10.2 Suspension Parameter Set 1
10.2.2 Guidance Impact Behaviour
We here present a series of figures which will serve to illustrate the effect of the wheelset guidance structures. At first, we disable the guidance structures, and simulate the freight wagon, pretending that no wheelset guidance exists. Figures 10.5(a) and 10.5(b) show the stable hunting behaviour that the freight wagon experiences at 25 m/s. However, as we lower the velocity, the periodic lateral hunting motion increases in amplitude, as discussed previously, and this is evident in figure 10.5(c) and 10.5(d) where we see the hunting motion grow at 20 m/s. Furthermore, at this speed, the wheelsets will actually begin to lose contact with the rails! This is why the simulation goes no further than it does.
When we enable the wheelset guidances, at 20 m/s, we see that the hunting amplitude no longer seems to grow unbounded, but actually achieves a stable amplitude of about 4 mm lateral movement for both wheelsets. This is illustrated in figures 10.5(e) and 10.5(e). This simulation is also supported by figure 10.6 in which we show an impact analysis. The top four figures show time histories of the impact forces in longitudinal and lateral direction on both wheelsets. The bottom two figures show the relative distances to the guidances. It is seen that only the rear wheelset impacts laterally.
By simulating the empty wagon atv = 40 m/s with guidances we achieved the results in figure 10.7. Due to the contraction of the hunting attractor we do not see any impact in this case.
We now examine more closely some strange looking phenomena, observed in the bifurcation diagrams generated earlier. The bifurcation diagram for the empty wagon has what seems to be two interesting discontinuities. The first interesting transition point occurs at around 10 m/s, and the second one at just under 14 m/s. Regarding the bifurcation diagram for the water loaded wagon we saw a discontinuity at aboutv = 19 m/s, and finally for the packed wagon we saw some strange behaviour at aboutv = 17 m/s.
A series of results is presented for this investigation, and which are laid out in in the rest of this section. These results illustrate time series for the motion of the wheelsets and car body, as well as the impact characteristics of the wheelsets. For the empty wagon we show simulations at v = 15 m/s,v = 13 m/s,v = 11 m/s andv = 9.5 m/s, in that order. This is followed by simulating the water loaded wagon at v = 20 m/s and v = 18 m/s. Finally, we have the packed wagon running at v = 17 m/s.
10.2 Suspension Parameter Set 1 95
(a) Longitudinal,v= 25 m/s.
0 5 10 15 20 25 30 35 40
(c) Longitudinal,v= 20 m/s.
0 5 10 15 20 25 30
(e) Longitudinal,v= 20 m/s.
0 5 10 15 20 25 30
Figure 10.5: (a),(b),(c) and (d) are simulations without guidances. (e) and (f) are simulations with guidances.
96 Results
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(e)
Relative lateral distance [m]
Impact Analysis disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.6: Simulation of the empty wagon with guidances. The velocity isv= 20 m/s. Regarding the clearance figures, we have illustrated the guidances by horizontal lines. (a) Front wheelset longi-tudinal impact forces. (b) Front wheelset lateral impact forces. (c) Rear wheelset longilongi-tudinal impact forces. (d) Rear wheelset lateral impact forces. (e) Longitudinal clearance illustrating no impact. (f) Lateral clearance illustrating impact on the rear wheelset.
10.2 Suspension Parameter Set 1 97
(b) Zoomed lateral.
0 2 4 6 8 10 12 14 16 18 20
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d) Zoomed yaw.
0 2 4 6 8 10 12 14 16 18
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(e) Longitudinal clearance.
0 2 4 6 8 10 12 14 16 18
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f) Lateral clearance.
Figure 10.7: Simulation of the empty wagon with guidances. The velocity isv= 40 m/s. We do not see any impact at this velocity, because the hunting attractor contracts for increasing velocity.
98 Results
Empty wagon running at v = 15 m/s
We can observe in the following figures that lateral movement of the wheelsets is rel-atively smooth, and that only the rear wheelset experiences impact with the freight wagon.
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.8: Simulation results of the empty wagon running atv= 15 m/s. (a) Lateral displacement.
(b) Zoomed lateral displacement, excluding car body lateral displacement. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 99
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.9: Impact analysis of the empty wagon running atv= 15 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
100 Results
Empty wagon running at v = 13 m/s
We observe in the following figures that lateral movement of the front wheelsets is no longer smooth, especially the movement of the rear wheelset.
In observing the lateral clearances, we see that both wheelsets now impact, and the forces are comparable to each other, although the rear wheelset impacts with greater force. Thus the discontinuity at about 14 m/s is probably brought about a transition from only the rear wheelset impacting, to both wheelsets impacting.
0 10 20 30 40 50 60
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.10: Simulation results of the empty wagon running atv= 13 m/s. (a) Lateral displacement.
(b) Zoomed lateral displacement, excluding car body lateral displacement. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 101
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.11: Impact analysis of the empty wagon running at v = 13 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
102 Results
Empty wagon running at v = 11 m/s
In order to investigate the discontinuity at about 10 m/s in the lateral behaviour of the freight wagon body, we performed simulations for 11 m/s and 9.5 m/s. Here, at 11 m/s, we can ascertain that behaviour is relatively similar to that for 13 m/s. Cheifly, both wheelsets are impacting against the freight wagon body, and with more or less the same intensity. In particular, the movement of the rear wheelset laterally is still erratic at its extrema.
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.12: Simulation results of the empty wagon running atv= 11 m/s. (a) Lateral displacement.
(b) Zoomed lateral displacement, excluding car body lateral displacement. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 103
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.13: Impact analysis of the empty wagon running at v = 11 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
104 Results
Empty wagon running at v = 9.5 m/s
At v = 9.5 m/s we can observe that behaviour is different that for v = 11 m/s. Of interest is the fact that although both wheelset still impact laterally against the freight wagon body, the rear wheelset no longer behaves erratically at its extrema.
In that both wheelsets still impact laterally, no significant effect is seen on the bi-furcation trace of any discontinuity with respect to either wheelset hunting, but the discrepancy is located with the lateral hunting of the car body. This jump can come about due to a change in the way forces are imparted upon the car body from the wheelsets during impact, in that now they are smoother than the erratic rear wheelset impacts experienced at v = 11 m/s.
0 10 20 30 40 50 60
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.14: Simulation results of the empty wagon running atv= 9.5 m/s. (a) Lateral displace-ment. (b) Zoomed lateral displacement, excluding car body lateral displacedisplace-ment. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 105
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.15: Impact analysis of the empty wagon running at v = 9.5 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
106 Results
Water loaded wagon running at v = 20 m/s
We here present time series data for a water loaded freight wagon running atv = 20 m/s.
After an initial transient, we see that the wagon settles into a low frequency hunting oscillation.
What merits special attention here is the impact behaviour of the wheelsets. The rear wheelset dominates in this role, since it is clearly the one impacting hardest. The front wheelset impacts, but not as hard as the rear wheelset. In fact, as velocity increases, the front wheelset will not impact at all with the freight wagon structure. Eventually, the rear wheelset won’t either, given sufficient velocity.
0 5 10 15 20 25 30
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.16: Simulation results of the water loaded wagon running at v = 20 m/s. (a) Lateral displacement. (b) Zoomed lateral displacement, excluding car body lateral displacement. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 107
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.17: Impact analysis of the water loaded wagon running atv= 20 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
108 Results
Water loaded wagon running at v = 18 m/s
After an initial transient, we see that the wagon settles into a low frequency hunting oscillation. Here, we take special note of the impact behaviour of the wheelsets. Both wheelsets now impact forcefully with the freight wagon structure, with nearly equal vigour. This indicates to us that the transition that takes place near the v = 19 m/s mark on the bifurcation trace figure 10.1(c) is one where the front wheelset begins to irritate the dynamics of the freight wagon more and more as it begins to impact, and its impacts increase in strength. Furthermore, the long period behaviour is what seems to lend a chaotic pattern to the bifurcation trace figure 10.1(c), but since we only sample the values for the bifurcation traces over a 3 second interval, we evade considering an entire wavelength of data, and thus we produce what seems to be a chaotic transition in the bifurcation trace.
0 5 10 15 20 25 30
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.18: Simulation results of the water loaded wagon running at v = 18 m/s. (a) Lateral displacement. (b) Zoomed lateral displacement, excluding car body lateral displacement. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 109
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis disp front left lat
disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.19: Impact analysis of the water loaded wagon running atv= 18 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
110 Results
Packed wagon running at v = 17 m/s
The strange behaviour in the bifurcation trace in the case of the packed wagon occurs as we slow down towards the nonlinear critical velocity. What actually occurs is that a new frequency is introduced in the lateral hunting motion. The period of this is beyond the 3 second sampling time, and introduces this strange behaviour in the bifurcation diagram. Had the sampling time been longer, we could have avoided this behaviour, but may have missed the fact that the hunting period begins to change.
In this section, we present a series of figures which illustrate the behaviour of the packed freight wagon at v = 17 m/s, which resides in this ‘strange’ region on the bifurcation trace. We clearly see that the period is about 8 seconds, which is clearly larger than the 3 second sampling time we use.
0 5 10 15 20 25 30
Yaw angle [rad]
Yaws
Yaw angle [rad]
Yaws
Front Wheelset Rear Wheelset Car Body
(d)
Figure 10.20: Simulation results of the packed wagon running atv= 17 m/s. (a) Lateral displace-ment. (b) Zoomed lateral displacement, excluding car body lateral displacedisplace-ment. (c) Yaw angle. (d) Zoomed yaw angle.
10.2 Suspension Parameter Set 1 111
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(c)
Relative longitudinal distance [m]
Impact Analysis
disp front left long disp front right long disp rear left long disp rear right long
(d)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(e)
Relative lateral distance [m]
Impact Analysis
disp front left lat disp front right lat disp rear left lat disp rear right lat
(f)
Figure 10.21: Impact analysis of the packed wagon running at v = 17 m/s. (a) Front wheelset lateral impact forces. (b) Rear wheelset lateral impact forces. (c) Longitudinal clearances. (d) Zoomed longitudinal clearance. (e) Lateral clearances. (f) Zoomed lateral clearances.
112 Results