Dynamic Analysis of Stresses and Evaluation of Service Life of Jointed Rails

PAPER

Hiroo KATAOKA Yuya OIKAWA Osamu WAKATSUKI Senior Researcher, Researcher, Senior Researcher, Track Structures & Components G., Track Technology Div.

Noritsugi ABE Nihonkido Kogyo Co., LTD

Jointed rails are replaced periodically in Japan. Their service life is governed mainly by the fracture at the joints. To evaluate the fatigue life of jointed rails, it is necessary to verify the stress distribution around fish-bolt holes and an S-N curve of jointed rails. Therefore, we carried out static loading tests in a laboratory and field tests to measure the stresses around the fish-bolt holes, and further dynamic stress analysis of jointed rails and bending fatigue tests of rails used in the field. The dynamic stress analysis model is composed of a beam model to calculate dynamic wheel/rail contact forces and a solid model to calculate stress distribution resulting from those contact forces. These models were validated using field test data. Based on the study results, we established a method to evaluate the fatigue life of jointed rails. In this method, we calculated the stresses under several combined conditions of jointed rail, vehicle type and vehicle speeds. The fatigue life was calculated by applying the stresses to the S-N curve. As a result, the rail replacement period have a potential to be extended except in cases of heavy wear between a fishplate and rail.

KeywordsKeywords: jointed rail, stress, fish bolt hole, fatigue, service life

1. Introduction 2. Jointed rail stress

To ensure operational safety, ultrasonic detection of Stress measurement positions are shown in Fig. 2. rails is carried out during maintenance, replacements The stresses were measured at 5 mm and 0 mm posi- made periodically to prevent rail fractures. The service tions away from the edge of fish-bolt holes in the 45- life of jointed rails is governed mainly by the fatigue frac- degree direction to the rail's longitudinal axis using ture at joints. There are several types of fracture, with uniaxial strain gauges. The reason for measuring at po- cracks tending to emanate from the paticularly prone sitions 5mm away is that the gauges at the 0 mm posi- fish-bolt holes, as shown in Fig. 1. As vehicles have be- tion might come in contact with the bolt holes and ren- come lighter, the number of fractured jointed rails has der the readings useless. The averages of measured val- decreased in recent years, so it is likely that rail replace- ues at 5 mm away from positions inside and outside track ment periods can be extended. gauge are called F1 (the average of F11 and F12) and F2 In order to verify the stress distribution around fish- (the average of F21 and F22) respectively, as shown in bolt holes, we had performed static loading tests and field Fig. 2. The measured values at 0 mm points are called tests as well as static stress analysis. Bending fatigue H1 and H2, as shown in Fig. 2. tests of new jointed rails had been also carried out. Running direction In this study, several tests, dynamic stress analysis and fatigue tests of used rails were carried out to evaluate service life accurately.

Inside: F11 Outside: F12

45-degree H1

5mm H2

Inside: F21 Outside: F22 Inside: inside track gauge Fig. 1 Rail fracture at a joint Outside: outside track gauge Fig. 2 Stress measurement positions

250 QR of RTRI, Vol. 46, No. 4, Nov. 2005 Table 1 Technical details of test track structure 40 H2max. Item Specifications Rail type 50kgN rail H1max.

) 20

Type for jointed rail 2 Joint Fastening （50kgN） type H1min. Other Type 5（for 50kgN） Railpad stiffness 110 MN/m (N/mm -40 Sleeper Joint Wooden tie for joint Stress amplitude type Other PC sleeper type 6 H2min. Sleeper spacing 39 sleepers / 25 m -80 01020304050 Fishbolt fastening 500 Nm torque Velocity (km/h) Fig. 4 Stress amplitudes under stepped joint and elastic 2.1 50kgN rail joint field test (1) support conditions

Running tests of a track vehicle on a tangent test increases. The negative peak value of H2 and the posi- track of a meter-gauge line were carried out to confirm tive peak value of H1 are caused by the impact wheel the basic characteristics of bolt hole stresses under clear load on the joint, so that the impact load increases un- substructure conditions. The technical details of test der stepped joint conditions. track structure are shown in Table 1. The rail was sawn into two parts, holes were drilled and rail joints as- 2.2 50kgN rail joint field test (2) sembled, so there were no irregularities on the top sur- faces of the jointed rails. To create another rail joint with In order to verify the relationship between impact a 1 mm step at the joint, shims were inserted between wheel load on the joint and stress variations, field tests the fishplates and the rail. Five sleepers around the joints were carried out with a test vehicle on which the wheel were wooden and the others were PC sleepers. load and lateral force were measured. Concrete supports were cast under the five wooden The test section was composed of ballasted track with sleepers and two supporting conditions were set, one by 50kgN rails on a 500 m radius curved section of meter- the insertion of rubber mats of 70 MN/m stiffness be- gauge line. The cant was 55 mm. The measurement was tween the concrete supports and wooden sleepers and performed at a low rail joint. The test vehicle was a Type- the other without rubber mats inserted (rigid support). 103 EMU used on local lines, set up for empty or loaded The stress variations around bolt holes at 5 km/h conditions. The velocity was set at between 10 km/h and under rigid support and no irregularity conditions are 70 km/h at 10 km/h intervals. shown in Fig. 3. The stress was set at 0 when the joint The ratio of lateral force to the wheel load was 0.02- bolts were fastened. The stresses of F11 and F12 decrease 0.12, which is small; therefore the stress variations were rapidly when the vehicle passed the joint gap. The analyzed relating to the wheel load. The wheel load was stresses of F11 and F12 as well as F21 and F22 have filtered out with a low-pass 100 Hz filter. Fig. 5 shows negative and positive smooth peak values behind the the relationship between the impact wheel load and the joints. These characteristics were consistent with past stress variations. F1min denotes the average of the mini- static test and analysis results. mum F11 and the minimum F12, and F2max and F2min Fig. 4 shows the maximum and minimum stress mean respectively the average of the maximum value of variations under stepped joint and elastic support F21 and F22 and the minimum value of F21 and F22. condintions. The stress amplitudes increase as velocity Each solid line in the figure shows a regression line. F2min correlates with the wheel load, however, F1min 20 and F2max don't correlate with the wheel load because Gap

) 10 2 40 0 F12

) 30 2 (N/mm -10 F11 − 7.54 Stress variation 20 F2max = 0.10 P -20 2 10 R = 0.26 -500 0 500 1000 0 20 F2min = − 0.21 P − 2.05 F21 -10 R2 = 0.66 ) 10 2 F1min = − 0.25 P − 7.93 -20 0 2 F22 R = 0.36 Stress amplitude (N/mm

(N/mm -10 -30

Stress variation -40 -20 0 20406080100120 -500 0 500 1000 Impact wheel load (kN) Distance (mm) Fig. 5 Relationship between impact wheel load and stress Fig. 3 Stress variations around bolt holes amplitude

QR of RTRI, Vol. 46, No. 4, Nov. 2005 251 the impact wheel load caused the former and the latter comotives passed. The ratio of stresses at the edge of the occurred at the point distant from the joint gap, as shown hole against those at a position 5 mm away at an angle in Fig. 3. of 45 degrees was less than 3.0. The results validate the previously calculated estimation that the ratio is less 2.3 60kg rail joint field test than 3.0. The bending stresses of the trailing rail measured 60kg rail joint field tests were carried out on a tan- at positions 280 mm away from the rail end are called gent section of ballasted track on a meter-gauge line. S1 (inside track) and S2 (outside track). They become We set three conditions on jointed rails, which were nor- greater in local train, limited express and locomotive mal state, with a loose sleeper and with a worn fish- order as shown in Fig. 6(b). The maximum value was 51 plate. The tests were carried out for limited express, N/mm2 under the worn fishplate condition when loco- local and freight trains. Inserting steel plates between motives passed. the rail and the sleepers adjacent to joints set the condition of a loose sleeper with a 3 mm gap between the 2.4 Static lateral loading tests sleeper and ballast. The worn fishplates were made artificially by inserting 1 mm cuts into their bottom end Static loading tests, performed on a rail with nine and top centers. sleepers, were carried out to clarify the effect of a lat- We clarified the effect of the vehicle speed, wheel eral load on the stresses. The sleepers were set on a rigid load and lateral force on the measured stress amplitudes bed, pressed down by anchor bolts and ballast mats be- under each condition by multiple regression analysis, tween the sleepers and the rigid bed with a stiffness of substituted the parameters averaged under each condi- 30 MN/m. The rail was subjected to a static load at points tion into the multiple regression equation and calculated 30 mm away from the rail end and the load angle ad- the amplitudes of stresses. The results are shown in Fig. justed to realize a predetermined ratio of lateral load to 6(a). The stress amplitudes around bolt holes in the fig- vertical load. The relationship between the ratio of lat- ure were measured when locomotives passed. eral load to constant vertical load and the stress ampli- The negative stress variations were large at H1, F11 tudes of inside and outside track gauge on their average and F12, as were the positive stress variations at H2, values are shown in Fig. 7. The average stress ampli- F21 and F22. The maximum stress amplitudes were 113 tudes with vertical load at 75 kN vary slightly with the N/mm2 at H1 and 125 N/mm2 at H2, occurring when lo- lateral load. It is likely that the average stress amplitudes mainly depend on vertical load and differences between stress amplitudes inside and outside the track Normal state Loose sleeper Worn fishplate gauge occur due to lateral load. F21 and F22 stress am- 120 plitudes near the loading point tend to increase with lat- Locomotive 㩷 90 eral load. 60 F21 F22 Average )

2 30 60 60 0 40 50kgN rail 40 60kg rail ) ) (N/mm

-30 2 20 2 20

Stress amplitude -60 0 0 (N/mm -90 -20 (N/mm -20 Stress amplitude -120 -40 Stress amplitude -40 H1 Average of H2 Average of -60 -60 F11, F12 F21, F22 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Measuring point Ratio of lateral load to Ratio of lateral load to vertical load vertical load (a) Stress amplitudes around bolt holes Fig. 7 Stress amplitudes under lateral loading (Vertical 60 load: 75 kN) Local train Limited express Locomotive 50 S1: inside track 3. Development of dynamic stress analysis model ) 2 S2: outside track 40 To evaluate rail stresses at joints, a dynamic stress 30 analysis model composed of a beam model to calculate dynamic force, and a solid model to calculate stresses 20

Stress (N/mm from the force was developed. The model was validated 10 using the test results, the points calculated being the same as those shown in Fig. 2. 0 S1S2 S1 S2 S1 S2 Measuring point 3.1 Analysis model (b) Bending stress Fig. 8 shows a whole model including vehicle/track Fig. 6 Stress in 60kg jointed rail test interaction model and finite element method (FEM)

252 QR of RTRI, Vol. 46, No. 4, Nov. 2005 model. The beam model used a Timoshenko beam as a The calculated stresses around bolt holes at 40km/h rail, a sleeper as mass, insert springs and dampers be- fluctuate after peak value due to impact load. The cal- tween the rail and sleepers as well as between sleepers culated peak stresses at positions 5mm away and at the and fixed points. Fishplates were modeled by using beam hole edge have good agreement with those in the tests elements connected to the rail by springs, the vehicle as shown in Fig. 10. modeled as a half body model. This model could take into Thus, this dynamic stress analysis model can pre- account rail discontinuity at the joints. The spring coef- dict roughly the stress variation of the jointed rail. How- ficient between rails and fishplate composed of eight el- ever, calculated dynamic forces are often reduced under ements was identified as 10 GN/m by comparing static the condition of stepped joints with low trailing rail. analyses results with those of the tests. The solid model was composed of a rail with half sleepers. Fine meshes were used to express the stress 4. Bending fatigue tests of used jointed rails concentration, which occurred around fish-bolt holes. For the analysis, we used the whole solid model first and Bending fatigue tests of used jointed rails, which go then the fine mesh model around fish bolt holes for which through an average accumulated passing tonnage of 330 the boundary condition was obtained from the displace- million gross tons (MGT) were carried out as shown in ment results of the previous analysis. Analyses were Fig. 11. The tests succeeded in making cracks at the edge carried out using a NASTRAN FEM package. of the hole and extending at a 45-degree angle, as shown in Fig.12. Based on the test results, an S-N curve express- 3.2 Validation using test results ing the remaining life of used jointed rails at the fracture probability of 50 % was obtained by weighted Probit analy- The model was validated using the results of the sis suitable for small sample fatigue data sets. To calcu- vehicle running tests under the stepped joint conditions. late the S-N curve, 10 items of data of actual rail break- Fig. 9 shows the comparison between the calculated rail ing stress were added. An S-N curve at an arbitrary frac- seat force and test results. Although the calculated peak ture probability was calculated from that at the probabil- value due to the impact load is sharper than that in the ity of 50% by assuming that standard deviation was con- tests, the calculated variation patterns are similar to stant. Fig. 13 shows the S-N curve and fatigue data. those in the tests at speeds of 10 km/h and 40 km/h.

Beam model calculating Solid model calculating Fine mesh model around dynamic force dynamic stress bolt holes

Car body (Calculating stress from displacement results of the previous analysis) Bogie V Unsprung mass Rail Railpad Sleeper

Rail Fishplate

Sleeper Fig. 8 Dynamic stress analysis model

100 100 100 100 Calculation Measurement 80 Measurement 80 Calculation 80 80 60 60 60 60 40 40 40 40 20 20 20 20 Rail seat force (kN) Rail seat force (kN) Rail seat force (kN) 0 0 0 Rail seat force (kN) 0 -1000 0 1000 -1000 0 1000 -1000 0 1000 -1000 0 1000 Distance (mm) Distance (mm) Distance (mm) Distance (mm) (a) Velocity: 10 km/h (b) Velocity: 40 km/h Fig. 9 Comparison of rail seat force under stepped joint condition

QR of RTRI, Vol. 46, No. 4, Nov. 2005 253 Measurement Gap H1 H2 Caluclation 200 40 40

150 20 20 ) 0 ) 0 2 2 100 -20 -20 (N/mm -40 (N/mm 50 -40 Stress variation Stress amplitude Dynamic force (kN) -60 -60 0 -80 -80 -1000 0 1000 -100 0 200 400 H1 Average H2 Average of F11, F12 of F21, F22 Distance (mm) Distance (mm) Measuring point (a) Calculated dynamic force (b) Calculated stress variation (c) Comparison with test at edge of holes results Fig. 10 Calculated stress amplitudes around bolt holes (stepped joint condition, velocity of 40 km/h)

S=−146logN+1407 Fatigue limit 444N/mm2 Unit : mm 10 Standard deviation 41N/mm2 800

700 130 77 ) 2 350 600 (N/mm Fig. 11 Bending fatigue test a 500 㱟

2 Failure 400 No failure

Pulsative stress amplitude 50 % S-N curve 300 104 105 106 107 Number of cycles Fig. 13 S-N curve of used jointed rail at 50% fracture Crack probability

Japanese railway companies and the rail life for replace- Fig. 12 Example of rail broken in fatigue test ment thus has the potential to be extended. However, the fatigue life under the worn fishplate condition was 5. Evaluation of remaining service life of jointed rail as short as about 10 MGT, suggesting that maintenance of the worn fishplate is important. The estimation was Miner's rule was adopted, modified so that the slope based on the results of tests under the worn fishplate in the area where the stress amplitude is under the fatigue limit becomes half that in the stress area over the Limited express, 50kgN Local train, 50kgN fatigue limit and the remaining fatigue life of used Locomotive, 50kgN Limited express, 60kg jointed rails evaluated. In the case of 50kgN rail, the Local train, 60kg Locomotive, 60kg field data measured in the past was used to estimate the 400 stresses. In the case of 60kg rail, the stresses in field high rail on curve data were relatively small because of small rail irregu- 300

larity in the field; therefore, stresses were corrected giv- ) 2 ing due consideration to the difference of the irregulari- 200 ties. Estimated stress amplitudes and the sum of remaining fatigue life and average accumulated passing ton- (N/mm 100 nage of 330 MGT are shown in Figs. 14 and 15. Stress amplitude The fatigue lives at the fracture probability of 0.1 % 0 under normal and loose sleeper conditions were over 820 Normal Worn Loose MGT for 50kgN rail and 1210 MGT for 60kg rail. They state fishplate sleeper are greater than the rail life for replacement adopted by Fig. 14 Estimated stress amplitudes around bolt holes

254 QR of RTRI, Vol. 46, No. 4, Nov. 2005 Limited express, 50kgN Local train, 50kgN 4. An S-N curve expressing the remaining life of used Locomotive, 50kgN Limited express, 60kg jointed rails, which go through an average accumu- Local train, 50kg Locomotive, 60kg lated passing tonnage of 330 MGT, was obtained from the results of the bending fatigue tests. 10000 evaluated high rail on curve 5. The fatigue lives at the fracture probability of 0.1 % remaining 1000 life under normal state and loose sleeper conditions were evaluated to be over 820 MGT for 50kgN rail and 1210 100 MGT for 60kg rail. The fatigue life under worn fish- average of (MGT) tonnage of plate conditions made artificially by inserting 1 mm 10 test rails cuts in them was as low as about 10 MGT. At the same

Fatigue life of bolt hole time, bending fatigue lives of jointed rails obtained 1 Normal Worn Loose from past study were over 690 MGT for 50kgN rail state fishplate sleeper and over 890 MGT for 60kg rail, therefore bending Fig. 15 Example of evaluated fatigue life of bolt hole fatigue must be taken into consideration when evaluating service life of jointed rails. condition made artificially by inserting 1 mm cuts in them. Thus, an estimated life under actual wear conditions may be different from that mentioned above. References At the same time, bending fatigue lives of jointed rails obtained from past study were over 690 MGT for 1) Cannon, D. F. Sinclair, J. and Sharpe, K. A., Improv- 50kgN rail and over 890 MGT for 60kg rail, therefore ing the Fatigue Performance of Bolt Holes in Rail- bending fatigue must be taken into consideration when way Rails by Cold Expansion, Proceedings of Fatigue, evaluating the service life of jointed rails. Corrosion Cracking, Fracture Mechanics & Failure Analysis, International Conference & Exposition, 1985. 6. Conclusions 2) Dukkipati, R. V. and Dong, R., The Dynamic Effects of Conventional Freight Car Running over a Dipped- To evaluate the fatigue life of jointed rails, the joint, Vehicle System Dynamics, 31, pp.95-111, 1999. stresses around fish-bolt holes were verified by static 3) Jenkins, H. H. Stephenson, J. E. Clayton, G. A. and loading tests, field tests and dynamic stress analysis. Morland, G. W., The Effect of Track and Vehicle Pa- Bending fatigue tests of rails used in actual track were rameters on Wheel/Rail Vertical Dynamic Forces, carried out and the fatigue lives evaluated under sev- Railway Engng J., pp.2-16, January, 1974. eral conditions. The following conclusions were obtained. 4) Kataoka, H. et al., Evaluation of Stresses around 1. It was verified that stress variation increased as ve- Fish Bolt Holes of Jointed Rails, In Proceedings of locity increases under the stepped joint condition with 7th International Heavy Haul Conference, Brisbane, high trailing rail, based on the results of field tests. Australia, pp.271-278, June, 2001. The peak stress value due to impact load correlated 5) Kataoka, H. et al., Evaluation of Service Life of with the wheel load measured on the vehicle. The Jointed Rails, In proceedings of World Congress on stress amplitudes obtained from 60kg rail field tests Railway Research, Koln,‥ Germany, November, 2001. were greatest under worn fishplate condition. 6) Knothe, KL. and Grassie, S. L., Modelling of Rail- 2. Static loading tests under lateral loading were car- way Track and Vehicle/Track Interaction at High ried out. The average stress amplitudes inside and Frequencies, Vehicle System Dynamics, 22, pp.209- outside the track gauge mainly depend on the verti- 262, 1993. cal load and some difference between them depends 7) Satou, Y. and Satou, Y., Life of Rail, Railway Techni- on the magnitude of lateral load. cal Research Report, No.476, 1965 (in Japanese). 3. Dynamic stress analysis model which consists of ve- 8) Thomas, J. and Abbas, B. A. H., Finite Element hicle/track interaction model and solid FEM model Model for Dynamic Analysis of Timoshenko Beam, were developed. The models were validated using the Journal of Sound and Vibration, 41, pp.291-299, test results. 1975.

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