Proceedings of ICTACEM 2014 International Conference on Theoretical, Applied, Computational and Experimental Mechanics December 27-29, 2014, IIT Kharagpur, India
ICTACEM-2014/221
Performance Evaluation of Steering Bogies on Various Tracks S. Pradhan, A. Menezes, A. K. Samantaray and R. Bhattacharyya Department of Mechanical Engineering, IIT, Kharagpur, India
ABSTRACT
For high speed rolling stock, running times can be reduced by enhancing the running speed of the train on curved portions of track. However, higher speed on curved track leads to large lateral forces, high frequency noises, wear of flanges and significant wheel load change at transition curves. In extreme case, there is a chance of derailment. To avoid derailment as well as hunting and to improve ride comfort of passengers and curving performance at high speed on curved path, tilting and/or steering bogies have been implemented. Running speed can be increased to some extent without affecting the ride comfort of passengers by using tilting bogies. With the help of steering bogies, speed can be increased on curved track by minimizing the lateral forces. Steering effect can also be affected by various design parameters of the curved tracks such as radius of curvature, cant/superelevation, and transition length. Cant also reduces the lateral force for both active and passive steering.
Keywords: Railway vehicle dynamics, Steering bogies, Ride comfort, Hunting, Derailment, Curved track.
1. INTRODUCTION High-speed rail-vehicles can run at speeds in excess of 350kmph on straight tracks and 250kmph on curved portions of tracks. Due to high speed on the curve, wheel exerts large lateral forces on the rails which causes wear of wheel flanges and rails and affects the dynamic behavior of bogies. Self-steering is achieved due to difference in rolling radii between the left and right wheels. If a wheel-set is moved laterally from its centered position, a difference in rolling radii arises 1. From Fig.1
γ e = ∆r 2l ,
(1)
where ∆r is instantaneous difference in rolling radii between left and right wheels and y is the lateral displacement from the centered position. For running stability of vehicles, equivalent conicity must remain in between 0.1 to 0.4. Low wheel tread gradient is helpful for high speed, but higher wheel tread gradient increases the curving performances.
S. Pradhan.: E-mail:
[email protected] , Telephone: 7501463364 A. K. Samantaray.: E-mail:
[email protected], Telephone: 9434031885, Address: IIT, Kharagpur, India
R
C
A
O
∆r = r2 − r1
y
B
l
r2
r1
D
l
y
(a)
(b) `Figure1. Equivalent conicity of wheel profile.
In modern high-speed trains, graded circular wheel tread configurations are used in which large numbers of arcs are joined next to each other 2. Such a graded profile reduces the contact area as well as contact bearing forces between wheel tread and rail. Also, the contact points during curving are uniformly distributed over the tread and lead to uniform wear instead of large localized wear. In a worn wheel, the tread gradient is larger as compared to a new wheel. As the centrifugal force causes the center of axle to move towards the outer side of the curved track, the presence of wheel-tread gradient leads to steering action in the curved portion of the track. In a worn wheel, self-steering effect is more as compared to a new wheel. But when the center of wheel tread is worn below the level of end of the tread, there can be significant deterioration of the vehicle’s dynamic performance, i.e., stability and ride comfort. 2. STEERING BOGIES There has to be compromise between stability on the straight track and good steering action in the curved track. Low conicity helps to achieve more speed on the straight track and for better curving performance, higher gradient is required. To achieve both high velocity as well as better curving performance, Shinkansen bogies use graded circular wheel tread configuration with nominal tread gradient 1:40. Bending stiffness and shear stiffness are the two parameters of primary suspension for stability and curving performance. For better curving performance, low bending stiffness is required which affects stability. To achieve better stability, shear stiffness should be increased. Shear stiffness helps to stabilize the vehicle and bending stiffness improves the curving performance (steering action) of the
wheel. The shear stiffness is responsible for critical speed of the vehicle while bending stiffness determines the angle of attack of the wheel-set in curves. When the wheel-sets of bogies are designed to take more or less radial position in the curved track as shown in Fig.(2) then the bogies are called radially steered bogies. In the case of steered bogie 3, the angle of attack is small which leads to lesser flange wear and track creep forces. Radially steered bogies are classified depending on the control principle used. In case of passive/ self –steering3, the working principles are, respectively, 1. Wheel-sets yawed by the wheel-rail contact forces. 2. Wheel-sets are rotated relative to vehicle body about the vertical direction. In both the above cases, the change in the kinematic of motion of wheel-set depends on radius of curvature. When wheel-sets are forced to occupy radial position in the curved track, the corresponding steering mechanism is called active steering. In active steering bogie, electric, hydraulic or pneumatic actuators are used to give yaw motion to the wheel-sets. Links, levers and sliders are used in between wheel-sets to operate different types of forced/ active steering mechanisms. Wheel flange
Wheel tread Large diameter
Small diameter
Travelling distance is less
Travelling distance is more
Figure 2. Self-steering characteristics of wheel-set.
Decreased anti-steering moment
Decreased angle of attack
Decreased lateral creep force
Figure 3. Active steering of rear wheel-set.
2.1. Active/ Assist/ Forced Steering: In forced steering, the axle can have yaw rotation relative to the bogie frame. The assist/forced steering3 can be achieved in different ways: 1. Axles can be connected by suitable linkage which can be actuated to force the wheels to take up radial positions on curved tracks. 2. Control torque can be applied to the wheel-set in the direction perpendicular to the plane of wheel-set. 3. Actuators can be used in the lateral direction of wheel-set, but ride quality is affected by this arrangement. 4. Wheel-set can be controlled by active torsional coupling between the wheels. Active primary suspension (actuators with primary suspension) along with passive components can be used in the same way of active secondary suspension3. Passive stiffness can be used to stabilize the kinematic oscillation (hunting instability) and actuator is used to provide better curving performance in the curved track. In case of active steering, stability and steering actions are considered separately. Equal longitudinal forces in the wheels lead to reduce wear and damage of the wheel and equal lateral forces are required to neutralize the centrifugal forces caused by cant deficiency or cant excess1. Same angle of attack is possible when actuators perfectly control the yaw angle with respect to bogie. The required yaw angle is determined from the radius of curvature of track, cant, velocity of vehicle and wheelbase. The steering performances on the curved track are not only dependent upon design of bogie but also the track configuration. 2.2. Design Parameters of Track The design parameters of track affect the dynamic behavior of the bogie. The major parameters are track gauge, cant / super-elevation, transition length of the curve (entry/exit curve), and radius of curvature in horizontal and vertical directions. These parameters are discussed in the subsequent sections. 2.2.1. Track gauge: The distance between the inner faces of rails is called track gauge. Different countries use different standard of gauges like broad gauge, meter gauge, narrow gauge as well as standard gauge. The gauge values are different for different countries. According to International Union of Railways (UIC), for high speed train, standard gauge is used whose value is 1435 mm.
Track gauge 14 mm
ϕt
Outer Rail
ht
Track plane
Inner Rail
2b0
ϕt
Horizontal plane Figure 4. Track gauge
Figure 5. Track cant
2.2.2. Track cant Track cant or super-elevation is defined as the difference between the inner and outer rail heights (as in Fig.5) in a curved path which is useful to compensate the unbalanced lateral acceleration. The angle can be calculated as ht , 2b0
ϕt = sin −1
(2)
where 2b0 is the track gauge. For example, 2b0=1435mm for standard gauge. 3.5e-4
0.0175 Constant cant angle
0.0125 c
b 0.01 0.075 Variable cant angle
0.05 0.025 0.0
Constant curve radius
2e-4 Variable curve radius
1.5e-4 1e-4
Zero curve radius
0.5e-4
3000 2000 Track abscissa
c
2.5e-4
Zero cant angle
o a 0.0 500 1000
b
3e-4
Track curvature
Track cant angle
0.015
4000 0.0
o 0
a 500 1000
2000
3000
4000
Track abscissa
(a)
(b) Figure 6. (a): Track curvature, (b) Track cant
2.2.3. Transition length of the curve The linear variation of curvature in the curved path is called transition curve which is clothoid type. It is used to join straight track to circular one or two curves together to allow continuous change in curvature. The clothoid type of the transition curve4 is given by (as shown in Fig. 6 (b))
ρ ( s= ) ρ0 +
s A2
(3)
= s s= 0 at the start of the transition curve, ρ is the curvature and A is a clothiod parameter. 0
Clothoid starts from straight line ( ρ0 = 0 ), has the length Lt and ends at the circle with constant radius of curvature
ρ = 1 R,
(4)
where R is the curve radius. 2.2.4. Dynamic properties of track Generally ballasted tracks or in some cases concrete slab tracks are used. Overt the time, the ballast loosens and deforms which causes minor track irregularities. Long wave track irregularities mainly affect vertical and lateral body vibrations which are the causes of ride discomfort. Rail surface irregularities/short wave irregularities are due to rail welds and wear of rail. Short wave irregularities cause fluctuation of the axle load, high frequency vibration, and increase the dynamic load on the track5. For soft subgrade, one resonance may occur at the frequency 20-40 Hz. When rail and sleepers vibrates on the ballast bed, the frequency range is 50-300 Hz. Here rail and sleepers provide mass and the ballast acts as spring and it also provides large amount of damping. Another resonance can be often found in the frequency range 200 to 600 Hz which is due to bouncing of the rail on rail pads. When the bending wave length of rail is twice the spacing of the sleepers, the corresponding resonance frequency is called pinned-pinned frequency which occurs at 1000 Hz. The nodes of the bending vibration of rail are at the support (sleeper) 6. The stability of vehicle is thus directly coupled with the properties of the track. Therefore, in this study, we will use a flexible ballasted track model with different levels of track irregularities. 3. MODELLING AND SIMULATION For modeling an active steering bogie, ADAMS (VI_rail) software is used. Link type steering mechanism consists of steering beam, steering lever and steering link7. In this steering mechanism, rotational displacement of bogie with respect to carbody is transmitted to axle through steering linkage. Steering angle is mostly dependant on radius of curvature of track, length of transition curve and running speed of the bogie. Here, link type forced steering is used in conventional bogie.
Primary suspension Lateral damper
Bump stop
Primary vertical damper Axle box Longitudinal damper Wheel-sets Axle Friction damper
Secondary suspension (Air spring) Bogie frame
Figure 7. Labelled diagram of bogie template developed in ADAMS (VI-rail)
Steering beam
Steering lever Steering link
Figure 8. Labelled diagram of steering bogie template developed in ADAMS (VI-rail)
For given radius of track at a particular position, the steering angle is defined by the angle by which each axle has to be turned in order to make wheels’angle of attack with the track
zero and align the axle with the radius of the track. This steering angle on a track without cant may be calculated as W 1 (5) = α sin −1 b × , 2 R where Wb is the wheel-base, α is the required steering angle and 1/ R = ρ is the curvature of
the track (See Fig.9). Steering angle in presence of cant angle may be calculated in terms of cant deficiency or cant excess depending on speed of the train. Then the instantaneous steering angle is 2 1 v 2 − φ gR Wb 1 2b0 v − ht gR −1 Wb α sin × × = = sin × × , 2 2b0 v 2 2 R 2 R v −1
(6)
where 2b0 is track gauge, φ is cant angle in radian, ht is the super-elevation, v is the velocity and g is the acceleration due to gravity. However, the computed angle goes out of bounds for large magnitude of can excess or deficiency. Thus, the steering angle is restricted within ±0.01 radians.
There are different types of tracks depending on the parameters such as radius of curvature, cant angle, transition length of the curve and irregularities. Here we have considered different types of tracks with measured irregularities.
Wb
α R
α α
α
R Figure 9. Steering angle of wheel set.
The yaw angles of wheel sets are controlled with respect to bogie. The required yaw angle is determined as defined above. We can increase the curving performance and reduce the lateral creep force by introducing steering mechanism. As a result, wear and tear of wheel (flange portion) reduces significantly.
4. RESULTS AND DISCUSSION By using the link type active mechanism, the derailment speed of the train is increased from 114m/s (410.4 km/h) to 134m/s (482.4 km/h) for same condition of the track. Active steering also offers the following advantages3: 1. Equal longitudinal creep between the wheels on the same axle. 2. Equal creep forces in the lateral direction between the wheel-sets of a vehicle. These results are shown in Figs. 10 to 12 when the vehicle moves at 100 m/s on a curved flexible ballasted track of radius of 4km and the track has no cant and no irregularities. 20000
30000
Longitudinal creep force (N)
15000
10000
5000
0.0
-5000
0
10
20 Time (s)
30
40
Figure 10. Longitudinal creep force of two wheels in the front axle of front bogie with no track cant.
Figure 11. Lateral creep of front wheels in front axle of front and rear bogies with no track cant.
Figure 12 shows that during perfect steering, angles of attack of the wheel-sets are equal. 0.15
Angle of attack (deg)
0.10
Angle of attack of front and rear wheels (right side)
0.05 0.0 -0.05
Angle of attack of front and rear wheels (left side)
-0.10 -0.15 0.0
10.0
20.0 Time (s)
30.0
40.0
Figure 12. Angle of attack of both wheel-sets of front bogie at 100m/s with no irregularities and no cant.
The wheel displacement and lateral creep force of steered and un-steered bogies are given in Figs. 13-14 which show the reduction in both with the use of the steering mechanism. 0.01
60000 50000 Without steering mechanism
Lateral creep force (N)
Lateral displacement (m)
Without steering mechanism
0.005
0
-0.005
40000 30000 20000
0
With steering mechanism
-0.01
With steering mechanism
10000
-10000 10
0
30
20 Time (s)
40
-20000 0
Figure 14. Wheel lateral displacement of Steered and Unsteered bogie at 100 m/s (360 km/h).
10
20 Time (s)
40
30
Figure 13. Lateral creep force of Steered and Unsteered bogie at 100 m/s (360 km/h).
The simulations of a vehicle with the designed steering bogie have been performed for the following track parameters. Track 1: Radius of curvature is 400m (small radius of curvature) and without cant. Track 2: Radius of curvature is 4000m (normal radius of curvature) and without cant. Track 3: Radius of curvature is 400m (small radius of curvature) and with cant angle of 0.1047 radian (super elevation=150mm). Track 4: Radius of curvature is 4000m (normal radius of curvature) and with cant angle of 0.1047 radian (super elevation=150mm). 40000
Track-1
Track-1
0.003 0.002
Lateral creep force (N)
Lateral displacement (m)
0.005 0.004
Track-3
Track-4
0.001 0 -0.001 -0.002 -0.003
Track-2
-0.004
30000 Track-3
20000 Track-2
Track-4
10000
-0.005 0
10
20
30
40
50
Time (s)
Figure 15. Lateral displacement of front left wheel at 35m/s (126 km/h) for different track conditions.
0
0
10
30 20 Time (s)
40
50
Figure 16. Lateral creep force of front left wheel at 35m/s (126 km/h) for different track conditions.
The derailment speed on 400m track radius of curvature is 40m/s whereas it is 134m/s on normal curved track. Therefore, simulations for comparison have been done at a common
speed of 35m/s. The lateral wheel displacements and creep forces for different tracks considered above are shown in Figs. 15-16. It is seen that both lateral wheel displacements as well as lateral creep forces decrease in the presence of cant in case of small curve radius (400m). But in presence of cant with large curve radius, cant reduces performance of steering bogie due to excess cant (150 mm at low speed of 35m/s). This is because on such large curve radius, the operating speed of the train should be much higher (around 100m/s or more) for the given cant. The effect of vibration on the passengers in the vehicle is measured in terms of the ride comfort which depends on displacements and accelerations felt by the passengers. Ride comfort for different tracks (with measured irregularities) is calculated by Sperling’s ride index method. The weighting function B is different for vertical and horizontal directions. The weighting factor B for ride comfort in horizontal direction is given by [8, 9] 1/2
1.911× f 2 + (0.25 × f 2 ) 2 = Bh 0.737 × (1 − 0.277 × f 2 )2 + (1.563 × f − 0.0368 × f 3 )2
(7)
and the weighting factor B for ride comfort in the vertical direction is given by
Bv = Bh /1.25
(8)
It is obvious that there is more weightage given to ride comfort in lateral (horizontal) direction. The ride index at any given frequency is defined as
Wz = (a 2 B 2 )1/ 6.67
(9)
where a is the amplitude of acceleration in cm/s2, B is the weighting factor and f is the frequency. The ride index is determined for each individual frequency, and total or overall ride comfort is calculated as W = (Wz16.67 + Wz2 6.67 + Wz36.67 + Λ + Wzn 6.67 )1/6.67 ztotal
(10)
A ride comfort value less than 3 means noticeable vibrations which is not very uncomfortable and a value less than 2 indicates a very pleasant ride. When ride comfort value is close to 1, the passangers can barely feel any vibration. The ride comfort for different track conditions for a vehicle equipped with the steering bogies is given in Table 1. These ride comfort values are obtained when the vehicle moves at a speed of 35 m/s (126 km/h) on a track with measured irregularity. The designed bogie gives extremely good ride comfort. In fact, the ride comfort reduces when the speed is increased. For this bogie designed for 360km/h on curved tracks, the worst case ride comfort is 2.96.
Table-1: Ride comfort for different tracks Track condition
Ride comfort (Wz) in Lateral direction
Ride comfort (Wz) in vertical direction
Curve radius = 400m, Cant angle=0 (Track 1)
1.9566
1.6871
Curve radius = 4000m, Cant angle=0 rad (Track 2)
1.28496
1.7098
Curve radius = 400m, Cant angle=0.1047 radian (Track 3)
1.78136
1.6997
Curve radius = 4000m, Cant angle=0.1047 rad (Track 4)
1.3125
1.6826
5. CONCLUSIONS We have designed a link type active steering bogie. By using this type steering mechanism, derailment speed on curved tracks is increased. The effects of different track conditions on the performance of steered bogies are discussed. Lateral creep force and lateral wheel displacements reduce with the designed steering bogie which improve the wheel wear. The track radius and cant angle are two important track parameters that affect the dynamic behavior. The designed bogie also improves the ride comfort of passengers. REFERENCES 1. A. H. Wickens, Fundamentals of rail vehicle dynamics, Swets & Zeitlinger, 2003. 2. I. Okamato, Shinkansen bogies, Japan Railway & Transport Review, 19, pp. 46-52, March 1999. 3. R. M. Goodall, & T. X. Mei, Active Suspensions, In: S. Iwnicki (Ed.) Handbook of railway vehicle dynamics, pp. 327-357, CRC Press, FL, 2006. 4. M. Lindahl, Track geometry for high speed railways: A literature survey & simulation of dynamic vehicle response, TRAIT-FKT Report 2001:54, ISSN 1103-470X. 5. S. Miura, H. Takai, M. Uchida & Y. Fukada, The mechanism of railway track, Japan Railway & Transport Review, pp.38-45, March 1998. 6. T. Dahlberg, Track issues, In: S. Iwnicki (Ed.) Handbook of railway vehicle dynamics, pp.143-179, CRC Press, FL, 2006. 7. I. Okamato, How bogies work, Japan Railway & Transport Review, 18, pp. 52-61, Dec. 1998. 8. K. Chandra & D. Ghosh Roy, A technical guide on oscillation trials, RDSO, MT-334, 2002. 9. K.V. Gangadharan, C. Sujata & V. Ramamurti, Experimental & analytical ride comfort evaluation of a railway coach, in: Proc. IMAC-XXII, Dearborn, Michigan, Paper #249, 2004.
