Диссертация (1025996), страница 20

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14 p.207. Zhang L. et al. Numerical Simulation Investigation on Flow Field of Axial BloodPump // Advances in Computer Science and Engineering. 2012. P. 223-229.159ПРИЛОЖЕНИЕП.1. Приведение модели динамики ротора к безразмерному видуПроведем обезразмеривание системы ((2.33), С. 55) с учетом введенных вТаблице 2 формул перехода. Тогда система (2.33) перепишется в видеEquation Chapter 1 Section 1x1′ = x2 ;cwηπr 2 S L2 lS L SβSx ′cm 2 x2 = −α 2 + cm S x x1 + m (−a1S L + a2 S L ) Sβ β1 + ...St2St2 2 iS+iSiS−iS0 i0 iAx iAx i+k A  −   + ... δS − ( x1S x − a1S L β1Sβ )  δS x + ( x1S x − a1S L β1Sβ )  x2 2 iS+iSiS−iS0 i0 iBx iBx i+k A  −   − ... δS x − ( x1S x + a2 S L β1Sβ )  δS x + ( x1S x + a2 S L β1Sβ ) −cwηπr 2 S L2 lS LΩSΩSβ β1 + Fx S F + Ax S F sin ( pSΩ tSt ) + ...+mΩ2 SΩ2eS x cos (ΩSΩ tSt );y1′ = y2 ;cwηπr 2 S L2 lS L SβSx ′cm 2 y2 = −β2 + cm S x y1 + m (a1S L − a2 S L ) Sβα1 + ...St2St2 2 i0 Si + iAy SiiS−iS0 iAy i −   + ...+k A  δS x − ( y1S x + a1S Lα1Sβ )  δS x + ( y1S x + a1S Lα1Sβ ) 2 2 i0 Si + iBy SiiS−iS0iByi+k A  −   + ... δS x − ( y1S x − a2 S Lα1Sβ )  δS x + ( y1S x − a2 S Lα1Sβ ) +cwηπr 2 S L2 lS LΩSΩ Sβα1 + Fy S F + Ay S F sin ( pSΩ tSt ) + ...160+mΩ2 SΩ 2eS x sin (ΩSΩ tSt );(П.1.1)α1′ = α 2 ;IxSβα 2 ′ = −I zSt2(ΩSΩcSβ β2 + m (a1S L − a2 S L ) S x y1 + ...2St)cma12 S L2 + a22 S L2 )(1 + km ) − 2a1a2 S L2 (1 − km ) α1 + ...(42 2 i0 Si + iAy SiiS−iS0 iAy i −   − ...+a1S L k A  δS x − ( y1S x + a1S Lα1Sβ )  δS x + ( y1S x + a1S Lα1Sβ ) +2 2 −i0 Si + iBy SiiSiS0 iBy i −   + ...−a2 S L k A  δS x − ( y1S x − a2 S Lα1Sβ )  δS x + ( y1S x − a2 S Lα1Sβ ) +M x S M + Bx S M sin ( pSΩ tSt ) + Ω2 SΩ2 γSβ ( I x − I z )cos(ΩSΩ tSt );β1′ = β2 ;IxSβSt2β2′ = I z(cΩSΩSβα 2 + m (−a1S L + a2 S L ) S x x1 + ...2St)cma12 S L2 + a22 S L2 )(1 + km ) − 2a1a2 S L2 (1 − km ) β1 − ...(422i0 Si + iAx Sii0 Si − iAx Si −   + ...−a1S L k A  δS x − ( x1S x − a1S L β1Sβ )  δS x + ( x1S x − a1S L β1Sβ ) 2 2 iS+iSiS−iS0 iBx i0 iBx i+a2 S L k A  −   + ... δS x − ( x1S x + a2 S L β1Sβ )  δS x + ( x1S x + a2 S L β1Sβ ) ++M y S M + By S M sin ( pSΩ tSt ) + Ω2 SΩ2 γSβ ( I x − I z )sin (ΩSΩ tSt ) ,где ( )′ – обозначена производная по безразмерному времени t .

Аргументы sin иcos – величины безразмерные, следовательно, масштаб SΩ =1.St161Вынесем S i2 за скобки и, разделив правые части уравнений (П.1.1) намножитель при переменной в левых частях, будем иметьx1′ = x2 ;cm S L Sβ St2cwηπr 2 S L2 lS L Stcm St2′x2 = −x1 +α2 +(−a1 + a2 ) β1 + ...Ixm2mS x22  i0 + iAxi0 − iAx+ −   + ...mS x  δS x − ( x1S x − a1S L β1Sβ )  δS x + ( x1S x − a1S L β1Sβ ) 222 2 k S S i0 + iBxi0 − iBx −   − ...+ A i t mS x  δS x − ( x1S x + a2 S L β1Sβ )  δS x + ( x1S x + a2 S L β1Sβ ) cwηπr 2 S L2 lS LΩStS F St2S F St2−β1 + Fx+ Axsin ( pt ) + Ω2e cos (Ω t );IxmS xmS xk A Si2 St2y1′ = y2 ;2 22cm S L Sβ St2cηπrSlSScSwLLtmty2′ = −β2 +y1 +(a1 − a2 )α1 + ...Ixm2mS x2 2 i0 + iAyii−k A Si2 St2 Ay0 −   + ...+mS x  δS x − ( y1S x + a1S Lα1Sβ )  δS x + ( y1S x + a1S Lα1Sβ ) 222 2 −i+iii k S S 0By0By+ A i t  −   + ...mS x  δS x − ( y1S x − a2 S Lα1Sβ )  δS x + ( y1S x − a2 S Lα1Sβ ) cwηπr 2 S L2 lS LΩStS F St2S F St2+α1 + Fy+ Aysin ( pt ) + Ω2e sin (Ω t );IxmS xmS xα1′ = α 2 ;Izcm S L S x St2′α 2 = − Ωβ2 +(a1 − a2 ) y1 + ...Ix2 I x Sβ+cm S L2 St24I x((a21(П.1.2))+ a22 )(1 + km ) − 2a1a2 (1 − km ) α1 + ...1622 2 −i0 + iAyii0Ay+a1 −   − ...I x Sβ  δS x − ( y1S x + a1S Lα1Sβ )  δS x + ( y1S x + a1S Lα1Sβ ) 222 2 +−iiii  k S S S 00ByBy−a2 A L i t  −   + ...I x Sβ  δS x − ( y1S x − a2 S Lα1Sβ )  δS x + ( y1S x − a2 S Lα1Sβ )  I S S2S S2+M x M t + Bx M t sin ( pt ) + Ω2 γ 1 − z  cos (Ω t );I x SβI x Sβ I x k A S L Si2 St2β1′ = β2 ;Izcm S L S x St2′β2 = Ωα 2 +(−a1 + a2 ) x1 + ...Ix2 I x Sβcm S L2 St2+a12 + a22 )(1 + km ) − 2a1a2 (1 − km ) β1 − ...(4I x()2 2 a1k A S L Si2 St2 i0 + iAxi−i0Ax− −   + ... δS x − ( x1S x − a1S L β1Sβ )  δS x + ( x1S x − a1S L β1Sβ ) I x Sβ22  a2k A S L Si2 St2 i0 + iBxi0 − iBx+ −  + ... δS x − ( x1S x + a2 S L β1Sβ )  δS x + ( x1S x + a2 S L β1Sβ ) I x Sβ I S M St2S M St2+ By+M ysin ( pt ) + Ω2 γ 1 − z sin (Ω t ). I x I x SβI x SβЗададим в качестве независимых единиц размерности следующие масштабыS x = δ,SL = l ,St =m,cmSi =P,R(П.1.3)где l – длина ротора, P – электрическая мощность, R – сопротивление,соответствующие единицам измерения: м, с, А.

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