Dynamic Features of a Planetary Speed Increaser Usable in Small Hydropower Plants

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1 Dynamic Features of a Planetary Speed Increaser Usable in Small ydropower Plants JALIU CODRUA, SAULESCU RADU, DIACONESCU DORIN, NEAGOE MIRCEA, CLIMESCU OLIVER Product Design and Robotics Department University ransilvania of Brasov Address Eroilor 9, Brasov ROMANIA cjaliu@unitbv.ro Abstract: - he planetary chain transmission analyzed in this paper as a speed increaser for small hydropower plants is proposed by the authors. he dynamic model of the chain speed increaser is presented in the paper, based on Lagrange and Newton-Euler methods. he paper approaches the appropriate kinematical and dynamic features of the transmission. he dynamic response is obtained by means of Matlab-Simulink software. Key-Words: - planetary speed increaser, dynamics, numerical simulation, small hydro. Introduction Usually, the speed increasers from the small hydropower plants multiply the input angular speed from to 5 times [,7]. But in the case of using electric generators with medium or high nominal speeds, the plant must include gearboxes with multiplication ratios over 5. he paper analyzes the case of a speed increaser with a multiplication ratio of, which can be used either in small hydro plants or wind turbines. he analyzed transmission is an innovative planetary chain increaser, which was proposed by the authors. he paper presents its dynamic modeling, as the first step in the design of the small hydropower plant control system. he paper approaches the appropriate kinematical and dynamic features of the speed increaser, based both on Lagrange and Newton-Euler methods. he dynamic response of the aggregate composed of a turbine speed increaser - generator is obtained by means of Matlab-Simulink software. m J a) J b Kinematical and Dynamic Aspects he first step in dynamical modelling consists in defining the structural and kinematical aspects of the transmission. hus, the planetary transmission contains: a fixed sun gear (, ), a satellite gear (), a semicoupling with pins () and a carrier (). he internal kinematical ratio i 0, the transmission ratio i, the interior efficiency η 0 and the transmission efficiency η can be calculated by means of relations () () [4,5,6]: ω ( ) = z = = = + + i i i () ω z DC Motor b) c) ω ω b, b m, m Brake d) Fig.. he scheme of the chain planetary increaser: a) the structural scheme, b) the dynamic scheme for the input element, c) the dynamic scheme for the output element and d) the block scheme of the considered machine (DC motor = water turbine, brake = electric generator). ISSN: ISBN:

2 ω ω ω = () i = = ω ω η0 =η =η η = = x ω η0 η =η = = () ω z where: i xy is the transmission ratio from element x to element y, while element z is considered blocked; ω represents the relative speed between elements x and xy y, and x from rel. () is given by ω ( ) x= sgnω = = sgn sgn, []. ω he transmission can be used in two structural cases: z < z and z > z. he multiplication ratio and the efficiency of the speed increaser in the two cases are represented in Fig.. he diagrams from Fig.,a highlight the fact that, for a multiplication ratio i =, the speed increaser with z < z has a smaller overall dimension ( z = 4, z = ) than in the case z > z ( z = 4, z = 6 ). he efficiency of the speed increaser with z < z is higher than in the second case (see Fig.,b). a) 6 4 z=4, z>z 0 z=4, z<z z b) -0. i efficiency z=4, z=6 z=4, z= Fig.. Simulations for the planetary speed increaser in the cases z<z and z>z of: a) the multiplication ratio and b) the efficiency. i Imposing the value of the transmission multiplication ratio at i =, the transmission ratio is done by relation (4): i = = i = = 0. 8 (4) i he angular speeds and accelerations transmission functions (rel. 5) can be established based on relation (), while the moments transmission function (rel. 6) based on relation () : ω i = ω ω ε ω = = ω ; ε = = ε (5) i i η=η ω = ω i η = ; (6) - in the case of neglecting friction, the moments transmission function is given by the following relation: = i = = 0. 8 ; - in the case of considering friction, the moments transmission function is: = i η = = Premises for Dynamic Modeling he speed increaser dynamic modeling relies on the following premises: in the dynamic modeling, the inertial effects due to the satellite gears rotation are neglected (their masses being considered in the axial inertial moment of the afferent carrier shaft), while the inertial effects of the mobile central elements are considered integrated into the shafts that materialize the external links of the planetary gears; under this premise, the static correlations between the external torques of each planetary gear are valid, while the dynamic correlations interfere only for the shafts that materialize the planetary gears external links. he mechanical inertia momentums of the two shafts (see Fig. ) are: J = 0.05; J = 0. 0 [ Kgm ] (7) the rubbing effect is considered by means of the efficiency η; the real machine (water turbine speed increaser generator) is replaced on the experimental stand by a machine of type: DC Motor increaser brake, in which the motor and the brake have the following mechanical characteristics: m = 0.ω m + 0 ; b = ωb [ Nm ] (8) ISSN: ISBN:

3 Fig. he Simulink scheme that models the motion equation of the planetary speed increaser in the numerical simulations, the following values for the kinematical and dynamic parameters are considered: - the satellite and sun gears teeth numbers are z = 4, z =, - the efficiencies of the pin coupling and chain transmission areη =.995, η = 4 he Dynamic Model In the dynamic modeling, the main objective is to determine the transmission functions for the angular speeds, accelerations and moments, relative to time: ω m = ωm( t), ω = ω( t), ω = ω ( t), ωb = ωb( t) ε m = ε m( t), ε = ε( t), ε = ε ( t), ε b = ε b( t) (9) m = m( t), = ( t), = ( t), b = b( t) he dynamic modeling is made by means of Fig., b,c and d, for the following cases: he motion equation is modeled by neglecting friction, and he motion equation is modeled by considering friction. 4. Case I, friction is neglected In this case the Lagrange method is being used: d Ec Ec = Q (0) dt ω ϕ According to Fig., the kinetic energy and generalized force have the following forms: E c = ( J ω + J ω) ; Q= m i + b () in which J, represents the mechanical inertia momentum of the input element, respectively J, for the output element. Deriving E c relative to time, it is obtained: d Ec d Ec =ε J+ε J ; = 0 () dt ω dt ϕ From relations () and () it results: ε J +ε J = m i + b () By replacing the known parameters into relation (), the dynamic equation when neglecting friction outcomes: [ J + J ( ) ] ( i ) ε (4) + ω[ 0 ] 0 ( ) = 0 After numerical replacements, the following motion equation results: ε ω = 0 (5) 4. Case II, friction is considered In this case, according to Fig.,b, c and d, it can be written the following system of equations, using the Newton-Euler method: + + = 0; i η + = 0; (6) Jε = m ; J ε = b. By solving system (6) and by taking into account friction, the equation used for modeling the machine dynamic system is obtained: [ J + J ( ) η] ( i ) ε + (7) + ω [ 0 η] 0 ( ) η = 0 After numerical replacements, the following motion equation results: ε ω = 0 (8) ISSN: ISBN:

4 5 Numerical Simulations he values of the output and input angular speeds in state-state regime ( ε = 0 ) are obtained from relations (5) and (8): - when friction is neglected: ω =.0, ω = 0. - when friction is considered: ω =.4508, ω = he Simulink scheme that models the motion equation of the planetary speed increaser is presented in Fig.. he machine dynamic response, considering the speeds, accelerations and moments, as functions of time, of the motor, speed increaser and brake are drawn in the Fig. 4. a) b) c) d) e) f) Fig. 4 Dynamic response of the aggregate: motor angular speed (a), input angular speed (b), output angular speed (c), brake angular speed (d), motor angular acceleration (e), input angular acceleration (f) ISSN: ISBN:

5 g) h) i) j) k) l) Fig. 4 Dynamic response of the aggregate: output angular acceleration (g), brake angular acceleration (h), motor moment (i), input moment (j), output moment (k) and brake moment (l). 4 Conclusion ) In certain conditions, the considered transmission can function in two constructive situations: z<z and z>z, the first one having higher values of the efficiency and a smaller overall dimension. ) he theoretical aspects, from which the dynamic response was obtained, are presented in the paper; the mechanical momentums of inertia and the motor mechanical characteristic (belonging to the turbine) and brake mechanical characteristic (belonging to the generator) were considered. ) As the dynamic modeling is being accomplished in order to compare the theoretical results with the experimental ones, obtained on the stand, the turbine is being replaced with a DC engine, and the generator is being replaced with a brake. he considered inertia mechanical momentums (see Fig. ) have as an input element, the engine rotor, the entering shaft with it s appropriate rolls, while for the output element, the exit shaft, brake rotor and the inertial effect of the satellite considered as a concentrated mass. 4) he analyzed planetary chain transmission increases the input speed times and decreases the input moment 5.88 times (see Fig. 4). ISSN: ISBN:

6 5) he system consisting of motor, speed increaser, brake starts practically, in the both cases, in about 0.4 s, after which enters in the steady-state regime. 6) he dynamic model is useful in the design of the control system for the small hydro stations and wind turbines. he system control program can be established by considering certain environmental conditions/seasons and by replacing the motor and the brake from the dynamic modeling with a turbine and a generator. 7) Based on the dynamic modeling, the authors will accomplish the design, manufacturing and testing of the speed increaser for an off-grid hydropower station in the framework of a research project. 5 Acknowledgements he authors will accomplish the design, manufacturing and testing of the speed increaser for stand-alone hydropower stations in the framework of the research project Innovative mechatronic systems for micro hydros, meant to the efficient exploitation of hydrological potential from off-grid sites, ID_40. he preparation and publishing of this paper were possible with the financial support of this research project. 6 CORRESPONDING ADDRESS Professor dr. eng. Codruta Jaliu ransilvania University of Brasov, Product Design and Robotics Department Eroilor 9, Brasov, Romania Phone/Fax: , cjaliu@unitbv.ro References: [] American Chain Association, Standard andbook of Chains: Chains for Power ransmission and Material andling, nd Edition, Dekker Mechanical Engineering [] Diaconescu, D., Products Conceptual Design (Romanian), ransilvania University Publishing ouse, Brasov, 005 [] arvey, A., Micro-hydro design manual, DG Publishing ouse, 005. [4] Jaliu, C., Diaconescu, D.V., Neagoe, M. and Săulescu R., Dynamic features of speed increasers from mechatronic wind and hydro systems, Proc. of EUCOMES 08, nd European Conf. on Mechanism Science, pp. 55-7, September 008, Springer Publishing ouse, Cassino, Italy, 008. [5] Neagoe, M. et al., A Conceptual Design Application Based On A Generalized Algorithm. he 9 th International DAAAM Symposium. pp , rnava, Slovakia, 008. [6] Neagoe, M., Diaconescu, D.V., Jaliu, C., Pascale, L., Săulescu, R. and Siscă, S., On a New Cycloid Planetary Gear used to Fit Mechatronic Systems of RES, OPIM 008. Proc. of the th Int. Conf. on Optimization pf Electrical and Electronic Equipment. Vol. II-B. Renewable Energy Conversion and Control, pp , Braşov, Romania, May 008, IEEE Catalogue 08EX996, 008. [7] Von Schon,.A.E.C., ydro-electric Practice - A Practical Manual of he Development of Water, Its Conversion o Electric Energy, And Its Distant ransmission, France Press, 007. ISSN: ISBN: