Analysis on the features and potential causes of wheel surface damage for heavy-haul locomotives

Journal Pre-proofs Analysis on the features and potential causes of wheel surface damage for heavy-haul locomotives Kaikai Lyu, Kaiyun Wang, Pengfei Liu, Yu Sun, Zhiyong Shi, Liang Ling, Wanming Zhai PII: DOI: Reference:

S1350-6307(19)30785-X https://doi.org/10.1016/j.engfailanal.2019.104292 EFA 104292

To appear in:

Engineering Failure Analysis

Received Date: Revised Date: Accepted Date:

3 June 2019 21 August 2019 4 November 2019

Please cite this article as: Lyu, K., Wang, K., Liu, P., Sun, Y., Shi, Z., Ling, L., Zhai, W., Analysis on the features and potential causes of wheel surface damage for heavy-haul locomotives, Engineering Failure Analysis (2019), doi: https://doi.org/10.1016/j.engfailanal.2019.104292

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Analysis on the features and potential causes of wheel surface damage for heavy-haul locomotives Kaikai Lyu 1, Kaiyun Wang 1,*, Pengfei Liu 2, Yu Sun 3, Zhiyong Shi 4, Liang Ling 1, Wanming Zhai 1 1 State

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

2 School 3 College 4

of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei, China

of Transportation Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu, China Department of Industrial Engineering, University of Florence, Florence, Florence, Italy

Highlights This paper presents the results of a systematic investigation of wheel damage in heavy-haul locomotive based on observations of the appearance of the surface damage in different locomotive types and running routes, and the influence of sand and braking modes were discussed. The results of MBD simulations and damage predictions were also supplemented. (1) Three types of cracks are commonly observed on wheel surface, circumferential cracks on field side, transverse cracks between 65-90mm from the back of flange, and transverse cracks near flange root. (2) The cracks between 65-90mm from flange back (concentrated on 80mm) propagate to greater depths, and require additional material removal during reprofiling. (3) In small curves with 400m radius, for locomotives with B0-B0 bogies, the predicted crack is located on 60-80mm from flange back (concentrated on 65mm), which have more chance to wear off. While for locomotives with C0-C0 bogies, the predicted crack is located on 65-90mm from flange back (concentrated on 80mm), and these cracks are easy to propagate. (4) With the increase of curve radius, the crack damage of wheels decreased significantly, and the position of cracks moves to wheels centre correspondingly.

Abstract With an aim of identifying the main causes of wheel surface damage occurred in heavy-haul locomotives, this paper presents the investigation on this intractable problem including field observed, site survey, and numerical simulation. The authors set out with a detailed description of the damage features and its propagation. By globally comparing the wheel states of four different types of locomotives and their running routes, the main causes of the surface damage are analysed, and further supplemented by the results of multi-body simulations and damage predictions. The influence of sand, liquid and braking modes on surface damage is also analysed. The results show that of all the three types of cracks commonly observed on wheels, only the cracks located between 65-90mm from flange back propagate deeply. The types of bogies have great influence on wheel surface damage. In

straight line operation, the braking forces will cause the transverse cracks near wheel centre, and the crack damage of wheels on locomotive with C0-C0 bogies is more severe than locomotive with 2(B0-B0) bogies, especially in large braking forces. In small curves, the transverse cracks occur on the outer wheels of the rear wheelsets for locomotive with C0-C0 bogies, and located on the band of 65-95mm (mainly concentrated on 80mm). While for locomotive with 2(B0-B0) bogies, the cracks occurred on the outer wheels of rear wheelsets concentrate on the position of 65mm, while the cracks at this position have more chance to wear off. With the increase of curve radius, the crack damage of wheels decreased significantly, and its location moves to wheel centre correspondingly. Keywords: wheel surface damage; heavy-haul locomotive; bogie type; braking force; small curve.

1. Introduction Chinese heavy-haul industry is developing rapidly in recent years, especially in terms of the axle load and length of train formation. In this process, the wheel surface damage is reported as an intractable issue for maintenance. The wheel surface damage does not usually cause catastrophic accidents thanks for the monitoring system, such as derailment mentioned in [1-4], but the maintenance cost on wheelset due to frequently wheel turning is greatly increased. Various wheel damages disturb the railway departments all over the world, and many studies are conducted to probe the mechanisms and seek for the practical solutions. Ekberg et al. [5] give an overview of the wheel/rail rolling contact fatigue (RCF), including predictive models and some prevention measures. Handa et al. [6, 7] investigate the dominating factors and countermeasures against the tread thermal cracks. Liu et al. [8] focus on wheel tread spalling by analysing two actual cases happened on locomotives, and by suppressing the longitudinal vibration of wheelset will extend the wheel service life. Some other investigations consider the entrance of fluid (water or lubricating oil) as main factor of crack propagation [9-11]. Moreover, several predictive models are developed to assess wheel surface damage, especially for the RCF. Two commonly used modes are the shakedown map and the damage function (T γ ), which are detailed in [12]. Both models are used to predict the fatigue damage of wheels and rails, and the results show good agreement with field observation [13-16]. To relieve this problem, the first step is to make an accurate identification of its main causes. The potential root causes of wheel RCF are identified and investigated for locomotives operating on the Iron Ore Line in northern Sweden and Norway, and some mitigating actions are proposed [17]. The location and direction of cracks can give evidence of its potential causes [18]. Therefore, associating the features of observed crack with the running conditions of vehicle is essential to investigate the wheel surface damage. The surface damage on wheels is often initiated by transient impact in the wheel-rail contact, but the deterioration along with the long-term operation is also noticeable. Therefore, the research into related problem exhibits high complexity, due to the necessary consideration of propagation. The problem of wheel surface damage for heavy-haul locomotives is challenging to railway operators. Investigations into this practical problem are necessary for better maintenance and safety management. This paper presents valuable measurements and observations in locomotive depot together with dynamic simulations, thus expecting to reveal the potential causes for wheel surface damage. The features of wheel surface damage occurred on heavy-haul locomotives are firstly demonstrated, which includes the damage types, crack position and direction, crack propagation and evolution.

Following, the wheel conditions of different locomotives operated in the same railway line are introduced and compared. Then, the potential causes of wheel surface damage are summarized based on field observation and comparison. Finally, the wheel surface damage is predicted adapting the shakedown map and damage function [12], which contributes to theoretical basis for the summarized causes. The current study might lead to a better understanding of the wheel surface damage especially for heavy-haul locomotives, and the presented ideas and suggestions are hopefully expected to be valuable for promoting further research on mitigating this problem.

2. Observations of the damage patterns The focus of this study was a locomotive that is widely used in Chinese heavy-haul railway, which has double three-axle bogies (each bogie has three motored axles, named C0-C0 bogie). The maximum traction weight is about 5000t, and the operating speed is about 70km/h for loaded and unloaded trains. This type of locomotive suffers serious wheel surface damage in some fixed lines, and the average service life of wheels is only 200,000-300,000km due to frequently wheel turning and is far less than the expected 600,000km. 2.1 Damage features More than 300 wheels with different service mileage were observed for obtaining the main feature of the surface damage, and the evolution of damage was also tracked by long-term observation. The most typical feature of the damage is serious cracks distributed on profile. Three types of cracks are commonly observed according to its position and direction, as shown in Figure 1.

(a)

(b)

(c)

Figure 1. Wheel surface cracks: (a) Circumferential cracks on field side, (b) Transverse cracks near wheel centre, and (c) Transverse cracks located at flange root.

The circumferential cracks in field side (i.e. furthest from wheel flange) of wheels can be found on most wheels, as shown in Figure 1(a). As observed, these cracks are usually uniform around wheel circumference and slightly curved in the end. The measured results show that these cracks are distributed between 75-100mm from flange back. However, the length of these cracks does not show obvious deterioration with the increase of service mileage, and also does not extend into serious spalling during observation, which indicates that the cracks usually do not propagate deep into the material. The second type of crack initiates near the centre of wheel tread, as shown in Figure 1(b). These cracks often show almost transverse (with shallow angles to wheel axle). The transverse cracks are

observed between 65-90mm from the back of wheel flange, slightly away from the wheel centre toward to field side. Another transverse crack is observed near flange root, as shown in Figure 1(c). These cracks are always less severe than the aforementioned transverse cracks. For the transverse cracks near tread centre and flange root, their opening directions usually are opposite. Other types of wheel surface damage are occasionally observed on the locomotives, such as indentation mainly caused by sand, angled cracks, and serious defects on wheel surface, as shown in Figure 2. But these types of damage do not show clear correlations with the service mileage of wheels.

(a)

(b)

(c)

Figure 2. Occasionally observed damages: (a) Indentation, (b) Angled cracks on field side, and (c) Serious defects near the centre of wheel profile.

2.2 Crack propagation When the depth of cracks exceeds a certain value, they can be detected and removed by wheel turning. The amount of turned material depends on the damage depth (i.e. the surface of wheels should not have obvious cracks and defects after wheel turning). Therefore, to determine which types of cracks propagated deep into material, the measurement was also carried out in wheel turning process. The wheels in turning have been running about 140,000km after renewal, which surface condition is shown in Figure 3(a). The three common cracks are all appearing on the surface, but the cracks near the centre of wheel are most serious. Figure 3(b) shows the surface condition after turned a depth of 1mm (i.e. wheel radius reduced 1mm). It is clearly found that only the transverse cracks near wheel centre are left, the other two types of cracks are both eliminated after turned a small depth. This can prove that the circumferential cracks on field side and the transverse cracks near wheel flange usually do not propagate deeply. Figure 3(c) shows the surface condition after turned a depth of 7mm, the transverse cracks near wheel centre are still not eliminated, but the amount of cracks decreased obviously. Finally, the total turned depth is 12mm until these transverse cracks are eliminated completely. According to the record of wheel turning, the cracks near the centre of wheels are usually deeper than other damage patterns, and are difficult to eliminate. Therefore, this paper mainly focuses on this type of crack.

(a)

(b)

(c)

Figure 3. Wheel surface conditions: (a) Before turning, (b) After turned 1mm, and (c) After turned 7mm.

2.3 Evolution of transverse cracks near wheel centre As observed in wheel turning process, the transverse cracks near the centre of wheels usually propagate deeply, causing the sharp reduction of wheel service life. One locomotive was tracked for showing the growth trend of these cracks. Three observations were made at approximately four monthly intervals (the wheel running about 10,000km per month), and the surface conditions of wheels were photographed at each observation. Figure 4 gives the surface conditions of the same wheel at three observed stages. It should be noted that the wheel is never turned or renewed between observations. From continuous observations, the sporadic mental pieces firstly appeared on the tread surface when running about 40,000km, as shown in Figure 4(a). With the increase of running distance, the sporadic pieces were distributed around the tread surface, and a rough band about 12mm can be obviously seen near the centre of wheels, as shown in Figure 4(b). At the running distance of 140,000km before wheel turning, large spalling pieces can be found in the rough band, as shown in Figure 4(c). Meanwhile, depth cracks were also detected, and the transverse cracks as shown in Figure 3(b) were found during wheel turning process. Therefore, the transverse cracks near wheel centre are closely associated with the small mental pieces, then extended to entire circumference, and propagated into the material meanwhile.

(a)

(b)

(c)

Figure 4. The surface conditions after running about: (a) 40,000km, (b) 80,000km, and (c) 140,000km.

Another fact is that these transverse cracks are rarely observed on the middle wheelsets, but are more serious on the third and fourth wheelsets. The data of wheel turning shows that more depths of material for the third and fourth wheelsets are usually turned to remove the transverse cracks.

3. Potential causes for wheel surface damage The wheel states of other locomotives, the operational lines, the sand quality and braking modes were also probed and observed, which are helpful for identifying the causes of wheel surface damage. 3.1 Influence of locomotive types Four types of locomotives were once used on a same railway line, and only the locomotive analysed above (named Type A) is still in used. The traction weight, bogie types, axle loads, wheel material grades, wheel profiles and surface conditions of these four types of locomotives are listed in table 1. Type B and Type C locomotives are both consisting of two coupled sections, each section with double two-axle bogies, (each bogie has two motored axles), named 2(B0-B0) bogies. And Type A and Type D locomotives are both with C0-C0 bogies. Table 1. The four types of locomotive

locomotive

bogie

Axle load (t)

Wheel material

Type A

C0-C0

25t

R7

Type B

2(B0-B0)

25t

R7

Type C

2(B0-B0)

23t

R9

Type D

C0-C0

23t

R9

Profile shape

Traction weight (t)

Running speed (km/h)

Surface damage Serious

JM3

5000

50-70

rare rare Serious

The traction weight and running speed of these four types of locomotives are almost same on a same railway line, but their bogie types are obviously different. The Type B and Type C locomotives with 2(B0-B0) bogies are rarely suffering wheel surface damage, whereas the Type A and Type D locomotives with C0-C0 bogies are often prone to serious wheel surface damage. The difference of bogie types means the number of axles is not the same, which further influence the traction or braking capacity. For Type A and Type D locomotives, each locomotive has six axles in total, but Type B and Type C locomotives consist of eight axles. The maximum traction or braking forces supplied by locomotives are limited by wheel/rail friction coefficient. When the friction coefficient is assumed the same, the maximum traction or braking forces of locomotives are depended on its total weight. With the same axle load, the tangential wheel/rail forces of type A and type D locomotives are more serious than type B and Type C locomotives in same operational condition, which result in more easily the tears of the material and further the surface cracks. From this point of view, the surface damage of locomotive wheels is closely related to the traction or braking capacity of the locomotives. 3.2 Influence of small curves In addition to the differences in traction and braking capacity, the locomotives with C0-C0 bogies also have disadvantage on curve negotiating compared to the locomotives with 2(B0-B0) bogies, especially in small radius curves. The Type A locomotive is mainly operating on fixed lines (named line A, at the length of about 190km), and its wheels suffer serious damage. The track geometry is obtained from track recording data. Figure 5 gives the distribution of left hand (negative radius) and right hand (positive radius) curves. It can be obviously found that the sharp curves with radii of 400-500m account for a large proportion in line A, almost about 16 percent of total length. When locomotive passes curve, larger wheelset

displacements, creepages, and tangential forces are produced. The curve radius and bogie wheelbase both significantly influence on the curving performance of locomotive. During curving, the wheel-rail contact conditions are more severe when traction or braking forces are applied.

Percentage of curve length

10 line A line B

8 6 4 2 0 -1200

-800

-400

0

400

800

1200

Curve Raidus (m)

Figure 5. Distribution of curves in two lines

The Type A locomotive is also used on the other railway line (named line B shown in Figure 5), the traction weight, running speed are roughly same as in line A. The conditions of wheel surface are observed and compared after same service mileage (both about 140,000km). Figure 6(a) shows the surface condition of a wheel running in line A with sharp curves, and there are severe transverse cracks near the centre of wheel. While for the wheels running in line B, shown in Figure 6(b), although sand indentation is commonly appearing on surface, the severe cracks are rarely seen. These observations give evidence that the sharp curves have obvious influence on the wheel surface cracks.

(a)

(b)

Figure 6. The conditions of wheel surface in: (a) Line A with sharp curves. (b) Line B without sharp curves.

3.3 Influence of sand quality The sand is used automatically when the adhesion of wheel/rail decreased. The appearance of the sand used previously is shown in Figure 7(a), and the typical appearance of the wheel surface is shown in Figure 7(b). There are more indentations appeared on the tread surface, in addition, the defects shown in Figure 2(c) are more frequent. Table 2. The compositions of old and new sands Sand

SiO2

Al2O3

Fe203

CaO

TiO2

Others

Old

79.88%

12.57%

1.81%

0.11%

0.24%

5.39%

New

96.62%

0.58%

0.52%

0.06%

0.04%

2.18%

As an improved measure, the sand is replaced, as shown in Figure 7(c). The colour of the new sand is more pure in appearance than old one. The chemical compositions of the two sands are listed in Table 2. The old sand contains much higher levels of aluminium oxide and ferric oxide, while the new sand is primarily silica. In addition, the ferric oxide may not be particularly hard, whereas the aluminium oxide will be harder than the silica, and hence expected to cause more indentations on wheel surface.

(a)

(b)

(c)

Figure 7. The sands: (a) Early used. (b) Obvious indentations on wheel surface. (c) New sand

The most significant improvement after sand replacement is the decrease of indentations and serious defects. But the surface cracks are still appeared and the service life of wheels is not extended significantly. The fact that changing the sand did not effectively relieve the cracking suggests that the root cause of tread crack has less relation with the sand. 3.4 Influence of lubrication oil and other fluid The presence of rail and wheel lubricating oil, rain and snow not only reduce wheel/rail adhesion coefficient, but also enter the cracks and accelerate their propagation. The observation of turning wheels shows that the deep cracks always appear black or brown colours, as shown in Figure 9, which means that the lubricated oil or water was trapped into these cracks.

(a)

(b)

Figure 9. The deep cracks with trace of: (a) Lubricating oil. (b) Water.

It is proven that the fluid (water, grease, oil, etc.) trapped into cracks will propagate the cracks deep into material [9-11]. The observation in the turning process gives the evidence that the lubricating oil and water are appearing in the cracks. In terms of fluid entrapment mechanism, only when the tangential force is opposite to the running direction, the fluid would possibly enter the cracks. In braking condition, the crack is pulled open by braking force acting at the surface, as shown in Figure

10(a). If there is fluid on the wheel/rail interface, it will trap into the cracks. The normal force will close the cracks with trapped fluid, and the incompressible fluid generates great stress which is helpful to the growth of cracks, as shown in Figure 10(b). Wheel

Wheel

V

V

Crack Braking force

Rail

(a)

Crack

Braking force

Rail

(b)

Figure 10. The influence of fluid on crack propagation: (a) Braking force open cracks. (b) The fluid propagates cracks.

3.5 Influence of braking modes Another relevant factor of the initiation and propagation of wheel surface damage is the thermal loads [19]. In railway wheels, thermal load is normally due to the friction heating from tread braking. During tread braking, the temperature of wheel surface rises, causing the reduction of fatigue strength of the material and even generating the brittle martensite near tread surface, which will further promote the initiation of surface crack. For Type A and Type B locomotives, they are both equipped with tread brakes on each wheel. However, on normal occasions, the tread braking is only used when running speed is less than 5km/h until to stop. And during the operation, the brake mode is mainly electric dynamic braking. The control system prevents the wheel from idling and therefore the high thermal load between wheel and rail is avoided. Hence, the crack damage is unlikely caused by tread braking.

3.6 Summary of potential causes The locomotive wheels experience a full range of curves, slopes, running speeds, traction and braking forces, or even climatic variation. Therefore, the main factors responsible for wheel surface damage are very difficult to determine. From the above analysis and comparison, some useful information can be obtained for identifying the potential causes for the wheel surface damage. (1) The types of bogies obviously influence the wheel surface damage. The wheels of locomotives with C0-C0 bogies are subjected to greater tangential forces than locomotives with 2(B0-B0) bogies in the same operational conditions. The greater wheel/rail tangential forces mean that more plastic deformation occurs on wheel surface material, eventually reaching the plastic strain limit of the wheel material, and hence cracks initiate. [12]. (2) The small radius curves are another reason responsible for the wheel surface damage, especially for locomotives with C0-C0 bogies, as the wheels of locomotives with 2(B0-B0) bogies are less prone to surface damage. (3) The replacement of sand is proven to decrease the indentations and serious defects, but it does not remove the surface cracks effectively. (4) The tread braking is almost used when the running speed is less than 5km/h until to stop,

therefore, the crack damage is unlikely caused by tread braking. (5) Even though the fluid will propagate the cracks, it is difficult to completely avoid in practice, and not all types of locomotives used in the same line suffer wheel surface damage. Therefore, the fluid is not likely to be the main reason for the severe surface damage that occurs on wheels of locomotives with C0-C0 bogies. In general, according to the field measurement and observation, the bogie types and the small radius curves are considered to be the main causes for the wheel surface damage of the locomotives with C0-C0 bogies. So, the wheel surface damage is further predicted using multi-body dynamic simulation, it is hoped will provide theoretical support for its potential causes.

4. Prediction of wheel surface damage Multi-body dynamic models were used to simulate the wheel/rail interaction of locomotives, and the calculated results were further post-processed using the predicted models for wheel surface damage. The Type A and type B locomotive were analysed because of their obvious difference in wheel conditions. 4.1 Multi-body dynamic models Based on the theory of vehicle-track coupled dynamics [20], the locomotive and track coupled models are established according to their actual parameters, the track sub-model is the typical ballasted track structure according to the operational line. Figure 12(a) shows the Type A locomotive with C0-C0 bogie, each traction unit consists of only one locomotive, and its wheels suffer serious wheel surface damage. Figure 12(b) shows the compared type B locomotive with 2(B0-B0) bogies. Each traction unit consists of two identical locomotives with B0-B0 bogies. The detailed introduction of the coupled models can be found in [21]. Only one dummy freight car is considered in the model to improve the computational efficiency. The dummy body has only one degree of freedom (longitudinal) to maintain constant speed. The traction and braking forces are applied to each wheelset. V

Dummy body

(a)

Freight

Locomotive

V

Dummy body

Freight

Locomotive A2

Locomotive A1

(b) Figure 12. Three-dimensional locomotive-track coupled models (elevation): (a) Type A locomotive with C0-C0 bogies. (b) Type B locomotive with 2(B0-B0) bogies.

The main parameters of the two types of locomotives used in simulation are list in Table 3. Table 3. Main parameters of locomotives used in simulation

Parameters Bogie type Wheel profile Carbody mass Bogie mass Wheelset mass Motor mass Wheelset radius Bogie distance Wheel base Free clearance of secondary lateral stopper Elastic clearance of secondary lateral stopper Stiffness of primary suspension along X axis Stiffness of primary suspension along Y axis Stiffness of primary suspension along Z axis Damping of primary suspension along Z axis Stiffness of secondary suspension along X axis Stiffness of secondary suspension along Y axis Stiffness of secondary suspension along Z axis Damping of secondary suspension along Y axis Damping of secondary suspension along Z axis

Units

Type A locomotive

Type B locomotive

/ / Kg Kg Kg Kg m m m mm mm MN/m MN/m MN/m kN·s/m MN/m MN/m MN/m kN·s/m kN·s/m

C0-C0 JM3 94960 7168 3131 3662 0.625 12.32 2.25/2 20 40 52.0e6 2.60e6 1.71e6 45.0e3 0.54e6 0.51e6 18.0e6 67.0e3 540.0e3

2(B0-B0) JM3 62600 5114 3131 3662 0.625 10.06 2.6 20 40 166.0e6 58.4e6 1.57e6 45.0e3 0.332e6 0.332e6 1.07e6 39.5e3 45.0e3

4.2 Predicted models of wheel surface damage The shakedown map and the damage function (Tγ model) are used to predict the wheel surface damage, the reliability and accuracy of these two models have been validated in many studies [14-16]. The shakedown map used for surface initiated cracks was proposed by Ekberg et al. [22], as shown in equation (1):

FI surf  f 

2 abk 3Fz

(1)

where f is the traction coefficient, a and b are the semi-axes of the Hertzian contact patch, k is the yield limit in cyclic shear of wheel material and Fz is the normal wheel/rail contact force. The wheel surface cracks is assumed to initiate when FIsurf>0 in high traction coefficient (f>0.3). The damage function for wheels was developed from a RCF damage model for rails [23]. The accumulated damage on contact patch is calculated to estimate the degree and location of cracks in wheel profile. Considering to the effects of liquid on the propagation of cracks, the cracks damage is only counted when the direction of longitudinal creep forces is opposite to the travel direction of wheels, while wear damage is always accumulated. The damage function to predict wheel RCF and wear is shown in equation (2):

T   Tx x  Ty y

(2)

where T is the tangential force and γ is the creepage acting on wheels. The x and y are referring to the longitudinal and lateral direction, respectively. According to the material property of the wheels on the studied locomotives, the values of parameters involved in the predicted models are listed in Table 4. Table 4. Parameters used in predicted models [12, 23] Predicted models

Parameters

Value

Shakedown map

Shear yield strength

311MPa

Damage function

Crack initiation threshold

20

Crack rate

3.6×10-6/revolution/N

Wear initiation threshold

100

Wear rate

-5.4×10-6/revolution/N

4.3 Predicted results under different traction and braking forces In the fixed railway line, the traction weight of Type A and type B locomotives are roughly same, and so are the provided traction and braking forces under the same conditions. The wheel surface damage of the two types of locomotives are predicted under different traction and braking forces. The locomotives are running in straight lines, and the speeds are both 70km/h. Figure 13 gives the predicted results from the damage function. Only the results of wheel 1R are presented for analysis, the ‘L’ and ‘R’ represent the left and right sides of the wheelset. The positive and negative forces in the figures represent traction and braking forces, respectively. And the positive damage is the crack damage whereas the negative damage is the wear damage [24].

-6

Damage (N/mm/wheel revolution)

12

×10

-400kN -300kN -200kN -100kN 0kN

8 4

100kN 200kN 300kN 400kN

0 -4 -8

0

20

(a)

40 60 80 100 Distance from Flange Back (mm)

120

140

-6

Damage (N/mm/wheel revolution)

12

×10

100kN 200kN 300kN 400kN

-400kN -300kN -200kN -100kN 0kN

8 4 0 -4 -8

0

20

40

60

80

100

120

140

Distance from Flange Back (mm) (b) Figure 13. Predicted damage of wheel 1R with different traction and braking forces using damage function: (a)

Type A locomotive. (b) Type B locomotive.

It can be found from Figure 13 that, in straight tracks, the crack damage are mainly caused by the braking forces, and the traction forces mainly cause wear damage. And with the increase of braking forces, the crack damage of wheels is increased significantly. From the comparison of values of damage, the wheels of Type A locomotive suffer more crack damage than Type B locomotive under the same braking forces. When the braking forces are both 400kN, the crack damage of Type A locomotives is about 11.03 × 10-6N/mm/wheel revolution, whereas the value is only 4.28 × 10-6N/mm/wheel revolution for Type B locomotive. The crack damage band of both the two locomotive types are both near the wheel centre, mainly located in the band of 60-90mm from flange back (concentrate on 70mm). According to the vertical relation between the resultant tangential forces and the crack angles [25], the braking forces will cause the transverse cracks in straight lines. Figure 14 gives the predicted results of wheel 1R of Type A locomotive using the shakedown map. With the increase of the braking forces, the values of FIsurf are increased obviously, which means that there are more surface cracks initiated on the wheels surface.

0.6

-400kN -300kN -200kN

FIsurf

0.3

-100kN 0kN

0.0

-0.3

-0.6

Constant forces 0

10

40

30

20

50

Time (s) Figure 14. Influence of braking forces on wheel damage of Type A locomotive using shakedown map.

Therefore, the calculated results show that the braking forces will cause the transverse cracks near wheel centre, and the crack damage of wheels on locomotive with C0-C0 bogies is more severe than locomotive with 2(B0-B0) bogies. With the same traction weight, there is more serious crack damage occurring on wheels of Type A locomotive than Type B locomotive. 4.4 Predicted results in small radius curves

(a)

100

×10

-6

Damage (N/mm/wheel revolution)

Damage (N/mm/wheel revolution)

As concluded in section 3, the small radius curves also have significant influence on the wheel surface damage, especially for locomotives with C0-C0 bogies. So, the wheel surface damage is predicted and compared in curve with 400m radius, and the running speed is set to 70km/h. Figure 15 gives the predicted results of all wheels on Type A locomotives using the damage function. When the locomotive traverses small curve, there is crack damage predicted in wheel 2R, wheel 3L, wheel 5R and wheel 6L. The other wheels suffer wear damage. It is to say that, the inner wheel of the second wheelset and the outer wheel of the third wheelset are more likely to have crack damage for both of the front and rear bogies in small curves. The cracks in wheels 2R and 5R are located in the band of 65-100mm from flange back, mainly concentrated in the position of 90mm. And the predicted cracks of wheels 3L and 6L are located on the band of 65-95mm, mainly in the position of 80mm. The values of predicted crack damage are about 5×10-6N/mm/wheel revolution.

0 Wheel 1L Wheel 1R

-100 -200 -300

0

20 40 60 80 100 120 Distance from Flange Back (mm)

140

(b)

10

×10

-6

0 Wheel 2L Wheel 2R

-10 -20 -30 -40

0

20 40 60 80 100 120 Distance from Flange Back (mm)

140

-6

0 Wheel 3L Wheel 3R

-10

-20

0

20 40 60 80 100 120 Distance from Flange Back (mm)

Damage (N/mm/wheel revolution)

(c)

(e)

Damage (N/mm/wheel revolution)

×10

10

×10

140

Wheel 5L Wheel 5R

-20 -30 0

-6

0 Wheel 4L Wheel 4R

-100 -200 -300

-6

-10

×10

0

20 40 60 80 100 120 Distance from Flange Back (mm)

(d)

0

-40

100

Damage (N/mm/wheel revolution)

Damage (N/mm/wheel revolution)

10

20 40 60 80 100 120 Distance from Flange Back (mm)

140

10

×10

140

-6

0 Wheel 6L Wheel 6R

-10

-20

0

20 40 60 80 100 120 Distance from Flange Back (mm)

(f)

140

Figure 15. Predicted damage of all wheels on Type A locomotive in small curve using damage function: (a) Wheelset 1. (b) Wheelset 2. (c) Wheelset 3. (d) Wheelset 4. (e) Wheelset 5. (f) Wheelset 6.

The angles of predicted cracks to wheelset axle are also calculated for the wheel 2R and wheel 3L according to longitudinal and lateral creep forces, as shown in Figure 16. The predicted cracks of the wheel 2R show steeper angles, about 65.8deg, and the angles of the cracks in the wheel 3L are shallow, about 22.3deg. The angles of wheel 5R and wheel 6L are as same as wheel 2R and wheel 3L, respectively. From the field observation, the cracks with shallow angles (close to transverse), as shown in Figure 1(b), have more chance to propagate deep. While the cracks with steeper angles (close to circumferential), as shown in Figure 1(a), are easier to remove. The predicted results show well corresponding to the field observation. 15 Wheel 2R Wheel 3L

Perecentage of the cracks

22.3deg 10

5

0

-5 -90

65.8deg

-60

-30

0

30

Angles of cracks (deg)

Figure 16. Distribution of the angles of predicted cracks.

60

90

×10

-6

0 Wheel 1L Wheel 1R

-100 -200 -300

0

20 40 60 80 100 120 Distance from Flange Back (mm)

Damage (N/mm/wheel revolution)

(a)

(c)

Damage (N/mm/wheel revolution)

100

100

×10

140

Wheel 3L Wheel 3R

-100

0

20 40 60 80 100 120 Distance from Flange Back (mm)

×10

-6

5

Wheel 2L Wheel 2R

0 -5 -10

-6

0

-200

10

0

20 40 60 80 100 120 Distance from Flange Back (mm)

(b) Damage (N/mm/wheel revolution)

Damage (N/mm/wheel revolution)

As contrasted with the predicted results for locomotive with C0-C0 bogies, the damages of all wheels for locomotives with 2(B0-B0) are also predicted when passing small curve, as shown in Figure 17.

140

(d)

10

×10

140

-6

Wheel 4L Wheel 4R

5 0 -5 -10

0

20 40 60 80 100 120 Distance from Flange Back (mm)

140

Figure 17. Predicted damage of all wheels on Type B locomotive in small curve using damage function: (a) Wheelset 1. (b) Wheelset 2. (c) Wheelset 3. (d) Wheelset 4.

It is seen that, wheels 2L and 4L suffer cracks damage, and the others suffer wear damage. The cracks are located in the band of 60-80mm from the flange back, mainly concentrated on the position of 65mm. And these cracks are with shallow angles (about 20deg). For the rear wheelsets of each bogie, the crack damages are predicted on the outer wheels, but its inner wheels suffer wear damage more often, and the position of the crack and the wear damage is roughly same. The distribution of left hand (negative radius) and right hand (positive radius) curves is almost same (see Figure 5) in the railway line, therefore, the cracks produced in small curve have chance to wear off in the next opposite curve. And this is the biggest difference of wheel crack damage between the two types of locomotives. Consequently, the wheels on locomotive with C0-C0 bogies will have more serious cracks than locomotive with 2(B0-B0) bogies. 4.5 Influence of curve radius on crack damage For the locomotive with C0-C0 bogies, in order to analyse the influence of curve radius on the wheel crack damage, the wheel 3L was chosen to analyse in different curves, as shown in Figure 18. It is clear seen that the curve radii have significant influence on the crack damage, and with the increase of curve radius, the crack damage shows obvious decreasing trend. When the curve radius is set to 400m, the value of predicted crack damage is about 5.38×10-6N/mm/wheel revolution. And when the curve radius increased to 600m, the corresponding crack damage decreases to 4.02 × 10-6N/mm/wheel revolution. Except for the values of the crack damage, the curve radius also influences the location of the crack damage on wheel profile. And when the curve radius is 400m, the

crack damage concentrates on the position of 80mm from flange back. With the increase of the curve radius, the position of crack damage moves to the centre of the wheel (70mm from flange back), and at this position, the cracks have more chance to wear off. When the curve radius is 800m, the position of crack damage is moved to the centre of wheel (70mm from flange back), and the value of crack damage decreased to 1.91×10-6N/mm/wheel revolution correspondingly. -6

8

×10

-6

6

Damage

Damage (N/mm/wheel revolution)

6

4

R400 R600 R800 R1000 R1200

4 2 0

2

×10

400 600 800 1000 1200 Curve radius (m)

0 -2 -4

0

20

40

60

80

100

120

140

Distance from Flange Back (mm)

Figure 18. Influence of curve radius on wheel damage.

Conclusions The wheel surface damage is one of the most serious and difficult problems for the railway industry. This paper presents the analysis of the features and potential causes of the wheel surface damage for locomotives running on a heavy-haul railway line. The main features associated with surface damage are described, and their potential causes are analysed based on field observation, site survey, and numerical calculation. Some conclusions can be drawn as follows: (1) Three types of cracks are commonly observed in the wheel surface, circumferential cracks on field side, transverse cracks between 65-90mm from back of flange, and transverse cracks near flange root. And only the cracks between 65-90mm propagate to greater depths, and require additional material removal during reprofiling. (2) From the tracking measurement, the transverse cracks which are the main focus of this paper are initiated from small metal pieces and gradually spread around wheel surface. These cracks further propagate and deteriorate with the increase of running distance. During turning process, the traces of water or lubricated oil are found. Improving the sand quality reduced the severity of surface pitting/indentation, but was not effective in eliminating the cracking. (3) In straight line operation, the braking forces will cause transverse cracks near wheel centre (located 60-90mm from flange back, concentrated on 65mm), and the crack damage of wheels on locomotive with C0-C0 bogies is more severe than locomotive with 2(B0-B0) bogies, especially under large braking forces. (4) In curves with 400m radius, the transverse cracks occur on the outer wheels of the rear wheelset (wheels 3L and 6L) for the locomotives with C0-C0 bogies, and located on the band of 65-95mm from flange back (mainly concentrated on 80mm). While for the locomotives with 2(B0-B0) bogies, the cracks occurring on the outer wheels of rear wheelset (wheels 2L and 4L) are located on 60-80mm from flange back (concentrated on 65mm), which have more chance to wear off.

(5) With an increase of the curve radius, the crack damage of wheels decreased significantly, and the position of the cracks moves to the wheels centre correspondingly. In all, the locomotives with C0-C0 bogies suffer more severe crack damage due to its bogie type, especially under large braking forces and in small curves. In our future work, the mitigated measures of the wheel surface damage will be investigated, mainly including the optimization of suspension parameters and the design of wheel profile.

Acknowledgements The authors would like to thank the State Key Laboratory of Traction Power for providing equipment and materials to this project, and the CRRC Datong Electric Locomotive CO., LTD for the cooperation and support. And the authors are grateful to the reviewers for valuable technical advice and help in improving the text of this paper.

Funding The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant No. 51825504, 51735012 and 51605315) and the Program of Introducing Talents of Discipline to Universities (111 Project) (Grant No. B16041), and this paper is also supported by the Doctoral Innovation Fund Program of Southwest Jiaotong University.

Conflict of interest The authors declared that they have no conflicts of interest to this work.

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