Estimation of dynamic behavior and energy efficiency of thrust hybrid bearings with active control

Transcription

1 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 Estimation of dynamic behavior and energy efficiency of thrust hybrid bearings with active control Alexander Babin Sergey Majorov Leonid Savin Abstract The resent aer considers analysis of world tendencies of alication of bearings with feedback control systems in various tyes of rotor machines. A ossibility of qualitative imrovement of oerational characteristics has been highlighted for bearings with integrated additional functions of automated diagnostics and active control of geometric rheological and force arameters. The resent aer features a mathematical model its imlementation in a form of an algorithm and numerical results including ressure and temerature distribution in a bearing in question load caacity and rotor s axial trajectories. A quality index has been formulated for thrust taered land hybrid bearings with a central feeding chamber that is based on a combination of minimum ower loss due to friction and stability of motion of a rotor. Various combinations of roughness and axial gas have been taken into account. Keywords mechatronics active control fluid-film bearings thrust bearings dynamic behavior energy efficiency. I. INTRODUCTION NTEREST in modelling and exerimental investigation of Iactive bearings arose with the evolution of what is commonly referred to as Industry 4. [1]. Synergy-based technological overla of mechanical engineering electrical engineering and information technologies enable smart machines and many cases emerge where traditional arts of machines could be relaced with mechatronic devices that extend functionality and enhance erformance of these machines. In the field of rotating machinery fluid-film bearings used to carry the load of a shaft are the most vital elements and thus become subjected to various enhancements including the ossibility to introduce active control systems. This work was suorted by the Ministry of Education and Science of the Russian Federation under Project no /4.6 (develoment and modernization of the test rig) and by the Russian Science Foundation under Project no (formulation and solution of the roblem in all sections of the resent aer). Alexander Babin is with the research lab Modelling of Hydro and Mechanical Systems at the Orel State University Orel Naugorskoe sh. 9 3 Russia (tel.: alex.mech.osu@gmail.com). Sergey Majorov is with the research lab Modelling of Hydro and Mechanical Systems at the Orel State University Orel Naugorskoe sh. 9 3 Russia ( sergeyostu@yandex.ru). Leonid Savin is with the deartment of Mechatronics Mechanics and Robotics at the Orel State University Orel Naugorskoe sh. 9 3 Russia ( savin@ostu.ru). The idea behind these enhancements is to not only rovide a stable oerational regime but also and very imortantly to increase energy efficiency of a machine. And ower loss in rotating machinery mainly occurs in bearings due to both friction and vibration. Machines subjected to loads varying in time or vibrations due to oerational regimes require certain sets of dynamic characteristics of bearings these sets are unique in each case making design of bearings a challenge. Investigation in the field of rotor s dynamic behaviour control in fluid-film bearings is carried out in the following fields: study of the ossibility of rofile adjustment of a ga between a rotor and a sleeve or a thrust disk of a bearing e.g. tilting-ad and some foil bearings [ 3]; study of the ossibility of alication of lubricants with adjustable arameters such as viscosity or density e.g. ferromagnetic fluids [4 5]; and study of hybrid fluid-film bearings [6 7] where load caacity is generated as a combination of hydrodynamic forces in the film and hydrostatic force from the lubricant sulied into a bearing under ressure where rotor s osition can be adjusted by means of electrohydraulic devises like servovalves. Alication of servovalves roved feasible in many alications with journal bearings [8-1]. There are however very few studies regarding the ossibility to aly the same aroach to thrust bearings. The urose of the resent aer is to introduce active control system to a traditional thrust taered land bearing and to estimate feasibility to use active control to enhance the erformance of the bearing in question. II. MATHEMATICAL MODEL OF AN ACTIVE THRUST HYBRID BEARING The oerational rincile of an ATHB (Figure 1) is as follows: the um (1) located in the tank with the fluid (water oil etc.) sulies the lubricant into the housing () of the bearing (3) which suorts the rotor (4) in the axial direction. The ressure data is acquired with the sensor (8). The data on the resent osition of the rotor is acquired with the roximity sensor (7). Data from the sensors is analogue and is acquired with the analogue inut modules of a DAQ system (5). This system also controls the servovalve (6) by means of adjusting the oening rate ξ generating an analogue voltage signal and the um (discrete outut module). ISSN:

2 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 Fig. 1 rincile diagram of an ATHB To simulate the oeration of an ATHB one has to ay close attention to two basic roblems: a roblem of hydrodynamic lubrication theory based on the Reynolds equation and the energy balance equation and a roblem of theory of automatic control. Merging a model of a hybrid bearing with a model of the control system yields a model of an active bearing. Here the controlled variable is the axial ga between the rotor s thrust disk and the bearing in question. By means of controlled suly of lubricant under ressure one could change the ressure distribution in the bearing thus controlling the value of the ga. The first stage is consequently modelling a assive thrust hybrid bearing (THB). The hoto and calculation diagram of a THB are resented in the Fig.. the following form: 1 F 1 h F rf r + r r + r r ω F (1) t where ω angular velocity of the shaft (rθ) local ressure F F 1 F Dowson s functions determined as in [11]: h dy h h ydy y F F F1 µ µ 1 F y dy µ F where h(θ) axial ga function µ(rθ) local viscosity which is determined as a distributed scalar value and is a function of temerature: µ µ e λ ( T T s ) where µ viscosity of the sulied fluid T s temerature of the sulied fluid λ temerature/viscosity coefficient. Here it has to be noted that the shae of the axial ga is modelled using Bezier curves that allow higher calculation accuracy of ressure gradient in the circumferential direction. In the Fig. 3 results of modelling and actual ga measurement are resented along with the hoto of the measuring setu. Fig. hoto of a THB (a) calculation diagram of a THB (b) Here R in and Rout are inner and outer radiuses of the bearing accordingly V r V θ and V y are velocity comonents in the olar coordinate system h minimum film thickness Θ angular extent of a single ad α angle of inclination of a ad. To obtain the ressure distribution the generalized Reynolds equation is derived to be solved iteratively with the energy balance equation which allows taking into account ossible viscosity variation in the fluid film due to temerature rise that occurs as a result of action of friction between the layers of the fluid. The generalized Reynolds equation takes Fig. 3 hoto of the rofile measurement system (a) comarison between rofile measurement and modelling (b) It could be seen that modelling results are accurate enough however there is a slight deviation due to mechanical treatment of the surface of the THB. In order to obtain the temerature distribution the energy equation taking into account the action of dissiation forces in the fluid is derived in the following form: ISSN:

3 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 h T h ωr T ρc µ r r µ r r () 1 1 h h ωr µ µ r µ r h where ρ density of the fluid c heat caacity of the fluid Т(rθ) local temerature. Equations (1) and () and the additional exressions are solved iteratively using a finite difference method with the following boundary conditions for ressure and temerature: T r Rout θ T T a θ Θ T r Rin T T θ θ r Rin s θ θ Θ θ s θ Θ θ Θ where s suly ressure a ambient ressure. The iteration rocess is then considered converged if the convergence criterion based on difference in load caacity of a bearing on the resent and the revious iteration. Character ressure and temerature distributions in thrust hybrid bearings are resented in the Fig. 4. Fig. 5 rotor-bearing dynamic system Under steady conditions the rotor takes the equilibrium osition when the hydrodynamic forces counterbalance the inertia forces i.e. R Y mg where m rotor s mass g freefall acceleration. When the rotor s osition changes under the influence of some imulse some additional forces start acting on the rotor so assuming these dislacements are relatively small the reaction force of a bearing could be linearized using Taylor series. The reaction force of the bearing could be determined as follows: Ry RY KY Y BY Y and consequently the motion law of the system is as follows: my B Y Y KYY F(t) (3) where F(t) is some external force as a function of time t. (3) is solved using the Runge-Kutta method of the 4 th order. In order to introduce the model of the control system to the develoed model of the bearing the structure of the named system has to be considered (Fig. 6). Fig. 6 Structure of the control system of an ATHB Fig. 4 ressure (a) and temerature (b) distribution in a THB Load caacity of a bearing is obtained by means of integration of ressure distribution over the area of the bearing: R Y z Θ Rout Rin ( r θ ) rdθdr where z number of fixed ads. To estimate dynamic behavior of a rotor on the ATHB a model of a dynamic system has to be develoed. The diagram is resented in the Fig. 5 The control system consists of a module that sets the value of a set oint (SP) and the data channel (D) the obtained data is comared to the set oint and the error ε is the used to generate a control signal by means of alication of a PID controller based regulator (R). The signal is then amlified (A) and sent to the actuator servovalve (SV) thus changing the suly ressure. These actions affect the osition of a rotor in the bearing (B) that could be subjected to some external force F(t). The aim of control is to maintain a desired value of the axial ga between the rotor and the THB. The control rincile is essentially regulation of in-flow ressure to increase or decrease the bearing s reaction force which results in increase or decrease of the axial ga. Here the regulator is the core element of the control system and is based on the PID control law where the outut signal is a function of the current error and the desired osition Ys (set oint): t ε ( t) u( t) K ε ( t) + K i ε ( t) dt + K d t where u(t) outut signal from the regulator K Ki Kd roortional integral and differential comonents of the regulator accordingly ε(t) error function. ISSN:

4 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 The kind of electrohydraulic actuators used in the resent research is simulated using the known relation between the ressure it sulies the lubricant with and the voltage on the inut of the valve. The most imortant term here is the time constant of the valve T SV i.e. the time it takes for a fully closed valve to fully oen. This is a crucial characteristic for systems subjected to high-frequency eriodic loads. The exression that allows simulation of a servo valve is as follows: d( t) TSV + ( t) K SV u( t) (4) dt where K SV gain coefficient of a servo valve u(t) control signal i.e. voltage on the servo valve s inut. The given equations (1) () (3) and (4) with additional exressions such as function of viscosity make a mathematical model of an ATHB which is going to subjected to study in the resent aer. III. NUMERICAL RESULTS AND DISCUSSION Problems of stability are the rimary roblems that are solved when develoing bearings for high-seed rotating machinery. Axial stability is considered in various tyes of ums for oil extraction aircraft and sacecraft engines etc. The urose of the resent study is to estimate the influence of the control system on the axial stability and energy efficiency of an ATHB. Stability analysis is based on estimation of the magnitude of oscillations of a rotor under comlex external axial loading and relies on the remise that the desired osition should be as close to the set oint as ossible. Energy efficiency estimation is based on calculation of ower loss due to friction: N FR M FRω Rout Θ where h ωrµ M FR r + rdθdr - friction torque. r h Rin Oeration of the ATHB has been modelled under the influence of a following external axial force: ωt π ωt π F( t) AD sin + sin + AD 1 5 where A D amlitude taken as N. In the Fig. 7 results of calculation of rotor s trajectories are shown for various A D settings. Fig. 7 results of rotor s trajectories calculation under various axial load (a) - A D 5 b) - A D 35 c) - A D 5 d) - A D 75) First the regulator has been tuned manually based on minimum transition eriod and control error. Chosen regulator arameters are: K 7.5 Ki15 Kd.5. Throughout this art the following modelling arameters were used : Rout.6 m Rin.3 m α.5 z 6 ISSN:

5 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 lubricant H 3⁰C ω 5 rad/s Tsv.5 s rotor s mass is 5.5 kg. In the Fig. 8 comarison results are shown for THB and ATHB regarding the stability and energy efficiency enhancement. case a machine is subjected to changing loads and needs to be designed with a sufficient level of rotor s ositioning accuracy it could be seen that introduction of a relatively simle in terms of simulation and execution control system greatly imroves the erformance of the bearing and the machine at a whole. IV. EXPERIMENTAL SETUP In order to verify the resented model and ossibly identify some new or unaccounted for effects a test rig has been develoed. A series of exeriments has been lanned for carrying out in the nearest future to suort the idea of an ATHB. A hoto of the test rig is resented in the Fig. 9 and in more detail in the Fig. 1. The main advantage of the develoed test rig is ossibility to study both radial and thrust active bearings at the same time. For verification uroses within the resent research it is lanned to only focus on ATHBs so instead of sliding journal bearings two rolling element bearings are installed so that there is such radial ga that the rotor could erform axial motion without restraining friction in these bearings. These bearings also rovide higher stability in radial direction. An ATHB is installed in its housing where one side is made of lexiglass in order to rovide some visual information like observable cavitation or turbulence etc. In Fig. 1a and Fig. 1b more detailed hotos of the servovalve setu and the ATHB are resented. Fig. 8 comarison results of oeration of THB and ATHB During simulations magnitude of oscillations has been calculated for comarison uroses and at frequency of 1 Hz the data on ower loss has been collected. Then a mean value of ower loss due to friction has been determined. It could be seen that alication of ATHB significantly decreases the magnitude of oscillations thus enhancing stability (Fig. 6a). With a ractically constant magnitude in the case of an ATHB magnitude of oscillations of a rotor increases in the case of a assive THB with the increase of the amlitude of the external axial force. Decrease of magnitude by the ATHB in this case is u to 85 % and the resulting trajectories are considered stable in comarison to a assive THB. Moreover the osition of the rotor only slightly deviates from the set oint which is very imortant in terms of ositioning accuracy. Comarison of ower loss due to friction (Fig. 6b) shows a 4% decrease in the case of the ATHB. And once more the value of ower loss remains constant in the whole range of simulated amlitudes whereas in the THB the ower loss increases with the increase of the amlitude of the axial external force. Based on the obtained numerical results it could be highlighted that the alication of ATHBs significantly increases stability and energy efficiency of a rotor machine. In Fig. 9 test rig with an ATHB (general view) ISSN:

6 INTERNATIONAL JOURNAL OF MECHANICS Volume 1 18 the height of the axial ga rovides less friction and enough hydrodynamic force allows energy efficiency to be significantly increased. Finally a test rig has been develoed to verify the obtained numerical results. Exerimental studies are the first ste of future research as it rovides initial data about the accuracy of the resented model. Possible identification of effects that have not been accounted for allows develoment of a more accurate model. ACKNOWLEDGMENTS This work was suorted by the Ministry of Education and Science of the Russian Federation under Project no /4.6 (develoment and modernization of the test rig) and by the Russian Science Foundation under Project no (formulation and solution of the roblem in all sections of the resent aer). Fig. 1 a) servovalve setu b) ATHB in more detail As shown in the Fig. 1a ressure is controlled right before the fluid enters the feeding chamber and it is ossible to also determine the temerature of the inflow. In order to determine whether radial oscillations occur that influence the erformance of the ATHB and to ossible determine shae deviation of the rotor s thrust disk four dislacement sensors are mounted around the thrust disk (Fig. 1b). One of these sensors is used to acquire data about rotor s osition for the control system to be used as current rotor s osition. V. RESULTS AND DISCUSSION Results resented in the resent aer show feasibility of alication of active ressure control to increase axial stability of rotors with thrust hybrid bearings. Numerical results show a more than 8% decrease of amlitude of vibration if active control is alied. It has also been determined that with varying amlitude of the external force the actual rotor s dislacement on the ATHB is more stable while amlitude of vibrations of the rotor on the assive THB increases. It has also been determined that energy efficiency of the rotor system increases in terms of decreased ower loss due to friction in the bearing. Along with decreased amount of energy dissiated due to vibrations ositioning of the rotor so that REFERENCES [1] E.A Lee Cyber Physical Systems: Design Challenges 11th IEEE International Symosium on Object Oriented Real-Time Distributed Comuting (ISORC) [] A. M. Haugaard Modeling of Flexible Tilting Pad Journal Bearings With Radial Oil Injection Proceedings of the STLE/ASME International Joint Tribology Conference [3] G. Aguirre Dynamic stiffness comensation with active aerostatic thrust bearings Proceedings of ISMA [4] H. Urreta Hydrodynamic bearing lubricated with magnetic fluids Journal of Physics Conference Series vol [5] A. Albagachiev Magnetic fluid in the regime of hydrodynamic lubrication Bulletin of the Bryansk Technical University vol [6] P. Kytka Alication of Feedforward-Disturbance-Comensation and Inut-Shaing to a Machine z-axis in Active Hydrostatic Bearings Proceedings of the 9th International Conference on Motion and Vibration Control [7] L.A. Savin Rotor trajectories in fluid-film bearings adjustment of them and energy efficiency arameters Proceedings of ICMMR MATEC Web of Conferences vol [8] F. G. Pierart Active lubrication alied to radial gas journal bearings. Part : Modelling imrovement and exerimental validation Tribology International vol [9] A. Chasalevri Imroving stability and oeration of turbine rotors using adjustable journal bearings Tribology Int vol. 14 (1) [1] D. C. Deckler Simulation and Control of an Active Tilting-Pad Journal Bearing STLE Tribol. Trans. vol [11] I. Chatzisavvas On the influence of thrust bearings on the nonlinear rotor vibrations of turbochargers Proceedings of ASME Turbo Exo 16: Turbomachinery Technical Conference and Exosition GT ISSN: