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Influence of the wheel diameter difference on the wheel/rail dynamic contact relationship of the heavy haul locomotive.

1. Introduction

With the development of railway technology, the load and speed of train have been qualitatively improved. At the same time, the wheel/rail wear problem is also aggravated, especially for heavy haul train. The wheel/rail contact relationship affects the running quality of railway vehicles and the maintenance costs directly (Froling 2006; Wang, Guo, and Liu 2011). In order to keep the railway vehicle with better dynamics performance, wheel turning and rail polishing is carried out frequently.

Aimed at the wheel/rail wear problem, many researches have been carried out from the wheel/rail rolling contact theory, experiment and simulation methods. Early studies on the wheel/rail wear issues were mainly focused on the wear behaviour of wheel/rail material with the aid of testing rig, and the abrasion value was judged by the frictional work between wheel and rail (Zobory 1997; Jendel 2002; Enblom and Berg 2005; Braghin, Lewis, and Dwyer 2006; Vuong et al. 2009; Gordana, Franklin, and Fletcher 2011; Pombo et al. 2011). The wheel wear test was carried out by Braghin, Lewis, and Dwyer (2006), based on the full size of wheel/rail rolling contact device, a model which can calculate the wear depth of wheel tread was put forward, and the wear of ETR500 in Rome-Florence line was simulated through the model. According to the Archard theory, Jendel (2002) carried out some research on the wear of the wheel in combination with the results of wheel/rail wear test, and summarises the wheel wear coefficient map in the clean and dry condition of wheel/rail contact environment. Based on the work of Jendel, Enblom and Berg (2005) considered the effect of elastic shear deformation and the brake method on wheel wear, put forward that elastic shear deformation has a great effect on the sliding speed of wheel tread wear. Simulation results show that the wheel tread wear will be increased on straight track under braking condition, and inner wheel wear will increase with the braking force on the curve track, while the outer wheel wear is on the contrary. The effects of traction direction and traction coefficient on wheel/rail wear problem in partial slip and full slip conditions were researched by Gordana, Franklin, and Fletcher (2011), respectively, and put forward that the traction coefficient has a greater impact on wheel/rail wear phenomenon.

Wheel wear phenomenon can be divided into uniform wear and non uniform wear, uniform wear mainly refers to the wheel tread wear along the wheel circumference direction are almost the same, which is mainly due to the abrasive wear, adhesive wear and plastic deformation; Non uniform wear includes certain non random wear due to wheel material defects and impact load factors, such as the wheel out of round, polygonal wheel et al. (Morys 1999; Nielsen and Johanssonand 2000). Wheel/rail wear will affect the wheel/rail contact geometry, unsatisfactory wheel/rail contact geometry relationship will deteriorate the dynamic performance of railway vehicle, and which will also have some negative effects on the railway vehicle components and the service life of track (Johanssonand and Nielsen 2002; Barke and Chiu 2005; Frohling, Ekberg, and Kabo 2008).

The measured wheel wear data with different wheel-sets of Daqin railway special coal line of China were shown in Figure 1 (Hu et al. 2010), it can be seen from Figure 1 that most of the heavy haul train exist unsymmetrical wear phenomenon, some railway vehicle even occur eccentric wheel wear to the same side of wheelset, which cause the railway vehicle has various forms of unsymmetrical wheel/rail contact phenomena (Ma et al. 2013). The wheel/rail contact dynamics modelling problems which considered the rail geometric irregularity was researched by Bogacz and Kowalska (2001), and the wheel/rail contact geometry relationship of the left and right wheel in the same wheelset was researched through a wheel/rail simple model. The effects of wheel/rail contact geometry relationship to the dynamic performance of locomotive under the limit state was researched by Oldrich Polach (2005).

Wheel/rail wear will lead to wheel diameter differences. Wheel diameter difference is referring to the difference of the rolling diameter of each wheelset in the same locomotive. In theory, the difference of the rolling diameter between left and right wheel in the same wheelset is the precondition of curve passing, so the existing of wheel diameter difference in some degree is favour to the curving passing of the railway vehicle. However, a wheel diameter difference on a straight track will result in different rolling radii of the left and right wheels, causing problems such as the unequal longitudinal creep force of wheels in the same wheelset, different distributions of vertical force, et al. (Swenson and Scott 1996). Thus, wheel diameter difference has a big influence on the running stability and safety of the railway vehicle.

The effect rules of wheel tread concave wear on wheel diameter difference was researched by Sawley and Wu (2005), put forward that the wheel tread concave wear changed the conicity of wheel tread. Thereby, the steering capability of wheelset was decreased and caused a greater attack angle through the curve negotiating, then the two points contact of the wheel/rail will seriously affecting the running stability of railway vehicle. Based on it, the relationship between wheel diameter difference which caused by wheel tread concave wear and the instability of the railway vehicle were analysed, and the wheel tread reprofile criterion of the North American freight car wheel tread were formulated. The effect of wheel diameter on wheel vibration frequency was researched by Cataldi-Spinola et al. (2003) through the Finite Element Analysis method, put forward that the wheel diameter will affect the vibration characteristics of wheel and it even will change the vibration frequency of some certain vibration mode.

Above researches have successfully solved many wheel/rail wear problems of railway vehicles, but there is rare research aimed at the wheel/rail dynamic contact relationship caused by the wheel diameter difference, and the existing researches are mainly focus on the coasting condition of railway vehicle, didn't considered the traction and braking cases in detail. Compared with the railway vehicle, locomotive needs to take the traction and braking condition into consider. In traction or braking condition, the wheel/rail dynamic contact relationship is different with the coasting condition. The effect of different types of wheel diameter difference on the wheel/rail dynamic contact relationship of heavy haul locomotive under coasting condition is researched firstly, and based on it, the difference of the wheel/rail contact relationship of locomotive between coasting condition and dynamic braking condition was simulated in detail.

In Section 2, the wheel diameter difference type was described firstly; Section 3 presented the standard of the wheel diameter difference; Section 4 gave the wheelset force statements; Section 5 presented the dynamic model which considered the wheel diameter difference and Section 6 discussed the simulation results.

2. Wheel diameter difference type

The wheel diameter difference in the same bogie, for example, can be represented as Figure 2, including the wheel diameter difference among four wheels of two wheelsets. Only taking the simplest wheel diameter difference of two wheels into consideration, there are six different forms, whereas for the three-axle bogie, there are 15 different types of wheel diameter differences.

For a two-axle bogie, according to the difference of position, the above six different wheel diameter differences can also be divided into four types, as shown in Figure 3, including the wheel diameter difference in the same phase (A), the wheel diameter difference of front the wheelset (B), the wheel diameter difference in anti phase (C) and the wheel diameter difference of the back wheelset (D).

3. Standard of wheel diameter difference

The wheel diameter difference has certain limit standards. The allowed wheel diameter differences for diesel locomotives in the medium maintenance standards of China are shown in Table 1.

As seen in Table 1, the wheel diameter difference of each wheel in the same locomotive can be 10 mm for minor maintenance. The wheel diameter difference in the same bogie should not be larger than 5 mm, whereas the largest wheel diameter difference of the same wheelset is just 1 mm.

In practical operation, when the wheel diameter difference is less than 1 mm it will be detected. Therefore, the wheel diameter difference value, especially in the same bogie, will not be too large. In the simulation analysis, the wheel diameter difference in the same bogie is usually no more than 3 mm.

4. Wheelset force statements

Assuming that the right wheel diameter of the front wheelset is smaller than others, the forces which the wheelsets suffers when the locomotive running along the track including wheel/rail creep force [T.sub.ij]; suspension force [F.sub.sij] of primary suspension system; lateral resilience force [F.sub.g] which generated by gravity stiffness and traction force or braking force [F.sub.j], as shown in Figure 4, in which, subscript i means direction, x means in longitudinal direction and y means in lateral direction, j is l means the left wheel while r means the right wheel.

As the two wheels of the same wheelset were connected rigidly through the wheel axle, the angular velocities of the two wheels in the same wheelset were equalled. When the right wheel diameter of the front wheelset is smaller than others, the running speed of left and right wheels in the same wheelset is different. According to the wheel/rail creep characteristics, the left and right wheel are under longitudinal creep force with different directions, which forms a yaw moment and makes the wheelset has a yaw angle in the clockwise direction. When the wheelset has a yaw angle with positive direction (along the clockwise direction), both the left and right wheels will suffer lateral creep forces pointing to the positive direction of the y axis, and the wheelset will occur lateral offset under the function of lateral creep forces, and adjusting itself constantly. The wheelsets must satisfy the following equilibrium equations (Chi et al. 2008).

{[T.sub.y] + [F.sub.sy] + [F.sub.g] =0 [M.sub.Tz] + [M.sub.sz] + [M.sub.gz] = 0 (1)

In which, [T.sub.y] is lateral creep force; [F.sub.sy] is lateral primary suspension force; [M.sub.Tz] is the yaw moment created by longitudinal creep force; [M.sub.sz] is the yaw moment created by the primary suspension system; [M.sub.gz] is the yaw moment created by the gravity angular stiffness.

The calculation formula of the wheel tread equivalent conicity is:

[[lambda].sub.g] = ([R.sub.l] - [R.sub.r])/2[y.sub.w] (2)

In which, [R.sub.l] and [R.sub.r] are the rolling radius of the left and right wheel, respectively; [[lambda].sub.g] is the wheel tread equivalent conicity. Based on it, the wheelset lateral offset [y.sub.w] which with wheel diameter difference can be acquired as shown in formula (3):

[y.sub.w] = ([R.sub.l] - [R.sub.r])/2[[lambda].sub.g] (3)

Form formula (3) can be seen clearly that the lateral offset of wheelset is proportional to the wheel diameter difference, and is inversely related to the wheel tread equivalent conicity. The bigger the wheel diameter difference, the greater the wheel/rail longitudinal creep force, so is the wheelset yaw angle. Thus, the wheel/rail lateral creep force caused for above reason is become greater, too.

When the locomotive is in traction or dynamic braking conditions, the wheelset is suffering the function of traction moment or braking moment from the traction motor. At present, the wheel/rail longitudinal creep force mainly consists of two parts, the original wheel/rail creep forces and the creep forces caused by traction or braking forces. If the creep force caused by traction or braking force is beyond some certain level, the direction of the wheel/rail creep force will change. For example, when the locomotive is in the dynamic braking condition, the wheel/rail longitudinal creep forces of the two wheels are both along the negative poison of x axis. This makes the wheelset yaw moment generated by longitudinal creep forces significantly reduced. And the yaw angle of wheelset and the lateral creep force reduced accordingly, so is the ability of the wheelset adjusting the rolling radius between left and right wheel. Therefore, the wheel diameter difference of the two wheels in the same wheelset is bigger when the locomotive is under traction or braking forces than that in coasting condition, and it will increase the wear of wheel/rail system, and deteriorate the phenomenon of wheel/rail unsymmetrical contact.

According to the analysis above, the existing of wheel diameter difference on the tangent track will let the wheelset offset to the side which has smaller wheel diameter, and increase the wheel/rail lateral creep force. At the same time, the chance of wheel flange contact with rail is increased as well, and deteriorate the wheel/rail wears. In addition, the existing of wheel diameter difference influence the ideal wheel/rail contact relationship and forming the phenomenon of wheel/rail unsymmetrical problem, especially in traction or dynamics braking condition.

5. Dynamics model

In order to study the effect of wheel diameter difference on wheel/rail dynamic contact relationship of heavy haul locomotive, the train model which consists of locomotive and [C.sub.80] special coal vehicle was established, as shown in Figure 5. To avoid the interference of many wheelsets on the simulation results, the locomotive model adopted a 2 ([B.sub.0]-[B.sub.0]) electric locomotive, which has the axle load of 25t. The locomotive and vehicle were connected through the coupler and polymer draft gear (Wu et al. 2016; Wu, Luo et al. 2017), it can traction 10,000 tons.

The dynamic model was established according to the structural and suspension parameters of the locomotive. The locomotive model is composed of eight wheelsets, 16 axleboxes, eight traction motors, four frames and two carbodies. Carbody and frames are connected by the secondary suspension system, which contains six spring sets and two lateral and two vertical dampers on each bogie. Bogies and wheelsets are connected by the primary suspension system which made of primary springs, traction bars and vertical dampers. One end of the traction motor hangs on the axle of wheelset and the other end hangs on the bogie. The primary suspension system and the secondary suspension system are modelled in accordance with the actual parameters. The traction force between carbody and bogies are transferred by the push--pull traction bar system. To gain accurate simulation results, the nonlinear factors of springs, dampers and coupler and buffer system also take into account. The model adopts the match of JM3 wheel and 60 kg/m rail, and the rail cant is 1/40. The main parameters of locomotive are shown in Table 2. Interactions between adjacent vehicles are important inputs for train dynamics simulations (Wu, Spiryagin et al. 2017). In order to consider the interaction between the locomotive and the neighboured freight vehicle under dynamic braking condition, a detailed dynamic model of the [C.sub.80] freight car with ZK6 type bogie and a dummy freight car model which only has 1 degree of freedom were also established.

Take the fourth bogie of the locomotive which neighboured the freight vehicle as research objective, the wheel/rail dynamic interaction with wheel diameter difference were simulated and researched, the change scope of wheel diameter difference in the same bogie was from -3 to 3 mm. The value of wheel diameter difference [D.sub.i], is supposed as the wheel diameter of the left wheel [D.sub.ij] subtracted the value of the right wheel [D.sub.ir], while the absolute wheel diameter difference [DELTA][D.sub.i], refers to the absolute value of the difference between the left and right wheel diameters, as following:

[D.sub.i] = [D.sub.il] - [D.sub.ir] (4)

[DELTA][D.sub.i] = |[D.sub.ij] - [D.sub.ir]| (5)

In which, the subscript i represents the wheel position. If the value of wheel diameter difference [D.sub.i] is positive, it indicates that the rolling diameter of right wheel is smaller than the normal diameter. If [D.sub.i] is negative, it indicates that the rolling diameter of left wheel is smaller. This includes wheel diameter difference in same phase, wheel diameter difference in anti phase and the wheel diameter difference of the two wheels in the same wheelset. The normal wheel diameter is 1250 mm, and all kinds of wheel diameter difference can be acquired through the initial setting of the wheel/rail contact geometry relationship.

6. Simulation results

6.1. Coasting condition

In order to avoid the influence of the track irregularity on the wheel/rail dynamic contact relationship, the train was running on the tangent track at 70 km/h without track irregularity. Different wheel diameter differences were set on the fourth bogie.

Take the eighth wheelset for example, the changes of wheel/rail longitudinal creepages of the eighth wheelset with the changes of wheel diameter difference were shown in Figure 6. (In this paper, WDD is short for wheel diameter difference). It can be seen clearly that the wheel diameter difference will cause the increase of wheel/rail longitudinal creepage, while the direction of the longitudinal creepage of the left and right wheels was opposite. The influence of the wheel diameter difference in anti phase on the longitudinal creepage is bigger than that of the wheel diameter difference in same phase. The changes of wheel/rail lateral creepages of the eighth wheelset with the change of the wheel diameter difference were shown in Figure 7. It can be seen that the wheel/rail lateral creepages of the two wheels in the same wheelset were almost the same. As the wheel diameter difference can form a large attack angle of wheelset, large wheel/rail lateral creepage can be caused by the wheel diameter difference in anti phase.

The wheel/rail lateral force mainly consists of the lateral component force of the wheel/rail contact normal force and the wheel/rail lateral creep force. Wheel diameter difference will lead to the change of wheel/rail contact angle, and thus the wheel/rail lateral force will also have been affected.

When the wheel diameter difference of the seventh wheelset [D.sub.7] < 0, it means the left wheel diameter is smaller than the normal wheel, the left and right wheel of the seventh wheelset will have a negative wheel/rail lateral creep force and cause the wheelset offset to the negative direction of y axis. At the same time, the eighth wheelset will also offset to the negative direction of y axis through the function of the suspension system. So there are positive wheel/rail lateral creep force on the two wheels of the eighth wheelset, the direction of the creep force is same as the direction of the lateral component of wheel/rail normal force of the left wheel, while it opposed to that of the right wheel. So in the case of [D.sub.7] < 0, the wheel/rail lateral force of left wheel will increase with the increase of [DELTA][D.sub.7], and the wheel/rail lateral force of right wheel will increase when the wheel/rail lateral creep force bigger than the lateral component force of wheel/rail normal force. If [D.sub.7] > 0, the situation is opposite.

If there is a wheel diameter difference on the eighth wheelset, it will produce a certain wheel/rail lateral creep force. If [D.sub.8] < 0, the eighth wheelset will have a negative lateral creep force on both wheels. For the left wheel, the direction of the wheel/rail creep force is opposite to the lateral component force of the wheel/rail contact normal force. While for the right wheel, the force direction is the same. So for the eighth wheelset, the wheel/rail lateral force of right wheel increase with the increase of [DELTA][D.sub.8], and the wheel/rail lateral force of left wheel increase with the increase of [DELTA][D.sub.8] along the negative direction when the wheel/rail creep force is bigger than the lateral component force of the wheel/rail contact normal force. If [D.sub.8] > 0, the situation is opposite to the situation of the [D.sub.8] < 0, shown in Figure 8.

From Figure 8 it can be seen clearly that the effect of wheel diameter difference in anti phase on wheel/rail lateral force is greater than that in same phase, which is mainly due to that the wheel diameter difference in same phase will cause the front and rear wheelsets driven the bogie offset lateral towards the direction of smaller diameter wheel. Therefore, there is a larger wheelset lateral displacement, but the attack angle is smaller, as shown in Figure 9. The wheel diameter difference in anti phase will cause the front and rear wheelsets offset lateral in opposite direction, which lead to a greater yaw movement of the bogie, and has a large wheelset yaw angle, the wheel/rail lateral creep force will increase at the same time.

The wheel wear number of the eighth wheelset with the change of wheel diameter difference is shown in Figure 10, in which the colour is darker means the wheel wear is serious, while the light colour represents the wheel wear is less. The change of the wheel wear number with the change of [D.sub.7] when [D.sub.8] = 0 is represented as solid line, and the dashed line represents the change of wear number with the change of [D.sub.8] when [D.sub.7] = 0. From Figure 10 it can be seen clearly that the wheel wear is almost in angular symmetrical distribution, and the wheel wear caused by wheel diameter difference in anti phase is far larger than that caused by wheel diameter difference in same phase. The maximum of wear number for the left wheel is happened when [D.sub.7] = 3 and [D.sub.8] = -3, and the value is 1002.96 N. The minimum value is nearly 0 for the standard wheelset. The maximum of the wheel wear for right wheel is happened when [D.sub.7] = -3 and [D.sub.8] = 3, and the value is 1005.9 N. The minimum value is also nearly 0 for the standard wheelset. So the wheel diameter difference in anti phase will greatly deteriorate the wheel/rail wear, while the wheel wear is kept in a low lever for the wheel diameter difference in same phase, which is mainly due to the lateral offset of front and rear wheelsets towards the same direction, it can effectively reduce the wheel diameter difference when locomotive is running on the tangent track, at the same time, it also can reduce the wheelset yaw angle and the creepage, so the wear number is small.

6.2. Dynamic braking case

Since the application of dynamic braking force, the running speed of the train will decrease steadily. In order to avoid the influence of speed and track irregularity during the simulation, the joint of the dummy vehicle was set with constant speed. Take the train running on the tangent track at 70 km/h for example. The dynamic braking force is applied on the wheelsets of the locomotive as braking torque. The maximum dynamic braking force of the locomotive is [F.sub.Bmax] = 461 kN, so each wheelset has a braking torque about:

[T.sub.Bmax] = [F.sub.bmax] * [R.sub.0]/8 = 461 kN x 0.625 m/B = 36 kN m (6)

During the simulation, the dynamic braking torque was set to be applied from 5 s, and it reached the maximum value after 10 s linear increasing, then it kept the maximum value, as shown in Figure 11.

The apply of the locomotive dynamic braking force will increase the wheel/rail longitudinal creepage, and change the direction of the wheel/rail longitudinal creepage and let the longitudinal creep force to the major component of the total wheel/rail creep force. The wheelset yaw angle and wheel/rail lateral creepage will decrease if the wheel diameter difference exists, as shown in Figures 12 and 13. From which can be seen that the longitudinal creepage of the left wheel increases with the increase of the wheel diameter difference [D.sub.7] and decreases with the increase of the wheel diameter difference [D.sub.8]. However, the change regular of the right wheel is opposite to the left wheel.

If the wheelset yaw angle is caused by its own wheel diameter difference, the wheel/rail lateral creepage of the wheels will reduce under the dynamic braking condition compared with the coasting condition. However, the wheel/rail lateral creepage of the wheels will increase under the dynamic braking condition compared with the coasting condition if the wheelset yaw angle is mainly affected by the seventh wheelset.

Therefore, if only the influence of the wheel diameter difference of eighth wheelset is considered, compared with the coasting condition, the wheel/rail lateral force under dynamic braking condition will both translate to the positive direction of y axis in some degree if [D.sub.8] [less than or equal to] 0. The situation is the opposite if [D.sub.8] > 0, the wheel/rail lateral force will shift to the negative direction of y axis. The wheelset lateral force of the eighth wheelset in dynamic braking condition is smaller than that in coasting condition, which is shown in Figure 14. The change regular of wheel/rail lateral force in dynamic braking condition is similar with that in coasting condition, but the value of wheel/rail lateral force is different.

The dynamic braking force will reduce the wheelset's ability of adjusting the wheel rolling radius of the two wheels in the same wheelset. Therefore, in the dynamic braking condition, the existing of wheel diameter difference not only can deteriorates the wheel/rail wear problem, but also cause the occurring of unsymmetrical flange wear phenomenon, and increase the wheel diameter difference further. The wheel wear statue of the eighth wheelset in dynamic braking case is shown in Figure 15. For the left wheel, the wear number is increased with the increase of [D.sub.7], and decreased with the increase of [D.sub.8]. On the contrary, the wear number of the right wheel is decreased with the increase of [D.sub.7], and increased with the increase of [D.sub.8]. The maximum value of wear number of the left wheel is at the point of [D.sub.7] = 3 and [D.sub.8] = -3 and the value is 3717.23 N. The minimum value of the left wheel wear number is at the point of [D.sub.7] = -3 and [D.sub.8] = 3 and the value is 110.68 N. The maximum value of the wheel wear of the right wheel is at the point of [D.sub.7] = -3 and [D.sub.8] = 3 and the value is 3670.69 N. The minimum value of the right wheel wear number is at the point of [D.sub.7] = 3 and [D.sub.8] = -3 and the value is 103.14 N. As the longitudinal creepage of the wheel with smaller diameter will increase and the wheel diameter difference in anti phase will increase the wheel/rail lateral creep force in braking condition, the maximum value of the wheel wear in the dynamic braking case will occur on the wheel with smaller diameter.

7. Conclusions

(1) The exists of wheel diameter difference will lead to the increase of wheelset yaw angle, which exacerbating the wear between wheel and rail. And the wear number of wheel diameter difference in anti phase is much larger than that in same phase, the influence of wheel diameter difference in anti phase on wheelset lateral force is also larger than that in same phase;

(2) Compared with coasting condition, the wheel/rail lateral force of smaller wheel will increase and the wheel/rail lateral force of bigger wheel will decrease under dynamic braking condition, the wheelset lateral force under dynamic braking condition is relatively smaller than coasting condition;

(3) When the locomotive is steady in dynamic braking condition, the wheel diameter difference is larger than coasting condition. So the wheel diameter difference will lead to wheel flange unsymmetrical wear in the dynamic braking condition and which will increase the wheel diameter difference further.

Acknowledgements

We thank the National Natural Science Foundation of China (grant number 51575458) for their aid and support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Ruiming Zou is a PhD candidate majoring in Vehicle Engineering in State Key Laboratory of Traction Power at Southwest Jiaotong University, China. His research interests mainly include dynamic characteristics of heavy-haul locomotive; longitudinal dynamics of heavy-haul train.

Weihua Ma is an associate researcher of State Key Laboratory of Traction Power at Southwest Jiaotong University, China. His research activities are mainly in the field of railway system dynamics, focusing on vehicle system dynamics and structure design of railway vehicle, include maglev vehicle.

Shihui Luo is a full professor of State Key Laboratory of Traction Power at Southwest Jiaotong University, China. His research activities are mainly in the field of railway system dynamics, focusing on vehicle system dynamics and structure design of railway vehicle, include maglev vehicle.

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Ruiming Zou, Weihua Ma and Shihui Luo

State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, China

ARTICLE HISTORY

Received 25 May 2017

Accepted 4 December 2017

CONTACT Weihua Ma [??] mwh@swjtu.cn

https://doi.org/10.1080/14484846.2018.1456787
Table 1. Limit value of wheel diameter differences in medium
maintenance standards (mm).

                    In same   In same    In same
Item                wheelset   bogie   locomotive

Design                 1.0      2.0       2.0
Medium maintenance     1.0      2.0       4.0
Minor maintenance      1.0      5.0      10.0

Table 2. Main parameters of locomotive.

Parameter                                        Unit

Axle load                                         t
Wheelset base                                     mm
Bogie base                                        mm
Coupler height                                    mm
Longitudinal stiffness of primary suspension     MN/m
Lateral stiffness of primary suspension          MN/m
Vertical stiffness of primary suspension         MN/m
Primary vertical damper   Velocity               m/s      0.1
                          Drawing damping force   N    4250
                          compressing damping     N    4450
                          force
Longitudinal stiffness of secondary suspension   MN/m
Lateral stiffness of secondary suspension        MN/m
Vertical stiffness of secondary suspension       MN/m
Secondary vertical        Velocity               m/s                0.1
damper                    Drawing damping force   N              9340
                          compressing damping     N              8500
                          force
Secondary lateral damper  Velocity               m/s      0.025     0.05
                          Drawing damping force   N    1540      3850
                          Compressing damping     N    1820      3440
                          force
Clearance of secondary stop                       mm

Parameter                                          Value

Axle load                                            25
Wheelset base                                      2800
Bogie base                                         8900
Coupler height                                      880
Longitudinal stiffness of primary suspension         36
Lateral stiffness of primary suspension               4.83
Vertical stiffness of primary suspension              2.91
Primary vertical damper   Velocity                    0.3
                          Drawing damping force  10,000
                          compressing damping    10,000
                          force
Longitudinal stiffness of secondary suspension        0.2265
Lateral stiffness of secondary suspension             0.2265
Vertical stiffness of secondary suspension            0.557
Secondary vertical        Velocity
damper                    Drawing damping force
                          compressing damping
                          force
Secondary lateral damper  Velocity                    0.075
                          Drawing damping force    4960
                          Compressing damping      4880
                          force
Clearance of secondary stop                      35 + 5 (elasticity)

Parameter

Axle load
Wheelset base
Bogie base
Coupler height
Longitudinal stiffness of primary suspension
Lateral stiffness of primary suspension
Vertical stiffness of primary suspension
Primary vertical damper   Velocity                              0.7
                          Drawing damping force            18,000
                          compressing damping              16,000
                          force
Longitudinal stiffness of secondary suspension
Lateral stiffness of secondary suspension
Vertical stiffness of secondary suspension
Secondary vertical        Velocity                    0.3
damper                    Drawing damping force  20,000
                          compressing damping    23,000
                          force
Secondary lateral damper  Velocity                    0.1       0.3
                          Drawing damping force    5820    11,310
                          Compressing damping      6200    11,650
                          force
Clearance of secondary stop
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Author:Zou, Ruiming; Ma, Weihua; Luo, Shihui
Publication:Australian Journal of Mechanical Engineering
Date:Jun 1, 2018
Words:6142
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