simulation of torsion moment at the wheel set of the railway vehicle ...

Mt = k$ Di(12) 4. Torsion moment at a Slippage of the Wheel set1D i = i-i i0di0~ 0 =dt(13)~ 0in the complex domain i0=(14)sdi~~ = in the complex domain i =(15)dtswhere k – torsion constant of driving shaft (4) – Fig. 2. Thetorsion constant of the leaves part of the driving shaft (i.e. part ofthe driving shaft from the jagged reductor to the near monoblockwheel) is k 1 55310 6 Nmrad 1 . Torsion constant of the longerpart of the driving shaft (i.e. part of the driving shaft from thejagged reductor to the further monoblock wheel) is k 2 9.810 6 Nmrad 1 [3]; θ 0 – banking of driving shaft (4) induced bythe wheel-rail system.3. Resonance Frequency of the wheel setAsi =0kiJ m D 2e0 + $ d n o $ s + k2transfer function W M is:2(16)Based on the former equations, we made a program in MAT-LAB-SIMULINK to simulate the torsion moment at the wheelset. We received a chronological variety of the torsion moment ofthe longer part of the driving shaft according to Fig. 4 when westarted from this simulation program. We assumed that a slippageof the wheel set appeared because of a nuisance value of the tractioncoefficient atD/ F ot2= = 1 (The traction coefficient atMthis environment is defined by the following term: F 2 n $ QM0n27924.8849n 1 = = 023 . ).D 121 .$ Q a $ 2000002 2We also assumed that the rotating moment of the shaft of thetraction electromotor for wavy direct current is determined by:33 2 161Mt ^ h = $ k0$ Isrd1+ cos 2~ t+ cos 4~tn=3233 33(21)= M ^1+ a cos 2~ t+a cos 4~thsrMFv)0n1 2v a (where M sr – in between value of the torque of the shaft of the tractionelectromotor for wavy direct current; a 1 16/33 – factoramplitude of a frequency 2f 2 50 100 Hz; a 2 1/33 – factoramplitude of a frequency 4f 4 50 200 Hz.Mt1Wt= =MkJ k J m D 2f m $ + es2 0 + $ d n op $h $ i 222k D J m2e0 + $ d n o $ si 2$JJ J m D 2Km $ e0 + $ d n oK2KkJ k J m D$ s2KK m $ + e2 0 + $ d n oh $ i 2L2NOO+ 1OOOP(17)The dominant poles of the transfer function W M define theresonance frequency of the wheel set. The resonance frequency ofthe wheel set is determined by the next equation:~ =kJ k J m D2m $ + e2 0 + $ d n oh $ i 2J J m D2m $ e0 + $ d n o2(18)Based on the equation (18), resonance frequencies of theleaves and longer of the driving shaft (4) – Fig. 2 – are:~ 1 = 526.87 sradrad~ 2 = 70.14 sec(19)(20)Fig. 4 Comparative value of the torsion moment of the longerpart of the driving shaft at a 1 16/33 of a frequency during2f 2 50 100 Hz the slippage of the wheel setCOMMUNICATIONS 3/2008 ●7