METHOD AND DEVICE FOR SPEED CHANGE BY THE EPICYCLIC GEAR TRAIN WITH STEPPED-PLANET GEAR SET

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Volodymyr MALASHCHENKO Lviv Polytechnic National University, Ukraine Oleh STRILETS RESEARCH WORKS OF AFIT Isse 38, s. 13 19, 2016 r. Volodymyr STRILETS 10.

1 Volodymyr MALASHCHENKO Lviv Polytechnic National University, Ukraine Oleh STRILETS RESEARCH WORKS OF AFIT Isse 38, s , 2016 r. Volodymyr STRILETS /afit National University of Water Management and Natre Resorces Use, Rivne, Ukraine METHOD AND DEVICE FOR SPEED CHANGE BY THE EPICYCLIC GEAR TRAIN WITH STEPPED-PLANET GEAR SET The article describes new method and device for continosly variable speed change management via compond epicyclic gearing with composite planet gears and closed circit hydrosystem, when the speed control element is either oter ring gear (annls) or the carrier or sn gear. In each case, the control element connected to closed circit hydrosystem and can be in motion or immovable depending on the bandwidth of hydrosystem s reglating throttle. We had held theoretical research and received graphic dependences between velocities of driving, control and driven elements by means of compter programing. Key words: speed change management, compond differential gear, stepped-planet gear set, closed circit hydrosystem, speed control element. 1. Introdction In the world of technology, there are widely known methods and devices for speed management that provide stepped or continosly variable change in velocity by the vale and direction with the se of respective gearboxes. However, these methods have many shortcomings. The main disadvantages of stepped speed management devices are the complexity of design, their large material consmption, the emergence of dynamic loads dring the transition from one speed to another, even in case of synchromesh sing. On the other hand, continosly variable speed devices have intense components wear de to the se of friction connections

2 14 Volodymyr MALASHCHENKO, Oleh STRILETS, Volodymyr STRILETS like brakes or lock-p cltches. All abovementioned redces the drability and reliability of certain device components and machine in general. Therefore, it cases the need in creation of new ways of speed management and devices, which eliminate those disadvantages. Advantages of sing the planetary gear train over other gear mechanisms has already been proven by a nmber of the world's scientists. Ths, in [6] it is shown that the classical planetary gear compared to helical gear is capable of achieving the gear ratio of 1:78 having 49% lower mass and volme, and 96% higher torqe density (torqe/volme ratio). In [2] a stdy presented on the possibility of redcing the mass of the planetary gear by the se of the maximm nmber of satellites. Also, some scholars [1] stdied the effect of the change of the tooth profile on the planetary gear dynamics. Or research focses on the development of speed control devices by combining the epicyclic gear (transmission with two degrees of freedom) with a closed circit hydrosystem. Recently, review of the methods and devices for the of speed change process management have been performed and their extensive analysis has been held [5, 7, 9]. The new classification for those methods and devices has been offered [4]. The possibility of speed change management via epicyclic gear train has been jstified [8]. The new patent-protected devices for speed change management via epicyclic gearing with closed circit hydrosystem have been developed. Nevertheless, for the implementation of any mechanical means, the comprehensive stdy of kinematic and power parameters is reqired, bt crrently flfilled insfficiently Prpose of the stdy is to rn theoretical and compter research of the dependences between velocity change of driving and driven gears cased by control gear movement in compond epicyclic transmission with composite planet gears set. 2. Reslts and discssion The article smmarizes the advantages of the method and devices for continosly variable speed change via stepped-planet epicyclic gearing with a closed circit hydrosystem. Those advantages inclde the possibility of speed change process atomation; dynamic loads redction; decreased components wear de to the absence of friction relationships, and simplified design. Strctre and operating principle of speed change device shown in Fig. 1, where yo can see the simplified scheme of epicyclic gearing (Fig. 1a) and a closed circit hydrosystem (Fig. 1b). The epicyclic gearing consists of a central gear 1 (sn gear), planets set 2, ring

Method and device for speed change by the epicyclic gear train with stepped-planet... 15 gear 3 (annls) and carrier 4 monted in framework 5.

3 Method and device for speed change by the epicyclic gear train with stepped-planet gear 3 (annls) and carrier 4 monted in framework 5. Planets set 2 is a pair of rigidly connected and longitdinally arranged gears of different radii and teeth nmber of z2 і z2. The closed circit hydrosystem 6 attached to the framework 5 and engaged with the control gear, i.e. annls, throgh the gearing 7. Hydrosystem 6 consists of hydralic pmp 8, pipelines 9, reglating throttle valve 10, check valve 11 and flid reservoir 12. Fig. 1. Epicyclic gearing with closed circit hydrosystem: a kinematic scheme, case of sn gear sed as inpts and annls control element; b scheme of closed circit ω4 = f ω3, ω1, 13 for ω1 = 100 rad/s hydrosystem; c graphical dependences ( ) In this case, speed change of the driven element carrier 4, is performed via annls 3. Sn gear 1, being a driving element, revolves with anglar velocity ω1 = const, so by means of closed circit hydrosystem 6 it is possible to change smoothly the velocity of the driven element carrier 4 (ω4). Annls 3, throgh the gearing 7, sets in motion the pmp 6, which pmps the flid in closed circit hydrosystem 6 consisting of pipelines 9 and so far open throttle valve 10. If we close the reglating throttle valve 10 it will stop the flow in hydrosystem 6, the pmp 6 will trn immovable and so will the annls 3 (ω3 = 0). Ths, depending on the bandwidth of reglating throttle valve 10, anglar velocity of annls 3 (ω3) changes from zero point to certain maximm vale ω3max, while changing the speed and possibly rotation direction of the carrier 4 (ω4). The relationship between anglar velocities in this transmission can be derived from well-known formla [3, 10] for fixed carrier train ratio: ω ω ω4 = 1 13 (1)

4 16 Volodymyr MALASHCHENKO, Oleh STRILETS, Volodymyr STRILETS where 13 fixed carrier train ratio between sn gear 1 and annls 3. Fig. 1a, illstrates the scheme of compond epicyclic gearing with planets set 2 made of a pair of rigidly connected and longitdinally arranged gears of different radii and teeth nmber of z2 і z2. Here, the sn gear 1 (z1) meshes with large planet 2 (z2), and the small planet 2 (z2 ) meshes with annls 3 (z3). Both meshes are external. Then, the fixed carrier train ratio will be: z = 2 z zz = z1 z2 zz (2) For greater clarity of the speed change natre in this device, we obtained ω4 = f ω3, ω1, 13 from the formla (1) sing a compter graphic dependences ( ) modeling. We sed different fixed carrier train ratio 13 = and anglar velocities ω1 of a driving gear. Those graphic dependences obtained for ω1 = 100 rad/s are showed at Fig. 1c. The next case considered is a similar compond epicyclic gear train with the control element carrier 4 (Fig. 2a). This time, carrier 4 is engaged with closed circit hydrosystem 6 throgh gearing 7, sn gear1 sed as inpts and annls3 sed as otpts. Fig. 2. Epicyclic gearing with closed circit hydrosystem: a kinematic scheme, case of sn gear sed as inpts and carrier is a control ω3 = f ω4, ω1, 13 for ω1 = 100 rad/s element; b graphical dependences ( ) If sn gear 1 is a driving element with anglar velocity ω1 = const, then changing the velocity of the carrier 4 (ω4) by means of closed circit hydrosystem 6 will transform the velocity of driven element annls 3 (ω3). In that case, carrier 4,

Method and device for speed change by the epicyclic gear train with stepped-planet... 17 throgh the gearing 7, sets in motion the pmp 6, which pmps the flid in closed circit hydrosystem 6.

5 Method and device for speed change by the epicyclic gear train with stepped-planet throgh the gearing 7, sets in motion the pmp 6, which pmps the flid in closed circit hydrosystem 6. Changing the bandwidth of reglating throttle valve 10 will reslt the increase of carrier 4 anglar velocity (ω4) from zero point to certain maximm vale ω4max, and the same time changing the velocity of the annls 3 (ω3). The relationship between anglar velocities can be fond from expression, where ω4 is variable: ω1 ω4(1 13 ) ω3 = 13 (3) obtained graphic dependences ( ) The expression (3) had been also programed, and for the case considered, we ω3 = f ω4, ω1, 13 for initial data same to the previos. Graphic dependences obtained for ω1 = 100 rad/s are showed at Fig. 2b. There is third case, also shold be mentioned, when driving element is a annls 3 and driven is the carrier 4 (Fig. 3a). Speed management is exected throgh sn gear 1 by means of closed circit hydrosystem 6, when we increase or decrease the bandwidth of throttle valve 10. Fig. 3. Epicyclic gearing with closed circit hydrosystem: a kinematic scheme, case of annls sed as inpts and sn gear is a control ω4 = f ω3, ω1, 13 for ω3 = 100 rad/s element; b graphical dependences ( ) The relationship between anglar velocities in sch transmission is described by the same expression (1), bt now ω1 is variable

6 18 Volodymyr MALASHCHENKO, Oleh STRILETS, Volodymyr STRILETS Again, for greater clarity of the speed change natre, we obtained graphic de- ω4 = f ω1, ω3, 13 from the same formla (1), bt with variable ω1, s- pendences ( ) ing a compter modeling. Graphic dependences obtained for fixed carrier train ratio 13 = and ω1 = 100 rad/s are showed at Fig. 3b. 3. Conclsions 1. Graphic dependences of velocity change in compond epicyclic gear trains with a closed circit hydrosystem, obtained by means of compter modeling, clearly confirming possibility of speed changes management between the driving and driven elements. 2. The applied research method of the dependences between the velocities of the elements in compond epicyclic gear trains with a closed circit hydrosystem, considering a control element to be either annls or carrier or sn gear, can be also applied to other compond epicyclic gearing analysis. 3. The reslting graphic dependence can be sed in designing of new devices for speed changes management and they are a scientific basis for frther research of mechanical means in engineering. References 1. Bahk C.J., Parker R.G.: Analytical investigation of tooth profile modification effects on planetary gear dynamics. Mechanism and Machine Theory, Iss. 70, Elsevier, Höhn B.R., Stahl K., Gwinner P.: Light-weight design for planetary gear transmissions. Gear Technology, Sept. 2013, Randall Pblications LLC, Kinytskyi Y.T.: Theory of mechanisms and machines. Nakova Dmka, Kyiv Malashchenko V.O., Strilets O.R., Strilets V.M.: Classification of methods and devices of the speed change process management in engineering. Hebezege nd Fördermittel, Iss. 3, Odessa Malashchenko V.O., Strilets O.R., Strilets V.M.: Overview and analysis of methods and devices of stepped speed change management in engineering. Blletin of National University of Water Management and Natre Resorces Use, Iss. 70, Rivne Pawar P. V., Klkarni P.R.: Design of two stage planetary gear train for high redction ratio. International Jornal of Research in Engineering and Technology, Vol.04, Iss. 06, esat Pblishing Hose, Bangalore Strilets O.: Speed change management via differential gear. Mashynoznavstvo, Iss. 6 (120), Lviv 2007.

7 Method and device for speed change by the epicyclic gear train with stepped-planet Strilets O.R.: Jstification of the speed change management capability via differential gearbox. Blletin of Engineering Academy of Ukraine, Iss. 2, Kyiv Strilets O.R.: Overview and analysis of methods and devices of speed change management in engineering. Abstracts of the 12 th International Symposim of Ukrainian Mechanical Engineers in Lviv, Uicker J.J., Pennock G.R., Shigley J.E.: Theory of Machines and Mechanisms. Oxford University Press, New York 2003.

8 20 Volodymyr MALASHCHENKO, Oleh STRILETS, Volodymyr STRILETS

INFLUENCE OF THE INCORRECT SETTINGS OF AXIAL COMPRESSOR INLET VARIABLE STATOR VANES ON GAS TURBINE ENGINE WORK PARAMETERS

Jornal of KONES Powertrain and Transport, Vol. 19, No. 3 01 INFLUENCE OF THE INCORRECT SETTINGS OF AXIAL COMPRESSOR INLET VARIABLE STATOR VANES ON GAS TURBINE ENGINE WORK PARAMETERS Pawe Wirkowski Polish