REVISTA ROMÃNÄ DE AUTOMATICÄ - IPA SA

More documents

Recommendations

Info

26 REVISTA ROMÂNĂ DE AUTOMATICĂ * M 2( ω2) * M1( ω1 ) 4 * M 2 ( ω2) * M1( ω1 ) 3 3 2 2 -4 -3 -2 1 -1 1 -4 -3 -2 -1 -1 1 2 3 4 5 i -1 1 2 3 4 5 i -2 -2 -3 -3 -4 -4 Fig. 2. Graphic M 2 ( ω ) i = − . Fig. 3. Graphic * M ( ω ) i −1 1 * 2 1 M 3 ( ω ) 1 = − . * M ( ω ) i −1 1 * 3 1 The displacement moment M ( * 2 ω 2) , because the resistant moment is negative, it follows that the transmission equation i will be from the domain ( −∞ ,0) ∪ (1, ∞) . If i < 0 the values | M 2( ω2) | | M ( ) | , 3 ω * * M ( ω ) M ( ω ) 1 1 1 * 3 1 are subunitary, if this 1 < i < 2 is over-unitary and this 2 < i the first value is over-unitary and the second one is sub-unitary. In conclusion, for the solution where the values of the resistant moment are low then we’ll chose i < 0 and for the case when the resistant moment at the automobiles wheels are high will be obtained the solution i > 2 . * The movements stability. The solution ω 1 , * ω , ω is obtained from the (16) system and * 2 3 * it is stabile even if Ωi = ωi 0 − ωi , i = 1, 2, 3 are going through zero. In this way will be studied the stability after the first approximation. Are obtained the linear approximations: * * * M ( ω + Ω ) = M ( ω ) + Ω M ( ) , 1 1 1 1 1 1 1p ω1 * * * 2 2 2 2 2 2 2 p ω 2 M ( ω +Ω ) = M ( ω ) +Ω M ( ) , * M ( ω + Ω ) = M ( ω ) + Ω M ( ) (18) * * 3 3 3 3 3 3 3 p ω 3 where by M ip were noted the functions derivates M ( * i ω i ) . By replacing the equations (12) and taking into account the notations α = AC − B i 1− i) β = * 2 [ M ( ω ) + (1 − i) M ( ω )] 1 * 2 1p 1 3 p 3 ( * M 2 3 p 3 AC − B γ = AC − B ( ω ) , * 2 [ M ( ω ) + i M ( ω )] 1 * 2 2 p 2 3 p 3 , (19) one obtained the linearly system of differential equations Ω& Ω& 1 = αC +βB ) Ω 1+ ( βC+γB ) ( Ω 2 = αB +βA) Ω 1+ ( βB+γA ) ( Ω The characteristic equation reads αC + βB − r or αB + βA βC + γB βB + γA − r = 0 2 2 , (20) (21) 2 r + Dr + E = 0 (22) where D = −( αC + 2βB + γA) , E = ( αC + βB)( βB + γA) − ( αB + βA)( βC + γB) (23) By making the calculations, from equations (23), (19) are obtained the results 1 D = − AC − B 1 E = 2 AC − B 2 * * 2 2 { CM ( ω ) + AM ( ω ) + [ i A + 2i(1 − i) B + (1 − i) C] M } * * 2 * * 2 [ M ( ω ) M ( ω ) + (1 − i) M ( ω ) M ( ω ) + i M M ] 1p 1p 1 1 2 p 2 2 p 2 2 p 2 2 p 2 1p 3 p 3 p (24)
REVISTA ROMÂNĂ DE AUTOMATICĂ 27 For the evaluation of the signs of the of the parameters D, E are taking into account the inequalities: 2 2 A > 0; C > 0; AC − B > 0; i A+ 2i(1 − i) B + (1 −i) C > 0 2 (25) that are deduced from the element calculations from the relation (2) Therefore, if M ip ( ω * i ), i = 1, 2, 3 are negative, then D > 0 ; E > 0 , the equation (22) has real negative solutions or complex solutions with the real part negative and thus Ω 1 → 0 , Ω and the movement is stabile. 2 → 0 4. CONCLUSION REFERENCES [1] Pandrea, N., Popa D.: Mecanisme. Teorie şi aplicaţii CAD, Ed. Tehnică, Bucureşti, 2000. [2] Popa, D., Chiroiu, V., L. Munteanu, J. Onisoru, A. Iarovici: On the modeling of hybrid systems, Proc. of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science, vol. 8, nr. 1, 2007. [3] Teodorscu, P. P.: Sisteme mecanice. Modele clasice, Ed.Tehnică, Bucureşti, vol. 1-3, 1984-1988-1997. [4] Dudiţă, FL: Mecanisme, Ed. Universitatea din Braşov, 1977. The mechanism used to couple three power sources is a planetary mechanism with two degrees of mobility. For such a planetary mechanism one makes the cinematic and dynamic analysis, finally resulting the differential equations of motion. The obtained equations for the steady-state are simple, they being useful to model the mechanism that can equipped a hybrid automobile. AR4-5.doc
Page 1 and 2: RRA, Vol. XXI, Nr. 4, pag. 1- 4, 20
Page 3 and 4: REVISTA ROMÂNĂ DE AUTOMATICĂ 3 T
Page 5 and 6: REVISTA ROMÂNĂ DE AUTOMATICĂ 5 O
Page 7 and 8: REVISTA ROMÂNĂ DE AUTOMATICĂ 7 V
Page 9 and 10: REVISTA ROMÂNĂ DE AUTOMATICĂ 9 f
Page 11 and 12: REVISTA ROMÂNĂ DE AUTOMATICĂ 11
Page 25: REVISTA ROMÂNĂ DE AUTOMATICĂ 25
Page 51: REVISTA ROMÂNĂ DE AUTOMATICĂ 51

REVISTA ROMÃNÄ DE AUTOMATICÄ - IPA SA

Create successful ePaper yourself

Delete template?

Save as template?

REVISTA ROMÃNÄ DE AUTOMATICÄ - IPA SA