Numerical simulation of hardfacing remanufacturing for large-scale damaged grinding roller

The present study is directed to the temperature and residual stress fields in the hardfacing remanufacturing for a large-scale grinding roller with damage. For this purpose, a numerical procedure for the hardfacing process based on the thermal cycle curve method was established, and the effectiveness of the proposed procedure was verified by the measurements of a multi-pass welding experiment with V-groove butt joint. A local model of bead-on-plate welding was used to check the heat source and extract the thermal cycle curve. The resulting thermal cycle curve was applied as a thermal load to the corresponding welding layer one by one. Based on the calculated material properties, the data files of the base metal (Grade:KmTBCr26) and the filling layers (Grade:ARCFCW9024) were re-developed to define the temperature-dependent physical and mechanical properties of the materials used in the hardfacing remanufacturing. The numerical simulation results reveal the changing trend and distribution of the temperature and residual stress fields during the hardfacing remanufacturing for the damaged grinding roller. The distribution of temperature and residual stress is very complicated due to the numerous welding layers in the hardfacing process. It is pointed out that with the increase of welding layers, the heat-affected zone of the grinding roller expands gradually, and the maximum tensile stress always appears at the position near the weld toe, which is prone to fatigue failure or interface peeling due to stress concentration.


Introduction
With the rapid development of the power and building material industry, various milling facilities are commonly used to pulverize coal gangues and cement aggregates in large-scale power and cement plants, respectively. The grinding roller is the central working part of the grinding equipment, which has a high damage rate due to the power-making process is achieved by the squeezing and grinding for the materials placed between them [1,2], so regular maintenance and replacement for these working parts become a necessity. If the abrasion-resistant layers of the grinding roller are mostly peeled off or unevenly worn, the rolling performance of the main working parts will be lost. Even worse, the surface cracks in the hardfacing layers spread to the substrate and may even cause the overall fracture of the equipment, resulting in a series of serious production accidents [3,4]. Therefore, the grinding roller must be repaired or replaced in time after severe wear to guarantee the long-term service safety of the equipment.
The so-called hardfacing technology means that unique welding materials with high wear resistance are deposited on the working surface of common metal parts by using built-up welding to improve the mechanical performance of working parts or repair the appearance dimensions of damaged components [5,6]. The thermal stresses generated during the hardfacing process will cause uniformly distributed, non-penetrating grid-like cracks on the surfacing layers, as shown in Fig. 1. The further propagation of these cracks may even cause sudden fracture of the grinding roller, and 1 3 two typical failure modes are shown in Fig. 2. The grinding roller commonly used in large-scale pulverizing equipment is faced with particular working environment and performance requirements. They are usually used as important working parts for crushing raw materials in cement and electric power industries, which have the characteristic of large volume, high economic value and complex maintenance and replacement [7][8][9]. In order to ensure the grinding effect, the damaged grinding roller needs to be replaced or repaired, and it is no doubt that it is uneconomical to replace the damaged roller frequently. Therefore, in the actual production, it is more and more common to use the hardfacing technology to remanufacture this kind of wear-resistant part. In the remanufacturing process of grinding rollers, the high abrasive flux-cored wire is usually deposited on the surface of the damaged roller by self-shielded open arc overlaying welding to restore its original size and function. However, hardfacing remanufacturing is a very complicated thermomechanical process due to the large wear-resistant parts being repaired and the difficulty of accurately measuring the thermo-physical properties for iron-chromium-based alloys [10,11]. This brings a significant obstacle to the numerical simulation of hardfacing remanufacturing for large-scale grinding rollers with damage.
Many researchers in industry and academia have mainly studied the hardfacing technology by using numerical simulation method. Sachajdak et al. [12] presented an application of the CFD-FVM model for thermal simulation of the GMAW hardfacing process. The developed model achieved a realizable compromise between accuracy and calculation efforts for engineering heat transfer analysis and showed high reliability by thermography measurements, particularly for heat transfer around the electric arc. Yang et al. [13] investigated the temperature and residual stress fields of medium-high carbon steel specimens after hardfacing based on a numerical model. The results showed that the compressive stress appears at the surface of the specimen when the martensite transformation occurs at the HAZ and hardfacing layer. Jiang et al. [14] performed a finite element analysis to estimate the residual stress and deformations in the repair weld of a stainless steel clad plate. The research results show that the heat input and welding layer number have significant effects on residual stress distribution, and using multi-layer welding and higher heat input can be helpful to decrease the residual stress. At the same time, Jiang et al. [15] also studied the effect of repair weld length on residual stress in the repair weld of a clad plate. It was found that when the repair length increased, the transverse residual stress in the weld and HAZ decreased, but the repair length had little effect on the longitudinal residual stress. In addition, the researches on the numerical simulation for the hardfacing also involve some other aspects, including the formation and evolution of cracks during the solidification of hardfacing layers [16], the flow of liquid metal in the molten pool during the hardfacing process [17] and the residual stress evaluation for different types of hardfacing processes and alloys [18][19][20][21].
A numerical simulation procedure for the hardfacing remanufacturing of damaged grinding roller was proposed based on the thermal cycle curve method in the present study. An appropriate average thermal cycle curve was obtained by the local model of bead-on-plate welding using a thermo-elastic-plastic finite element analysis. The effectiveness of the proposed numerical procedure was validated by a V-groove butt joint welding experiment. The local and global mesh models of the damaged grinding roller were established, and then the temperature and residual stress  fields in the hardfacing layers and substrate of the grinding roller were analyzed to show areas prone to fatigue failure or interface peeling. The proposed numerical framework may serve as a tool for predicting the temperature and residual stresses fields as an evaluation standard for the hardfacing remanufacturing of the worn grinding roller.

Theoretical background for hardfacing simulation
The following introduces the theoretical background involving the numerical simulation of hardfacing remanufacturing for the grinding rollers.

Thermal cycle curve method
The hardfacing remanufacturing of grinding rollers usually needs to repeatedly build up dozens of layers or even more wear-resistant weld beads, which leads to complex temperature and stress fields. In the numerical simulation of multipass welding using the thermal cycle curve method, some typical welding joints are selected, and their corresponding mesh models are established. After the welding heat source is checked, the thermal elastic-plastic finite element analysis is performed to extract the average thermal cycle curve in the welding zone for corresponding joints. Then, the obtained thermal cycle curve is applied to the corresponding weld bead successively as an initial thermal load. The specific implementation process for the multi-pass welding based on the thermal cycle curve method is shown in Fig. 3.  Welding experiment measurements can also obtain the thermal cycle curve. Suppose some welds adopt different process parameters (such as different filler wires, interlayer preheating temperature, welding current, voltage). In that case, the thermal cycle curves applied to different welds also have corresponding differences. In a word, the thermal cycle curve used should accurately reflect the welding thermal cycle history experienced by the welds to ensure the reliability of the numerical simulation for multi-pass welding. The case of using the thermal cycle curve method to simulate the build-up welding process is shown in Fig. 4.

Multi-pass welding simulation based on SYSWELD
As a professional welding numerical simulation software, SYSWELD was jointly developed by AREVA and ESI, which fully realized the coupling calculations of mechanical, thermal conduction and metallurgy [22,23]. The material database of SYSWELD provides the thermo-physical and mechanical properties of commonly used steel, aluminum alloy and cast iron and considers the influence of various metallographic microstructures on the material properties, including ferrite, pearlite, martensite, bainite and austenite. The chewing gum method proposed by ESI is used to define the materials which have not been deposited in the welds. This method avoids the element self-locking phenomenon, which is easy to occur in killing or activating elements. By giving a minimum value to the relevant parameters such as the elastic modulus, thermal conductivity and specific heat of the weld materials, the undeposited metal material is approximately treated as hot air; with the continuous deposition of the welds, the mechanical properties of the undeposited weld return to normal. Some code definitions of the thermo-physical properties for not-yet-deposited materials are given below. For the hardfacing remanufacturing of the grinding roller studied in this study, the material properties of the grinding roller and the iron-based surfacing alloy are quite special, but these materials are not recorded in the SYSWELD database, so secondary development is needed. To this end, ESI has a special tool named Material-Data-Manager to establish a material database, which can input material properties in the form of excel tables and can also modify the plastic strain hardening law of materials. When setting the material properties in the finite element numerical analysis, the material database file with the format of *. mat can be directly loaded. In this study, the above-mentioned development tool was used to establish the specialized material database required for hardfacing remanufacturing of grinding roller.

Selection and verification of heat source model in SYSWELD
Choosing a suitable heat source model has an important influence on the practical implementation of welding numerical simulation. The hardfacing remanufacturing Fig. 6 The specimen and measuring points    [24,25], which divided the heat source into two ellipsoids along the welding direction, as shown in Fig. 5. This model considers the difference in arc heat along the thickness of the plate and the digging and stirring effects of the welding beam. Its mathematical formula is as follows: The heat flux distribution inside the ellipsoid in the front half is and the heat flux distribution inside the ellipsoid in the rear half is where, η is arc efficiency; I is welding current; U is arc voltage; f f and f r are the distribution coefficients of the total input power in the front and rear parts of the molten pool, f f + f r = 2; a, b 1 , b 2 and c are the distribution parameters of the double ellipsoid heat source model. Among them, a represents the weld pool length, b and c affect the melting width and penetration respectively.    SYSWELD has a built-in double ellipsoid heat source model and provides a professional heat source calibration module-heat input fitting. By checking the heat source parameters, the heat source model used in the welding simulation can be more in line with the actual welding process. Its parameters are usually determined based on engineering experience and experimental results for the double ellipsoid heat source model. The steps of heat source calibration based on SYSWELD are as follows: (1) Firstly, select the initial values of the distribution parameters of the heat source model for trial calculations based on engineering experience. The initial value can be determined by referring to the proportional coefficient of the experimental measurements of the molten pool when the welding reaches the quasi-steady state; (2) Secondly, compare the temperature field and molten pool obtained in trial calculations with the experimental results, and adjust the parameters of the heat source model in a targeted way; (3) Finally, substitute the correction values of the parameters into the heat source model to calculate the quasisteady temperature field again, and repeat the adjustments until the appropriate parameters of the heat source model are determined. Save the calibrated heat source model function as a *.fct file for subsequent implementation in the numerical simulation for hardfacing remanufacturing of grinding roller.

Verification of numerical simulation method for hardfacing
To verify the effectiveness of the above methods applied to the hardfacing process, the multi-pass welding of V-groove butt joint in the literature [26] was taken as an example, the thermal cycle curve method was used to implement the numerical simulation of this case and the numerical results were compared with the experimental measurements.

Material and welding specimen
It is necessary to introduce the butt welding process with V-groove in the literature [26] in this section. Chang et al. [26] carried out a welding experiment on buttwelded joints with V-groove and used X-ray diffraction to measure the residual stresses near the welding line. The length, width and thickness of the experimental specimen are 110 mm, 30 mm and 4.5 mm, respectively, with a V-shaped groove filled with three layers of welds. The geometry and dimensions of the welding specimen are illustrated in Fig. 6. Seven measuring points, located in the area near the weld, as shown in Fig. 6 and Table 1, were measured by an X-ray diffractometer. TIG welding is used to implement the deposition of the three-layer welding in the V-groove joint. This is a simple multi-pass welding  case, which is suitable for verifying the numerical methods used in the research. Table 2 shows the welding sequence and its corresponding process parameters. The material used in this specimen is carbon structural steel named A36, and its chemical composition is shown in Table 3. A36 is an American standard carbon structural steel with a microstructure mainly composed of ferrite and pearlite, by the standard ASTM A36/A36M-03A [27]. The temperature-dependent thermal physical properties and mechanical properties of ASTM A36 are shown in Figs. 7 and 8, respectively [26]. However, there is no such material as A36 in the SYSWELD material database. Through comparison, it is found that the chemical composition of S355J2G3 steel in the SYSWELD database is similar to that of A36, as shown in Table 4. S355J2G3 is a kind of low-alloy high-strength structural steel that implements the European standard EN10025-2 [28]. Given the similarities between the two sheets of steel, based on the material properties of S355J2G3 and the secondary development method described in Sect. 2.2, the special data file of A36 was produced by using Material-Data-Manager, which was used to define the material properties in the subsequent numerical modeling of multi-pass butt-joint welding.

Numerical modeling of the cited case
A numerical model for multi-pass butt-joint welding was carried out using the thermal cycle curve method in this section. The mesh model of welding specimen was established using Visual Mesh 8.0, which mainly includes two types: (1) local mesh model for heat source checking and extraction of thermal cycle curve; (2) global mesh model for multi-pass welding simulation. These two kinds of mesh models are shown in Figs. 9 and 10, respectively. Because the size of this specimen is relatively small, the local model has only one layer of weld bead compared with the global model. Considering the computation time and calculation accuracy, the meshes near the weld zone are finer, while relatively coarser meshes are used in the region away from the weld. The number of nodes and elements in the local mesh model is 21,297 and 25,536, respectively, while those in the global mesh model are 25,536 and 27,886, respectively. When performing mechanical analysis, it is necessary to impose appropriate constraints on the model to prevent its rigid-body displacement and rotation, just as shown in Fig. 11.

Heat source check and thermal cycle curve extraction
Before implementing the numerical calculation for the multi-pass butt-joint welding, the heat source must be checked first to obtain a reasonable heat source model describing the welding heat input. By calculating the quasi-steady temperature field, the distribution parameters of the double ellipsoid heat source model were adjusted according to the method described in Sect. 2.3 to make the weld pool or thermal cycle curve match the actual one. Save the calibrated heat source model function and name it in the format of *. fct. The heat source parameters after calibration are shown in Table 5. The quasi-steady temperature field refers to the state in which the temperature reaches a relative equilibrium during the welding process. The weld morphology obtained in this state can best reflect the correct heat source model. The simulated quasi-steady temperature field is shown in Fig. 12, and the comparison between the simulated molten pool and the experimental one is shown in Fig. 13. After obtaining the calibrated heat source model, the numerical simulation of the initial weld pass in the local mesh model was performed by calling the heat source function file. The nodes in the cross section of the weld, as shown in Fig. 14, were used to extract the corresponding welding thermal cycle curves in the quasi-steady state and then average them to obtain the average thermal cycle curve, as shown in Fig. 15. The comparison between the numerically calculated and experimentally measured thermal cycle curves is shown in Fig. 16. It can be found from Fig. 16 that the maximum temperature in the thermal cycle curve obtained by the numerical calculation is slightly higher than that of the experimental curve, but in general, the two curves are in good agreement. Therefore, the calculated thermal cycle curve can be used for subsequent multi-pass butt-joint welding simulation. When implementing this multi-pass welding simulation, the parameters such as the start and end time of each layer of weld bead are shown in Table 6.

Comparison of numerical and experimental results
The thermal cycle curve obtained in Sect. 3.3 was sequentially loaded to each weld layer according to the welding sequence and time. Accordingly, each weld layer experienced a welding heating process based on the thermal cycle curve. Taking the third layer of weld as an example, the temperature distribution of the specimen after the deposition is shown in Fig. 17. It can be seen that the temperature in the molten pool is the highest, with a large temperature gradient, and the temperature away from the weld zone gradually decreases. Each weld will rise to 1311 °C within 1.3 s after the beginning of welding, and the temperature change trend is consistent with the calculated average thermal cycle curve. The displacement in the Z-direction was used to measure the angular deformation. Each weld will cause angular deformations after welding, which is due to the uneven heat input on the upper and lower surfaces of the specimen during the  welding process, resulting in inconsistent shrinkage. The angular distortions of the specimen after the third welding pass are shown in Fig. 18. The maximum Z-direction of the specimen after the welding of the first, second and third layers is 0.564 mm, 0.886 mm and 1.110 mm, respectively, as shown in Fig. 19. It can be seen from Fig. 19 that the angular deformation increases with the deposition of the welding layer. Although the subsequent weld pass will make  the angular deformation larger on the basis of the previous one, the rate of its increase will slow down. This is consistent with the research results of Yan [29]. This phenomenon is that the cooled weld bead provides an obstacle to the continuous deformation of the specimen by increasing the stiffness of the welded joint. In short, the cumulative effects of each weld in multi-pass welding make the deformation more severe than that in single-pass welding. The residual stresses obtained by numerical simulation were compared with the experimental measurements to verify the effectiveness of the numerical method used for the hardfacing remanufacturing of the grinding roller. The welding test in literature [26] measured the residual stresses of 7 measuring points near the weld area, and the distribution of the measuring points is shown in Fig. 6. In order to facilitate comparison, the measuring path in the numerical model is consistent with that in the welding test, as shown in Fig. 20. The comparison of longitudinal and transverse residual stresses obtained by experiment and numerical simulation is shown in Figs. 21 and 22, respectively. It can be seen from the figures that the peak value of longitudinal residual stress appears near the weld, presenting a tensile stress state of nearly 400 MPa, and a compressive stress state far away from the weld zone; while the peak value of the transverse residual stress is smaller, which also appears in the area close to the weld, about 45 MPa. The transverse residual stress far away from the weld zone gradually decreases and transforms from tension to compression, but it is always smaller in magnitude than the longitudinal residual stress. By comparing the residual stress curves obtained by numerical simulation and Hardfacing layers Fig. 25 The grinding roller under hardfacing   experimental measurement, it can be seen that the change trends of the two curves are similar, and they are in good agreement. Only a few measuring points have great differences, which may be caused by many simplifications in the numerical model and experimental measurement errors. Through comparative analysis, it can be concluded that the thermal cycle curve method used in this study achieves a better balance between the calculation efficiency and accuracy, so it is more suitable for the numerical simulation of the hardfacing remanufacturing of grinding roller.

Numerical modeling for remanufacturing of grinding roller
This section takes the HRM2800 grinding roller as an example to conduct numerical simulation, focusing on the temperature distribution and residual stress field in the grinding roller substrate and hardfacing layers. Figure 23 shows the HRM 2800 grinding roller with groovelike wear in the middle of the working surface. The repair process of the worn roller is as follows: First, perform dyeing flaw detection on the base material of the damaged roller to confirm whether cracks are penetrating through the base material; then, use carbon arc gouging to remove the remaining surfacing layers, and use flux-cored wire with high chromium cast iron type to fill the defects such as pits in the grinding roller matrix; finally, an angle grinder is used to smooth the filled buttering layer, and the remaining cavities are filled to the original size layer by layer to complete the remanufacturing of the worn grinding roller. The specific process is shown in Fig. 24. The grinding roller under surfacing repair is shown in Fig. 25. The remanufacturing parameters used for HRM 2800 grinding roller are shown in Table 7. It is worth pointing out that due to the relatively thin buttering, tempering and capping layers, the numerical modeling in this paper focuses on the filling layer, which accounts for the majority of the surfacing layers.

Calculation of material parameters and establishment of material database
Up to now, the wear resistance of high chromium cast iron has been studied mainly using experiments [30]. There are few numerical simulations on high chromium cast iron materials, and their high-temperature thermo-physical parameters are also rare, which brings difficulties to the numerical modeling. In this paper, JMatPro is used to calculate various high-temperature physical properties of high chromium cast iron and other materials. It is a powerful calculation software for phase diagrams and high-temperature performances of metal materials. According to the compositions of the material, the performance parameters that change with temperature during the solidification process can be calculated [31,32]. The grade of high chromium cast iron used for HRM 2800 grinding roller is KmTBCr26, and its chemical composition is shown in Table 8. When the cast iron module of JMatPro is used for calculation, it is necessary to set reasonable parameters to ensure the calculation accuracy. The calculation module for cast iron is shown in Fig. 26. There are mainly two forms of carbon in cast iron: graphite and cementite (Fe 3 C). In white cast iron, almost all carbon exists in the form of Fe 3 C. Therefore, the matrix type of cast iron after solidification is set to pearlite. Since only a tiny part of the base metal is heated to melt and participates in the molten pool reaction, the thermo-physical parameters when it is fully diffused to the equilibrium state are selected in this paper. The temperature-dependent physical parameters of the base metal KmTBCr26 calculated through solidification are shown in Fig. 27. The hardfacing layers of the remanufactured grinding roller adopt the high chromium cast iron flux-cored wire ARCFCW9024 developed by Beijing ARC Xinxing Co., Ltd. Its chemical composition is shown in Table 9, and the calculated temperature-dependent material properties of ARCFCW9024 are shown in Fig. 28.
Because there is no function to calculate the mechanical properties of white cast iron in the cast iron module of JMatPro, its mechanical parameters can be obtained by consulting the Ref. [16,33]. The research data in the literature [33] shows that the tensile strength of high chromium white cast iron (Cr content, 34%) at room temperature (25 °C), 700 °C and 1000 °C is 415 MPa, 200 MPa and 50 MPa, respectively. Ma et al. [16] conducted a numerical simulation study on the chromium carbide overlays welded on the surfaces of ASTM A36 steel plate. Because brittle materials generally do not have a yield state, 90% of the ultimate tensile strength at room temperature is defined as its yield strength, while yield strength at other temperatures is obtained by linear interpolation. In this paper, a similar approach was adopted to produce the temperaturedependent yield stress curve of high chromium cast iron, as shown in Fig. 29.   According to the material database development method in Sect. 2.2, the data files of the base metal (Grade: KmTBCr26) and the filling layers (Grade: ARCFCW9024) were re-developed based on the calculated material properties, and they were named as W_HighCrCastIron. mat and W_ARC9024.mat, respectively. The developed material data files were loaded in the SYSWELD welding wizard to implement numerical simulation. Since the buttering layer and capping layer are generally very thin compared with the filling layers, these two layers are ignored for simplification.
Only two kinds of materials, including base metal and filling layers, were considered in the numerical modeling for hardfacing remanufacturing of grinding roller.

Establishment of mesh model for hardfacing remanufacturing
Establishing a suitable mesh model is one of the key conditions for numerical simulation. When implementing the numerical simulation of grinding roller remanufacturing, it is

Weld bead
Base metal necessary to establish two types of mesh models, namely the whole model and the local model. The geometrical dimensions of the worn roller used for remanufacturing are shown in Fig. 30, which is the basis for establishing the global mesh model. In this study, the model of bead-on-plate welding was used to check the heat source and extract the heat cycle curve, and the corresponding geometric model is shown in Fig. 31. For the sake of simplification, it is approximately considered that the wear area of the grinding roller and the wear-resistant weld beads are rectangular, which does not affect the understanding of the distribution regularity of temperature and residual stress caused by hardfacing remanufacturing. Since the grinding rollers used in industrial production are generally large and the wear-resistant layers are thick, it needs a large number of computing resources to carry out the overall 3D finite element analysis, so a 2D plane strain model of grinding roller was used for numerical simulation of hardfacing remanufacturing. The number of nodes and elements in the established plane strain model is 72,447 and 72,346, respectively, as shown in Fig. 32. The mesh model of beadon-plate welding is shown in Fig. 33. In mechanical analysis, boundary constraints are imposed on the global and local mesh models to prevent rigid body displacement and rotation.

Thermal cycle curve for hardfacing remanufacturing
In this study, the local mesh model of bead-on-plate welding was used for heat source verification, and the process parameters adopted consisted of those of hardfacing remanufacturing for grinding roller. Within 2 s after arcing, the temperature field of the bead-on-plate welding enters a quasi-steady state, as shown in Fig. 34, and the morphology of the molten pool basically no longer changes. It can be seen from Fig. 34 that the maximum temperature in the molten pool obtained numerically is about 2000 °C, which is basically consistent with the maximum temperature of the molten pool measured experimentally in the literature [34]. By adjusting the parameters of the heat source model, the simulated weld pool and heat-affected zone are shown in Fig. 35. It is considered that the molten pool will be formed above 1500 °C, which is consistent with the melting temperature of chromium carbide overlays set in literature [16]. The temperature in the heataffected zone is the austenitizing temperature, which is about 750 °C [35]. The validated heat source model was obtained and saved as a *.fct format file, which was called to simulate the temperature field of the bead-on-plate welding, and the average thermal cycle curve was obtained by averaging the thermal cycle curves of the nodes in the weld cross section, as shown in Fig. 36. The average thermal cycle curve was saved as a function file named Repair_weld. trc, which was then used to replace the moving heat source for numerical simulation of hardfacing remanufacturing.

Simulation process and parameters for hardfacing
When the worn grinding roller is remanufactured by hardfacing, the buttering layer needs to be planed to facilitate subsequent processing. In order to simulate the stress release during the planing of the buttering layer, the welding layer W2 is regarded as a planed layer. The first two layers (W1-W2) were overlaid first, then W2 was set as dummy materials to calculate the equilibrium state after removing the W2 layer, and then the surfacing process of W2 to W6 was calculated; at this time, W1 was regarded as a filled metal layer. The simulation process of grinding roller hardfacing remanufacturing is shown in Fig. 37. The welding parameters should be strictly controlled during the hardfacing remanufacturing for grinding roller. It is generally required that the initial temperature of the grinding roller substrate should not be lower than 40 °C. In this study, the preheating temperature and ambient temperature were set to be 40 °C, and the interpass temperature was controlled below 80 °C. Table 10 shows the relevant parameter set in the numerical simulation of hardfacing remanufacturing for the grinding roller.  According to the given calculation process and parameters, the numerical simulation of hardfacing remanufacturing for the grinding roller was carried out. It mainly includes three parts: (1) Numerical simulation of W1-W2 welding layers; (2) Equilibrium calculation of removing W2 layer; (3) Numerical simulation of W2-W6 welding layers.
The numerical results were discussed in the following section. Figure 38 shows the temperature field of the first welding layer W1 at different welding times. It can be seen from this figure that at the initial time t = 0.245 s, the whole welding layer W1 starts to heat up, and the maximum temperature that can be reached is about 209 °C. When t = 4.22 s, the welding layer W1 heats up to the maximum temperature and then begins to cool down until t = 15 s when it drops to about 80 °C, which means the end of a thermal welding cycle. At this time, the base metal temperature at the bottom area connected with the welding layer W1 is higher, up to 250 °C, so that the temperature in the upper part of the welding layer W1 is low. The temperature in the lower part is high. The temperature difference between the upper and lower layers causes greater thermal stress, which may lead to the delamination between the welding layer W1 and the substrate of the grinding roller. The temperature change of the second welding layer W2 is similar to that of W1, as shown in Fig. 39. Due to the heating of the W2 layer, the existing W2 layer is heated again, but the peak temperature is lower than that of the previous thermal cycle. The maximum temperature appears in the W1 layer after the surfacing of the W2 layer at t = 30 s. As the hardfacing process progresses, the heataffected zone of the grinding roller substrate also expands and extends radially to the depth of the roller. Since the whole heating process is controlled by a given thermal cycle curve, it is ensured that the interpass temperature meets the welding process requirements. Figures 40 and 41 show the axial (S11), radial (S22) and hoop (S33) residual stresses caused by surfacing W1 and W2, respectively. It can be concluded that the residual stress area caused by the welding layer W2 is larger than that of the welding layer W1. This is because W2 additionally applies a thermal cycle to the substrate and the welds on the basis of W1 heating. It can be seen from Fig. 40 that the peak values of residual stress in the three directions of S11, S22 and S33 caused by W1 are 599, 481 and 751 MPa, respectively, and the peak values of residual stress in the three directions (S11, S22 and S33) caused by W2 are 600, 493 and 763 MPa, respectively. The residual stress caused by W2 is slightly larger than that of W1. The welding layers W1 and W2 both have a smaller peak value and distribution area for the radial   stress (S22), while the peak value and distribution area for the hoop stress (S33) are relatively large. This distribution is similar to the hoop stress in the multi-pass butt welding of 9Cr-1Mo steel pipe conducted by Deng [36], and the magnitude of residual stress is close to that of longitudinal stress in the multi-pass welding of S355J2 thick plate [37]. Excessive hoop tensile stress (S33) will cause many short transverse cracks on the surface of hardfacing layers. It can be seen from these two figures that the residual tensile stress is basically distributed at the junction of the welding layer and the grinding roller substrate, and the maximum tensile stress appears near the weld toe. This is because the metal materials in this area are first heated to expand, and when it is cooled and contracted, tensile stress is generated due to the constraints of the surrounding materials. Correspondingly, there is a balanced compressive stress zone at the bottom and around the tensile stress zone due to the need for internal stress balance. The axial compressive stress (S11)

Numerical simulation of W1-W2 welding layers
is basically distributed at the bottom of the tensile stress zone, while the hoop compressive stress (S33) is distributed around the tensile stress zone. As the number of welding layers increases, the stress state in the previous welding layer also changes. After the surfacing of welding layer W2, the tensile stress in W1 decreases correspondingly, and some areas change from tensile stress state to compressive stress state since the alternating thermal cycles change the residual stress state in the original area. This is basically consistent with the distribution of residual stress in repair welds for a stainless steel clad plate studied by W. C. Jiang [14].
The grinding roller substrate and hardfacing layers are all brittle materials of high chromium cast iron, so it is suitable to use the maximum principal stress criterion to judge whether the material fails [16]. Figure 42 shows the principal stress distribution of W1 (Fig. 42a) and W2 (Fig. 42b). It can be seen that the maximum principal stresses of welding layers W1 and W2 are 751 MPa and 763 MPa, respectively. The stress distribution in the middle of the welding layer is relatively uniform, while the distribution at both ends of the welding layer is quite different. The inner area of the welding layer is generally in a state of tensile stress, while the bottom of the welding layer is in a state of compressive stress, and the maximum tensile stress occurs at the weld toe area where the welding layer connects with the grinding roller substrate. This is because the sharp geometric transition of the welding toe tends to produce stress concentration, and fatigue failure or interface peeling is easy to occur at the location. Therefore, the parts to be repaired should be polished smoothly during hardfacing remanufacturing to avoid sharp geometric transitions. The distribution of principal stress also indicates that the latter welding layer will affect the stress state in the previous welding and surrounding areas.

Equilibrium calculation of removing W2 layer
The welding layer W2 was set as dummy material to simulate the planning process of the buttering layer. Set the material properties and process parameters in the program, and call the previous step's calculation files to restart the numerical calculation. Figures 43 and 44 show the temperature and maximum principal stress distributions before and after the removal of welding layer W2, respectively. It can be seen from the figure that the highest temperature before and after the removal of welding layer W2 is 290 °C and 220 °C, respectively, and the principal peak stress is 763 MPa and 650 MPa, respectively. This indicates that the temperature decreases to a certain extent after the removal of welding layer W2, but its distribution characteristics do not change significantly. After removing the welding layer W2, the temperature of welding layer W1 is still the highest and gradually decreases along the radial direction of the grinding roller. The peak value of principal stress still appears at the weld toe connecting the welding layer and the grinding roller substrate, and the inner part of the welding layer is in the state of tensile stress and gradually changes to the state of compressive stress in the grinding roller substrate. However, due to the removal of the welding layer W2, the distribution and magnitude of the compressive stress have changed. This indicates that the residual stress in the hardfacing repair zone has been released after removing the W2 layer, and a new equilibrium state has been reached again.

Numerical simulation of W2-W6 welding layers
After calculating the equilibrium state for the removal of welding layer W2, the mesh model of the grinding roller was updated. Weld layer W1 was defined as the completed group and named as "WELD_FINISHED". The surface elements of the completed welding layer W1 were added to the cooling surface group "AIR", and then the result files obtained from the previous equilibrium calculation were called to restart the engineering files for numerical simulation of welding layers W2-W6. The temperature and residual stress fields in the hardfacing process of welding layers W2 to W6 are discussed below.

Temperature field analysis of welding layers W2 to W6
The hardfacing simulations of welding layers W2 to W6 were carried out on the basis of the equilibrium state calculations. Figure 45 shows the temperature fields of welding layers W2-W6. It can be seen that the interpass temperature of welding layers W2 to W5 is maintained at 80 °C due to the use of a thermal cycle curve to control the welding heating process. The welding layer W6 was kept at room temperature for 30 s after surfacing. Due to the heat conduction between the filled welding layers and the W6 layer, the welding layer W6 is higher than 80 °C, and its maximum temperature is 262 °C, which is lower than that of other welding layers. Generally speaking, the distribution of the temperature field formed by each welding layer is basically similar. The maximum temperature always appears near the bottom of the welding layers due to the proximity to the welding heat source and gradually decreases along the radial direction of the grinding roller, spreading in an arc shape. The temperature at the toe of each welding layer is higher, which will cause greater thermal stress. As the number of surfacing layers increases, the range of the heat-affected zone is also expanding, and the filled welding layers are repeatedly affected by multiple thermal cycles of the subsequent welding layers. The measuring line located in the middle of the grinding roller, as shown in Fig. 46, is used to measure the temperature of the welding layers from the outer surface to the inner surface. The temperature curves of different welding layers at the points along the measuring line are shown in Fig. 47. It can be seen from the figure that near the outer surface of the grinding roller, since some welding layers (W2 to W5) have not been overlaid, the temperature Distance along the measuring line /mm measured here is actually the ambient temperature, which is kept constant at 40 °C. The shape and magnitude of the temperature curves for the welding layers W2 to W5 are similar, but there is an inevitable delay between the curves, which is caused by the unfilled welding layers at the temperature points being measured. It can be seen from each curve that when the temperature rises to about 80 °C, a gentle step area is formed, and the length of the step is the height of the current welding layer. The curves show that the temperature rises rapidly near the bottom of the welding layer, reaching a maximum value of about 300 °C, and the temperature away from the welding layer gradually decreases. However, with the increase of the number of surfacing layers, the heat-affected area of the grinding roller expands, resulting in a gradual flattening trend of the temperature curves for the subsequent welding layers. After the surfacing of welding layer W6, the whole grinding roller was kept in the air for 30 s, so the maximum temperature decreased. The changing trend of the W6 curve is more gentle than that of other curves, which means that the temperature distribution of the grinding roller tends to be uniform after hardfacing remanufacturing.

Residual stress field analysis of welding layers W2 to W6
The maximum principal stress distribution after hardfacing from W2 to W6 is shown in Fig. 48. It can be seen from the figure that the positions of the maximum tensile principal stress in different welding layers are basically the same, and they all appear at the welding toe where the welding layer connects with the substrate of the grinding roller, just as shown in the dashed box in Fig. 48. The inside and bottom of the welding layer are in tensile and compressive stress states, respectively, and the residual stresses at the weld toe of the welding layer change from compression to tension. The tensile stress and compressive stress appear alternately in each surfacing layer. The substrate of the grinding roller at the bottom and both sides of the hardfacing layers are in the state of compressive stress, and tensile stress, respectively, and this distribution trend of residual stress is pronounced in the welding layer W6. Two measuring paths were selected for residual stress measurement, as shown in Fig. 49. Path 1 is located in the middle of the hardfacing repair zone of the grinding roller, while path 2 is located at the interface between the surfacing layers and the grinding roller base materials. Figure 50 shows the residual stresses measured along path 1. It can be seen that in the area without hardfacing, the residual stress is zero. With the progress of the hardfacing process, the residual stress curves gradually shift to the left. Figure 50a, c and d shows axial stress, hoop stress and maximum principal stress, respectively. The curve shapes and changing trends of these three types of residual stresses are similar, but they are different in magnitude. When the measuring points reach the filled welding layers, considerable tensile stress appears rapidly and remains stable inside the weld layer area. When the measuring points leave the filled welding layers, it decreases rapidly to the compressive stress, indicating a sizeable compressive stress area at the bottom of each welding layer after surfacing. With the increase of the measuring distance, the residual compressive stress gradually rises and tends to zero, which shows that the residual stress in the substrate of the grinding roller far away from the hardfacing repair zone is already very small and can be ignored. The stress curves from the welding layer W3 to W6 show a fluctuation from the tensile stress state to the compressive stress state caused by the change of stress state between the latter and the previous welding layer. With the increase of the welding layer, the number of fluctuations between the tensile and compressive stress states also increases, but the amplitude of the stress tends to decrease. This fluctuation of the stress state is particularly obvious in the curve of the welding layer W6. This is because the numerical calculation of W6 includes a cooling time of 30 s, which plays a crucial role in releasing the residual stress. Therefore, the maximum stress value and stress amplitude of the curve W6 are smaller than those of other welding layers, and the fluctuations between the tension and compression stress states are more regular. Figure 51b shows the radial stresses of different welding layers. It can be seen that the radial stress inside the hardfacing repair zone is all compressive stress, which decreases with the increases of the measuring distance. When it decreases to a certain extent, there is an increasing trend. The radial stress curve of the W6 layer is different from that of other welding layers, which is due to the redistribution of residual stress in the cooling stage of hardfacing remanufacturing. Figure 52 shows the residual stress distribution along measuring path 2, which is significantly different from that along measuring path 1 in the middle of the hardfacing repair zone. The curves of axial and radial stresses are similar in shape, as shown in Fig. 51a, b, respectively. It can be seen that there is a large residual tensile stress near the weld toe, and then the tensile stress decreases  Distance along the path 1/ mm gradually. There is a relatively large axial compressive stress, while the radial compressive stress is smaller. With the increase of the welding layer, the residual stress fluctuates to a certain extent, but the stress amplitude of the latter welding layer is smaller than that of the previous welding layer. This is because the latter welding layer has a heating effect on the previously completed welding layer, equivalent to a heat treatment to promote the residual stress release. The curves of hoop stress and maximum principal stress are basically similar in shape, as shown in Fig. 51c, d, respectively. It can be seen that the residual stress in the area close to the weld toe rises quickly; in the range of the weld layer, the residual stress rises slowly to the maximum; far away from the welding layer, the stress decreases rapidly until the compressive stress appears, but the compressive stress is smaller than the tensile stress in magnitude. Similarly, the axial stress and the maximum principal stress also fluctuate to a certain extent. The amplitude of stress fluctuation decreases in the completed welding layer, but the fluctuation frequency increases with the increase of the welding layers. After the surfacing of welding layer W6, these two types of stress are mainly in a tensile state, and the stress distribution tends to be uniform in the grinding roller. The influence of the number of welding layers on the peak value of residual stress is shown in Fig. 52. It can be seen that the peak residual stress decreases with the increase of the welding layer. Compared with the welding layer W1, the hoop, axial and radial residual stresses of the W6 layer are reduced by about 23.7%, 30.1% and 56.9%, respectively. This is because the thermal effect of the subsequent welding layer is equivalent to applying a stress relief tempering on the completed surfacing layer, which is consistent with the research conclusions drawn by W. C. Jiang et al. [14].

Conclusions
In this paper, a numerical simulation procedure was implemented for the hardfacing remanufacturing of worn grinding roller, and the following research conclusions can be summarized based on the research results: (1) A numerical procedure for hardfacing remanufacturing of damaged grinding roller based on thermal cycle curve method was proposed, and a welding experiment of V-groove butt joint was used to verify the effectiveness of the proposed numerical procedure. Through the thermo-elastic-plastic finite element analysis, an appropriate average thermal cycle curve was obtained by the local model of bead-on-plate welding, which was applied as a thermal load to the corresponding welding layers in the hardfacing remanufacturing for grinding roller. (2) The high-temperature physical properties of iron-based wear-resistant materials were calculated using JMatPro software. Based on the calculated material properties, the data files of the base metal (Grade: KmTBCr26) and the surfacing layers (Grade: ARCFCW9024) were obtained through the secondary development of the material database, which was used to define the temperature-dependent physical and mechanical properties of the materials used in the hardfacing remanufacturing. (3) The numerical calculation results show that the distributions of temperature and residual stress fields are very complicated in the hardfacing process, due to the repeated thermal cycles caused by numerous welding layers. In general, the maximum temperature always appears close to the bottom zone of the welding layers and gradually decreases along the radial direction away from the welding layers. The temperature in the area near the weld toe of each welding layer is higher, which will cause greater thermal stress. As the surfacing layers increase, the heat-affected area of the grinding roller expands, and the filled welding layers are subjected to repeated thermal cycles of the subsequent welding layers. (4) The number of surfacing layers has a significant effect on the peak value of residual stress. The peak residual stress decreases with the increase of the welding layer. Compared with the welding layer W1, the hoop, axial and radial residual stress of welding layer W6 are reduced by about 23.7%, 30.1% and 56.9%, respectively. This can be explained by the fact that the heating of the subsequent welding layer promotes the residual stress release in the previously filled welding layers. (5) Under the influence of many surfacing layers, residual stress distribution shows a great fluctuation in the grinding roller, and the state of residual stress changes between tension and compression with the different positions of surfacing layers. The inside of the welding layer is generally in a state of tensile stress, while the bottom part of the welding layer is generally in a state of compressive stress. The maximum residual Stress stress always appears in the vicinity of the weld toe connecting the welding layer and the substrate, which is easy to cause fatigue failure or interface peeling for the repaired roller, so special attention should be paid to this part in the hardfacing remanufacturing for the damaged grinding roller.