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Analysis of rail milling as a rail maintenance process: Simulations and experiments
Wear 438-439 (2019) 203029
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Analysis of rail milling as a rail maintenance process: Simulations and experiments
T
Wilhelm Kubina,∗, Werner Davesb,c, Richard Stockd a
Linsinger Maschinenbau Gesellschaft m.b.H., Austria Materials Center Leoben Forschung GmbH, Austria c Institute of Mechanics, Montanuniversitaet Leoben, Austria d LINMAG GmbH, 994 Lillooet Rd., North Vancouver, BC, V7J 2H5, Canada b
A R T I C LE I N FO
A B S T R A C T
Keywords: Rail maintenance Rail milling Finite element simulation Wheel/rail interaction Residual stresses Microscopic investigation
The maintenance process rail milling and the rolling contact behavior of a milled rail are analyzed in detail. By using commercial finite element programs the milling process and the rolling-sliding contact of a wheel on a milled rail are simulated with 3D and 2D methods. These results are compared to experimental results and metallographic investigations of a milled rail after an actual milling process and after milling tests that were done in track together with a European infrastructure manager (IM). A satisfying agreement is shown by comparing the obtained numerical results with the experimental results and metallographic investigations.
1. Introduction Continuously increasing demands on rail transportation result in higher dynamic axle loads, train speeds and volume of traffic. This leads to increasing requirements on rail materials to resist wear and rolling contact fatigue (RCF). Typical RCF defects like “squats”, “head checks”, “spalling” and “shelling” as well as other defects like “wheel burns” or “corrugation” can impact ride comfort and safety and will reduce rail life. To keep rails in a functional and safe condition and to prevent premature rail failure, different rail maintenance strategies can be applied. The two commonly used maintenance technologies to extend rail lifetime are rail grinding and rail milling. This paper is focusing on 3D and 2D simulations of the maintenance process rail milling and the rolling contact behavior of a milled rail in service. Milling as such is primarily used in industrial machining processes and is a rather new application for rail maintenance services. Rail milling can be described as a dry rotational cutting process that results in a reprofiled rail head without producing “new” RCF defects. In addition, it is a safe, clean and spark-free process and has a very high level of geometrical accuracy, which means that the measurements of the longitudinal and transversal profile after milling show quite lower values than the threshold values of the European Norm EN 13,231-3:2012. A further advantage of this process is the possibility to remove several millimeter deep defects in only one pass. Fig. 1 shows schematically the assembly milling tool/rail head with a close-up view of the interaction region. Simulations and
∗
metallographic investigations can help to get a better understanding of this very complex metal machining process and its influence on the wheel/rail rolling-sliding contact behavior. Several finite element studies deal with the description of machining processes in general. Predictions of the chip formation, the cutting forces and the temperature field in the process zone are demonstrated in Refs. [1–6]. Various studies focus on the cutting process and deal with the machining-induced residual stresses [7,8]. Description of the milling process in general concerning the temperature, the load conditions and the milling forces are investigated in Refs. [9–11]. Simulations for the description of the contact between rough surfaces are investigated in different ways. Studies of contact between single asperities regarding the damage behavior and contact pressure distribution are presented in Refs. [12–14]. Investigations of rough surfaces with purely elastic material behavior deal with the contact pressure and stress distribution can be found in Refs. [15–18]. Contact simulations with rough surfaces or single asperities under pure normal loading and with an elastic-plastic material behavior are performed in Refs. [19–24]. Numerical studies deal with the rail/wheel rollingsliding contact between two rough surfaces and with elastic-plastic material behavior are demonstrated in Refs. [25–29]. This paper aims to present 3D and 2D finite element simulations of the milling process as rail maintenance and the rolling-sliding contact of a wheel on a maintained rail by milling. The milling model results are compared to experimental and metallographic investigations of a
Corresponding author. E-mail address: [email protected] (W. Kubin).
https://doi.org/10.1016/j.wear.2019.203029 Received 15 January 2019; Received in revised form 12 June 2019; Accepted 23 August 2019 Available online 24 August 2019 0043-1648/ © 2019 Published by Elsevier B.V.
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Fig. 2. 3D milling model with the selected boundary conditions and detailed views of the used rail profile and the insert distribution.
and detailed views of the used rail profile and the location of the inserts in the tool holder segment. For a detailed study of the rail milling process with respect to the temperature field and the stress field in the process zone and resulting milling force a 2D model was set up using the finite element program Abaqus/Explicit and an Arbitrary-Lagrangian-Eulerian (ALE) method. This method merges a pure Lagrangian method with a pure Eulerian method to separate the mesh motion from the material flow which is often used in high dynamic nonlinear numerical calculations like milling. It prevents a large distortion of the finite element mesh and allows simulating a stable machining process. The numerical model represents a part of a rail head next to the milling area and one milling insert with a common edge radius, a negative rake angle and a positive clearance angle. The milling process is simulated accurately without any artificial numerical influences by applying a set of well-chosen boundary conditions and dimensions on the rail part and the milling insert. Special features of the model are the assumption of an initial chip with Eulerian boundary conditions to allow a material outflow at the rail top surface and the assumption of Eulerian boundary conditions on the left side of the rail to allow a material inflow. With the assumption of Lagrangian boundary conditions on the right side, the rail part is able to grow in size, which gives a general picture of the machined rail. In this 2D numerical study, a detailed investigation of the milling process is made about the resulting milling force and the development of the temperature field and stress field in the process zone and the machined rail. The mesh of the rail part is partitioned with different kinds of continuummechanical formulations to guarantee a stable milling simulation. For partition 1, a pure Lagrangian formulation is used, where the motion of the material and the mesh are merged. In the regions of partition 2, a mixture of the Lagrangian and Eulerian formulation is used, which enables a combined motion of the material and the mesh in a horizontal direction and a separated motion in vertical direction. A pure Eulerian formulation is used in partition 3, where the material flows through a fixed mesh. The edge nodes of the initial chip are coupled with a kinematic constraint to prevent a high distortion of elements during the change of the chip thickness. The simulated milling insert is moveable by using a reference point at the top of the tool tip which is tied to an analytical rigid body. For a transient cutting process with non-constant uncut chip thickness, the milling insert can be moved in vertical direction, but it is fixed in horizontal direction. In this numerical research, a thermo-mechanical coupled analysis is performed to predict the temperature field and the stress field in rail, chip and milling insert. The assembly of the 2D milling model with the chosen boundary conditions is shown in Fig. 3.
Fig. 1. Assembly of the milling tool (tool holder and cutting inserts) and a rail head with a close-up view of the interaction region.
milled rail after an actual milling process at the test track of the company partner LINSINGER/LINMAG in Austria. Besides the results of the rolling-sliding contact simulation are compared to experimental results of milling tests that were done in track together with a European IM in summer 2017.
2. Simulation models 2.1. Milling models A general picture of the whole milling process can be shown in a 3D model set up with the finite element code DEFORM 3D V11.1. This FE program was used due to its fast and robust remapping algorithm which is needed to calculate such a complex machining process in 3D. The milling tool is modeled as a rigid body, and for the material description of the rail head an elastic-plastic behavior is used. For both parts, the rail and the tool holder, tetrahedral elements with a higher element density at the top surface of the rail head and the insert area of the tool holder are taken to model the chip formation process accurately. The simulated rail head has a typical 60E2 profile and is fixed in space by using vertical and horizontal constraints at its bottom. In the simulation the tool holder segment has fifteen cutting inserts in three rows where five inserts are attached per each row. The friction coefficient μ and the heat transfer coefficient are set to 0.4 and 11−09 W/m2K respectively. On the center point of the tool holder an angular velocity . φ and a feed rate x˙ are applied. A theoretical milling depth of about 1 mm is used in this study. The actual milling depth can be higher or lower due to the positioning of the insert in the tool holder and the deformation state of the worn rail profile. Fig. 2 shows the assembly of the milling tool and the rail head with the chosen boundary conditions 2
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Table 3 JC parameters of the R260 rail steel. A [MPa]
B [MPa]
C
ε˙0
n
m
Troom [K]
Tmelt [K]
304.1
861.6
1.53e-02
1
0.144
0.633
293
1793
temperatures, made at the Materials Center Leoben in Austria, and experimental data at elevated strain rates of rail steels demonstrated in Ref. [33] were used to calculate the required JC parameters. The calculated parameters which represent a standard rail material of the steel grade R260 are presented in Table 3. 2.2. Rolling-sliding contact model In a second step, a 2D finite element model has been developed using ABAQUS/Standard for cyclic investigations of a wheel rollingsliding on a machined rail. The model consists of a part of a rail head and a wheel and includes the profile and surface roughness of a machined rail. To consider the influence of the milling process on the rolling contact and fatigue behavior of a machined rail, it is necessary to map the results of measurements, such as surface roughness and the residual stress field, onto the rolling-sliding contact model. In the simulation the wheel is described with elastic material behavior and the rail with plastic kinematic hardening behavior published in Ref. [26]. With these models the cyclic plastic deformation of remaining milling facets, the change of the surface roughness and the resulting residual stress field of machined rails can be determined after some passes of a wheel. Fig. 4 shows the assembly and the chosen boundary conditions of the rolling-sliding simulation with a schematic close-up view of the milling facets area. The facets dimensions, the length fz and the height H, depend on the chosen set of milling parameters like milling velocity, feed and tool holder radius. The three idealized facets are modeled with a length fz of 5.36 mm and a height H of 11.9 μm. The remaining surface of the rail part stays flat. This is a valid method for analyzing the influence of the roughness during a rolling-sliding contact, which has been reported in Ref. [26]. In this study, normal loads FN of about 7 kN,
Fig. 3. The 2D milling model with the chosen partitions and boundary conditions. Table 1 Model and process parameters of the milling simulation. Parameter
Value
horizontal cutting velocity vx & feed [mm/s] max. uncut chip thickness uy (max) [μm] shear stress limit τmax [MPa] friction coefficient μ Quinney-Taylor coefficient β milling time tmilled [ms]
3750 389 290 0.4 0.9 6.8
The horizontal component of the milling velocity vx(t) and the feed of the milling insert are applied on the inflow surface of the rail part. The combination of the horizontal velocity and the feed is nearly constant and is set to a value of 3750 mm/s in this case. By using the vertical component of the milling velocity and the milling time a vertical displacement uy(t) is calculated and applied as a linear amplitude on the reference point of the milling insert. In this case one milling insert has to remove a maximum uncut chip thickness of 389 μm in a milling time of 6.8 ms for a theoretical rail milling depth of about 1 mm. In the simulation a friction coefficient μ of 0.4 and an artificial shear stress limit of 290 MPa are used due to the chosen process parameters, numerical material tests and a combination of the calculation methods for the friction coefficient published in Refs. [30–32]. The heat produced by contact flows 50 to 50 into the milling insert and the rail part. For the conversion of the plastically dissipation energy to heat a Quinney-Taylor coefficient of 0.9 is used. An overview of the model and process parameters for this study is given in Table 1.
2.1.1. Material parameter The used elastic and thermos-physical material parameters of the rail part and the uncoated milling insert are shown in Table 2. In addition the Johnson-Cook (JC) constitutive material model is used to describe the plastic behavior of a standard rail material of the steel grade R260. An example of the JC constitutive equation is given in Ref. [9]. For the plastic rail material description tensile tests at different Table 2 Elastic and thermo-physical properties of the rail material and the tool material. Properties
Rail material (R260)
Tool material (K20)
Density ρ [kg/m³] Conductivity λ [W/mK] Specific heat c [J/kgK] Young's Modulus E [MPa] Poisson's ratio υ [−]
7850 42 490 219,000 0.29
14,750 88 296 630,000 0.22
Fig. 4. 2D rolling-sliding model with the chosen boundary conditions and a schematic close-up of the milling facet area. 3
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Fig. 5. Cross section of the used rail samples (above) and the simulated rail head (below) before and after the milling process. On the right side of the figure a qualitative comparison of the real and simulated chips is shown.
12 kN and 19 kN with accelerating and braking slip values of 0.0%, 0.5%, 1.0% and 1.5% are applied. The normal loads have to be recalculated by using the load transfer methodology published in Ref. [27] and correspond approximately to wheel loads of about 4 t, 8 t and 16 t. The developed contact patches have lengths of 11.6 mm, 14.3 mm and 17.8 mm and nominal maximum contact pressures of 0.8 GPa, 1.0 GPa and 1.4 GPa regarding the studied normal load cases.
Fig. 6. Close-up views of the rail surface before (left column) and after (right column) rail reprofiling by an experimental milling test.
3. Results and discussion Surface contour measurements help to get a general picture of the rail profile on a milled rail. For the analysis of the rail reprofiling process by milling an arbitrary rail contour was milled on a typical 60E2 profile in an experimental test made at the construction facility of Linsinger/LINMAG in Austria. Fig. 5 above shows a superimposition of the cross section of the rail head before milling, colored in red, and the cross section of the rail head after rail reprofiling, colored in green. By comparing the superimposed rail head cross sections, a precise reprofiled rail head without any contour imperfections can be shown due to rail milling in only one pass. For the validation of the obtained simulation results, Fig. 4 below represents the cross section of the nonmachined rail head, colored in red, superimposed by the cross section after the simulated milling process, colored in blue. The similarity between metallographic investigations and simulations can be shown by comparing the profile change, shown on the left side in Fig. 5, and the produced chips, shown on the right side in Fig. 5. The difference between the experiment and the simulation is only about 3% by comparing the maximum milling depth at the gauge corner of the rail. With these results an acceptable agreement between the real and the simulated milling process can be shown. For a better visualization of the rail surface conditions and the quality of the rail head after the reprofiling process by milling, Fig. 6 represents microscopic investigations at 200× magnification of the rail head at three locations in transversal direction before and after milling. An uneven and rough rail surface condition can be seen at the nonmachined rail head, colored in red in Fig. 6 (left column). In contrast the milled rail head shows a smooth surface condition without damage and micro-cracks, colored in green in Fig. 6 (right column). For the detailed analysis of the rail milling process, the obtained results of the 2D simulation are needed. In Fig. 7a the development of the resulting total milling force per plane thickness concerning the milling time of one milling insert during one pass is shown for a maintenance process with the previously mentioned set of milling parameters. At the beginning of the simulated milling process, the milling force fluctuates as a result of the first impact between tool and workpiece, the inertia effects, the initial chip flow, the thermal softening behavior of the chip and elastic deformation of the tool tip. The total milling force increases until the maximum uncut chip thickness is
Fig. 7. a) Development of the total milling force per plane thickness with respect to the milling time of one insert. b) The influence of the uncut chip thickness on the maximum resulting milling force for various analyzed sets of milling parameters.
reached. A maximum amount of around 900 N/mm is obtained after 1.4 ms. Afterwards, the milling force decreases nearly to the zero level in a period of about 5.4 ms. The amount of the milling force depends
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Fig. 9. The development of temperature in the rail, chip and the milling insert during the simulated milling process at five chosen milling time states.
and at not more than 300° the material can be regarded as uninfluenced by temperature. For the verification of the obtained simulation results metallographic investigations of the rail head after the experimental milling test were made, shown in Fig. 10 at 100× magnification. The left orange framed picture shows the microstructure of the rail head in transversal direction. The microstructure of the rail head in longitudinal direction is illustrated in the right green framed picture. The used and partitioned rail sample for the metallographic investigation is shown in Fig. 10 above. The microstructure in both directions, longitudinal and transversal, appears uninfluenced by temperature as an unchanged pearlitic microstructure is found. No visible surface roughness is recognizable in the pictures between the milling facets. Fig. 11 shows the average values of measured and simulated residual stresses in relation to rail depth in a) axial direction and b) transverse direction. The residual stress measurements were done at milled and traffic loaded rail samples after a time interval of 11 days in track and about 120,000 tons of loading, represented by the red dotted
Fig. 8. The development of the Von Mises stress in the rail, chip and the milling insert during the simulated milling process at five chosen milling times.
mainly on the maximum uncut chip thickness and thus on the material resistance of the workpiece. Several milling parameters, like milling velocity, milling depth and feed rate can be changed and if the same maximum uncut chip thickness is maintained, the milling force stays at the same level. Fig. 7b shows the development of the maximum total milling force with respect to the uncut chip thickness for various sets of milling parameters. The change of the above mentioned milling parameters shows no influence on the resulting total milling force, shown in Fig. 7b. The maximum resulting milling force per plane thickness demonstrates a linear behavior with increasing the uncut chip thickness. The distribution of the Von Mises stress in the rail and the tool is presented in contour plots at defined milling times in Fig. 8. During the whole milling process the Von Mises stress distribution in the rail stays nearly constant. A maximum stress value of about 1.0 GPa is reached, which corresponds to a typical nominal contact pressure of an 8 t wheel in the wheel-rail interaction system (numerically predicted). Therefore, it is assumed that milling influence on the rail is comparable to a standard wheel loading. In the milling insert the Von Mises stress increases significantly and reaches its maximum – localized at the tool tip – at the end of the milling process. The decrease of the uncut chip thickness is accompanied by a higher decrease of the tool-chip contact area resulting in a stress peak in the tool. Due to this stress peak, damage can be initiated preferred at the tip of the milling insert. The obtained temperature result of the 2D milling simulation is illustrated in Fig. 9. The development of the temperature field in the milling area of the insert and the rail head is shown in counter plots at five chosen milling time states. A temperature of about 800° is reached in the chip nearby the contact surface after a milling time of 1.4 ms. This temperature stays constant until a milling time of 3 ms. Afterwards it decreases and reaches a value of 600° at the end of the simulated milling process. The temperature at the surface of the milling insert shows its maximum value of about 900° after a milling time of 5 ms which subsequently decreases to 700° nearby the surface of the insert tip. The highest temperature at the surface of the machined rail is about 300° and this indicates no significant thermal influence on the remaining rail material during and after milling. The simulation demonstrates that the main part of the produced heat flows into the chip and the milling insert. Only a small part flows into the machined rail
Fig. 10. Metallographic investigation of a rail head after the experimental milling test. 5
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4. Conclusions This numerical and experimental study shall help to better understand and optimize rail re-profiling processes. Additionally, it shows that rail milling is an appropriate maintenance process which can remove rail defects, keeping the rail material and the rail microstructure in its initial state. From the developed simulations and experiments, the following main conclusions can be made:
• A similarity between metallographic investigations of a rail head • • •
•
Fig. 11. The average values of the measured and simulated residual stresses over the rail depth in a) axial direction and b) transverse direction.
lines, and after 7 months in track and about 2,300,000 tons of loading, represented by the green dashed lines. The measurements of a worn rail sample out of the same track without maintenance action are represented by the blue dashed-dotted lines in the diagrams. Five measurement points on each analyzed rail head in lateral direction are averaged, to get typical residual stress profiles for the tested rail condition. The simulated residual stresses, represented by the black continuous lines, are the average values of all simulated load and slip cases after five cycles of rolling-sliding contact. In the simulations the influence by the surface roughness in submicron range was not taken into account and therefore no values are indicated for the first 30 μm at the rail surface. The axial residual stresses of the worn rail sample and the milled and traffic loaded rail sample after 11 days in track show almost the same development with increasing rail depth, demonstrated in Fig. 11a. After 7 months in track the axial residual stresses decrease further, and higher compressive stresses are detected. The simulated axial residual stress values and the measured results of the rail sample after 7 months in track show in average almost the same development with respect to the depth. The transverse residual stress values of the milled and traffic loaded rail samples are far more in the compressive range as in the worn rail, demonstrated in Fig. 11b. The same behavior is found in the simulations. This is valid for the transverse direction and axial direction. Lower residual stress values in the non-maintained (worn) rail can be explained, since residual stresses will be reduced by cracks. The exact load and refurbishing history of this rail is unknown and it is probably only a pure coincidence that the milled and 0.12 MGT loaded rail (red dotted line) has nearly the same axial residual stresses. The obtained results of the rolling-sliding contact simulation match satisfactorily with the measurements of the in-track-test samples, especially the rail sample after 7 months of slight (approximately 2.3 MGT of loading) traffic in track.
after a milling test and the 3D simulations of the milling process is shown by comparing the profile change and the produced chips. A reprofiled rail head without visible contour imperfections is produced due to rail milling in one pass. The resulting milling force depends linearly on the maximum amount of the uncut chip thickness. An increase of the maximum uncut chip thickness raises the material resistance of the workpiece and thus the milling force. The Von Mises stress distribution in the rail directly after the cut stays nearly constant during the whole milling process. A maximum stress value of about 1.0 GPa is reached, which corresponds to a typical loading by an 8 t wheel in the wheel-rail interaction system. The results of the milling simulation show that a maximum temperature of about 300° is reached at the surface of the machined rail. Such temperatures do not influence the remaining rail material during and after milling. Metallographic investigations demonstrate an unchanged pearlitic microstructure and no phase changes, like martensitic layers, after rail milling, which confirm the numerical results. By comparing the development of residual stresses in the rollingsliding contact simulation and the measurements of the in-track-test a satisfying agreement is shown. The measurements and the simulations show compressive residual stress fields after a specified time/tons of loadings in track.
Declaration of interest None. Acknowledgement The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center “Integrated Computational Material, Process and Product Engineering (IC-MPPE)” (Project No 859480). This program is supported by the Austrian Federal Ministries for Transport, Innovation and Technology (BMVIT) and for Digital and Economic Affairs (BMDW), represented by the Austrian research funding association (FFG), and the federal states of Styria, Upper Austria and Tyrol. References [1] C.Z. Duan, T. Dou, Y.J. Cai, Y.Y. Lin, Finite element simulation and experiment of chip formation process during high speed machining of AISI 1045 hardened steel, Int. J. Recent Trends Eng. 1 (2009) 46–50. [2] P.J. Arrozola, D. Ugarte, J. Montoya, A. Villar, S. Marya, Finite element modeling of chip formation process with Abaqus/ExplicitTM 6.3, in: E. Oñate, D.R.J. Owen (Eds.), Proceedings of VIII International Conference on Computational Plasticity, Barcelona, September 5-8, 2005, CIMNE, 2005. [3] M. Abouridouane, F. Klocke, D. Lung, D. Veselovac, The mechanics of cutting: insitu measurement and modelling, Procedia CIRP 31 (2015) 246–251. [4] X. Man, D. Ren, S. Usui, C. Johnson, T.D. Marusich, Validation of finite element cutting force prediction for end milling, Procedia CIRP 1 (2012) 663–668. [5] T. Özel, T. Altan, Process simulation using finite element method – prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling, Int. J. Mach. Tool Manuf. 40 (2000) 713–738. [6] S.M. Afazov, S.M. Ratchev, J. Segal, Modelling and simulation of micro-milling cutting forces, J. Mater. Process. Technol. 210 (2010) 2154–2162.
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Analysis of rail milling as a rail maintenance process: Simulations and experiments
T
Wilhelm Kubina,∗, Werner Davesb,c, Richard Stockd a
Linsinger Maschinenbau Gesellschaft m.b.H., Austria Materials Center Leoben Forschung GmbH, Austria c Institute of Mechanics, Montanuniversitaet Leoben, Austria d LINMAG GmbH, 994 Lillooet Rd., North Vancouver, BC, V7J 2H5, Canada b
A R T I C LE I N FO
A B S T R A C T
Keywords: Rail maintenance Rail milling Finite element simulation Wheel/rail interaction Residual stresses Microscopic investigation
The maintenance process rail milling and the rolling contact behavior of a milled rail are analyzed in detail. By using commercial finite element programs the milling process and the rolling-sliding contact of a wheel on a milled rail are simulated with 3D and 2D methods. These results are compared to experimental results and metallographic investigations of a milled rail after an actual milling process and after milling tests that were done in track together with a European infrastructure manager (IM). A satisfying agreement is shown by comparing the obtained numerical results with the experimental results and metallographic investigations.
1. Introduction Continuously increasing demands on rail transportation result in higher dynamic axle loads, train speeds and volume of traffic. This leads to increasing requirements on rail materials to resist wear and rolling contact fatigue (RCF). Typical RCF defects like “squats”, “head checks”, “spalling” and “shelling” as well as other defects like “wheel burns” or “corrugation” can impact ride comfort and safety and will reduce rail life. To keep rails in a functional and safe condition and to prevent premature rail failure, different rail maintenance strategies can be applied. The two commonly used maintenance technologies to extend rail lifetime are rail grinding and rail milling. This paper is focusing on 3D and 2D simulations of the maintenance process rail milling and the rolling contact behavior of a milled rail in service. Milling as such is primarily used in industrial machining processes and is a rather new application for rail maintenance services. Rail milling can be described as a dry rotational cutting process that results in a reprofiled rail head without producing “new” RCF defects. In addition, it is a safe, clean and spark-free process and has a very high level of geometrical accuracy, which means that the measurements of the longitudinal and transversal profile after milling show quite lower values than the threshold values of the European Norm EN 13,231-3:2012. A further advantage of this process is the possibility to remove several millimeter deep defects in only one pass. Fig. 1 shows schematically the assembly milling tool/rail head with a close-up view of the interaction region. Simulations and
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metallographic investigations can help to get a better understanding of this very complex metal machining process and its influence on the wheel/rail rolling-sliding contact behavior. Several finite element studies deal with the description of machining processes in general. Predictions of the chip formation, the cutting forces and the temperature field in the process zone are demonstrated in Refs. [1–6]. Various studies focus on the cutting process and deal with the machining-induced residual stresses [7,8]. Description of the milling process in general concerning the temperature, the load conditions and the milling forces are investigated in Refs. [9–11]. Simulations for the description of the contact between rough surfaces are investigated in different ways. Studies of contact between single asperities regarding the damage behavior and contact pressure distribution are presented in Refs. [12–14]. Investigations of rough surfaces with purely elastic material behavior deal with the contact pressure and stress distribution can be found in Refs. [15–18]. Contact simulations with rough surfaces or single asperities under pure normal loading and with an elastic-plastic material behavior are performed in Refs. [19–24]. Numerical studies deal with the rail/wheel rollingsliding contact between two rough surfaces and with elastic-plastic material behavior are demonstrated in Refs. [25–29]. This paper aims to present 3D and 2D finite element simulations of the milling process as rail maintenance and the rolling-sliding contact of a wheel on a maintained rail by milling. The milling model results are compared to experimental and metallographic investigations of a
Corresponding author. E-mail address: [email protected] (W. Kubin).
https://doi.org/10.1016/j.wear.2019.203029 Received 15 January 2019; Received in revised form 12 June 2019; Accepted 23 August 2019 Available online 24 August 2019 0043-1648/ © 2019 Published by Elsevier B.V.
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Fig. 2. 3D milling model with the selected boundary conditions and detailed views of the used rail profile and the insert distribution.
and detailed views of the used rail profile and the location of the inserts in the tool holder segment. For a detailed study of the rail milling process with respect to the temperature field and the stress field in the process zone and resulting milling force a 2D model was set up using the finite element program Abaqus/Explicit and an Arbitrary-Lagrangian-Eulerian (ALE) method. This method merges a pure Lagrangian method with a pure Eulerian method to separate the mesh motion from the material flow which is often used in high dynamic nonlinear numerical calculations like milling. It prevents a large distortion of the finite element mesh and allows simulating a stable machining process. The numerical model represents a part of a rail head next to the milling area and one milling insert with a common edge radius, a negative rake angle and a positive clearance angle. The milling process is simulated accurately without any artificial numerical influences by applying a set of well-chosen boundary conditions and dimensions on the rail part and the milling insert. Special features of the model are the assumption of an initial chip with Eulerian boundary conditions to allow a material outflow at the rail top surface and the assumption of Eulerian boundary conditions on the left side of the rail to allow a material inflow. With the assumption of Lagrangian boundary conditions on the right side, the rail part is able to grow in size, which gives a general picture of the machined rail. In this 2D numerical study, a detailed investigation of the milling process is made about the resulting milling force and the development of the temperature field and stress field in the process zone and the machined rail. The mesh of the rail part is partitioned with different kinds of continuummechanical formulations to guarantee a stable milling simulation. For partition 1, a pure Lagrangian formulation is used, where the motion of the material and the mesh are merged. In the regions of partition 2, a mixture of the Lagrangian and Eulerian formulation is used, which enables a combined motion of the material and the mesh in a horizontal direction and a separated motion in vertical direction. A pure Eulerian formulation is used in partition 3, where the material flows through a fixed mesh. The edge nodes of the initial chip are coupled with a kinematic constraint to prevent a high distortion of elements during the change of the chip thickness. The simulated milling insert is moveable by using a reference point at the top of the tool tip which is tied to an analytical rigid body. For a transient cutting process with non-constant uncut chip thickness, the milling insert can be moved in vertical direction, but it is fixed in horizontal direction. In this numerical research, a thermo-mechanical coupled analysis is performed to predict the temperature field and the stress field in rail, chip and milling insert. The assembly of the 2D milling model with the chosen boundary conditions is shown in Fig. 3.
Fig. 1. Assembly of the milling tool (tool holder and cutting inserts) and a rail head with a close-up view of the interaction region.
milled rail after an actual milling process at the test track of the company partner LINSINGER/LINMAG in Austria. Besides the results of the rolling-sliding contact simulation are compared to experimental results of milling tests that were done in track together with a European IM in summer 2017.
2. Simulation models 2.1. Milling models A general picture of the whole milling process can be shown in a 3D model set up with the finite element code DEFORM 3D V11.1. This FE program was used due to its fast and robust remapping algorithm which is needed to calculate such a complex machining process in 3D. The milling tool is modeled as a rigid body, and for the material description of the rail head an elastic-plastic behavior is used. For both parts, the rail and the tool holder, tetrahedral elements with a higher element density at the top surface of the rail head and the insert area of the tool holder are taken to model the chip formation process accurately. The simulated rail head has a typical 60E2 profile and is fixed in space by using vertical and horizontal constraints at its bottom. In the simulation the tool holder segment has fifteen cutting inserts in three rows where five inserts are attached per each row. The friction coefficient μ and the heat transfer coefficient are set to 0.4 and 11−09 W/m2K respectively. On the center point of the tool holder an angular velocity . φ and a feed rate x˙ are applied. A theoretical milling depth of about 1 mm is used in this study. The actual milling depth can be higher or lower due to the positioning of the insert in the tool holder and the deformation state of the worn rail profile. Fig. 2 shows the assembly of the milling tool and the rail head with the chosen boundary conditions 2
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Table 3 JC parameters of the R260 rail steel. A [MPa]
B [MPa]
C
ε˙0
n
m
Troom [K]
Tmelt [K]
304.1
861.6
1.53e-02
1
0.144
0.633
293
1793
temperatures, made at the Materials Center Leoben in Austria, and experimental data at elevated strain rates of rail steels demonstrated in Ref. [33] were used to calculate the required JC parameters. The calculated parameters which represent a standard rail material of the steel grade R260 are presented in Table 3. 2.2. Rolling-sliding contact model In a second step, a 2D finite element model has been developed using ABAQUS/Standard for cyclic investigations of a wheel rollingsliding on a machined rail. The model consists of a part of a rail head and a wheel and includes the profile and surface roughness of a machined rail. To consider the influence of the milling process on the rolling contact and fatigue behavior of a machined rail, it is necessary to map the results of measurements, such as surface roughness and the residual stress field, onto the rolling-sliding contact model. In the simulation the wheel is described with elastic material behavior and the rail with plastic kinematic hardening behavior published in Ref. [26]. With these models the cyclic plastic deformation of remaining milling facets, the change of the surface roughness and the resulting residual stress field of machined rails can be determined after some passes of a wheel. Fig. 4 shows the assembly and the chosen boundary conditions of the rolling-sliding simulation with a schematic close-up view of the milling facets area. The facets dimensions, the length fz and the height H, depend on the chosen set of milling parameters like milling velocity, feed and tool holder radius. The three idealized facets are modeled with a length fz of 5.36 mm and a height H of 11.9 μm. The remaining surface of the rail part stays flat. This is a valid method for analyzing the influence of the roughness during a rolling-sliding contact, which has been reported in Ref. [26]. In this study, normal loads FN of about 7 kN,
Fig. 3. The 2D milling model with the chosen partitions and boundary conditions. Table 1 Model and process parameters of the milling simulation. Parameter
Value
horizontal cutting velocity vx & feed [mm/s] max. uncut chip thickness uy (max) [μm] shear stress limit τmax [MPa] friction coefficient μ Quinney-Taylor coefficient β milling time tmilled [ms]
3750 389 290 0.4 0.9 6.8
The horizontal component of the milling velocity vx(t) and the feed of the milling insert are applied on the inflow surface of the rail part. The combination of the horizontal velocity and the feed is nearly constant and is set to a value of 3750 mm/s in this case. By using the vertical component of the milling velocity and the milling time a vertical displacement uy(t) is calculated and applied as a linear amplitude on the reference point of the milling insert. In this case one milling insert has to remove a maximum uncut chip thickness of 389 μm in a milling time of 6.8 ms for a theoretical rail milling depth of about 1 mm. In the simulation a friction coefficient μ of 0.4 and an artificial shear stress limit of 290 MPa are used due to the chosen process parameters, numerical material tests and a combination of the calculation methods for the friction coefficient published in Refs. [30–32]. The heat produced by contact flows 50 to 50 into the milling insert and the rail part. For the conversion of the plastically dissipation energy to heat a Quinney-Taylor coefficient of 0.9 is used. An overview of the model and process parameters for this study is given in Table 1.
2.1.1. Material parameter The used elastic and thermos-physical material parameters of the rail part and the uncoated milling insert are shown in Table 2. In addition the Johnson-Cook (JC) constitutive material model is used to describe the plastic behavior of a standard rail material of the steel grade R260. An example of the JC constitutive equation is given in Ref. [9]. For the plastic rail material description tensile tests at different Table 2 Elastic and thermo-physical properties of the rail material and the tool material. Properties
Rail material (R260)
Tool material (K20)
Density ρ [kg/m³] Conductivity λ [W/mK] Specific heat c [J/kgK] Young's Modulus E [MPa] Poisson's ratio υ [−]
7850 42 490 219,000 0.29
14,750 88 296 630,000 0.22
Fig. 4. 2D rolling-sliding model with the chosen boundary conditions and a schematic close-up of the milling facet area. 3
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Fig. 5. Cross section of the used rail samples (above) and the simulated rail head (below) before and after the milling process. On the right side of the figure a qualitative comparison of the real and simulated chips is shown.
12 kN and 19 kN with accelerating and braking slip values of 0.0%, 0.5%, 1.0% and 1.5% are applied. The normal loads have to be recalculated by using the load transfer methodology published in Ref. [27] and correspond approximately to wheel loads of about 4 t, 8 t and 16 t. The developed contact patches have lengths of 11.6 mm, 14.3 mm and 17.8 mm and nominal maximum contact pressures of 0.8 GPa, 1.0 GPa and 1.4 GPa regarding the studied normal load cases.
Fig. 6. Close-up views of the rail surface before (left column) and after (right column) rail reprofiling by an experimental milling test.
3. Results and discussion Surface contour measurements help to get a general picture of the rail profile on a milled rail. For the analysis of the rail reprofiling process by milling an arbitrary rail contour was milled on a typical 60E2 profile in an experimental test made at the construction facility of Linsinger/LINMAG in Austria. Fig. 5 above shows a superimposition of the cross section of the rail head before milling, colored in red, and the cross section of the rail head after rail reprofiling, colored in green. By comparing the superimposed rail head cross sections, a precise reprofiled rail head without any contour imperfections can be shown due to rail milling in only one pass. For the validation of the obtained simulation results, Fig. 4 below represents the cross section of the nonmachined rail head, colored in red, superimposed by the cross section after the simulated milling process, colored in blue. The similarity between metallographic investigations and simulations can be shown by comparing the profile change, shown on the left side in Fig. 5, and the produced chips, shown on the right side in Fig. 5. The difference between the experiment and the simulation is only about 3% by comparing the maximum milling depth at the gauge corner of the rail. With these results an acceptable agreement between the real and the simulated milling process can be shown. For a better visualization of the rail surface conditions and the quality of the rail head after the reprofiling process by milling, Fig. 6 represents microscopic investigations at 200× magnification of the rail head at three locations in transversal direction before and after milling. An uneven and rough rail surface condition can be seen at the nonmachined rail head, colored in red in Fig. 6 (left column). In contrast the milled rail head shows a smooth surface condition without damage and micro-cracks, colored in green in Fig. 6 (right column). For the detailed analysis of the rail milling process, the obtained results of the 2D simulation are needed. In Fig. 7a the development of the resulting total milling force per plane thickness concerning the milling time of one milling insert during one pass is shown for a maintenance process with the previously mentioned set of milling parameters. At the beginning of the simulated milling process, the milling force fluctuates as a result of the first impact between tool and workpiece, the inertia effects, the initial chip flow, the thermal softening behavior of the chip and elastic deformation of the tool tip. The total milling force increases until the maximum uncut chip thickness is
Fig. 7. a) Development of the total milling force per plane thickness with respect to the milling time of one insert. b) The influence of the uncut chip thickness on the maximum resulting milling force for various analyzed sets of milling parameters.
reached. A maximum amount of around 900 N/mm is obtained after 1.4 ms. Afterwards, the milling force decreases nearly to the zero level in a period of about 5.4 ms. The amount of the milling force depends
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Fig. 9. The development of temperature in the rail, chip and the milling insert during the simulated milling process at five chosen milling time states.
and at not more than 300° the material can be regarded as uninfluenced by temperature. For the verification of the obtained simulation results metallographic investigations of the rail head after the experimental milling test were made, shown in Fig. 10 at 100× magnification. The left orange framed picture shows the microstructure of the rail head in transversal direction. The microstructure of the rail head in longitudinal direction is illustrated in the right green framed picture. The used and partitioned rail sample for the metallographic investigation is shown in Fig. 10 above. The microstructure in both directions, longitudinal and transversal, appears uninfluenced by temperature as an unchanged pearlitic microstructure is found. No visible surface roughness is recognizable in the pictures between the milling facets. Fig. 11 shows the average values of measured and simulated residual stresses in relation to rail depth in a) axial direction and b) transverse direction. The residual stress measurements were done at milled and traffic loaded rail samples after a time interval of 11 days in track and about 120,000 tons of loading, represented by the red dotted
Fig. 8. The development of the Von Mises stress in the rail, chip and the milling insert during the simulated milling process at five chosen milling times.
mainly on the maximum uncut chip thickness and thus on the material resistance of the workpiece. Several milling parameters, like milling velocity, milling depth and feed rate can be changed and if the same maximum uncut chip thickness is maintained, the milling force stays at the same level. Fig. 7b shows the development of the maximum total milling force with respect to the uncut chip thickness for various sets of milling parameters. The change of the above mentioned milling parameters shows no influence on the resulting total milling force, shown in Fig. 7b. The maximum resulting milling force per plane thickness demonstrates a linear behavior with increasing the uncut chip thickness. The distribution of the Von Mises stress in the rail and the tool is presented in contour plots at defined milling times in Fig. 8. During the whole milling process the Von Mises stress distribution in the rail stays nearly constant. A maximum stress value of about 1.0 GPa is reached, which corresponds to a typical nominal contact pressure of an 8 t wheel in the wheel-rail interaction system (numerically predicted). Therefore, it is assumed that milling influence on the rail is comparable to a standard wheel loading. In the milling insert the Von Mises stress increases significantly and reaches its maximum – localized at the tool tip – at the end of the milling process. The decrease of the uncut chip thickness is accompanied by a higher decrease of the tool-chip contact area resulting in a stress peak in the tool. Due to this stress peak, damage can be initiated preferred at the tip of the milling insert. The obtained temperature result of the 2D milling simulation is illustrated in Fig. 9. The development of the temperature field in the milling area of the insert and the rail head is shown in counter plots at five chosen milling time states. A temperature of about 800° is reached in the chip nearby the contact surface after a milling time of 1.4 ms. This temperature stays constant until a milling time of 3 ms. Afterwards it decreases and reaches a value of 600° at the end of the simulated milling process. The temperature at the surface of the milling insert shows its maximum value of about 900° after a milling time of 5 ms which subsequently decreases to 700° nearby the surface of the insert tip. The highest temperature at the surface of the machined rail is about 300° and this indicates no significant thermal influence on the remaining rail material during and after milling. The simulation demonstrates that the main part of the produced heat flows into the chip and the milling insert. Only a small part flows into the machined rail
Fig. 10. Metallographic investigation of a rail head after the experimental milling test. 5
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4. Conclusions This numerical and experimental study shall help to better understand and optimize rail re-profiling processes. Additionally, it shows that rail milling is an appropriate maintenance process which can remove rail defects, keeping the rail material and the rail microstructure in its initial state. From the developed simulations and experiments, the following main conclusions can be made:
• A similarity between metallographic investigations of a rail head • • •
•
Fig. 11. The average values of the measured and simulated residual stresses over the rail depth in a) axial direction and b) transverse direction.
lines, and after 7 months in track and about 2,300,000 tons of loading, represented by the green dashed lines. The measurements of a worn rail sample out of the same track without maintenance action are represented by the blue dashed-dotted lines in the diagrams. Five measurement points on each analyzed rail head in lateral direction are averaged, to get typical residual stress profiles for the tested rail condition. The simulated residual stresses, represented by the black continuous lines, are the average values of all simulated load and slip cases after five cycles of rolling-sliding contact. In the simulations the influence by the surface roughness in submicron range was not taken into account and therefore no values are indicated for the first 30 μm at the rail surface. The axial residual stresses of the worn rail sample and the milled and traffic loaded rail sample after 11 days in track show almost the same development with increasing rail depth, demonstrated in Fig. 11a. After 7 months in track the axial residual stresses decrease further, and higher compressive stresses are detected. The simulated axial residual stress values and the measured results of the rail sample after 7 months in track show in average almost the same development with respect to the depth. The transverse residual stress values of the milled and traffic loaded rail samples are far more in the compressive range as in the worn rail, demonstrated in Fig. 11b. The same behavior is found in the simulations. This is valid for the transverse direction and axial direction. Lower residual stress values in the non-maintained (worn) rail can be explained, since residual stresses will be reduced by cracks. The exact load and refurbishing history of this rail is unknown and it is probably only a pure coincidence that the milled and 0.12 MGT loaded rail (red dotted line) has nearly the same axial residual stresses. The obtained results of the rolling-sliding contact simulation match satisfactorily with the measurements of the in-track-test samples, especially the rail sample after 7 months of slight (approximately 2.3 MGT of loading) traffic in track.
after a milling test and the 3D simulations of the milling process is shown by comparing the profile change and the produced chips. A reprofiled rail head without visible contour imperfections is produced due to rail milling in one pass. The resulting milling force depends linearly on the maximum amount of the uncut chip thickness. An increase of the maximum uncut chip thickness raises the material resistance of the workpiece and thus the milling force. The Von Mises stress distribution in the rail directly after the cut stays nearly constant during the whole milling process. A maximum stress value of about 1.0 GPa is reached, which corresponds to a typical loading by an 8 t wheel in the wheel-rail interaction system. The results of the milling simulation show that a maximum temperature of about 300° is reached at the surface of the machined rail. Such temperatures do not influence the remaining rail material during and after milling. Metallographic investigations demonstrate an unchanged pearlitic microstructure and no phase changes, like martensitic layers, after rail milling, which confirm the numerical results. By comparing the development of residual stresses in the rollingsliding contact simulation and the measurements of the in-track-test a satisfying agreement is shown. The measurements and the simulations show compressive residual stress fields after a specified time/tons of loadings in track.
Declaration of interest None. Acknowledgement The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center “Integrated Computational Material, Process and Product Engineering (IC-MPPE)” (Project No 859480). This program is supported by the Austrian Federal Ministries for Transport, Innovation and Technology (BMVIT) and for Digital and Economic Affairs (BMDW), represented by the Austrian research funding association (FFG), and the federal states of Styria, Upper Austria and Tyrol. References [1] C.Z. Duan, T. Dou, Y.J. Cai, Y.Y. Lin, Finite element simulation and experiment of chip formation process during high speed machining of AISI 1045 hardened steel, Int. J. Recent Trends Eng. 1 (2009) 46–50. [2] P.J. Arrozola, D. Ugarte, J. Montoya, A. Villar, S. Marya, Finite element modeling of chip formation process with Abaqus/ExplicitTM 6.3, in: E. Oñate, D.R.J. Owen (Eds.), Proceedings of VIII International Conference on Computational Plasticity, Barcelona, September 5-8, 2005, CIMNE, 2005. [3] M. Abouridouane, F. Klocke, D. Lung, D. Veselovac, The mechanics of cutting: insitu measurement and modelling, Procedia CIRP 31 (2015) 246–251. [4] X. Man, D. Ren, S. Usui, C. Johnson, T.D. Marusich, Validation of finite element cutting force prediction for end milling, Procedia CIRP 1 (2012) 663–668. [5] T. Özel, T. Altan, Process simulation using finite element method – prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling, Int. J. Mach. Tool Manuf. 40 (2000) 713–738. [6] S.M. Afazov, S.M. Ratchev, J. Segal, Modelling and simulation of micro-milling cutting forces, J. Mater. Process. Technol. 210 (2010) 2154–2162.
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