Design and numerical characterization of a new planetary transmission

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Design and numerical characterization of a new planetary transmission BALBAYEV, Gani, CECCARELLI, Marco and CARBONE, Giuseppe <http://orcid.

1 Design and numerical characterization of a new planetary transmission BALBAYEV, Gani, CECCARELLI, Marco and CARBONE, Giuseppe < Available from Sheffield Hallam University Research Archive (SHURA) at: This document is author deposited version. You advised to consult publisher's version if you wish to cite from it. Published version BALBAYEV, Gani, CECCARELLI, Marco and CARBONE, Giuseppe (2014). Design and numerical characterization of a new planetary transmission. International journal of novative technology and research, 2 (1), Copyright and re-use policy See Sheffield Hallam University Research Archive

2 GANI BALBAYEV Almaty University of Power Engeerg and Telecommunication, Almaty, Kazakhstan MARCO CECCARELLI University of Casso and South Latium, Casso, Italy GIUSEPPE CARBONE University of Casso and South Latium, Casso, Italy. Abstract This paper describes design and characterization of a novel planetary transmission that can be used to adjust transmission ratio accordg to externally applied load. A basic modelg has been formulated to characterize both its design and operation. A detailed 3D CAD model has been proposed order to vestigate operation feasibility of proposed design solution. A proper dynamic model has been developed with MSC ADAMS softw. Simulation tests have been carried out and results discussed to validate proposed design solution. Key words: Mechanical Transmissions, Gears, Planetary Gears, Design, Simulation. I. INTRODUCTION Gearboxes used various types of dustrial machery to provide suitable torque while reducg speed from a rotatg power source by usg gear ratios. Gearboxes used many applications, such as wd turbes, conveyors, dragles, bridges and many or machers. Gears also used differential drives of automobiles, fal drives of tractors and heavy macheries maly as reducer. The efficiency of gear tras depends on many factors such as type and profile of teeth profile, contact stresses, number and type of beargs. These factors have been studied with recent approaches [3], [10] and [13]. Planetary gear transmissions commonly used applications where a large speed reduction is required as poted out [12] and [8]. Several design solutions have been proposed literature, like for example [5], [14] and [1]. For example a cambased fitely variable transmission can be used for contuously variable transmission, which can also achieve any transmission ratio, [5]. This mechanism consists of two ma parts, namely a cam mechanism and a planetary gear set. Cam-based CVT (contuously variable mechanism) can be more complex than ors, [5]. In case of a speed reducer, a gear box with conical gears consists of 8 conical gears. Two of m horizontal and 6 pions located vertically. Each pairs of pions locked toger. But this mechanism design order to obta any speed ratios it is necessary to change value of pion or horizontal gear, [14]. Magnetic planetary gears can be also a solution for gearboxes, when y consist of a sun gear, four planetary gears, and a rg gear. But each gear must have an axially permanent magnet that is sandwiched between two yokes made of electromagnetic soft iron. Magnetic gears have ma advantage for a low mechanical loss, but transmission torque is usually very low as poted out [11]. Planetary gears can be designed as a contuously variable transmission as proposed for example [4]. This mechanism can change gear ratio dependg on load through two degrees of freedom and eventually by usg a brake, [4]. Theoretical and experimental study of pushg CVT dynamics is presented [1], where work is focused to design advanced CVT systems with improved efficiency. A mechanism with a planetary gear set and a torque converter is designed as a contuously variable transmission [2]. This mechanism has two degrees of freedom and makes uses of an external torque to start movement, [2]. Open issues can be still identified efficiency smoothly changg reduction ratio dependg on external load to output shaft. This paper describes a design of a new planetary transmission with two degrees of freedom. The ma purpose of this new planetary transmission with two degrees of freedom is related to capability at adaptg operation to variable loadg conditions by preservg efficiency and put-output load ratio. Basic prciples of this type of gear box presented [6] and [7] and this paper gives furr developments efficiency of planetary transmission. The proposed design solution provides a motion of output lk with a speed that is versely proportional to shaft loadg. These features suitable for usg proposed design practical applications such as differential planetary gear box transmissions for vehicles, metal cuttg tools, wd turbes and or transmission applications needg smooth control of ratio reduction but adaptation to a variable load. A proper dynamic model has been developed with MSC ADAMS softw to provide formation on feasibility of proposed design solution. Simulation tests have been carried out and results discussed for validatg proposed design and characterizg its operation. II. THE IDEA FOR A NEW PLANETARY TRANSMISSION A planetary mechanism contas at least one rigid body which rotates about its own axis and at same ISSN All rights Reserved. Page 735

3 time revolves about anor axis. Pots of this body will generate epicycloids or hypocycloids trajectories. Therefore a planetary mechanism is often called as an epicyclic or cyclic mechanism. A planetary mechanism can be obtaed by mountg a rigid body that is often referred to as a planet, on a crank p. The crank is generally called arm or carrier, [9]. The proposed new planetary transmission can be considered a CVT with a planetary gear set. In this paper a new solution is considered for improvg efficiency of planetary transmissions. This mechanism has two mobile planetary gear sets with an asymmetrical design. The asymmetrical design gives special operation features. The special operation features can be recognized smoothly changg reduction ratio as dependg on load of output shaft. Referrg to Fig.1 new planetary transmission is conceived with two degrees of freedom with a mechanism consistg of an put carrier H 1, an output carrier H 2, central (sun) gears 1 and 4, which fixed on a shaft, satellites 2 and 5, central ternal gears 3 and 6 which fixed toger. Gears form a closed mechanical cha with a differential operation. Carrier H 1 transfers put drivg force to closed mechanical cha and carrier H 2 transfers output resistance force. Motion starts at fixed output carrier with one degree of freedom. At this time satellite 5 is output lk. To transmit motion from put carrier H 1 to output carrier H 2 satellite 5 must be locked and this can be obtaed thanks also to friction at gear contacts. This is peculiarity of proposed system. The put carrier H 1 moves gear 2 that pushes both gears 1 and 3 that transmit different forces to gears 6 and 4 correspondgly. Thus, gear 5 moves by different forces comg from its contacts with gears 6 and 4, and refore carrier H 2 moves. In addition mechanism will be able to work with two degrees of freedom because of possibility of activatg a second degree of freedom when satellite 5 will be unlocked by overcomg frictions at gear teeth contacts. Because of its functiong this mechanism can be applied as gearbox of cars, metal cuttg maches and where is necessary smoothly to change reduction ratio of transmissions. This mechanism can start movement without usg additional device, when force can overcome friction on satellites. This planetary transmission can change reduction ratio like CVT as dependg on an external load of output carrier. Ma design characteristics of proposed design related to two put mobile lks, namly two degrees of freedom, stepless operations, smoothly and automatically changg reduction ratio dependg on load at output shaft. The operation advantages of this mechanism smoothly and automatically changg reduction ratio dependg on load of output lk and possibility to start movement without usg any additional device. This mechanism can be a suitable transmission solution for any non constant operation, sce it is able to adapt its operation to variable load. (а) (b) Figure 1 A kematic scheme for a new planetary gear box with design parameters: (a) longitudal view; (b) cross-section view. A kematic characterization of mechanism can be expressed as function of parameters of external torques on carriers M H1, M H2 and put angular velocity ω H1. Referrg to Fig.1, kematic relations among angular velocities of gears with z 1, z 2, z 3, z 4, z 5, z 6 teeth can be expressed form 1 H1 u (1) 13 3 H1 1 H 2 ( H 2) u (2) 46 3 H 2 Where ( 2) z6 u H 46 (3) z H 2 H1 H1 / H 2 4 M M (4) When z i number of teeth gear (i=1,..,6). From Eqs. (1) and (2) angular velocities ω 3, ω 1 of gears 3 and 1 can be obtaed as ( u 1) ( u 1) ( H 2) 13 H1 46 H 2 3 (5) ( H 2) u13 u46 1 u13 ( 3 H1) H1 (6) A fairly easy numerical example can be carried out for an application for a wd turbe, Fig.2. Assumg from wd flow ω H1 =100 rpm and M H1 = 15 ; M H2 = 14, (Fig.1), output and termediate angular velocities ω H2, ω 1, ω 3 and ternal forces can be computed with proposed model through Eqs. (1) to (6) by considerg ω 4 = ω 1, ω 6 = ω 3. From Eq. (4) angular velocity of output carrier is computed as ω H2 = 75 rpm. From Eqs. (5) and (6) angular velocities of gears 1 and 3 computed as ω 1 =250 rpm and ω 3 =50 rpm, respectively. ISSN All rights Reserved. Page 736

Figure 2 A wd turbe with a proposed planetary gear box: (1-blades; 2-put shaft; 3-planetary gear box transmission 4-output shaft; 5-generator; 6-tower). III.

3 shows an exploded CAD design of planetary gear box with followg ma components, referrg to Fig.

satellite; 12-put carrier. The full mechanical design of mechanism with housg is shown Fig.4. Figure 3 A CAD exploded assembly of a new gear box design.

4 Figure 2 A wd turbe with a proposed planetary gear box: (1-blades; 2-put shaft; 3-planetary gear box transmission 4-output shaft; 5-generator; 6-tower). III. A MECHANICAL DESIGN AND VIRTUAL MODEL A CAD design of a gearbox with planetary gear set has been worked out Solid Works softw. Fig.3 shows an exploded CAD design of planetary gear box with followg ma components, referrg to Fig.1: 1-output carrier; 2-bearg; 3-output satellite; 4- spdle of output satellite; 5-bearg; 6-bearg of ternal gears; 7-gearshuft; 8-sun gear; 9-epicyclic gears; 10-put satellite; 11-spdle of put satellite; 12-put carrier. The full mechanical design of mechanism with housg is shown Fig.4. Figure 3 A CAD exploded assembly of a new gear box design. The proposed planetary transmission consists of a mechanical planetary gear set without additional devices such as torque converters or electronic parts. General design characteristics have been selected for practical applications of transmission, like for example, wd turbe stallations. A wd turbe stallation can be identified, for example, by referrg to a small wd turbe of 5 kw power and with average wd speeds of m/s, Fig.2. All geometrical parameters have been defed with CAD model Figs.3 and 4. The design parameters can be sized for wd application Fig.2 with a maximum high D ( Fig.1b) of 180 mm and a maximum longitudal size L ( Fig.1a) of 110 mm. The put and output shafts have a diameters of 32 mm and 30 mm, respectively. The overall weight is 5 kg if made of steel. Figure 4 Mechanical design of a new planetary gear box Fig.2: 1-output carrier; 2-bearg; 3-housg; 4-gear shaft; 5-output satellite; 6-epicyclic gears; 7-put satellite; 8-cover; 9-sun gear; 10-put carrier. IV. SIMULATION RESULTS A dynamic simulation of planetary gear box has been carried out by usg MSC ADAMS softw. The MSC ADAMS model of proposed planetary gear box is presented Fig.5. Input values such as angular velocity, put and output torque, stiffness, dumpg coefficients, and friction forces have been defed accordgly as listed Table 1. Input angular velocity and torque have been set as a constant values of 100 rpm and 15. Output torque is variable. All gears spur gears with module 1 mm. Friction coefficient of gears has been set as equal to 0.2 by referrg to a contact of steep surfaces. Table 1 summarizes ma or parameters that have been assumed by referrg to feasible values for a real case of study considerg material, penetration depth and force exponent. All geometrical dimensions have been set as by referrg to models Figs. 3 and 4. After settg above-mentioned parameters significant attention has been addressed properly modelg all constrats and jots order to achieve a reliable operation of proposed model as a feasible mechanical design. Figure 5 ADAMS model of gear box design Fig. 3 and 4: a) ADAMS model; b) contacts between ternal gear and satellite; c) contacts between sun gear and satellite. ISSN All rights Reserved. Page 737

5 Gani Balbayev* et al. / (IJITR) INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY Y AND RESEARCH Volume No.2, Issue No. 1, December January 2014, TAB BLE 1 Inpu ut parameters for simulation of model Fig. 4 Parameter Value Inpu ut angular velocity Input torqu ue Outp put angular velocity Plots Fig. 6 Output torque Variablee (14-15) Dampg 40 Young s modulus E+005 Density E-006 Penetration depth 0.1 Force exponent 1.8 Units rpm rpm N* *sec/mmm N/mm* m**2 kg/ /mm**3 mmm Several cases of study have been com mputed order to vestigate dyn namic behavior of prop posed transmission. In part ticular, prelimary tests have been carried out by considerg a constant put speed as 1000 rpm and torque ass 15 and variable outpu torque as The outpu torque is prescribed by alte ernative suitable ope eration n, y have been verif fied that outputt speed, accordance with expected smooth variable transmission ratio and constant outputt power. Examples of results thatt have been obta aed reported plot ts of Figs.6 to 12. Angular velocities of put and output epicyclic ternal gears presented Fig. 6. The epicyclic ternal gears rotate with same speed approximately of 108 rpm. Fig. 7 shows plotss of computed angular velocities of sun gears. The put and outpu sun gears rota ate with same speeds. Angular velocities of pu ut and outputt planet gears presented Fig. 8. Angular velocity of put planet gear approximately is 250 rpm. Angular velocity of outpu planet gearr approximately is 125 rpm. Fig. 9 shows plotss of computed torques of epicyclicc ternal gears. Torq que reaches 32 at 2.5 seco ond, after this time system works properly with app proximately value of 29. Fig. 10 shows plot of computed torques of sun gears and torq que valu ue approximately is 75. Computed results of conta act forces between gear rs presented Fig. 11 and 12. In Fig contact forces plotted as dur ng simulated motion for a full rotation of outp put shaf ft. Fig..11 shos ows plots of computed cont tactt forces between put satellite and ternal gear, whichh is related to Fig. 5 (c). Considerg curve Fig. 11, t approximately highest contact force of 1.1 N appears at 2.5 second and contact forc ce decreases to 0.2 N at 7..5 second. This suddenly change of contact forc ces at 2..5 second can be thought as due maly to friction at gear teeth cont tacts, whil le system is startg a motion. Next changg off contact forces at 7.5 second can be thought t due to variable applied load to output shaft. Computed results s of contact c forces of output planet gear and output t ternal i nal gear presented enteded Fig. 12, which h is related to Fig. 5 (b). The highesst contact force of 1.1 N appes pes at 2.5 second and contact ct force of 0.5 N is computed at 7.5 second. The values of contact ct forces crease by creasg ng values s off external ernal loads s on output shaft. Figure 6 Computed plot of angular speed of put and output ternal gears. Figure 7 Computed plot of angular speed of sun gears. Figure 8 Computed plot of angular speed of put (contuous le) ) and output (dot le) planet gears. Figure 9 Computed plot of f torque of ternal gears. Figure 10 Computed plot of torque of sun gears. Figure 11 Computed plot of contact forces between planet gears and ternal gears Fig.5 (c). ISSN http: :// w.ijitr.com All rights Reserved. Page 738

6 Figure 12 Computed plot of contact forces between planet gears and sun gears Fig.5 (b). V. CONCLUSION A planetary gear box with two degrees of freedom has been studied from aspects of mechanical design and kematic modelg. A mechanical design and 3D CAD model of a planetary gear box with two degrees of freedom have been proposed order to adapt operation to variable loadg. Design of planetary gearbox is shown kematic scheme. The formulated equations tested by numerical examples. A proper dynamic model and simulations have been carried out MSC ADAMS environment. Simulation results show that proposed planetary gear box has suitably constant output values both terms of speed and torque. The simulation results also show that proposed gear box smoothly changes reduction ratio at constant put speed. Contact forces between gears small enough to use proposed system under expected loadg conditions. VI. ACKNOWLEDGMENTS The first author likes to acknowledge JSC Center of International Program "Bolashak" of Republic of Kazakhstan for supportg his PhD study and research at LARM University of Casso and South Latium Italy, academic year REFERENCES [1]. Carbone, G., Mangialardi, L., Bonsen, B., Tursi, C., Veenhuizen, P. A. (2007). CVT dynamics: Theory and Experiments. Mechanism and Mache Theory 42(1): [2]. Crockett, J. S. (1990). Shiftless contuouslyaligng transmission. Patent of USA 4,932,928, Cl. F16H 47/08U.S.Cl. 475/51; 475/47. [3]. Fetvaci, C. (2010). Defition of volute spur gear profiles generated by gear-type sharper cutters. Mechanics Based Design of Structures and Maches 38(4): [4]. Harries, J. (1991). Power transmission system comprisg two sets of epicyclical gears. Patent of Great Brita GB (A). [5]. Derek, F., L., Dennis, W. H. (2006). The Operation and Kematic Analysis of a Novel Cam-based Infitely Variable Transmission. ASME 2006 International Design Engeerg Technical Conferences and Information engeerg conference l(3): 1-6. [6]. Ivanov, K. (2012). Design of Tood Contuously Variable Transmission Form of Gear Variator. Balkan Journal of Mechanical Transmissions (BJMT). 2(1): [7]. Ivanov, K. (2001). Force Adaptation of Two- Mobile Gear Mechanisms. Almaty: Kazgos INTI Publications,( Russian). [8]. Kaharman, A., Dg, H. (2010). A Methodology to Predict Surface Wear of Planetary Gears under Dynamic Conditions. Mechanics Based Design of Structures and Maches, 38: [9]. Levai, Z. (1968). Structure and Analysis of Planetary Gear Tras. Journal Mechanisms 3: [10]. Muni, D. V., Muthuveerappan, G. (2009). A comprehensive study on asymmetric ternal spur gear drives through direct and conventional gear design. Mechanics Based Design of Structures and Maches 37(4): [11]. Niguchi, N., Hirata, K. (2012). Transmission Torque Analysis of a Novel Magnetic Planetary Gear Employg 3-D FEM. IEEE Transactions on Magnetics 48(2): [12]. Patel, P. (2009). Design and Analysis of Differential Gearbox. Report, U.V. Patelcolliege of Engeerg, Kherva: Ganpat University. [13]. Thirumurugan, R., Muthuveerappan, G. (2011). Critical loadg pots for maximum fillet and contact stresses normal and high contact ratio spur gears based on load sharg ratio. Mechanics Based Design of Structures and Maches 39(1): [14]. Yaghoubi, M., Mohtasebi, S. (2010). Design and Simulation of a New Bevel Multi-Speed Gear box for Automatic Gearboxes. Science Journal Report and Opion, 2:1-7. ISSN All rights Reserved. Page 739

MARCO CECCARELLI University of Cassino and South Latium, Cassino, Italy

GANI BALBAYEV Almaty University of Power Engineering and Telecommunication, Almaty, Kazakhstan MARCO CECCARELLI University of Cassino and South Latium, Cassino, Italy GIUSEPPE CARBONE University of Cassino