STTIONRY ND TRNSIENT VIBRTIONS OF DVI VIBROINSULTION SYSTEM. Jerzy Michalczyk, ul.zagorze c, 3 398 Cracow, Poland Piotr Czuak, ul. Szujskiego /4, 3-3 Cracow, Poland address for correspondence Grzegorz Cieplok, ul.graniczna 7a, 4-48 Myslowice, Poland. e-mail: czuak@uci.agh.edu.pl DEPRTMENT OF MECHNICS ND VIBRO-COUSTICS University of Mining and Metallurgy, Cracow, Poland. BSTRCT: nalysis of the new, patented, hydraulic dynamic viroinsulator system of the DVI type is presented in the paper. The descried device applied to the classical viroinsulation system, sujected to harmonic load, significantly improves its efficiency y means of generating additional forces shifted in phase y π angle against forces eerted y elastic suspensions. This viroinsulator, contrary to the Frahm s one, does not increase the numer of degrees of freedom of the system. The analytical solution of a stationary motion as well as computer simulations of transient resonance phenomena together with eperimental confirmations of the results are included in the paper. Semiactive system designed for variale angular velocity of eciting force is also analysed. Key words: dynamic antiresonant viroinsulation, viratory machine, semiactive systems..introduction n idea of the dynamic antiresonant viroinsulation [] in relation to the force viroinsulation is ased on the generation of additional dynamic forces eing in anti-phases and of equal values with the forces transmitted to the ase y a classic viroinsulation system. The task can e solved y passive elements if only the viroinsulating system performs sinusoidal motion and is not heavily dumped. By adding a certain inert system to supporting springs the theoretical alancing of forces transmitted from the virating oject to the ase can e achieved. This will not limit the static stiffness of the system. The effect occurs in the system shown in Fig. []. Fig. nalysed model of the viroinsulating system.
The machine ody, m, in a steady state, performs harmonic virations (t). The viroinsulation system of elasticity and dumping constants, K and respectively, is influencing the foundation M not only y a static component originated from the machine weight ut also y a dynamic component connected with cyclic deformation of springs K and the damper. This force causes virations (t) of the foundation M, on which the reaction R(t) acts from the side of the ase. Into this system a container with liquid was attached in such a way that its ody was affied to the foundation. The container consists of two chamers, upper and lower, closed y pistons (memranes) of surface. Both chamers are connected y a channel of diameter containing liquid of a mass m c. Memranes are stiffly affied to the machine ody. Fig. 8 shows the diagram of the DVI ruer-oil viroinsulator. ssuming machine ody motion as (t)=xsin(t), the equation of the foundation motion derived on the ases of Lagrange s method is as follows: M + m c && + & + + K = X t mc X t + X t K R + = sin( ) cos( ) + sin( ) () where: - viscous damping coefficient in channel. It has een assumed that there is a laminar flow in the channel. The condition for the rest of the foundation M, in a steady state, is the zeroing of the right-hand side of equation (). Since our aim is that the reaction transmitted into surroundings would e zero, R =, finally the condition for non-transmitting of virations to the ase is given y the formula: + + X t m sin( ) c X cos( t) + X sin( t ) K = Two cases should e considered:.. In the first case none of the parameter value will satisfy the equation. In the second case the equation will take the form: () X t m sin( ) c + X sin( t) K = (3) Hence, the condition for zeroing of the force transmitted into the foundation at a weak dumping value can e formulated as: c m = K (4) what can e satisfied for > only. In real situations where >> the aove condition can e written, in an approimation, as: mc K (4a) If, at the given frequency,, the viroinsulator parameters m c,, and K are selected in such a way as to satisfy the equation (4), the force transmitted to the machine foundation will theoretically e of zero value.
This happens, ecause forces generated y elastic elements and those connected with the inertia of liquid present in the viroinsulator channel cancel each other. Those forces are in an anti-phase and have equal amplitudes and frequencies. It can e derived that the transmission coefficient p of the system equals: R( t) p = P ma = s can e seen from equation (5) the viroinsulating system with the damping element descried aove has only one resonance range, while systems with dynamic dampers have two such ranges, one eing in the direct vicinity of the working frequency [3]. n (5). SIMULTION OF THE RUBBER-OIL VIBROINSULTOR Previously analyzed model which allows to derive the condition for zeroing of the force transmitted into the ase does not illustrate several significant phenomena occurring in real systems. It does not include e.g. resonance phenomena, influence of mass and dumping in liquid on the viration amplitude in steady state conditions, etc. In order to e ale to estimate those phenomena the simulating model of the two-rotor viratory machine was uilt (Fig. ) [4]. H l a I e ϕ m y a l m e I ϕ H h m,i h β k t mc ky y t m c ky k y Fig..The model of a viroinsulated two-rotor machine The simulated system was symmetrical towards the y ais. Simulation was performed for such values of initial parameters for which the sum of unalanced forces in the y direction, in the steady state, equals: F = 468[N]. Paper [4] deals with the simulation of the aove system performed for typical parameters. The diagram presented in Fig. 3 gives the comparison of the forces transmitted to the ase in the steady state for the system viroinsulated y the ruer-oil viroinsulator (roken line) and the system not insulated in such a way (solid line). The analyzed type of a viroinsulator allows to lower the force value transmitted to the ase - in the steady working point - to 8.3 % of the value of the classic viroinsulation (oth of the same static stiffness). Fig. 4 presents the amplitude-frequency characteristics of the forces transmitted to the ase. The force transmitted y a classic viroinsulator is shown y a roken line, while the one transmitted y the oil-ruer viroinsulator is shown y a solid line. This diagram was determined on the ases of steady states otained in the time simulations. The resonance amplitude of the machine equipped with a viroinsulator is more than two times lower than the resonance amplitude of the machine operating without that viroinsulator for the case of a stationary resonance.
.. 4. 6. 8.. 5. 4. 3. P [N ].. punk t pracy ustalonej. Fig. 3 Forces transmitted to the ase y two types of viroinsulation. [rad/s] Fig. 4 The dependence of forces transmitted to the ase on the forced frequency. π 3. STRTEGY OF OPERTING THE RUBBER-OIL INSULTOR. The inherent defect of the presented aove solution is that at the start-up of the machine the suspension system equipped with the viroinsulator ehaves only slightly etter than the system of a classic suspension. Therefore in the presented herey paper the possiility of controlling the inner diameter of the channel inside the viroinsulator was investigated. The channel (3) inside the viroinsulator, shown in Fig. 5, can e constructed in such a way that its inner part has a regulated diameter enaling to control the area of the channel (3) as a function of an angular frequency of virations. Schematic presentation of the semiactive viroinsulation is given in Fig.5. 6 7 α 3 8 4 5 9 Fig. 5 Diagram of a semiactive viroinsulator It is possile to control the inner diameter of the channel (3) y regulating the amount of liquid in the space etween the mandrel (8) and a ruer clamping ring (). By means of that the cross area of the channel can e regulated. The system of two ellows (4) and (5) allows to retain the constant amount of liquid inside the viroinsulator preventing any ecessive increase of pressure to act on ruer memranes (9). The amount of liquid in each part of the viroinsulator is controlled y the change of the position of the lever. Thus in transient states the diameter d can e adjusted to the actual value of an angular frequency of viration in such a way that equation 4 will e satisfied all the time. The semiactive system was applied to the previously simulated system. The forces transmitted to the ase during the start-up and the steady operation are shown in diagrams in Fig. 6 and Fig. 7 for the system with the semiactive viroinsulator and the typical DVI viroinsulator respectively. For the start-up operation of the system with the semiactive viroinsulator.5 times lowering of the force transmitted to the ase was otained.
Fig. 6 Forces transmitted to the ase y the system with the semiactive viroinsulator. Fig. 7 Forces transmitted to the ase y the system with the typical DVI viroinsulator 4. EXPERIMENTL PRT The ruer-oil viroinsulator with a rectilinear channel was designed and constructed for eperimental purposes (Fig.8) in which ruer memranes have elasticity of constant K. 86 7 -ody -memranes 3-channel - korpus 4-mandrel - memrany fied to the machine 3 - kana³ 5-foundation 4 - trzpieñ 6-machine 5 - podstawa ody 6 - ziornik górny 7 - ziornik dolny 8 - korpus maszyny Fig.8. The diagram of the DVI ruer-oil viroinsulator. In accordance with equation (4), it was designed in such a way as to transmit to the ase the minimal force at the eciting frequency of 5 Hz. The viroinsulator was sujected to the kinematic eciting force of the frequency regulated in the range from 3 to 5 Hz and the viration amplitude equalled app..5 mm. - viroinsulator - fiing of viroinsulator 3- force sensor 4- measuring system 5- direct-current motor 6- supply system 7- tachogenerator Fig.9. The scheme of the eperimental set up. The viroinsulator was sujected to the kinematic ecitation y a slider crank mechanism. t the opposite side of the viroinsulator the measurements of the force transmitted were made. The aim of measurements was to otain the dependence of the maimal amplitudes of the force transmitted to the ase on the frequency of the kinematic eciting.
Eperiments were performed for two different cases. When the ruer-oil viroinsulator is filled with liquid the force connected with its inertia should oppose the one generated y elastic memranes (oth forces are in an anti-phase) and this reduces the force value transmitted to the ase. When the viroinsulator is empty the system ehaves as a classic ruer viroinsulator. Plots of force vs. frequency for the two types of viroinsulators are shown in Fig.. The dependence of the force transmitted to the ase on the forced frequency for the ruer-oil viroinsulator and the ruer one are shown y solid and roken lines respectively. Fig. gives the comparison of the force transmitted to the ase versus time (at forced frequency equal 5 Hz) for the ruer-oil viroinsulator and for the classic one. The force transmitted y the ruer-oil viroinsulator equals 5 N while the one transmitted y ruer insulator equals 8 N. 3.. F[N]... 5.. 5.. 5. f[hz] Fig.. Plot of force vs. frequency Fig.. Plot of force vs. time 5. CONCLUSIONS. The analysed type of a viroinsulator allows to lower the force value transmitted to the ase in the steady working point to 8.3 % of the value of the classic viroinsulation (oth of the same static stiffness).. The resonance amplitude of the machine equipped with a viroinsulator is more than two times lower than the resonance amplitude of the machine operating without that viroinsulator for the case of a stationary resonance. 3..5 times lowering of the force transmitted to the ase was otained for the start-up operation of the system with the semiactive viroinsulator. 4. Eperimental results fully confirmed the correct action of the ruer-oil viroinsulator. The reduction of the force value transmitted to the ase at the working point was 3.6 times larger than in the case of the classic viroinsulator. REFERENCES. G.Done, 978, Viration Control y Passive Means Other than Using Damping, Dynamika maszyn, Ossolineum, Wroclaw, 63-6.. J. Michalczyk, 9. 8. 996, Wiroizolator, Pat. RP No. 75447. 3. J.Michalczyk, G. Cieplok, 999, Wysokoaktywne uklady wiroizolacji i redukcji drgan, Coll. Columinum, Cracow. 4. J.Michalczyk, P.Czuak, 999, naliza teoretyczna i adania symulacyjne antyrezonansowego wiroizolatora dynamicznego, Mechanika, Tom 8, Zeszyt.