play (between valve body and securing catches) is cancelled Coulombfriction represents cooperation between valve body and securing catches,? springs characteristics are linear and described by stiffness coefficient c,? description of hydraulic system is based on concentrated parameter model,? the model does not represent influence pipes on valve body vibrations.List of major symbols:SymbolParameterDimension in SIap1leakage coefficientm4s/kgAathrottle valve gap aream2c1equivalent stiffness of valve centring springsN/mczequivalent stiffness of springs fixing valve in holderN/mCq1throttle valve flow ratio dtpiston diametermffrequencyHzgEarth s accelerationm/s2hvalve-sleeve pair gap thicknessmHHeaviside step function k1, k2damping in respectively valve-sleeve pair and housing-holder pairNs/mlpiston lengthml0gap of valve body and securing catchesmm1mass of piston valve and 1/3 of spring masskgm2mass of distributor housingkgp1pressure before distributorPap2pressure after distributorPapzsink line pressurePa?p2throttle valve pressure dropPassmaximum gap widthmttimeswexcitation vibration amplitudemQptheoretical pump deliverym3/sxmgap lengthmxpmutual shift of valve and housing edgesmX1displacement of piston valvemX2displacement of distributor housingm?2coefficient of friction of valve housing against securing catches ?icoefficient of friction of valve housing against holder base ?working liquid densitykg/m3?angular frequencyrad/sVibration insulation of hydraulic system control components241Model (1) also takes into account the interaction between the valve housing and se-curing catches 5 (Figure 1). A numerical solution in the form of a “ transmission func-tion” , understood as a ratio of valve housing vibration acceleration amplitude a2 toexcitation vibration acceleration amplitude a0, is shown in Figure 3.00,511,522,533,544,51015202530354045505560f Hza2/a0 -Fig. 3. Proportional distributor housing vibration acceleration amplitude a2 relativeto excitation vibration acceleration amplitude a0 for f = 1060 HzAn analysis of the simulation results shows a considerable gain in housing vibra-tion amplitude at a frequency of about 20 Hz. This is due to resonance since the massof the vibrating valve amounts to about 4.5 kg and the equivalent stiffness of the holdersprings is 86 000 N/m. Hence a gain in distributor housing vibration amplitude is ob-served in the range of 10 30 Hz (ineffective vibration insulation).This means that valve insulation which will widen the insulation zone and reducethe resonance zone should be proposed. The black-box approach (Figure 4) was adoptedto solve the problem.Different forms of the insulating element can be assumed. The introduction of a vi-bration insulator with quasi-zero stiffness significantly contributes to the minimizationof valve housing vibrations. The ideal characteristic of the vibration insulator withquasi-zero stiffness is described by the following Equation 13:,cos)(2)2(sin)(222222111HHHwHwwHHwHlxxlcPxcclcPxF? (2)M. STOSIAK242where:c1w, c2w stiffness of respectively the main spring and the compensation spring,?H angle of initial, original inclination of the side arm to axis y,P1H, P2H initial spring tensions in position ?H N,lH length of the side arm in position ?H.m2m1?111cos?txX?222cos?txX?tww?cos0c1k1l0?Fig. 4. Black-box approach to valve vibration insulationThe total stiffness of such a vibration insulator in the excitation direction (the di-rection of the external mechanical vibration) is:.coscoscos)(22)(222222222221?HHHHHHHwHwwlxllxlcPccxc? (3)Thus the fourth equation of model (1) can be written as:?. 0coscoscos)(2222222222222222112112122?wXlXllXlcPccXXkXXcXmHHHHHHHwHww? ? (4)Exemplary solutions of model (1) supplemented with Equation (4) are shown in thefigures below for excitation frequency f = 10 60 Hz.An analysis of the simulation results shows that thanks to the use of the vibrationinsulator with quasi-zero stiffness the vibration of the valve housing can be considera-bly reduced. However, because of its dimensions such an insulator cannot be used insmall spaces. Therefore materials with good vibration insulation properties and suit-able for the use in small spaces should be sought. It seems that special pads (mats) formounting hydraulic valves on them could meet the requirements. Such materials shouldalso be resistant to hydraulic fluids and extreme ambient temperatures. Using theVibration insulation of hydraulic system control components243black-box approach one can select an insulator material characteristic ensuring effec-tive vibration insulation in a wide excitation range.00,050,10,150,20,250,31015202530354045505560f Hza2/a0 -Fig. 5. Proportional distributor housing vibration acceleration amplitude a2 relativeto excitation vibration acceleration amplitude a0 for f = 1060 Hz00,050,10,150,20,250,30,351015202530354045505560f Hza2/a0 -Fig. 6. Proportional distributor housing vibration acceleration amplitude a2 relativeto excitation vibration acceleration amplitude a0 for f = 1060 HzM. STOSIAK244The results of the application of a vibration insulator with characteristic xkxc?222and c2 = 20 000 N/m and k2 = 50 Ns/m are shown in Figure 6. In this case, the fourthequation of model (1) should be supplemented with a nonlinear vibration insulatorcharacteristic.When a vibration insulator with a nonlinear damping characteristic (k2 = 250 Ns/m)and linear stiffness (c2 = 20 000 N/m) 222xkxc? is used to insulate base vibrationsthe valve housing vibrations are as shown in Figure 7.00,511,522,51015202530354045505560f Hza2/a0 -Fig. 7. Proportional distributor housing vibration acceleration amplitude a2 relativeto excitation vibration acceleration amplitude a0 for f = 10 60 HzFigures 5 and 6 show that such a nonlinear vibration insulator characteristic can beselected that the insulation will be effective in the whole considered excitation fre-quency range.The problem of influence of mechanical vibrations on valve was considered in theo-retical and experimental way. Theoretical considerations were based on numericalcalculations according to mathematical model. For some theoretical considerationsexperimental tests were done using test stand (hydraulic simulator, valve holder, springset).3. Experimental testsA test rig enabling the generation of mechanical vibrations characterized by a pre-scribed frequency was built to experimentally verify the theoretical results and conclu-Vibration insulation of hydraulic system control components245sions. The investigated valve Mannesmann-Rexroth proportional distributor type4WRE 6 E08-12/24Z4/M fixed in the holder was mounted on the test rig and sub-jected to external mechanical vibrations (photo 1). Tests were done without pipesconnected to valve.A linear hydrostatic drive simulator Hydropax ZY25 made by Mannesmann-Rexroth,capable of generating vibrations up to 100 Hz, was the source of external mechanicalvibrations. Main component of simulator of linear hydrostatic drive is servo valve whichcontrols hydraulic cylinder. The simulator consists three main parts: hydraulic part,control part and control software. Displacement of simulator table is controlled bydisplacement transducer and its acceleration is controlled by accelerometer. On simu-lator table the tested valve was mounted. Electrical control signal for simulator wassupported by external harmonic signal generator. The simulator is described in moredetail in 4. The proportional distributor was placed in the special holder andbilaterally supported with springs (there were two springs connected in parallel oneach of the sides). Preliminary tests were carried out for springs with an equivalentstiffness of 86 000 N/m and a pre-deflection of 2 mm. The external excitation pa-rameters are shown in Table 2.Photo 1. Proportional distributor placed in special holder and bilaterally supported with springs, during testingTable 2. Amplitude of vibrations acting on tested hydraulic distributorf Hzw0 m300.000483350.000406400.000366450.000269500.000214550.000145600.0000522Figure 8 shows an overall valve vibration diagram for the external excitation, i.e.a ratio of proportional distributor housing acceleration amplitude a2 to excitation vi-bration amplitude a0 versus a frequency of 25 60 Hz.M. STOSIAK246It appears from the diagram shown in Figure 8 that for a system of springs withequivalent stiffness cz = 86 000 N/m and a proportional distributor with a mass of4.5 kg the vibration insulation is effective (transmission function a2/a0 1) in thegiven external vibration frequency range. As a result of the insulation, the distributorhousing vibration amplitude and the distributor slide-valve vibration amplitude de-crease 5. Consequently, the amplitude of the pressure fluctuations due to the excita-tion of distributor slide-valve vibrations also decreases. However, in the case of sosimple vibration insulation, resonance may be generated at external vibration frequen-cies other than the ones used in the test. Therefore, as Figures 5 and 6 indicate, a vi-bration insulation element with other properties and characteristics, e.g. with nonlinearstiffness and with damping, should be used.00,20,40,60,811,22530354045505560f Hza2/a0 -Fig. 8. Proportional distributor housing vibration acceleration amplitude a2 relativeto excitation vibration acceleration amplitude a0 for f = 2560 Hz4. ConclusionIt has been shown that there is a need to reduce the vibration of the hydraulicvalves with which machine tools and mobile machines are commonly equipped. Theuse of vibration insulators in the form of springs whose characteristics are linearresults in a reduction in valve housing vibration acceleration amplitude at certainexternal vibration frequencies, but it may be conducive to resonance at other fre-quencies. Comparison of results presented on Figure 3 and Figure 8 shows, that dif-ferences between model and test are not great for frequency range 35 60 Hz. Thebiggest differences are observed in resonant area (25 Hz). It follows from the pre-sented cases of vibration insulation (Figures 5 8) that materials with linear charac-Vibration insulation of hydraulic system control components247teristics should be used in order to extend the range of effective vibration insulation.Thanks to the use of a vibration insulator with a nonlinear characteristic the valvehousing vibration acceleration amplitude was reduced by a few tens of percent: byover 90% for the vibration insulator with quasi-zero stiffness and by about 80% forthe vibration insulator whose stiffness or damping was proportional to displacementor velocity to the second power. A reduction in valve housing vibration will lead toa reduction in slide-valve vibration, particularly in the resonant vibration range. Asa result, the pressure fluctuations and the emitted noise (particularly in a low fre-quency range) will decrease and the precision of the motions of the hydraulic receiv-ers will increase. Vibration insulators in such applications should also satisfy othercriteria, such as: resistance to changes in ambient temperature, resistance to hydrau-lic fluids, and small geometric dimensions. Therefore, besides having proper phys-icochemical properties, a vibration insulator should have a standardized design suit-able for typical connection plates for hydraulic valves.References1 Lisowski E., Szewczyk K.: Theoretical determination of multi-piston axial-flow pumpdelivery fluctuations (in Polish), Sterowanie i Nap?d Hydrauliczny, No. 1, 1984, pp. 3 6.2 Kud?ma Z.: Frequency of the free vibration of a relief valve and a hydraulic system (inPolish), Sterowanie i Nap?d Hydrauliczny, No. 3, 1990, pp. 27 30.3 Amini A., Owen I.: A practical solution to the problem of noise and vibration in a pres-sure-reducing valve, Experimental Thermal and Fluid Science, No. 10, 1995, pp. 136 141.4 Misra A., Behdinan K., Cleghorn W.L.: Self-excited vibration of a control valve due tofluid-structure interaction, Journal of Fluids and Structures, Vol. 16, No. 5, 2002, pp. 649665.5 Stosiak M.: The effect of the low-frequency mechanical vibrations of the base on the con-trol component of the hydraulic valve (in Polish), in: Rozwj maszyn i urz?dze? hydrau-licznych, Edit. Wac?aw Kollek, Wroc?aw, Wydaw. Wroc. Rady FSNT NOT, Vol. 11,No. 2 3, 2006, pp. 83 94.6 Stosiak M.: An influence of mechanical vibrations of ground for pressure pulsation inhydraulic system (in Polish), Hydraulika i Pneumatyka, No. 3, 2006, pp. 5 8.7 Engel Z.: Protection of the environment against vibrations and noise (in Polish), Wy-dawnictwo Naukowe PWN, Warsaw, 2001.8 Leea E.C., Nianb C.Y., Tarng Y.S.: Design of a dynamic vibration absorber against vibra-tions in turning operations, Journal of Materials Processing Technology, Vol. 108, 2001,pp. 278 285.9 Grajnert J.: Vibration insulation in machines and vehicles (in Polish), Oficyna Wy-dawnicza Politechniki Wroc?awskiej, Wroc?aw, 1997.10 Pytlik A.: Vibrations in hydraulic systems of mechanized casing section (in Polish),Nap?dy i Sterowanie, Vol. 10, No. 4, 2008, pp. 121 130.11 Krylov V., Pickup S., McNuff J.: Calculation of ground vibration spectra from heavymilitary vehicles, Journal of Sound and Vibration, Vol. 329, No. 115, 2010, pp. 30203029.M. STOSIAK24812 Kollek W., Kud?ma Z., Maga K., Stosiak M.: Disturbances in the operation of propor-tionally controlled hydrostatic systems (in Polish), Nap?dy i Sterowanie, Vol. 6, No. 5,2004, pp. 53 57.13 Joint publication edited by ?wider J., Kazimierczak J.: Computer-aided design of machinevibration and noise reducing systems (in Polish), WNT, Warsaw, 2001.Wibroizolacja elementw steruj?cych uk?adw hydraulicznychW artykule skupiono si? na problemie oddzia?ywania zewn?trznych drga? mechanicznychna zawory hydrauliczne. Omwiono skutki tych oddzia?ywa?. Przeprowadzono analiz? teore-tyczn? wp?ywu charakterystyki wybranych izolatorw na redukcj? drga? korpusu zaworu hy-draulicznego. Przedstawiono wst?pne badania eksperymentalne dla prostych przyk?adw izo-latorw.