1 Introduction
2 Design methodology
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a model of the object built based on an integrated multiphysics, multiscale, probabilistic simulation approach;
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an evolving set of data relating to the object;
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a means of dynamically updating or adjusting the model in accordance with the data;
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mirror and predict activities/performance over the life of its corresponding physical twin.
3 General concept for the development of a realistic locomotive multibody model
3.1 Background
3.2 Locomotive model acceptance procedure
3.3 Development of a locomotive model
3.4 LMAP stage 1
3.5 LMAP stage 2
3.6 LMAP stage 3
4 Key engineering operational aspects with uncertainties in the system modelling and prediction approaches
4.1 Friction at the wheel-rail interface
4.1.1 Friction in locomotive traction studies—Why is friction important for locomotive traction studies?
4.1.2 Friction characterisation—How is friction characterised in locomotive traction studies?
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Small-scale laboratory testThese tests are conducted to gain a fundamental understanding of friction. The advantages of such an approach are control over test parameters, ease to prepare the test specimen, easy data acquisition, and low cost. The specimens used in these tests are extracted/cut from the larger bodies. Thus, scaling of the contact condition is essential to represent the real-world condition. The main approaches used in this test are pin-on-disc [49, 50], twin-disc [51, 52], or scaled roller rig [53, 54].
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Full-scale laboratory testTo exactly represent the wheel-rail contact condition and reduce the uncertainty due to the scaling problem, full-scale test rigs are also in use to characterise the friction condition. The available full-scale test rig can be classified into three categories [55]: locomotive test rig, bogie test rig, and wheelset test rig. With the locomotive test rig, more parameters can be evaluated with higher accuracy which decreases respectively with bogie and wheelset rigs. However, the higher accuracy needs a trade-off with the higher cost of operation and maintenance.
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Field test utilising special instrumented vehicleInstrumented bogies and instrumented wheelsets are used to quantify the friction at wheel-rail contacts [56, 57]. Since the testing is performed under real-world scenarios, the results are reliable. However, it is one of the costlier approaches, a possible variation of parameters during the test (e.g. variation of lateral creepage) is limited and control over the test parameters may be challenging.
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Field instruments capable of measuring the traction-slip relationship
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Locomotive field tests
4.1.3 Friction models—How is friction characterised in the numerical model?
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Coulomb model
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Rational model
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Exponential model
S.N. | Friction models | References |
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1 | \(\mu =\frac{{\mu }_{\mathrm{s}}}{1+0.23v}\) | [67] |
2 | \(\mu =\frac{{\mu }_{\mathrm{s}}(f,W,V)}{1+\alpha \left(f,W,V\right)v}\) | [68] |
3 | \(\mu =0.15+\frac{0.45}{3+v}\) | [69] |
4 | \(\mu =\frac{0.03}{0.2+v}+\frac{15}{100+{v}^{2}}\) | |
5 | \(\mu =\frac{0.3}{2+v}+\frac{15}{100+{v}^{2}}\) | [65] |
S.N. | Friction models | References |
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1 | \(\mu ={\mu }_{\mathrm{s}}(\left(1-A\right){\mathrm{e}}^{-Bv}+A)\) | |
2 | \(\mu =0.175+0.175{\mathrm{e}}^{-1.5v}\) | [73] |
3 | \(\mu =0.32+0.18{\mathrm{e}}^{-6v}\) | [74] |
4 | \(\mu =0.15+0.15{\mathrm{e}}^{-{\mathrm{log}}^{2}\frac{v}{3}}\) | [69] |
5 | \(\mu =0.33+0.18{\mathrm{e}}^{-{\mathrm{log}}^{2}\frac{v}{1.25}}\) | [66] |
4.2 Advances in contact models for traction studies
4.3 Wheel-rail wear in traction studies
Wear model | KTH | Sheffield | British | Florence | Budapest | Coimbra |
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Material | ||||||
Rail | UIC 900A, UIC1100 | UIC 900A | BS11 | UIC60 | BS11 | EN 260 |
Wheel | R7 | R8T | R8T | ORE S1002 | Unknown | R7 |
Friction condition | Dry, lubricated | Dry, wet | Dry | Dry | Dry | Dry |
5 Parallel computing in locomotive traction studies
5.1 Parallel computing basics
5.2 MPI-based parallel co-simulation
5.3 TCP/IP and OpenMP-based parallel co-simulation
5.4 Locomotive traction simulations using parallel computing
Location (km) | Model | Traction force (kN) | Adhesion force utilisation (%) | Equivalent adhesion coefficient |
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3.15 | LTD | 460 | 100 | 0.350 |
2D | 400 | 87 | 0.305 | |
3D | 416 | 90 | 0.315 | |
3.3 | LTD | 460 | 100 | 0.350 |
2D | 390 | 85 | 0.298 | |
3D | 410 | 89 | 0.312 |
6 Design of novel power technologies through advanced locomotive studies
6.1 Modelling technique of hybrid locomotives
General information | Diesel-electric | Hybrid |
Power type | Diesel-electric | Electric (battery) |
Wheel arrangement (UIC/AAR) | Co–Co/C–C | Co–Co/C–C |
Dimensions (approximately) | ||
Length (mm) | 21,200 | 21,200 |
Width (mm) | 2950 | 2950 |
Height (mm) | 4245 | 4245 |
Locomotive weight (t) | 136.2 | 136.2 |
Axle load (t) | 22.7 | 22.7 |
Topology of electric power transmission system | AC–DC–AC | DC–AC |
Wheel diameter (mm) | 1066 | 1066 |
Power plant and battery system data | ||
Power output (gross) (kW) | 3356 | – |
Battery system maximum discharge/charge capacity (kW) | 3100/5000 | |
Battery system specification (MWh) | 5 | |
Performance figures | ||
Traction power (kW) | 3100 | 3100 |
Tractive effort | ||
Maximum starting traction effort (kN) | 600 | 600 |
Maximum continuous traction effort (kN) | 520 | 520 |
Maximum dynamic braking power (kW) | – | 5000 |
Maximum dynamic braking effort (kN) | 325 (from 50 to near 0 km/h) | 325 (from 50 to near 0 km/h) |
6.2 Using simulation tools to assess locomotive design outcomes
7 Challenges in the development of locomotive models and digital twins
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Friction mapping The exact representation of friction conditions in the V-model Stage 3 (see Fig. 2) based on the locomotive position on the track should be implemented in the model. There are a great number of complexities associated with the introduction of the changes in friction conditions into the model. These are associated with the existing friction models having no explicit physical interpretation [72]. Some limited research activities in this area are in progress [112, 113]. There are almost no research activities in terms of numerical modelling on the distribution of lubricants along the track and across the top of the rail under operational conditions.
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Environmental conditions There are no exact models or studies on how the environmental conditions should be introduced in digital twins. The recent research shows that the weather has a significant influence on the train operational results [117]. It is also necessary to consider other external loads that might act on a locomotive such a wind, wind gusts, etc. There is a question regarding how to connect simulations to the meteorology database and how to use such data in the detailed analysis.
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Wear mapping and RCF Most rail wear models are built on the data delivered for specific wheel and rail materials. Most researchers currently use these models that can be considered as indicators only for possible wear and RCF developments. There are some developments in this area [93]. However, questions exist on how the laboratory measurements should be transferred into a real-world application scenario [118, 119] and how worn wheel and rail profiles should be introduced in the model for long-term track studies, especially, for cases where mixed train operations (for example, passenger and freight) are in progress.
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Train simulations This area progresses very well in terms of the improvements that have recently been made [22]. However, some challenges still exist as part of operational uncertainties. One such challenge relates to train resistance [120, 121] and virtual driver modelling issues considering that each train driver uses his own driving strategy. It might not be a problem for unmanned train operations because they are based on predefined algorithms.
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Software implementation The continuing improvement in computer technology requires development of more capable algorithms for co-simulation and parallel computing tasks considering that the V-model described in this paper is a multidisciplinary-based model.