Introduction
Tab.1 Comparisons among different railway dampers: Parallel configurations |
Damper | Potential power/W | Regenerated power/W | Regenerated power efficiency/% |
---|---|---|---|
Primary vertical damper | 39.07 (low) | 1.47 (low) | 3.75 (high) |
Secondary lateral damper | 4790.00 (high) | 12.47 (high) | 0.67 (low) |
Secondary vertical damper | 25.82 (very low) | 0.32 (very low) | 1.25 (moderate) |
Secondary yaw damper | 3700.00 (moderate) | 3.03 (moderate) | 0.08 (very low) |
Tab.2 Values of the parameters of a typical passenger rail vehicle [41] |
Symbol | Definition | Value | Symbol | Definition | Value | |
---|---|---|---|---|---|---|
mveh | Total vehicle mass | 3.3×104 kg | Bwb | Bogie wheelbase | 2.6 m | |
mbd | Carboy mass | 2.508×104 kg | Hbd | Body height | 1.57 m | |
mbg | Total bogie frame mass | 4.18×103 kg | Hbg | Bogie height | 0.5 m | |
mws | Per wheelset mass | 1.12×103 kg | Wr | Wheel radius | 0.45 m | |
ksl | Secondary lateral stiffness (per axle box) | 1.672×106 N/m | Hslbdh | Secondary lateral damper body end height | 0.53 m | |
csl | Secondary lateral damping (per damper×2) | 2.507598×104 N∙s/m | Hslbgh | Secondary lateral damper bogie end height | 0.56 m | |
ksv | Secondary vertical stiffness (per axle box) | 1.3672×105 N/m | Hsvt | Secondary vertical damper body end height | 0.96 m | |
csv | Secondary vertical damping (per damper×4) | 1.337386×104 N∙s/m | Hsvb | Secondary vertical damper bogie end height | 0.895 m | |
ksy | Secondary yaw stiffness (per axle box) | 2.09×105 N/m | Hsyt | Secondary yaw damper body end height | 0.61 m | |
csy | Secondary yaw damping (per damper×4) | 6.687×106 N∙s/m | Hsybgh | Secondary yaw damper bogie end height | 0.53 m | |
kpv | Primary vertical stiffness (per axle box) | 7.599×105 N/m | Hpvt | Primary vertical damper height (top) | 0.81 m | |
cpv | Primary vertical damping (per damper×8) | 4179.33 N∙s/m | Hpvb | Primary vertical damper height (bottom) | 0.29 m | |
cped (Case 1) | Electrical damping (PRDs, cped) | See Fig. 1(a) | Lhl | Half body length | 12 m | |
cped (Case 2) | Electrical damping (PRDs, cped) | See Fig. 1(b) | Lhw | Half body width | 1.4 m |
Note: Case 1: Total damping coefficient of the primary damper= cpv + cped; cpv = 4.17933×103 N∙s/m; Case 2: Total damping coefficient of the primary damper= cped, cpv = 0 N∙s/m. |
System modeling
Rail vehicle model
Track irregularity
Tab.3 General track data characteristics and descriptions [42] |
Track | Line speed/(km∙h–1) | Length/km | Standard deviation (lateral)/mm | Standard deviation (vertical)/mm | Description |
---|---|---|---|---|---|
110 | 110 | 5 | 3.04 | 5.12 | A low-speed, 110 km/h (70 mile/h) piece of UK track, lower-quality cross-country track |
160 | 160 | 5 | 2.46 | 2.77 | A mainline UK track, 160 km/h (100 mile/h), typical of better-quality cross-country and lower-quality intercity routes |
200 | 200 | 5 | 1.42 | 2.39 | A good-quality piece of UK mainline track, 200 km/h (125 mile/h), typical of high-speed intercity tracks |
225 | 225 | 5 | 1.36 | 2.00 | Top-quality UK track, 225 km/h (140 mile/h), example of the best intercity track |
270 | 270 | 4 | 1.04 | 1.81 | Top-quality German ICE track, 270 km/h (170 mile/h) |
Power regenerating damper
Tab.4 Values of key parameters of the PRDs |
Am/m2 | Dm/(10−6 m3) | kT/(Nm∙A–1) | kV/(V∙rad–1∙s) | ηv/% | ηm/% | r/Ω | R (Case 1) /Ω | R (Case 2)/Ω |
---|---|---|---|---|---|---|---|---|
0.000127 | 8.2 | 0.925 | 0.925 | 92 | 95 | 10 | 1, 5, 10, 20, 50 | 0.5, 1, 2, 5, 10 |
Ride comfort
Tab.5 NMV evaluation scales for ride comfort [36] |
Scale for NMV | Comfort index |
---|---|
NMV<1.5 | Very comfortable |
1.5≤NMV<2.5 | Comfortable |
2.5≤NMV<3.5 | Medium |
3.5≤NMV<4.5 | Uncomfortable |
NMV≥4.5 | Very uncomfortable |
Running safety
Analysis, results, and discussion
Ride comfort and running safety
Tab.6 Ride comfort assessment (95th percentile weighted RMS acceleration (mean ride comfort)) under different vehicle speeds (load: 1 Ω) |
Running speed/(mile∙h–1) | Body center | Pivot 1 | Pivot 2 |
---|---|---|---|
Case 1 | |||
25 | 0.6285 | 0.8265 | 0.9730 |
50 | 0.6924 | 1.3738 | 1.1074 |
75 | 0.8178 | 1.3696 | 1.4633 |
100 | 1.0422 | 1.7284 | 2.1450 |
Case 2 | |||
25 | 0.6229 | 0.8158 | 0.9596 |
50 | 0.6790 | 1.3459 | 1.0770 |
75 | 0.8045 | 1.2948 | 1.4520 |
100 | 1.0401 | 1.7243 | 2.1318 |
Tab.7 Ride comfort assessment (95th percentile weighted RMS acceleration (mean ride comfort)) under different vehicle speeds (viscous damper) |
Running speed/(mile∙h–1) | Body center | Pivot 1 | Pivot 2 |
---|---|---|---|
25 | 0.6285 | 0.8265 | 0.9730 |
50 | 0.6924 | 1.3738 | 1.1074 |
75 | 0.8178 | 1.3696 | 1.4633 |
100 | 1.0422 | 1.7284 | 2.1450 |
Tab.8 Ride comfort assessment (95th percentile weighted RMS acceleration (mean ride comfort)) under different electrical loads (speed: 100 mile/h) |
Load resistance/Ω | Body center | Pivot 1 | Pivot 2 |
---|---|---|---|
Case 1 | |||
1.0 | 1.0422 | 1.7284 | 2.1450 |
5.0 | 1.0422 | 1.7284 | 2.1450 |
10.0 | 1.0422 | 1.7284 | 2.1450 |
20.0 | 1.0422 | 1.7284 | 2.1450 |
50.0 | 1.0422 | 1.7284 | 2.1450 |
Case 2 | |||
0.5 | 1.0401 | 1.7243 | 2.1318 |
1.0 | 1.0442 | 1.7367 | 2.1484 |
2.0 | 1.0507 | 1.7580 | 2.1702 |
5.0 | 1.0597 | 1.8010 | 2.2202 |
10.0 | 1.0668 | 1.8705 | 2.2781 |
Tab.9 Low-speed flange climbing track cases |
Radius/m | Cant/mm | Gauge widening/mm | Transition length/m | Distance from the start of the runoff transition to the center of dip/m |
---|---|---|---|---|
90 | 25 | 19 | 7.5 | 0.000 (top), 7.500 (bottom) |
150 | 100 | 13 | 30 | 6.000 (top), 16.883 (bottom) |
200 | 150 | 6 | 45 | 6.000 (top), 16.883 (bottom) |
Tab.10 Y/Q low-speed flange climbing case under 1 Ω electrical load |
Radius (transition*)/m | Y/Q | ||
---|---|---|---|
Case 1 | Case 2 | Case 3 (viscous damper) | |
90 (bottom) | 0.714 | 0.714 | 0.714 |
90 (top) | 0.699 | 0.699 | 0.683 |
150 (bottom) | 0.605 | 0.605 | 0.605 |
150 (top) | 0.760 | 0.760 | 0.761 |
200 (bottom) | 0.726 | 0.723 | 0.715 |
200 (top) | 0.676 | 0.675 | 0.676 |
Note: *Distance from the start of runoff transition to the center of dip |