Volodymyr MALASHCHENKO RESEARCH WORKS OF AFIT Lviv Polytechnic National University, Ukraine Issue 38, s. 13÷19, 2016 r. Oleh STRILETS Volodymyr STRILETS 10.1515/afit-2016-0002 National University of Water Management and Nature Resources Use, Rivne, Ukraine

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

The article describes new method and device for continuously variable speed change man- agement via compound epicyclic gearing with composite planet and closed circuit hy- drosystem, when the speed control element is either outer ring gear (annulus) or the carrier or sun gear. In each case, the control element connected to closed circuit hydrosystem and can be in motion or immovable depending on the bandwidth of hydrosystem’s regulating throttle. We had held theoretical research and received graphic dependences between ve- locities of driving, control and driven elements by means of computer programing.

Key words: speed change management, compound differential gear, stepped-planet gear set, closed circuit hydrosystem, speed control element.

1. Introduction

In the world of , there are widely known methods and devices for speed management that provide stepped or continuously variable change in veloc- ity by the value and direction with the use 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 consump- tion, the emergence of dynamic loads during the transition from one speed to an- other, even in case of synchromesh using. On the other hand, continuously variable speed devices have intense components wear due to the use of friction connections

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like brakes or lock-up . All abovementioned reduces the durability and reli- ability of certain device components and in general. Therefore, it causes the need in creation of new ways of speed management and devices, which elimi- nate those disadvantages. Advantages of using the planetary over other gear mechanisms has already been proven by a number of the world's scientists. Thus, 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 volume, and 96% higher torque density (torque/volume ratio). In [2] a study presented on the possibility of reducing the mass of the planetary gear by the use of the maximum number of satellites. Also, some scholars [1] studied the effect of the change of the tooth profile on the planetary gear dynamics. Our research focuses on the development of speed control devices by com- bining the epicyclic gear ( with two degrees of freedom) with a closed circuit 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 jus- tified [8]. The new patent-protected devices for speed change management via ep- icyclic gearing with closed circuit hydrosystem have been developed. Nevertheless, for the implementation of any mechanical means, the comprehensive study of kin- ematic and power parameters is required, but currently fulfilled insufficiently Purpose of the study is to run theoretical and computer research of the de- pendences between velocity change of driving and driven gears caused by control gear movement in compound epicyclic transmission with composite planet gears set.

2. Results and discussion

The article summarizes the advantages of the method and devices for contin- uously variable speed change via stepped-planet epicyclic gearing with a closed circuit hydrosystem. Those advantages include the possibility of speed change pro- cess automation; dynamic loads reduction; decreased components wear due to the absence of friction relationships, and simplified design. Structure and operating principle of speed change device shown in Fig. 1, where you can see the simplified scheme of epicyclic gearing (Fig. 1a) and a closed circuit hydrosystem (Fig. 1b). The epicyclic gearing consists of a central gear 1 (sun gear), planets set 2, ring

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gear 3 (annulus) and carrier 4 mounted in framework 5. Planets set 2 is a pair of rigidly connected and longitudinally arranged gears of different radii and teeth num- ber of z2 і z2’. The closed circuit hydrosystem 6 attached to the framework 5 and engaged with the control gear, i.e. annulus, through the gearing 7. Hydrosystem 6 consists of hydraulic pump 8, pipelines 9, regulating throttle valve 10, check valve 11 and fluid reservoir 12.

Fig. 1. Epicyclic gearing with closed circuit hydrosystem: a – kinematic scheme, case of sun gear used as inputs and annulus – control element; b – scheme of closed circuit ω= ωω (4) hydrosystem; c – graphical dependences 4fu( 31,,13 ) for ω1 = 100 rad/s

In this case, speed change of the driven element – carrier 4, is performed via annulus 3. Sun gear 1, being a driving element, revolves with angular velocity ω1 = const, so by means of closed circuit hydrosystem 6 it is possible to change smoothly the velocity of the driven element – carrier 4 (ω4). Annulus 3, through the gearing 7, sets in motion the pump 6, which pumps the fluid in closed circuit hy- drosystem 6 consisting of pipelines 9 and so far open throttle valve 10. If we close the regulating throttle valve 10 – it will stop the flow in hydrosystem 6, the pump 6 will turn immovable and so will the annulus 3 (ω3 = 0). Thus, depending on the bandwidth of regulating throttle valve 10, angular velocity of annulus 3 (ω3) changes from zero point to certain maximum value ω3max, while changing the speed and possibly rotation direction of the carrier 4 (ω4). The relationship between angular velocities in this transmission can be derived from well-known formula [3, 10] for fixed carrier train ratio:

ωω− (4) 13u13 ω4 = (1) − (4) 1 u13

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(4) where u13 – fixed carrier train ratio between sun gear 1 and annulus 3. Fig. 1a, illustrates the scheme of compound epicyclic gearing with planets set 2 made of a pair of rigidly connected and longitudinally arranged gears of different radii and teeth number of z2 і z2’. Here, the sun gear 1 (z1) meshes with large planet 2 (z2), and the small planet 2 (z2’) meshes with annulus 3 (z3). Both meshes are external. Then, the fixed carrier train ratio will be:

z z zz (4) =−−=2 3 23 u13  (2) z1 z 2′′ zz 12

For greater clarity of the speed change nature in this device, we obtained ω= ωω (4) graphic dependences 4fu( 31,,13 ) from the formula (1) using a computer (4) = modeling. We used different fixed carrier train ratio u13 1...10 and angular ve- locities 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 compound epicyclic gear train with the control element – carrier 4 (Fig. 2a). This time, carrier 4 is engaged with closed circuit hydrosystem 6 through gearing 7, sun gear1 used as inputs and annulus3 used as outputs.

Fig. 2. Epicyclic gearing with closed circuit hydrosystem: a – kinematic scheme, case of sun gear used as inputs and carrier is a control ω= ωω (4) element; b – graphical dependences 3fu( 41,,13 ) for ω1 = 100 rad/s

If sun gear 1 is a driving element with angular velocity ω1 = const, then chang- ing the velocity of the carrier 4 (ω4) by means of closed circuit hydrosystem 6 will transform the velocity of driven element – annulus 3 (ω3). In that case, carrier 4,

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through the gearing 7, sets in motion the pump 6, which pumps the fluid in closed circuit hydrosystem 6. Changing the bandwidth of regulating throttle valve 10 will result the increase of carrier 4 angular velocity (ω4) from zero point to certain max- imum value ω4max, and the same time changing the velocity of the annulus 3 (ω3). The relationship between angular velocities can be found from expression, where ω4 is variable:

ωω−−(1u(4) ) ω = 14 13 (3) 3 (4) u13

The expression (3) had been also programed, and for the case considered, we ω= ωω (4) obtained graphic dependences 3fu( 41,,13 ) for initial data same to the pre- vious. Graphic dependences obtained for ω1 = 100 rad/s are showed at Fig. 2b. There is third case, also should be mentioned, when driving element is a an- nulus 3 and driven is the carrier 4 (Fig. 3a). Speed management is executed through sun gear 1 by means of closed circuit hydrosystem 6, when we increase or decrease the bandwidth of throttle valve 10.

Fig. 3. Epicyclic gearing with closed circuit hydrosystem: a – kinematic scheme, case of annulus used as inputs and sun gear is a control ω= ωω (4) element; b – graphical dependences 4fu( 31,,13 ) for ω3 = 100 rad/s

The relationship between angular velocities in such transmission is described by the same expression (1), but now ω1 is variable

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Again, for greater clarity of the speed change nature, we obtained graphic de- ω= ωω (4) pendences 4fu( 13,,13 ) from the same formula (1), but with variable ω1, us- ing a computer modeling. Graphic dependences obtained for fixed carrier train ratio (4) = u13 1...10 and ω1 = 100 rad/s are showed at Fig. 3b.

3. Conclusions

1. Graphic dependences of velocity change in compound epicyclic gear trains with a closed circuit hydrosystem, obtained by means of computer 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 compound epicyclic gear trains with a closed circuit hydrosystem, considering a control element to be either annulus or carrier or sun gear, can be also applied to other compound epicyclic gearing analysis. 3. The resulting graphic dependence can be used in designing of new devices for speed changes management and they are a scientific basis for further research of mechanical means in .

References

1. Bahk C.J., Parker R.G.: Analytical investigation of tooth profile modification effects on planetary gear dynamics. “ and Machine Theory”, Iss. 70, Elsevier, 2013. 2. Höhn B.R., Stahl K., Gwinner P.: Light-weight design for planetary gear transmissions. “Gear Technology”, Sept. 2013, Randall Publications LLC, 2013. 3. Kinytskyi Y.T.: Theory of mechanisms and . Naukova Dumka, Kyiv 2002. 4. Malashchenko V.O., Strilets O.R., Strilets V.M.: Classification of methods and devices of the speed change process management in engineering. „Hebezeuge und Fördermittel”, Iss. 3, Odessa 2015. 5. Malashchenko V.O., Strilets O.R., Strilets V.M.: Overview and analysis of methods and devices of stepped speed change management in engineering. „Bulletin of National Uni- versity of Water Management and Nature Resources Use”, Iss. 70, Rivne 2015. 6. Pawar P. V., Kulkarni P.R.: Design of two stage planetary gear train for high reduction ratio. “International Journal of Research in Engineering and Technology”, Vol.04, Iss. 06, eSAT Publishing House, Bangalore 2015. 7. Strilets O.: Speed change management via differential gear. „Mashynoznavstvo”, Iss. 6 (120), Lviv 2007.

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8. Strilets O.R.: Justification of the speed change management capability via differential gearbox. „Bulletin of Engineering Academy of Ukraine”, Iss. 2, Kyiv 2015. 9. Strilets O.R.: Overview and analysis of methods and devices of speed change management in engineering. Abstracts of the 12th International Symposium of Ukrainian Mechanical Engineers in Lviv, 2015. 10. Uicker J.J., Pennock G.R., Shigley J.E.: Theory of Machines and Mechanisms. Oxford University Press, New York 2003.

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