Spectral Optimization of the Suspension System of High-speed Trains

More documents

Recommendations

Info

D. Younesian et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 98-103 by intersection of the surfaces is taken as the optimal values. The Genetic Algorithm is seeking for four optimal parameters of the primary and secondary suspension so that the level of acceleration becomes minimum and simultaneously the level of shear stress in coil spring remains less than a specific value (500Mpa). Fig. 3: Flow chart of the implemented Genetic Algorithm Table 2: Mechanical Properties of the wagon body Parameter Symbol Value body length body mass body mass inertia L BD 20 m M 40 ton BD I 1.3.3X10 BD 6 kgm 2 Bogie mass M BG 1200 kg Wheel set mass M w 1180 kg Number of spring rings N 10 Springs shear module G 80 GPa Spring diameter D 0.2 m Non-dimension accel- -eration and shear stress Primary suspension spring diameter (m) Secondary suspension damping (NS/m) Optimal point Fig. 4: Geometrical depiction of the optimization procedure In order to validate the optimization procedure, effects of positive and negative deviations with respect to the optimal values of the properties of the suspension systems obtained for v=20 m/s and e=2 m are illustrated in Fig. 5 and 6. These Figures are numerically verifying the optimization procedure. In all the Figures deviation σ denotes actual value divided by the optimal value. 101 Non dimension acceleration and shear stress 8 7 6 5 4 3 2 1 acceleration stress 0 0.5 0.7 0.9 1.1 1.3 1.5 Fig. 5: Effects of deviations with respect to the optimal coil spring diameter of the secondary suspension system Acceleration (m/s 2 ) 0.0366 0.0364 0.0362 0.036 0.0358 0.0356 0.0354 0.0352 Primary Suspension Secondary Suspension 0.035 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Fig. 6: Effects of deviations with respect to the optimal damping of both suspension systems In Figs. 7 and 8 the effects of deviation with respect to optimal spring diameter of secondary suspension system on acceleration and stress in time domain are shown. As it is seen, the acceleration values obtained for σ = 0. 5 (half of the optimal diameter) are less than values of optimal system ( σ = 1 ) however the spring shear stress is remarkably larger than values of optimal system and vice versa for σ = 1. 5 . So it can be concluded that the optimized system leads to minimum acceleration with a shear stress less than the allowable stress (500 MPa). Acceleration (m/s 2 ) 1. 0. 0 0 0. 1 1. 2 2. -0.5 - 2 1 -1.5 Time(s) Fig. 7: Effect of deviations with respect to the optimal coil spring diameter of the secondary suspension (acceleration) Tables 3 and 4 are demonstrating how much error may happen in case of any positive or negative deviation with respect to the optimal values. It is seen that RMS of the shear stress increases with decreasing of the spring diameter up to 500 MPa and contrarily, RMS value of the acceleration decreases. σ σ 1 σ=0.5 σ=1.0 σ=1.5
Shear stress (MPa) 395 375 355 335 315 295 275 D. Younesian et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 98-103 × . 13 × 3 σ=0.5 0.5 σ=1.0 1 σ=1.5 1.5 255 0 0.5 1 Time (s) 1.5 2 2.5 Fig. 8: Effects of deviations with respect to the optimal coil spring diameter of the secondary suspension system (shear stress) Table 3: Effects of deviations with respect to the optimal values of the spring coil diameter of the primary suspension system Coefficient Acceleration (σ ) RMS(m/s 2 Stress RMS ) (MPa) 0.5 0.03 2605.5 0.6 0.0304 1362.0 0.7 0.0310 1215.3 0.8 0.0321 844.2671 0.9 0.0335 615.1957 1.0 0.0351 465.5598 1.1 0.0369 363.3230 1.2 0.0387 290.8722 1.3 0.0401 237.9541 1.4 0.0413 198.3112 1.5 0.0421 167.9688 Table 4: Effects of deviations with respect to the optimal values of the damping of the primary suspension system Coefficient Acceleration (σ ) RMS(m/s 2 Stress RMS ) (MPa) 0.5 0.0365 499.43 0.6 0.0359 499.404 0.7 0.0355 499.3790 0.8 0.0353 499.3790 0.9 0.0352 499.3401 1.0 0.0351 499.3250 1.1 0.0352 499.3119 1.2 0.0352 499.3006 1.3 0.0353 499.2907 1.4 0.0354 499.2820 1.5 0.0355 499.2743 Optimum values for the damping of primary and secondary suspensions are illustrated respectively in Figs. 9 and 10 for different eccentricity values. As it is seen, optimal damping values for the primary and secondary suspensions are both decreasing functions of the operational speeds. It is also seen that for large values of eccentricity (e> 4 m) trend of variations of the optimal values becomes significantly different. In other words, for eccentricity values lower than 4 meters one can assume that eccentricity has no significant effect on the optimal values of primary suspension damping. Variation of the optimal values of the coil spring diameter of the primary and secondary suspensions is illustrated in Fig. 11 for different operational speeds. As it is seen dependency of the optimal diameters on the operational speed is much lower than optimal damping 102 values. It is also seen that the optimal value of the primary suspension coil spring diameter is generally larger than secondary suspension in the whole speed range. It is also seen that dependency of the secondary suspension optimal stiffness on the operational speed is lower than that of primary suspension system. Optimal Cps (Ns/m) 210000 200000 190000 180000 170000 160000 150000 140000 130000 15 20 25 30 35 40 45 50 55 Fig. 9: Optimal value of the primary suspension system damping Optimal Css (Ns/m) 190000 180000 170000 160000 150000 140000 130000 120000 15 20 25 30 35 40 45 50 55 Fig. 10: Optimal value of the secondary suspension system damping dss and dps (m) 0.055 0.0545 0.054 0.0535 0.053 0.0525 0.052 Speed (m/s) Speed (m/s) dps dss 0.0515 18 28 38 48 58 68 78 88 Speed (m/s) Fig. 11: Optimal value of the coil spring diameter for both suspension systems Influences of the track quality on the optimal values of damping are illustrated in Fig. 12.”Track 1” denotes class 4 and “track2” denotes class 5 in Table 1. As it is seen, optimal value of the primary suspension damping decreases when the track quality becomes worse and in contrary, optimal values of the secondary suspension damping increases. This conclusion is very well adopted with reality because locking effect may happen for large values of the primary suspension damping because it is directly connected to the rail irregularities. Locking phenomena (Large damping forces at high frequency) is e=2 e=4 e=6 e=2 e=4 e=6
Page 1 and 2: D. Younesian et al. 2009. Int. J. V
Page 3: D. Younesian et al. 2009. Int. J. V

Spectral Optimization of the Suspension System of High-speed Trains

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?