Authors: N.A. Feoktistov, A.A. Yumabayev, E.V. Skripkin, A.V.Monastyrsky
Keywords: Bimetallic rolling roll, combined mold, working layer, core, computer modelling, finiteelement method, voltage, deformation.
The article discusses the results of computer modeling of residual stresses in a rolling roll. When producing rolling rolls by centrifugal casting, even minor deviations from technological production parameters can lead to the appearance of cracks in the casting body. These cracks and chips typically form during heat treatment as a result of the combined action of residual stresses and deformations. To assess the factors influencing the level of residual stresses in the roll barrel after crystallization, computer modeling was carried out using the PolygonSoft tool.
The purpose of this work is to analyze the influence of various factors on the formation of a rolling roll in a casting mold, as well as to evaluate the possibility of controlling these factors to optimize casting technology and obtain higher-quality workpieces. During the modeling process, the dynamics of temperature changes, the stress-strain state throughout the entire volume of the roll, and the level of residual stresses in the working layer were determined.In addition, the maximum temperature gradients that arise during the transition from the hotter end to the colder central regions of the roll’s working layer were identified, since these gradients lead to the greatest stresses in those areas.
Rolling mill rolls (RMR) are the primary working tool in hot and cold rolling mills. The work rolls perform the plastic deformation of metal in its hot or cold state.
In metallurgy, rolling mill rolls are classified as follows [1]:
By function: roughing rolls, profile rolls, and sheet rolls.
By the type of work performed: work rolls and backup rolls.
By their structural characteristics: with or without an internal axial hole; monolithic, two-layer, composite; cast as a single piece or with bands.
By material: cast iron, steel, and hard alloys.
By manufacturing technology: cast, forged, heat-treated, or non-heat-treated.
By hardness class:
Cast iron rolls: soft, semi-hard, and hard.
Steel rolls: groups A, B, C, D.
Backup rolls provide strength and rigidity while alleviating the loads sustained by work rolls during the rolling process.
The object of study is a three-layer rolling mill roll, a bimetallic product composed of a working layer, an intermediate layer, and a core, each made of different alloys.
The working layer is made of a wear-resistant alloy (NiCr, NiCr-CE, NiCr).
The intermediate layer is manufactured using alloyed cast iron.
The core is composed of high-strength cast iron.
Modern technology for manufacturing rolling mill rolls involves producing the working and intermediate layers using a centrifugal casting machine, followed by assembling the mold and pouring the core material. The development of this technology has enabled the use of highly wear-resistant and hard alloys for the working layer, while employing more cost-effective high-strength cast iron for the core [2].
The objective of this study is to analyze the influence of various factors on the formation of rolling mill rolls in the casting mold and to evaluate the feasibility of controlling these factors to optimize the casting technology and produce high-quality castings.
The manufacturing of rolling mill rolls (RMR) is a complex process. Minor deviations in the technology can result in the following defects [2–5]:
During melting and pouring: cavities and inclusions, adhesions, hot cracks, non-metallic inclusions, lack of cohesion between layers.
During machining: chipping in the roll neck and body, dimensional discrepancies with the design specifications, grinding crack networks, among others.
During heat treatment: non-homogeneous structure, high residual stresses, among others.
During operation: fatigue-induced chipping, detachment of specific areas of the body, wear-induced crack networks, among others.
Casting defects that fall within machining tolerances are corrected through machining. However, defects on the working surface of the roll body are generally irreparable.
A significant portion of the defects that form in RMR are cracks. These can occur during the crystallization of molten metal in the mold and during the heat treatment of the castings. The primary cause of cracks is residual stresses, as well as the associated accumulated plastic deformations that arise during heat treatment. The combination of these factors forms the stress-strain state (SSS) of the rolling mill roll.
In the initial stage of production, the formation of the cast structure and the development of residual stresses are determined by the following key technological parameters [6]:
Thermal regimes for pouring the working layer and the core.
Geometric characteristics of the part.
Cooling rate of the casting in the mold.
Mechanical properties of the materials used.
Evaluating the influence of these factors on the level of residual stresses, as well as their qualitative distribution within the roll body, is more effectively performed through computational simulation.
Modern computational simulation methods for casting processes allow for the analysis of thermophysical, hydrodynamic, and crystallization processes that occur during the filling of the mold cavity with molten metal and the solidification of the part [7].
Casting process simulation software operates based on different calculation methods, such as the finite difference method, the finite element method, and the control volume method [8].
The object of study is a sheet rolling mill roll with a high-chromium cast iron working layer. This roll consists of three layers: the working layer, the intermediate layer, and the core.
Working layer: Manufactured by centrifugal casting from highly alloyed cast iron, with a chromium content of 15–17%.
Intermediate layer: Made of alloyed cast iron.
Core: Poured using the gravity casting method with high-strength cast iron.
The approximate weight of each component is as follows:
Working layer: 4,300 kg.
Intermediate layer: 450 kg.
Core: 12,300 kg (see Figure 1).
Figure 1. Model of the rolling mill roll: a, b – working and intermediate layers; c – core.
During heat treatment, chipping and cracking occur on the surface of the working layer (see Figure 2) due to stresses that exceed the material's strength limit during heating or cooling. These defects form during the solidification and heat treatment of the casting, as well as under high-temperature conditions during the roll’s operation in the rolling mill.
Figure 2. Chipping and cracks in the rolling mill roll.
To perform an accurate evaluation of residual stresses, a computational simulation of the roll manufacturing process was conducted.
The casting process simulation system "PoligonSoft" was used as the tool. Calculations in the software were performed using the finite element method (FEM), which enables modeling of the metal crystallization processes within the mold [9].
The FEM allows for the analysis of bodies composed of different materials, evaluation of regions of any shape, and application of various boundary conditions. This is achieved by dividing the initial geometry of the casting into finite elements (in "PoligonSoft," tetrahedrons with four vertices are used).
Independent meshes are used for all bodies within the analysis region, enabling the modeling of contacts between bodies. This approach provides a reasonably accurate evaluation of the qualitative distribution and quantitative characteristics of residual stresses [10].
The preparation for the simulation and mesh generation were performed using the integrated mesh generator "SALOME." For the volumetric mesh obtained, representing the elements of the roll and the casting mold, the initial and boundary conditions for the casting parameters were defined in the "Master" preprocessor. These parameters included:
Pouring temperature.
Temperature of the working layer.
Alloy characteristics.
Properties of the combined casting mold, among others.
Using the "Mirage" postprocessor, results were observed at control points in the form of sequentially changing values, such as temperatures, stress intensities, and deformations at each calculated time step.
The dynamics of temperature changes were measured using sensors installed at the center of the working layer at control points located at the following distances from the end:
1 ~ 20 mm,
2 ~ 635 mm,
3 ~ 1270 mm,
4 ~ 1905 mm,
5 ~ 2520 mm.
To determine the temperature field, Fourier's heat conduction equation (1) with phase transition (2) was used:
(1)
Where: a=λ/ρC - - thermal diffusivity coefficient; qv - - internal heat source power; C – specific heat capacity.
(2)
Where: L – amount of heat released during the phase transition (solidification); fs – fraction of the solid phase.
At external boundaries, heat exchange with the environment is calculated using Newton's law of cooling (3) and Stefan-Boltzmann's law of thermal radiation (4).
(3)
Where: q – heat flux density; aK – - convection heat transfer coefficient; T1 – temperature at the contact zone between the working layer and the molten metal; T2 – temperature at the contact zone between the working layer and the mold.
(4)
Where: q – heat flux density; ε – reduced emissivity value of each surface involved in the radiative heat exchange process; σ = 5,67 × 10⁻⁸ W/(m²×K⁴) – Stefan-Boltzmann constant.
The calculation of residual stresses was performed using the "Hook" stress solver at control points of the working layer, located at equal distances from the end of the roll body: 1 ~ 20 mm, 2 ~ 317,5 mm, 3 ~ 635 mm, 4 ~ 952,5 mm, 5 ~ 1270 mm, 6 ~ 1587,5 mm, 7 ~ 1905 mm, 8 ~ 2222,5 mm, 9 ~ 2520 mm.
The set of elastoplastic properties for each temperature of the casting, required to calculate the stress-strain state (SSS), is presented in the form of graphs in Figure 3 [11, 12].
Figure 3. Graphical representation of the mechanical properties of the working layer: a) Young's modulus, MPa; b) Poisson's ratio; c) Coefficient of linear thermal expansion, 1/K; d) Strength limit, MPa; e) Hardening coefficient, MPa; f) Strength limit, MPa.
The basis for calculating stresses and deformations is the temperature fields formed during the solidification and cooling of the casting. During solidification, the temperature within the casting is distributed non-uniformly due to varying wall thicknesses, different materials in the casting mold, pouring duration, and other factors. As a result, deformations occur within the casting, generating stresses [13].
To model the solidification and cooling processes of the roll casting, the following initial temperature values were set:
Molding mixture: 20°C.
Mold: 400°C.
Working layer: 1150°C.
Core: 1350°C [14].
Calculations were performed until the casting reached a temperature of 400°C.
The working layer cooled to this temperature in 18 hours.
The roll core reached 400°C in 23 hours.
Thermal fields were calculated with maximum approximation to real production conditions. Subsequently, cooling curves for the working layer of the rolling mill roll were generated (see Figure 4).
Figure 4. Dynamics of temperature changes in the working layer at control points: 1 ~ 20; 2 ~ 635; 3 ~ 1270; 4 ~ 1905; 5 ~ 2520 mm, and cooling rates during specific time intervals.
The curves obtained from temperature changes in the working layer were conditionally divided into four zones, within which the cooling rates of the molten metal in the mold were calculated.
In the first stage, the temperature of the working layer decreases rapidly after pouring: within 15 minutes, the temperature drops at a rate of 13°C/min. According to Newton's law, the heat exchange power between two bodies increases with a greater temperature difference. In other words, after the roll core is poured with molten metal, the temperature difference between the casting mold and the working layer is very high, causing rapid heat exchange. The mold heats up from the roll’s working layer to 700°C within 2 hours, after which the heating of the mold slows down.
The second stage is characterized by slower cooling: the cooling rate is 2.04°C/min near the ends (points 1 and 5) and 1.75°C/min near points 2, 3, and 4. This is because the ends of the casting have a larger contact surface, and the casting shapes of the necks maintain ambient temperature after assembly for pouring.
The third stage is distinguished by a uniform cooling rate throughout the working layer, which is 0.84°C/min. During this interval, the temperatures between the casting and the mold nearly equalize.
The fourth stage is characterized by a uniform cooling rate at all control points, at 0.58°C/min. A slight deviation is due to the different thermal conductivities of the materials: the thermal conductivity of the molding mixture is 0.17 W/(m×K), while that of the chill mold is 29 W/(m×K) [15]. Therefore, the roll’s working layer in contact with the chill mold cools faster.
The cooling process of the rolling mill roll to 400°C takes 23 hours. During this period, thermophysical processes occur within the casting body, influencing the structural-phase state of the roll. As a result, changes in the volume of the structural composition occur, leading to the stress state of the roll. In the next stage, an analysis of residual stresses after cooling the roll to 50°C was conducted (see Fig. 5).
Figure 5. Residual stresses in the working layer at control points:1…9 – 20; 317.5; 635; 952.5; 1270; 1587.5; 1905; 2222.5; 2520 mm, respectively.
Analysis of the data shows that the minimum residual stresses occur at the extremities (points 1 and 9) and in the central section of the working layer (point 5), where the residual stress values do not exceed 100 MPa. The maximum residual stresses (exceeding 160 MPa) are observed at a distance of 300 mm (points 2 and 8) from the lower and upper ends of the working layer.
It is worth noting that this extreme pattern of residual stress distribution is related to the magnitude of the temperature gradient along the roll body. Since heating from the ends and working areas of the roll body leads to a local temperature equilibrium in the extreme zone, the gradient in this area is minimal. As a result, low residual stresses are observed in the extremities (see Figure 6).
Figure 6. Intensity of deformations and residual stresses in the cast body of the roll (maximum stresses and deformations are highlighted in red).
A similar qualitative pattern is observed in the center of the roll body. In this area, heating occurs from the working surface and is significantly slower than at the extremities. As a result, the temperature gradient along the radius is also low.
The maximum temperature gradients occur during the transition from the hotter zones at the extremities to the cooler central areas of the roll’s working layer; it is precisely in these areas that the maximum stresses arise.
The stress-strain state of the roll is formed due to metal cooling, contraction challenges, and phase transformations.
Deformations are most intense at the hot spots of the casting, i.e., where the alloy crystallization completes last. In the case of the roll, these points correspond to the central parts of the upper and lower necks (see Figure 6). As a result, restricted contraction is observed in these areas of the casting, which, in turn, generates stress fields at the boundary conditions between the working layer and the core of the rolling mill roll.
Thus, the areas of maximum stress identified in the casting body during the simulation closely correspond to the defects formed during the roll production (see Figure 2).
Computational simulation enabled a more efficient and detailed study of the processes occurring in the casting, identifying the most critical areas for the formation of chipping and cracks.
Using the "PoligonSoft" casting process simulation system, the temperature fields and the stress-strain state of the rolling mill roll were calculated. This allowed for an analysis of the cooling dynamics of the casting, temperature changes in the mold, and residual stresses after casting. The calculations showed that, initially, the cooling rate of the working layer is 13°C/min, later decreasing to 0.56°C/min. The casting reaches 400°C in 23 hours. Residual stresses along the working layer range between 100 and 160 MPa, while at the interface between the working layer and the core, they reach 300 MPa.
It was determined that the areas with maximum residual stress concentrations correspond to the zones of discontinuities in the casting, identifying this stress state as one of the causes of crack formation in the working layer of the rolling mill roll.
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Translated by A.J. Camejo Severinov
Original text in Russian
Assessment of the stressstate of a rolling roll usingcomputerized modeling
Development of Quenching Technology for Steel Parts Using Computer Modeling
Numerical Simulation of the Formation Conditions of Castings with Exothermic Sleeves
Application of a new porosity model for predicting shrinkage defects in castings
Imitative model of the formation of shrinkage cavities and macroporosity
Quantitative Estimation of Formation of Shrinkage Porosity by the Niyama Criterion
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